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KS2, KS3, GCSE, A Level, IB, Scottish Higher Maths

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List of Topics Covered by LiveMaths

  • Edexcel A Level Maths
  • C1
  • Algebra and Functions
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • C2
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Coordinate Geometry
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90°
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Differentiation
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ= 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities
  • Integration
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • Moments
  • Introducing Moments
  • The Turning Effect of a Force
  • Basic Moments Example 1
  • Basic Moments Example 2
  • Basic Moments Example 3
  • Basic Moments Example 4
  • Basic Moments Example 5
  • Basic Moments Example 6
  • Basic Moments Example 7
  • Moments and Equilibrium
  • Moment Problems Involving Equilibrium Example 1
  • Moment Problems Involving Equilibrium Example 2
  • Moment Problems Involving Equilibrium Example 3
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Representation of Data Collected in Samples
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Measures of Location
  • Introduction
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • Measures of Dispersion
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Coding
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Correlation
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • MEI A Level Maths
  • C1
  • Algebra
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Effect of Transformations on a Point Example 1
  • Cubic Curves
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Simplifying Algebraic Fractions
  • Algebrain Fractions Example 1
  • Algebrain Fractions Example 2
  • Algebrain Fractions Example 3
  • Algebrain Fractions Example 4
  • Algebrain Fractions Example 5
  • Algebrain Fractions Example 6
  • Polynomials
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Language of Mathematics
  • Number Sets
  • Number Sets
  • Problem Solving
  • Problem Solving Example 1
  • Problem Solving Example 2
  • Problem Solving Example 3
  • Problem Solving Example 4
  • Converse of a Statement
  • Converse of a Statement - Example 1
  • Converse of a Statement - Example 2
  • Logic
  • Logic Example 1
  • Logic Example 2
  • Logic Example 3
  • Logic Example 4
  • Logic Example 5
  • Proof
  • Methods of Proof Example 1 - Exhaustion
  • Methods of Proof Example 2 - Exhaustion
  • Methods of Proof Example 3 - Disproof by Counter Example
  • Methods of Proof Example 4 - Disproof by Counter Example
  • Methods of Proof Example 5 - Deduction
  • Methods of Proof Example 6 - Deduction
  • Methods of Proof Example 7 - Contradiction
  • Methods of Proof Example 8 - Contradiction
  • C2
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90°
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • NM
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • S3
  • Correlation
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Kinematics
  • Projectiles
  • Introduction to Projectile Motion
  • Horizontal Projection Example 1
  • Horizontal Projection Example 2
  • Projection at an Angle Projection Example 1
  • Projection at an Angle Projection Example 2
  • Projection at an Angle Projection Example 3
  • Projection at an Angle Projection Example 4
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Representation of Data Collected in Samples
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Measures of Location
  • Introduction
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • Measures of Dispersion
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Coding
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Other Measures of Dispersion
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 1
  • Collecting Like Terms
  • Algebra and Functions
  • OCR A Level Maths
  • C1
  • AQA A Level Maths
  • C1
  • Algebra and Functions
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • C2
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Geometric Sequences
  • Introduction to Geometric Sequences
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90 degrees
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Differentiation
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities
  • CCEA A Level Maths
  • C1
  • Algebra and Functions
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Algebra
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • C2
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Coordinate Geometry
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Introduction
  • Introduction to Geometric Sequences
  • Geometric Sequences
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90 degrees
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • Kinematics
  • Projectiles
  • Introduction to Projectile Motion
  • Horizontal Projection Example 1
  • Horizontal Projection Example 2
  • Projection at an Angle Example 1
  • Projection at an Angle Example 2
  • Projection at an Angle Example 3
  • Projection at an Angle Example 4
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Representation of Data Collected in Samples
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Measures of Location
  • Introduction
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • Measures of Dispersion
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Coding
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Correlation
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • Moments
  • Introducing Moments
  • The Turning Effect of a Force
  • Basic Moments Example 1
  • Basic Moments Example 2
  • Basic Moments Example 3
  • Basic Moments Example 4
  • Basic Moments Example 5
  • Basic Moments Example 6
  • Basic Moments Example 7
  • Moments and Equilibrium
  • Moment Problems Involving Equilibrium Example 1
  • Moment Problems Involving Equilibrium Example 2
  • Moment Problems Involving Equilibrium Example 3
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Equilibrium
  • Centre Of Mass for a Compound Shape Example 5
  • Lamina Suspended From Point Example 1
  • Lamina Suspended From Point Example 2
  • Lamina Suspended From Point Example 3
  • Lamina on an Inclined Plane Example 1
  • Lamina on an Inclined Plane Example 2
  • Lamina on an Inclined Plane Example 3
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Representation of Data Collected in Samples
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Measures of Location
  • Introduction
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • Measures of Dispersion
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Coding
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • C2
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Exponentials and Logarithms
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Geometric Sequences
  • Introduction to Geometric Sequences
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90 degrees
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Representation of Data Collected in Samples
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Measures of Location
  • Introduction
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • Measures of Dispersion
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Coding
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Correlation
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • C3
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • General Motion in the Plane Example 1
  • General Motion in the Plane Example 2
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Equilibrium
  • Centre Of Mass for a Compound Shape Example 5
  • Lamina Suspended From Point Example 1
  • Lamina Suspended From Point Example 2
  • Lamina Suspended From Point Example 3
  • Lamina on an Inclined Plane Example 1
  • Lamina on an Inclined Plane Example 2
  • Lamina on an Inclined Plane Example 3
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • Conservation of Energy
  • Introduction to the Concept of Conservation of Energy
  • Object Sliding Down a Smooth Slope
  • Object Sliding Down a Rough Slope
  • Object Falling, No Air Resistance
  • Object Falling, Constant Air Resistance
  • Object Sliding Up Slope, No Resistance
  • Object Sliding Up Slope Against Friction
  • Rolling Hills Example 1
  • Rolling Hills Example 2
  • Power
  • The Definition of Power
  • Acceleration and Maximum Speed on a Level Road
  • Car on a Slope
  • Power generated by a Pump
  • Collisions
  • Conservation of Linear Momentum Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Newton's Law of Restitution
  • Introduction
  • Newton's Law of Restitution Example 1
  • Newton's Law of Restitution Example 2
  • Newton's Law of Restitution Example 3
  • Newton's Law of Restitution Example 4 - Collision With a Wall
  • Successive Impacts
  • Problems Involving Successive Impacts -Example 1
  • Problems Involving Successive Impacts -Example 2
  • Problems Involving Successive Impacts -Example 3
  • Equilibrium
  • Equilibrium Revision
  • Revision Example 1
  • Revision Example 2
  • More Complex Equilibrium Problems Involving Rigid Bodies
  • Equilibrium Problems Involving Rigid Bodies Example 1
  • Equilibrium Problems Involving Rigid Bodies Example 2
  • Equilibrium Problems Involving Rigid Bodies Example 3
  • Ladder Problems
  • Ladder Problems Example 1
  • Ladder Problems Example 2 Part a
  • Ladder Problems Example 2 Part b
  • Logarithmic Graphs
  • Logarithmic Graphs Example 1
  • Logarithmic Graphs Example 2
  • Logarithmic Graphs Example 3
  • C4
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Introduction
  • General Motion of a Particle
  • Displacement as a Function of Time Example 4
  • Displacement as a Function of Time Example 3
  • Displacement as a Function of Time Example 2
  • Displacement as a Function of Time Example 1
  • Introduction to Displacement as a Function of Time
  • Displacement as a Function of Time
  • Projection at an Angle Example 4
  • Projection at an Angle Example 3
  • Projection at an Angle Example 2
  • Projection at an Angle Example 1
  • Horizontal Projection Example 2
  • Horizontal Projection Example 1
  • Introduction to Projectile Motion
  • Projectiles
  • M2
  • Kinematics
  • Type I - Linear Factors Only in Denominator Example 4
  • Tangents and Normals
  • Introduction to The parabola
  • The Parabola
  • FP2
  • Coordinate Geometry
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Type IV - Improper Fractions Example 1 (Leads to Type I)
  • Type IV - Improper Fractions Example 2 (Leads to Type III)
  • Type IV - Improper Fractions Example 3 (Leads to Type II)
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Numerical Integration
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Numerical Integration
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Integration
  • Numerical Integration
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Spearman's Rank
  • Introduction to Spearman's Rank
  • Spearman's Rank Example 1
  • Spearman's Rank Example 2
  • Spearman's Rank Example 3
  • Meaning of Correlation Coefficient
  • IB Studies
  • IB
  • Algebra
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Arithmetic Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • Descriptive Statistics
  • Introduction
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Differential Calculus
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Equations
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Exponential Graphs
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90?
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Quadratics
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Trigonometry
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Two Variable Statistics
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Spearman's Rank
  • Introduction to Spearman's Rank
  • Spearman's Rank Example 1
  • Spearman's Rank Example 2
  • Spearman's Rank Example 3
  • Meaning of Correlation Coefficient
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • S2
  • The Binomial and Poisson Distributions
  • The Binomial Distribution
  • Introduction to the Binomial Distribution
  • Binomial Examples - Example 1
  • Binomial Examples - Example 2
  • Binomial Examples - Example 3
  • Binomial Examples - Example 4
  • The Expecation and Variance for a Binomial Distribution
  • Expectation and Varaince Example 1
  • Expectation and Varaince Example 2
  • Expectation and Varaince Example 3
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • Poisson Examples - Example 4
  • The Binomial and Poisson Distributions
  • Which Distribution?
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • Continuous Random Variables
  • Introduction to Continuous Random Variables
  • Continuous Random Variables - Intro Part 1
  • Continuous Random Variables - Intro Part 2
  • Continuous Random Variables - Intro Part 3
  • Continuous Random Variables - Intro Part 4
  • Probability Density Functions
  • Probability Density Function - Example 1
  • Probability Density Function - Example 2
  • Probability Density Function - Example 3
  • Cumulative Distribution Functions
  • Cumulative Distribution Functions - Intro Part 1
  • Cumulative Distribution Functions - Intro Part 2
  • Cumulative Distribution Functions - Example 1
  • Cumulative Distribution Functions - Example 2
  • Cumulative Distribution Functions - Example 3
  • Cumulative Distribution Functions - Example 4
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • Continuous Distributions
  • The Continuous Uniform Distribution (Rectangular)
  • Introduction to the Rectangular Distribution
  • The Mean and Variance
  • Rectangular Distribution Example 1
  • Rectangular Distribution Example 2
  • Rectangular Distribution Example 3
  • Approximating Binomial Distribution Using the Normal Distribution
  • Approximating Binomial with Normal Intro
  • Approximating Binomial with Normal Example 1
  • Approximating Binomial with Normal Example 2
  • Approximating Poisson Distribution Using the Normal Distribution
  • Approximating Poisson with Normal Intro
  • Approximating Poisson with Normal Example
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Parabola Examples 1
  • Parabola Examples 2
  • Parabola Examples 3
  • Parabola Examples 4
  • Parabola Examples 5
  • Parabola Examples 6
  • Parabola Examples 7
  • The Ellipse
  • Introduction to the Ellipse Part 1
  • Introduction to the Ellipse Part 2
  • Tangents and Normals
  • Ellipse Examples 1
  • Ellipse Examples 2
  • Ellipse Examples 3
  • Ellipse Examples 4
  • Ellipse Examples 5
  • Ellipse Examples 6
  • Ellipse Examples 7
  • The Hyperbola
  • Introduction to the Hyperbola Part 1
  • Introduction to the Hyperbola Part 2
  • The Rectangular Hyperbola
  • Tangents and Normals Part 1
  • Tangents and Normals Part 2
  • Hyperbola Examples 1
  • Hyperbola Examples 2
  • Hyperbola Examples 3
  • Hyperbola Examples 4
  • Hyperbola Examples 5
  • Hyperbola Examples 6
  • C3
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • C4
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • M2
  • Kinematics
  • Displacement as a Function of Time
  • Introduction to Displacement as a Function of Time
  • Displacement as a Function of Time Example 1
  • Displacement as a Function of Time Example 2
  • Displacement as a Function of Time Example 3
  • Displacement as a Function of Time Example 4
  • General Motion of a Particle
  • Introduction
  • General Motion in the Plane Example 1
  • General Motion in the Plane Example 2
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Equilibrium
  • Centre Of Mass for a Compound Shape Example 5
  • Lamina Suspended From Point Example 1
  • Lamina Suspended From Point Example 2
  • Lamina Suspended From Point Example 3
  • Lamina on an Inclined Plane Example 1
  • Lamina on an Inclined Plane Example 2
  • Lamina on an Inclined Plane Example 3
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • S2
  • The Binomial and Poisson Distributions
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • The Poisson Distributions
  • The Poisson Distribution
  • Poisson Examples - Example 4
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • Continuous Random Variables
  • Introduction to Continuous Random Variables
  • Continuous Random Variables - Intro Part 1
  • Continuous Random Variables - Intro Part 2
  • Continuous Random Variables - Intro Part 3
  • Continuous Random Variables - Intro Part 4
  • Probability Density Functions
  • Probability Density Function - Example 1
  • Probability Density Function - Example 2
  • Probability Density Function - Example 3
  • Cumulative Distribution Functions
  • Cumulative Distribution Functions - Intro Part 1
  • Cumulative Distribution Functions - Intro Part 2
  • Cumulative Distribution Functions - Example 1
  • Cumulative Distribution Functions - Example 2
  • Cumulative Distribution Functions - Example 3
  • Cumulative Distribution Functions - Example 4
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Hypothesis Test Example 4
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • C3
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Integration
  • Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • C4
  • Parametric and Implicit Equations
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • M2
  • Kinematics
  • Projectiles
  • Introduction to Projectile Motion
  • Horizontal Projection Example 1
  • Horizontal Projection Example 2
  • Projection at an Angle Example 1
  • Projection at an Angle Example 2
  • Projection at an Angle Example 3
  • Projection at an Angle Example 4
  • Displacement as a Function of Time
  • Introduction to Displacement as a Function of Time
  • Displacement as a Function of Time Example 1
  • Displacement as a Function of Time Example 2
  • Displacement as a Function of Time Example 3
  • Displacement as a Function of Time Example 4
  • General Motion of a Particle
  • Introduction
  • General Motion in the Plane Example 1
  • General Motion in the Plane Example 2
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • Vectors
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • S2
  • Expection Algebra
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Hypothesis Test Example 4
  • Correlation
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • C3
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • C4
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type II - Quadratic Factor in Denominator Example 1
  • Type II - Quadratic Factor in Denominator Example 2
  • Type II - Quadratic Factor in Denominator Example 3
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Type IV - Improper Fractions Example 1 (Leads to Type I)
  • Type IV - Improper Fractions Example 2 (Leads to Type III)
  • Type IV - Improper Fractions Example 3 (Leads to Type II)
  • Parametric Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • M2
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Equilibrium
  • Centre Of Mass for a Compound Shape Example 5
  • Lamina Suspended From Point Example 1
  • Lamina Suspended From Point Example 2
  • Lamina Suspended From Point Example 3
  • Lamina on an Inclined Plane Example 1
  • Lamina on an Inclined Plane Example 2
  • Lamina on an Inclined Plane Example 3
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • Statics
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • S2
  • The Poisson Distribution
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • Poisson Examples - Example 4
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • The Normal Distribution
  • Approximating Binomial Distribution Using the Normal Distribution
  • Approximating Binomial with Normal Intro
  • Approximating Binomial with Normal Example 1
  • Approximating Binomial with Normal Example 2
  • Approximating Poisson Distribution Using the Normal Distribution
  • Approximating Poisson with Normal Intro
  • Approximating Poisson with Normal Example
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Hypothesis Test Example 4
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • Correlation
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • Spearman's Rank
  • Introduction to Spearman's Rank
  • Spearman's Rank Example 1
  • Spearman's Rank Example 2
  • Spearman's Rank Example 3
  • Meaning of Correlation Coefficient
  • C3
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • C4
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • M2
  • Kinematics
  • Projectiles
  • Introduction to Projectile Motion
  • Horizontal Projection Example 1
  • Horizontal Projection Example 2
  • Projection at an Angle Example 1
  • Projection at an Angle Example 2
  • Projection at an Angle Example 3
  • Projection at an Angle Example 4
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Centre Of Mass for a Compound Shape Example 5
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • Dynamics
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • S2
  • The Poisson Distribution
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • Poisson Examples - Example 4
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • Continuous Random Variables
  • Introduction to Continuous Random Variables
  • Continuous Random Variables - Intro Part 1
  • Continuous Random Variables - Intro Part 2
  • Continuous Random Variables - Intro Part 3
  • Continuous Random Variables - Intro Part 4
  • Probability Density Functions
  • Probability Density Function - Example 1
  • Probability Density Function - Example 2
  • Probability Density Function - Example 3
  • Cumulative Distribution Functions
  • Cumulative Distribution Functions - Intro Part 1
  • Cumulative Distribution Functions - Intro Part 2
  • Cumulative Distribution Functions - Example 1
  • Cumulative Distribution Functions - Example 2
  • Cumulative Distribution Functions - Example 3
  • Cumulative Distribution Functions - Example 4
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • Continuous Distributions
  • Approximating Binomial Distribution Using the Normal Distribution
  • Approximating Binomial with Normal Intro
  • Approximating Binomial with Normal Example 1
  • Approximating Binomial with Normal Example 2
  • Approximating Poisson Distribution Using the Normal Distribution
  • Approximating Poisson with Normal Intro
  • Approximating Poisson with Normal Example
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Hypothesis Test Example 4
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • WJEC A Level Maths
  • C1
  • Algebra and Functions
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Algebra
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)sup>n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • C2
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities
  • Coordinate Geometry
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Integration
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • C3
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • C4
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Integration
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • M1
  • Modelling
  • Particle
  • The Particle
  • String and Rod
  • The String and the Rod
  • Surface
  • Surfaces
  • Examples
  • Creating a Model from a Situation Example 1
  • Creating a Model from a Situation Example 2
  • Creating a Model from a Situation Example 3
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • Vertical Motion Under Gravity
  • Applying Constant Acceleration Formulae to Vertical Motion Example 1
  • Applying Constant Acceleration Formulae to Vertical Motion Example 2
  • Applying Constant Acceleration Formulae to Vertical Motion Example 3
  • Applying Constant Acceleration Formulae to Vertical Motion Example 4
  • Applying Constant Acceleration Formulae to Vertical Motion Example 5
  • Velocity -Time Graphs
  • Using Velocity-Time Graphs Example 1
  • Using Velocity-Time Graphs Example 2
  • Using Velocity-Time Graphs Example 3
  • Using Velocity-Time Graphs Example 4
  • Applying Formulae to Vectors
  • Formulae Applied to Vectors Example
  • Statics
  • Resultant of Two Forces
  • Finding the Resultant of Two Forces Using Trigonometry Example 1
  • Finding the Resultant of Two Forces Using Trigonometry Example 2
  • Finding the Resultant of Two Forces Using Trigonometry Example 3
  • Finding the Resultant of Two Forces Using Trigonometry Example 4
  • Resolving Forces and Resultant Forces
  • Resolving Forces into two components
  • Finding Resultant Forces by Resolving Forces Example 1
  • Finding Resultant Forces by Resolving Forces Example 2
  • Finding Resultant Forces by Resolving Forces Example 3
  • Finding Resultant Forces by Resolving Forces Example 4
  • Finding Resultant Forces by Resolving Forces Example 5
  • Forces in Equilibrium
  • Forces in Equilibrium Example 1
  • Forces in Equilibrium Example 2
  • Forces in Equilibrium Example 3
  • Types of Force
  • Forces in Equilibrium Example 4
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Dynamics
  • Introducing Newton's Laws
  • Newtons 1st Law
  • Newton's 2nd Law
  • Newton's 3rd Law
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Applying Newton's Second Law Example 3
  • Applying Newton's Second Law Example 4
  • Applying Newton's Second Law Example 5
  • Applying Newton's Second Law Example 6
  • Applying Newton's Second Law Example 7
  • Applying Newton's Second Law Example 8
  • Applying Newton's Second Law Example 9
  • Applying Newton's Second Law Example 10
  • Applying Newton's Second Law Example 11
  • Applying Newton's Second Law Example 12
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3
  • The Motion of Connected Bodies Example 4
  • The Motion of Connected Bodies Example 5
  • The Motion of Connected Bodies Example 6
  • The Motion of Connected Bodies Example 7 Part 1
  • The Motion of Connected Bodies Example 7 Part 2
  • Momentum and Impulse
  • Introducing Momentum
  • Introducing the Concept of Impulse
  • More about Impulse
  • Momentum and Impulse Example 1
  • Momentum and Impulse Example 2
  • Conservation of Momentum
  • Conservation of Linear Momentum Example 1
  • Conservation of Linear Momentum Example 2
  • Conservation of Linear Momentum Example 3
  • Conservation of Linear Momentum Example 4
  • Conservation of Linear Momentum Example 5
  • Conservation of Linear Momentum Example 6
  • Moments
  • Introducing Moments
  • The Turning Effect of a Force
  • Basic Moments Example 1
  • Basic Moments Example 2
  • Basic Moments Example 3
  • Basic Moments Example 4
  • Basic Moments Example 5
  • Basic Moments Example 6
  • Basic Moments Example 7
  • Moments and Equilibrium
  • Moment Problems Involving Equilibrium Example 1
  • Moment Problems Involving Equilibrium Example 2
  • Moment Problems Involving Equilibrium Example 3
  • Centre of Mass
  • Finding the Centre of Mass
  • Particles on a Line Example 1
  • Particles on a Line Example 2
  • Particles on a Plane Example 1
  • Particles on a Plane Example 2
  • Particles on a Plane Example 3
  • Standard Results
  • Compound Figures
  • Centre Of Mass for a Compound Shape Example 1
  • Centre Of Mass for a Compound Shape Example 2
  • Centre Of Mass for a Compound Shape Example 3
  • Centre Of Mass for a Compound Shape Example 4
  • Equilibrium
  • Centre Of Mass for a Compound Shape Example 5
  • Lamina Suspended From Point Example 1
  • Lamina Suspended From Point Example 2
  • Lamina Suspended From Point Example 3
  • M2
  • Kinematics
  • Projectiles
  • Introduction to Projectile Motion
  • Horizontal Projection Example 1
  • Horizontal Projection Example 2
  • Projection at an Angle Example 1
  • Projection at an Angle Example 2
  • Projection at an Angle Example 3
  • Projection at an Angle Example 4
  • Displacement as a Function of Time
  • Introduction to Displacement as a Function of Time
  • Displacement as a Function of Time Example 1
  • Displacement as a Function of Time Example 2
  • Displacement as a Function of Time Example 3
  • Displacement as a Function of Time Example 4
  • Work, Energy and Power
  • Work
  • Introduction to the Concept of Work Done by a Force
  • Basic Work Example
  • Work Done Against Gravity Example 1
  • Work Done Against Gravity Example 2
  • Work Done Against Friction
  • Work Done against Gravity and Friction - Object on Slope Example 1
  • Force at an Angle to the Direction of Motion Example 1
  • Force at an Angle to the Direction of Motion Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 2
  • Work Done against Gravity and Friction - Object on Slope Example 3
  • Work Done by a Water Pump in Raising Water
  • Energy
  • Introducing the Concept of Energy
  • Kinetic Energy Example 1
  • Kinetic Energy Example 2
  • Work Done and Kinetic Energy Gain Example 1
  • Work Done and Kinetic Energy Gain Example 2
  • Potential Energy Example 1
  • Potential Energy Example 2
  • Vectors
  • Vector and Scalar Quantities
  • Vectors and Scalars
  • Vectors to Represent Displacement
  • Displacement Problems Example 1
  • Displacement Problems Example 2
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Unit Vectors
  • Unit Vectors Introduction
  • Adding and Subtracting Vectors Example 1
  • Adding and Subtracting Vectors Example 2
  • Modulus (Magnitude) of a Vector Given in i, j Form
  • Unit Vector in a Given Direction
  • Resolving Vectors
  • Horizontal and Vertical Components Example 1
  • Horizontal and Vertical Components Example 2
  • Horizontal and Vertical Components Example 3
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Using Vectors to Represent Velocity and Acceleration
  • Introduction to Position Vectors
  • Using Vectors to Represent Velocity and Acceleration Example 1
  • Using Vectors to Represent Velocity and Acceleration Example 2
  • Using Vectors to Represent Velocity and Acceleration Example 3
  • Relative Position and Velocity
  • The Concept of Relative Position
  • The Concept of Relative Velocity
  • Problems Involving Vectors
  • An Extended Problem Involving the Use of Vectors Part 1
  • An Extended Problem Involving the Use of Vectors Part 2
  • S1
  • Modelling
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • Miscellaneous Example
  • Correlation
  • Scatter Diagrams
  • Scatter Diagrams and Correlation Part 1
  • Scatter Diagrams and Correlation Part 2
  • Product Moment Correlation Coefficient
  • The Concept of the PMCC Part 1
  • The Concept of the PMCC Part 2
  • The Concept of the PMCC Part 3
  • Calculating the PMCC Example 1
  • Calculating the PMCC Example 2
  • Calculating the PMCC Example 3
  • Example Using Coding
  • Interpretation
  • Interpretation of r
  • Regression
  • Linear Regression
  • Explanatory and Response Values
  • The Least-Squares Regression Line
  • The Least Squares Regression Line
  • Calculating the Least Squares Regression Line
  • Application and Interpretation
  • Interpolation and Extrapolation
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • The Binomial and Poisson Distributions
  • The Binomial Distribution
  • Introduction to the Binomial Distribution
  • Binomial Examples - Example 1
  • Binomial Examples - Example 2
  • Binomial Examples - Example 3
  • Binomial Examples - Example 4
  • The Expecation and Variance for a Binomial Distribution
  • Expectation and Varaince Example 1
  • Expectation and Varaince Example 2
  • Expectation and Varaince Example 3
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • Poisson Examples - Example 4
  • The Binomial and Poisson Distributions
  • Which Distribution?
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • Continuous Random Variables
  • Introduction to Continuous Random Variables
  • Continuous Random Variables - Intro Part 1
  • Continuous Random Variables - Intro Part 2
  • Continuous Random Variables - Intro Part 3
  • Continuous Random Variables - Intro Part 4
  • Probability Density Functions
  • Probability Density Function - Example 1
  • Probability Density Function - Example 2
  • Probability Density Function - Example 3
  • Cumulative Distribution Functions
  • Cumulative Distribution Functions - Intro Part 1
  • Cumulative Distribution Functions - Intro Part 2
  • Cumulative Distribution Functions - Example 1
  • Cumulative Distribution Functions - Example 2
  • Cumulative Distribution Functions - Example 3
  • Cumulative Distribution Functions - Example 4
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • S2
  • Continuous Distributions
  • The Continuous Uniform Distribution (Rectangular)
  • Introduction to the Rectangular Distribution
  • The Mean and Variance
  • Rectangular Distribution Example 1
  • Rectangular Distribution Example 2
  • Rectangular Distribution Example 3
  • Approximating Binomial Distribution Using the Normal Distribution
  • Approximating Binomial with Normal Intro
  • Approximating Binomial with Normal Example 1
  • Approximating Binomial with Normal Example 2
  • Approximating Poisson Distribution Using the Normal Distribution
  • Approximating Poisson with Normal Intro
  • Approximating Poisson with Normal Example
  • Hypothesis Tests
  • Definitions
  • Populations
  • Sampling
  • Sampling Example
  • Bias
  • What is a Statistic?
  • Sampling Distributions
  • Sampling Distribution Example 1
  • Sampling Distribution Example 2
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 3
  • Hypothesis Test Example 4
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • D1
  • Critical Path Analysis
  • Introduction
  • Introduction to CPA
  • Drawing a Network
  • Drawing a Network Example 1
  • Drawing a Network Example 2
  • Drawing a Network Example 3
  • Analysis of a Network
  • Time Analysis Example 1
  • Time Analysis Example 2
  • Time Analysis Example 3
  • Cascade (Gantt) Charts
  • Cascade Example 1
  • Cascade Example 2
  • Scheduling
  • Scheduling Example 1
  • Scheduling Example 2
  • D1
  • Critical Path Analysis
  • Introduction
  • Introduction to CPA
  • Drawing a Network
  • Drawing a Network Example 1
  • Drawing a Network Example 2
  • Drawing a Network Example 3
  • Analysis of a Network
  • Time Analysis Example 1
  • Time Analysis Example 2
  • Time Analysis Example 3
  • Cascade (Gantt) Charts
  • Cascade Example 1
  • Cascade Example 2
  • Resource Histograms
  • Resource Histogram Example 1
  • Resource Histogram Example 2
  • FP1
  • Complex Numbers
  • Introduction
  • Introduction to Complex Numbers
  • Simplifying Expressions
  • Adding and Subtracting
  • Multiplying
  • Quadratics
  • Solving a Quadratic with Complex Roots
  • Real and Imaginary Parts
  • Real Parts, Imaginary Parts and Conjugates
  • Realising the Denominator
  • Multiplying Through By Conjugate
  • Solving Equations
  • Equating Real and Imaginary Parts
  • Finding Z
  • The Argand Diagram
  • Argand Example 1
  • Modulus and Locus Example 1
  • Modulus and Locus Example 2
  • Modulus and Argument Intro
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Modulus and Argument Example 5
  • Roots of Polynomials
  • Roots of Polynomials Example
  • The Binomial Distribution
  • The Binomial Distribution
  • Introduction to the Binomial Distribution
  • Binomial Examples - Example 1
  • Binomial Examples - Example 2
  • Binomial Examples - Example 3
  • Binomial Examples - Example 4
  • The Expecation and Variance for a Binomial Distribution
  • Expectation and Varaince Example 1
  • Expectation and Varaince Example 2
  • Expectation and Varaince Example 3
  • Hypothesis Testing
  • Hypothesis Test Example 1
  • Hypothesis Test Example 2
  • Hypothesis Test Example 4
  • Trees
  • Minimum Spanning Trees
  • Introduction
  • Kruskal's Algorithm Example 1
  • Kruskal's Algorithm Example 2
  • Prim's Algorithm Example 1
  • Prim's Algorithm Example 2
  • Prim's Algorithm in a table
  • Trees
  • Minimum Spanning Trees
  • Introduction
  • Kruskal's Algorithm Example 1
  • Kruskal's Algorithm Example 2
  • Prim's Algorithm Example 1
  • Prim's Algorithm Example 2
  • Prim's Algorithm in a table
  • Route Inspection
  • The Route Inspection Algorithm
  • Introduction
  • Route Inspection Example
  • Shortest Path
  • Dijkstra's Algorithm
  • Dijkstra Example
  • Linear Programming
  • Graphical Solution
  • Formulating a Linear programming Problem
  • Representing a LP Problem Graphically
  • Using the Graph to Solve a Linear Programming Problem
  • The Simplex
  • Forming an Initial Tableau
  • Solving a Simplex Tableau
  • The Simplex Explained
  • Shortest Path
  • Dijkstra's Algorithm
  • Dijkstra Example
  • Linear Programming
  • Graphical Solution
  • Formulating a Linear programming Problem
  • Representing a LP Problem Graphically
  • Using the Graph to Solve a Linear Programming Problem
  • Coordinate Systems
  • Intrinsic Coordinates
  • Introduction to Intrinsic Coordinates
  • Intrinsic Coordinates Example 1
  • Intrinsic Coordinates Example 2
  • Intrinsic Coordinates Example 3
  • Radius of Curvature
  • Introduction to Radius of Curvature
  • Radius of Curvature Example 1
  • Radius of Curvature Example 2
  • Series
  • Summation by Method of Differences
  • Differences Example 1
  • Differences Example 2
  • Differences Example 3
  • Using Standard Results
  • Standard Results Example
  • Proof by Induction
  • Introduction to Proof by Induction
  • Induction Example 1
  • Induction Example 2
  • Induction Example 3
  • Induction Example 4
  • Induction Example 5
  • FP1
  • Inequalities
  • Solving Inequalities
  • Introduction to Solving Inequalities
  • Inequalities Example 1
  • Inequalities Example 2
  • Inequalities Example 3
  • Inequalities Example 4
  • Solving Inequalities Involving Modulus
  • Inequalities Example 5
  • Inequalities Example 6
  • Inequalities Example 7
  • Series
  • Summation by Method of Differences
  • Differences Example 1
  • Differences Example 2
  • Differences Example 3
  • Using Standard Results
  • Standard Results Example
  • Proof by Induction
  • Introduction to Proof by Induction
  • Induction Example 1
  • Induction Example 2
  • Induction Example 3
  • Induction Example 4
  • Induction Example 5
  • First Order Differential Equations
  • Separable Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Family of Solution Curves
  • Example 1
  • Example 2
  • Exact Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • General First Order Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Polar Coordinates
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Areas of Regions for Polar Curves
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Tangents Parallel to and Perpendicular to the Intitial Line
  • Introduction
  • Example
  • FP3
  • Complex Numbers
  • Tranformations of the Complex Plane
  • Complex Number Transformations Introduction
  • Transformation Examples
  • Complex Number Transformations Example 1
  • Complex Number Transformations Example 2
  • Complex Number Transformations Example 3
  • Complex Number Transformations Example 4
  • Complex Number Transformations Example 5
  • Invariant Points
  • Invariant Points Example
  • Complex Numbers
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Numerical Methods
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Linear Interpolation
  • Interval Bisection
  • Newton-Raphson
  • Summary of Numerical Methods
  • 2nd Order Differential Equations
  • 2nd Order Differential Equations with Constant Coeeficients
  • Introduction to 2nd Order Differential Equations
  • Real Distinct Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Complex Roots to the Auxiliary Equation
  • Complimentary Function and Particular Integral
  • CF & PI Example 1
  • CF & PI Example 2
  • CF & PI Example 3
  • CF & PI Example 4
  • CF & PI Example 5
  • CF & PI Example 6
  • CF & PI Example 7
  • Using Substitutions to Solve Differential equations
  • Using Substitutions Example 1
  • Using Substitutions Example 2
  • Using Substitutions Example 3
  • Shape
  • Trigonometry
  • Years 9, 10, 11
  • Introduction
  • Introduction to Trigonometry
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Harder Examples
  • Multi-Step Trig Problems Example 1
  • Multi-Step Trig Problems Example 2
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1
  • Three Dimensional Problems Example 2
  • Data
  • Probability
  • Years 9, 10, 11
  • Tree Diagrams
  • Introduction to Tree Diagrams - Part 1
  • Introduction to Tree Diagrams - Part 2
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Tree Diagrams Example 3
  • Tree Diagrams Example 4
  • Tree Diagrams Example 5
  • Tree Diagrams Example 6
  • GCSE Maths
  • Shape Space and Measure
  • Trigonometry - Right Angle Triangles
  • Introduction
  • Introduction to Trigonometry (9, 10, 11)
  • Finding a Side
  • Finding a Side Example 1 (9, 10, 11)
  • Finding a Side Example 2 (9, 10, 11)
  • Finding a Side Example 3 (9, 10, 11)
  • Finding a Side Example 4 (9, 10, 11)
  • Finding a Side Example 5 (9, 10, 11)
  • Finding a Side Example 6 (9, 10, 11)
  • Finding an Angle
  • Finding an Angle Example 1 (9, 10, 11)
  • Finding an Angle Example 2 (9, 10, 11)
  • Finding an Angle Example 3 (9, 10, 11)
  • Harder Examples
  • Multi-Step Trig Problems Example 1 (9, 10, 11)
  • Multi-Step Trig Problems Example 2 (9, 10, 11)
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1 (9, 10, 11)
  • Three Dimensional Problems Example 2 (9, 10, 11)
  • Converting Between Decimals and Fractions (Advanced)
  • Converting Between Decimals and Fractions (Advanced) Example 1
  • Converting Between Decimals and Fractions (Advanced) Example 2
  • Converting Between Decimals and Fractions (Advanced) Example 3
  • Converting Between Decimals and Fractions (Advanced) Example 4
  • Converting Between Decimals and Fractions (Advanced) Example 5
  • Converting Between Decimals and Fractions (Advanced) Example 6
  • Standard Form Advanced
  • Advanced Standard Form Example 1
  • Advanced Standard Form Example 2
  • Advanced Standard Form Example 3
  • Advanced Standard Form Example 4
  • Advanced Standard Form Example 5
  • Advanced Standard Form Example 6
  • Advanced Standard Form Example 7
  • Number Sequences and Patterns
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms for Number Sequences
  • Finding the nth Term Example 1
  • Finding the nth Term Example 2
  • Finding the nth Term Example 3
  • Finding the nth Term Example 4
  • Number Sequences and Patterns Extension
  • nth Terms for Number Sequences
  • Number Sequence Extension Work Example 1
  • Number Sequence Extension Work Example 2
  • Number Sequence Extension Work Example 3
  • Number Sequence Extension Work Example 4
  • Percentages Advanced
  • Profit and Loss
  • Percentage Profit and Loss Example 1
  • Percentage Profit and Loss Example 2
  • Percentage Profit and Loss Example 3
  • Percentage Profit and Loss Example 4
  • Percentage Profit and Loss Example 5
  • Income Tax
  • Income Tax Calculations Example 1
  • Income Tax Calculations Example 2
  • Percentages Advanced Extension
  • Income Tax
  • Income Tax Calculations Example 3
  • Income Tax Calculations Example 4
  • Sale Reductions
  • Sale Reductions Example
  • Finding the Original Quantity
  • Finding the Original Quantity Example 1
  • Finding the Original Quantity Example 2
  • Finding the Original Quantity Example 3
  • Finding the Original Quantity Example 4
  • Interest
  • Interest Example 1
  • Interest Example 2
  • Interest Example 3
  • Interest Example 4 - Simple and Compound Interest
  • Interest Example 5 - Compound Interest
  • Extra Fraction Work
  • Fractions
  • Expressing one Quantity as a Fraction of Another
  • Finding a Fraction of a Quantity
  • Finding Whole Given Fraction Example 1
  • Finding Whole Given Fraction Example 2
  • Finding Whole Given Fraction Example 3
  • Percentages
  • Finding Whole Given Percentage Example 1
  • Finding Whole Given Percentage Example 2
  • Ratio
  • Introduction to Ratio
  • Simplifying Ratios Example 1
  • Simplifying Ratios Example 2
  • Simplifying Ratios Example 3
  • Simplifying Ratios Example 4
  • Simplifying Ratios Example 5
  • Ratio and Fraction
  • Ratio and Proportion
  • Ratio
  • Dividing in Given Ratio Example 1
  • Dividing in Given Ratio Example 2
  • Dividing in Given Ratio Example 3
  • Equivalent Ratios Introduction
  • Equivalent Ratios Example 1
  • Equivalent Ratios Example 2
  • Equivalent Ratios Example 3
  • Equivalent Ratios Example 4
  • The Form 1:n Example 1
  • The Form 1:n Example 2
  • The Form 1:n Example 3
  • Direct Proportion
  • Direct Proportion Introduction
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Inverse Proportion
  • Inverse Proportion Introduction
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers Introduction
  • Surds
  • Surd Introduction
  • Simplifying Surds Example 1
  • Simplifying Surds Example 2
  • Simplifying Surds Example 3
  • Rationalising Denominators
  • General Problems
  • Irrational Miscellaneous Example 1
  • Irrational Miscellaneous Example 2
  • Rational and Irrational Numbers Extension
  • An Infinite Number!
  • How Many Irrational Numbers Are There?
  • Indices Advanced
  • Review
  • Review of Indices so Far
  • The Power mn
  • The Power mn Example 1
  • The Power mn Example 2
  • Fractional Indices
  • Introduction to the Fractional Index 1/n
  • Fractional Indices Example 1
  • Fractional Indices Example 2
  • Introduction to the Fractional Index m/n
  • Fractional Indices Example 3
  • Fractional Indices Example 4
  • Fractional Indices Example 5
  • Fractional Indices Example 6
  • GCSE-F
  • Number
  • Integers
  • Addition
  • Adding Integers Example 1
  • Adding Integers Example 2
  • Carrying Figures Explained
  • Adding Integers Example 3
  • Subtraction
  • Subtracting Integers Example 1
  • Borrowing Digits Explained
  • Subtracting Integers Example 2
  • Addition and Subtraction
  • Mixed Example 1
  • Rounding
  • Rounding Integers Example 1
  • Rounding Integers Example 2
  • Rounding Integers Example 3
  • Multiplying
  • Introduction to Multiplying Integers
  • Multiplying Integers by 10, 100 etc.
  • Multiplying Two Integers Example 1
  • Multiplying Two Integers Example 2
  • Multiplying Two Integers Example 3
  • Multiplying Algebraic Expressions Example 1
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 1
  • Introduction to Algebra
  • Algebra Basics
  • Introduction to Algebra
  • Algebra
  • Inverse Proportion Example 3
  • Inverse Proportion Example 2
  • Inverse Proportion Example 1
  • Inverse Proportion
  • Inverse Proportion Introduction
  • Direct Proportion Example 3
  • Direct Proportion Example 2
  • Direct Proportion Example 1
  • Direct Proportion Introduction
  • Direct Proportion
  • The Form 1:n Example 3
  • The Form 1:n Example 2
  • The Form 1:n Example 1
  • Equivalent Ratios Example 4
  • Equivalent Ratios Example 3
  • Equivalent Ratios Example 2
  • Equivalent Ratios Example 1
  • Equivalent Ratios Introduction
  • Dividing in Given Ratio Example 3
  • Dividing in Given Ratio Example 2
  • Ratio and Proportion
  • Ratio
  • Dividing in Given Ratio Example 1
  • Ratio and Fraction
  • Simplifying Ratios Example 5
  • Simplifying Ratios Example 4
  • Simplifying Ratios Example 3
  • Simplifying Ratios Example 2
  • Simplifying Ratios Example 1
  • Ratio
  • Introduction to Ratio
  • Finding Whole Given Percentage Example 2
  • Finding Whole Given Percentage Example 1
  • Percentages
  • Finding Whole Given Fraction Example 3
  • Finding Whole Given Fraction Example 2
  • Finding Whole Given Fraction Example 1
  • Finding a Fraction of a Quantity
  • Fractions
  • Expressing one Quantity as a Fraction of Another
  • Extra Fraction Work
  • Finding the Original Quantity Example 4
  • Finding the Original Quantity Example 3
  • Finding the Original Quantity Example 2
  • Finding the Original Quantity Example 1
  • Finding the Original Quantity
  • Percentages Advanced
  • Finding the nth Term Example 4
  • Finding the nth Term Example 3
  • Finding the nth Term Example 2
  • nth Terms for Number Sequences
  • Finding the nth Term Example 1
  • Continuing a Sequence Example 3
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 1
  • Number Sequences and Patterns
  • Continuing a Sequence
  • Introduction to Recurring Decimals
  • Recurring Decimals
  • Reviewing Fraction Work Example 2
  • Reviewing Fraction Work Example 1
  • Fraction Review
  • Reciprocals
  • Reciprocals Introduction
  • Range of Values for a Corrected Number Example 8
  • Range of Values for a Corrected Number Example 7
  • Range of Values for a Corrected Number Example 6
  • Range of Values for a Corrected Number Example 5
  • Range of Values for a Corrected Number Example 4
  • Range of Values for a Corrected Number Example 3
  • Range of Values for a Corrected Number Example 2
  • Range of Values for a Corrected Number Example 1
  • Working With Numbers
  • Range of Values for a Corrected Number
  • The Meaning of the Zero Index
  • The Zero Index
  • Introduction to Standard Form Example 6
  • Introduction to Standard Form Example 5
  • Introduction to Standard Form Example 4
  • Introduction to Standard Form Example 3
  • Introduction to Standard Form Example 2
  • Introduction to Standard Form
  • Introduction to Standard Form Example 1
  • Negative Indices Example 3
  • Negative Indices Example 2
  • Negative Indices Example 1
  • Negative Indices
  • Second Index Law Example 2
  • The Second Index Law
  • Second Index Law Example 1
  • First Index Law Example 2
  • First Index Law Example 1
  • The First Index Law
  • Indices and Standard Form
  • Indices
  • Introduction to Indices
  • Decreasing a Quantity by a Given Percentage
  • Increasing a Quantity by a Given Percentage
  • Finding One Quantity as a Percentage of Another Example 2
  • Finding One Quantity as a Percentage of Another Example 1
  • Finding a percentage of a Quantity Example 4
  • Finding a percentage of a Quantity Example 3
  • Finding a percentage of a Quantity Example 2
  • Finding a percentage of a Quantity Example 1
  • Percentage of a Quantity
  • Percentages, Fractions and Decimals Example 3
  • Percentages, Fractions and Decimals Example 2
  • Percentages, Fractions and Decimals Example 1
  • Percentages, Fractions and Decimals
  • Introduction to Fractions and Percentages Example 4
  • Introduction to Fractions and Percentages Example 3
  • Introduction to Fractions and Percentages Example 2
  • Introduction to Fractions and Percentages Example 1
  • Percentages and Fractions
  • Introduction to Decimals and Percentages Example 3
  • Introduction to Decimals and Percentages Example 2
  • Percentages and Decimals
  • Introduction to Decimals and Percentages Example 1
  • Introduction
  • Introduction to Percentages
  • Percentages
  • Mixed Operations on a Calculator Involving Decimals
  • Dividing Decimals on a Calculator
  • Multiplying Decimals on a Calculator
  • Subtracting Decimals on a Calculator
  • Adding Decimals on a Calculator
  • Calculator Guide
  • Rounding to Significant Figures
  • Rounding to Decimal Places Example 2
  • Rounding to Decimal Places Example 1
  • Rounding to the Nearest Whole Number
  • Rounding
  • Directed Numbers
  • Decimals and Directed Numbers
  • Dividing Decimals by Decimals Example 4
  • Dividing Decimals by Decimals Example 3
  • Dividing Decimals by Decimals Example 2
  • Dividing Decimals by Decimals Example 1
  • Dividing Decimals by Decimals Introduction
  • Dividing Decimals by 10, 100 etc.
  • Dividing Decimals
  • Multiplying Decimals by Decimals Example 3
  • Multiplying Decimals by Decimals Example 2
  • Multiplying Decimals by Decimals Example 1
  • Multiplying Decimals by an Integer
  • Multiplying Decimals by 10, 100 etc.
  • Multiplying Decimals
  • Subtraction of Decimals
  • Subtracting Decimals
  • Adding Decimals
  • Addition of Decimals
  • Putting Decimals Into Numerical Order
  • Ordering Decimals
  • Introduction to Decimal Fractions
  • Decimals
  • Meaning of Decimals
  • Dividing Mixed Numbers on the Calculator
  • Dividing Fractions on the Calculator
  • Multiplying Mixed Numbers on the Calculator
  • Multiplying Fractions on the Calculator
  • Subtracting Mixed Numbers on the Calculator
  • Subtracting Fractions on the Calculator
  • Adding Mixed Numbers on the Calculator
  • Calculator Guide
  • Adding Fractions on the Calculator
  • Fractions with Mixed Operations Example 4
  • Fractions with Mixed Operations Example 3
  • Fractions with Mixed Operations Example 2
  • Using BIDMAS
  • Fractions with Mixed Operations Example 1
  • Directed Numbers
  • Directed Numbers and Fractions
  • Dividing - Whole Number and Mixed Number
  • Dividing - Dealing with Whole Numbers
  • Dividing - Dealing with Mixed Numbers
  • Dividing Fractions Example 2
  • Dividing Fractions Example 1
  • Dividing Fractions
  • Miscellaneous Example
  • Multiplying - Whole Number and Mixed Number
  • Multiplying - Dealing with Whole Numbers
  • Multiplying - Dealing with Mixed Numbers
  • Multiplying Fractions Example 2
  • Multiplying Fractions Example 1
  • Multiplying Fractions
  • Mixed Add and Subtract Example 2
  • Mixed Add and Subtract
  • Mixed Add and Subtract Example 1
  • Subtracting - Dealing with Mixed Numbers Example 2
  • Subtracting - Dealing with Mixed Numbers Example 1
  • Subtracting Using a Common Denominator Example 2
  • Subtracting Using a Common Denominator Example 1
  • Subtracting Fractions
  • Subtracting Fractions with the Same Denominator Example 1
  • Adding - Dealing with Mixed Numbers
  • Adding Using a Common Denominator Example 2
  • Adding Using a Common Denominator Example 1
  • Adding Fractions with the Same Denominator Example 2
  • Adding Fractions
  • Adding Fractions with the Same Denominator Example 1
  • Equivalent Fractions Example 3
  • Equivalent Fractions Example 2
  • Equivalent Fractions Example 1
  • Equivalent Fractions
  • Introduction
  • Introduction to Fractions
  • Fractions
  • Lowest Common Multiple Example 3
  • Lowest Common Multiple Example 2
  • Lowest Common Multiple
  • Lowest Common Multiple Example 1
  • Highest Common Factor Example 2
  • Highest Common Factor Example 1
  • Highest Common Factor
  • Expressing a Number as a Product of Primes
  • Divisibility Tests for Integers
  • Introduction to Prime Numbers
  • Prime Numbers
  • Multiples of Integers
  • Factors of Integers
  • Factors, Multiples, Prime Numbers
  • Factors and Multiples
  • Directed Numbers on the Calculator
  • BIDMAS on the Calculator Example 2
  • BIDMAS on the Calculator Example 1
  • Dividing Integers on the Calculator
  • Multiplying Integers on the Calculator
  • Subtracting Integers on the Calculator
  • Calculator Guide
  • Adding Integers on the Calculator
  • Dividing Directed Numbers
  • Multiplying Directed Numbers
  • Subtracting Directed Numbers
  • Adding Directed Numbers
  • Directed Numbers
  • Introduction to Directed Numbers
  • Mixed Operations with Integers - BIDMAS Example 2
  • Mixed Operations with Integers - BIDMAS Example 1
  • Mixed Operations
  • Dividing Two Integers Example 3
  • Dividing Two Integers Example 2
  • Dividing Two Integers Example 1
  • Dividing
  • Dividing Integers by 10, 100 etc.
  • Multiplying Two Integers Example 4 - Practical Example
  • Multiplying Algebraic Expressions Example 2
  • Basic Equations
  • Forming Simple Equations
  • Forming Simple Equations From Information Given
  • Solving Simple Equations
  • Equation as a Balance
  • Solving Simple Equations Example 1
  • Solving Simple Equations Example 2
  • Solving Simple Equations Example 3
  • Solving Simple Equations Example 4
  • Harder Equations
  • Collecting Like Terms Review
  • Harder Equations Example 1
  • Harder Equations Example 2
  • Harder Equations Example 3
  • Harder Equations Example 4
  • Basic Inequalities
  • Introduction to Inequalities
  • Introduction to Inequalities
  • Solving Simple Inequalities
  • Solving Simple Inequalities Example 1
  • Solving Simple Inequalities Example 2
  • Solving Simple Inequalities Example 3
  • Solving Simple Inequalities Example 4
  • Solving Simple Inequalities Example 5
  • Basic Formulae
  • Words and Symbols
  • Finding a Formula Example 1
  • Finding a Formula Example 2
  • Finding a Formula Example 3
  • Finding a Formula Example 4
  • Substitution
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Numbers into Formulae Example 5
  • Directed Numbers Review Example 1
  • Directed Numbers Review Example 2
  • Substituting with Directed Numbers Example 1
  • Substituting with Directed Numbers Example 2
  • Algebraic Products
  • Single Bracket
  • Expanding with a Single Bracket Example 1
  • Expanding with a Single Bracket Example 2
  • Expand and Simplify
  • Expanding Brackets Extension Example
  • Pair of Brackets
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Squaring a Bracket
  • Expanding (x + a)(x - a)
  • Pair of Brackets Extension Example
  • Expand and Simplify Extension Example
  • Factorising into a Single Bracket
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising into a Pair of Brackets
  • Factorising into a Pair of Brackets Example 1
  • Factorising into a Pair of Brackets Example 2
  • Factorising into a Pair of Brackets Example 3
  • Factorising into a Pair of Brackets Example 4
  • Factorising into a Pair of Brackets Example 5
  • Factorising into a Pair of Brackets Example 6
  • Factorising into a Pair of Brackets Example 7
  • Factorising into a Pair of Brackets Example 8
  • Factorising into a Pair of Brackets Example 9
  • Factorising into a Pair of Brackets Example 10
  • The Difference of 2 Squares
  • The Difference of 2 Squares Example 1
  • The Difference of 2 Squares Example 2
  • The Difference of 2 Squares Example 3
  • The Difference of 2 Squares Extension Example
  • Formulae with Brackets
  • Expanding Brackets Review
  • Expanding Brackets Review Example 1
  • Expanding Brackets Review Example 2
  • Expanding Brackets Review Example 3
  • Formulae with Brackets
  • Formulae with Brackets Example 1
  • Formulae with Brackets Example 2
  • Formulae with Brackets Example 3
  • Further Equations
  • Equations with Brackets
  • Solving Equations with Brackets Example 1
  • Solving Equations with Brackets Example 2
  • Further Inequalities
  • Inequalities with Brackets
  • Solving Inequalities with Brackets Example 1
  • Solving Inequalities with Brackets Example 2
  • Simultaneous Equations
  • Algebraic Solution
  • Simultaneous Equations Algebraic Solution Example 1
  • Simultaneous Equations Algebraic Solution Example 2
  • Simultaneous Equations Algebraic Solution Example 3
  • Simultaneous Equations Algebraic Solution Example 4
  • Simultaneous Equations Algebraic Solution Example 5
  • Simultaneous Equations Algebraic Solution Example 6
  • Simultaneous Equations Algebraic Solution Example 7
  • Simultaneous Equations Algebraic Solution Example 8
  • Graphical Solution
  • Simultaneous Equations Graphical Solution Example 1
  • Simultaneous Equations Graphical Solution Example 2
  • No Solutions or Infinite Solutions
  • No Solutions or Infinite Solutions
  • Problem Solving
  • Problem Solving Example 1
  • Problem Solving Example 2
  • More Formulae
  • Deriving Formulae
  • Deriving Formulae Example 1
  • Deriving Formulae Example 2
  • Deriving Formulae Example 3
  • Deriving Formulae Example 4
  • Substitution into Formulae
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Expressions into Formulae
  • Rearranging Formulae
  • Rearranging Formulae Example 1
  • Rearranging Formulae Example 2
  • Rearranging Formulae Example 3
  • Rearranging Formulae Example 4
  • nth Terms for Sequences
  • Finding nth Terms Example 1
  • Finding nth Terms Example 2
  • Finding nth Terms Example 3
  • Finding nth Terms Example 4
  • Graphs of Straight Lines
  • Vertical Lines
  • Equations of ines Parallel to the Y-Axis
  • Horizontal Lines
  • Equations of ines Parallel to the X-Axis
  • The Line y = x
  • The Line y = x
  • Plotting Lines from Equations
  • Plotting Lines Example 1
  • Plotting Lines Example 2
  • Plotting Lines Example 3
  • The Equation of a Straight Line
  • Equations of Straight Lines Introduction
  • Equations of Straight Lines Example 1
  • Equations of Straight Lines Example 2
  • Intersection
  • The Interection of Two Lines
  • The Interection of Two Lines Example 1
  • Parallel Lines
  • Parallel Lines Introduction
  • The Equations of Parallel Lines Example 1
  • The Equations of Parallel Lines Example 2
  • Perpendicular Lines
  • Perpendicular Lines Introduction
  • Gradients of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 2
  • Quadratic Equations
  • Solving Quadratic Equations
  • Introduction to Quadratic Equations Part 1
  • Introduction to Quadratic Equations Part 2
  • Introduction to Quadratic Equations Part 3
  • Solving Quadratic Equations by Factorising Example 1
  • Solving Quadratic Equations by Factorising Example 2
  • Solving Quadratic Equations by Factorising Example 3
  • Solving Quadratic Equations by Factorising Example 4
  • Solving Quadratic Equations by Factorising Example 5
  • Solving Quadratic Equations by Factorising Example 6
  • Solving Quadratic Equations by Factorising Example 7
  • Forming and Solving
  • Trial and Improvement
  • Solving Equations by Trial and Improvement Example 1
  • Solving Equations by Trial and Improvement Example 2
  • Solving Equations by Trial and Improvement Example 3
  • The Quadratic Formula
  • Solving Quadratic Equations Using The Formula Example 1
  • Solving Quadratic Equations Using The Formula Example 2
  • Solving Quadratic Equations Using The Formula Example 3
  • Solving Quadratic Equations Using The Formula Example 4
  • Completing the Square
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • The Meaning of Completed Square Form
  • Solving Quadratics by Completing the Square
  • Quadratic Equations Extension
  • Completing the Square
  • Deriving the Quadratic Formula
  • Quadratic Graphs
  • Plotting Quadratic Graphs
  • Plotting Quadratic Graphs Example 1
  • Plotting Quadratic Graphs Example 2
  • The Shape of a Quadratic
  • Happy or Sad?
  • Other Tables
  • Other Tables Example 1
  • Other Tables Example 2
  • Indices
  • Indices with Algebra
  • The First Index Law
  • The Second Index Law
  • The Power mn
  • Using the Index Laws Example 1
  • Negative Indices
  • Fractional Indices
  • Ratio and Proportion
  • Ratio Revision
  • Ratio Revision Example 1
  • Ratio Revision Example 2
  • Ratio Revision Example 3
  • Expressing a Ratio in the Form 1:n Example 1
  • Expressing a Ratio in the Form 1:n Example 2
  • Dividing in a Given Ratio Example 1
  • Dividing in a Given Ratio Example 2
  • Dividing in a Given Ratio Example 3
  • Direct Proportion
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Direct Proportion Example 4
  • Direct Proportion Example 5
  • Inverse Proportion
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Inverse Proportion Example 4
  • Inverse Proportion Example 5
  • Algebraic Fractions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Multiplying and Dividing
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Lowest Common Multiples
  • Lowest Common Multiples (Algebraic) Example 1
  • Lowest Common Multiples (Algebraic) Example 2
  • Lowest Common Multiples (Algebraic) Example 3
  • Lowest Common Multiples (Algebraic) Example 4
  • Adding and Subtracting
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Adding and Subtracting Algebraic Fractions Example 7
  • Equations
  • Solving Equations Involving Fractions Example 1
  • Solving Equations Involving Fractions Example 2
  • Solving Equations Involving Fractions Example 3
  • Advanced Formulae
  • Substitution
  • Substituting Numbers in Standard Form Example 1
  • Substituting Numbers in Standard Form Example 1 - Calculator Guide
  • Substituting Numbers in Standard Form Example 2
  • Substituting Numbers in Standard Form Example 2 - Calculator Guide
  • Substituting Numbers in Standard Form Example 3
  • Substituting Numbers in Standard Form Example 3 - Calculator Guide
  • Rearranging Formulae
  • Rearranging Formulae (Advanced) Example 1
  • Rearranging Formulae (Advanced) Example 2
  • Rearranging Formulae (Advanced) Example 3
  • Rearranging Formulae (Advanced) Example 4
  • Rearranging Formulae (Advanced) Example 5
  • Rearranging Formulae (Advanced) Example 6
  • Rearranging Formulae (Advanced) Example 7
  • Miscelaneous Example
  • Miscellaneous Example
  • Advanced Inequalities
  • Quadratic Inequalities
  • Solving Quadratic Inequalities Example 1
  • Solving Quadratic Inequalities Example 2
  • Solving Quadratic Inequalities Example 3
  • Solving Quadratic Inequalities Example 4
  • Advanced Graphs
  • Using a Quadratic Graph
  • Using a Quadratic Graph to Solve Quadratic Equations
  • Cubic Graphs
  • Cubic Graphs Example 1
  • Cubic Graphs Example 2
  • Cubic Graphs Example 3
  • Cubic Graphs Example 4
  • Reciprocal Graphs
  • Introducation to Reciprocal Graphs
  • Reciprocal Graphs Example 1
  • Reciprocal Graphs Example 2
  • Shapes of Graphs
  • Shapes of Graphs Introducation
  • Shapes of Graphs Example 1
  • Shapes of Graphs Example 2
  • Using General Graphs
  • Using General Graphs Example 1
  • Using General Graphs Example 2
  • Using General Graphs Example 3
  • Using Gradients of Graphs
  • Using Gradients of Graphs Introduction
  • Using Gradients of Graphs Example 1
  • Using Gradients of Graphs Example 2
  • Using Gradients of Graphs Example 3
  • Algebraic Proof
  • Proving Statements Using Algebra
  • Proof Example 1
  • Proof Example 2
  • Proof Example 3
  • Proof Example 4
  • Simultaneous Equations Linear and Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 4
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 5
  • Algebra
  • Algebra Basics
  • Introduction to Algebra
  • Introduction to Algebra
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Multiplying Algebraic Expressions Example 1
  • Multiplying Algebraic Expressions Example 2
  • Basic Equations
  • Forming Simple Equations
  • Forming Simple Equations From Information Given
  • Solving Simple Equations
  • Equation as a Balance
  • Solving Simple Equations Example 1
  • Solving Simple Equations Example 2
  • Solving Simple Equations Example 3
  • Solving Simple Equations Example 4
  • Shape Space and Measure
  • Basic Area
  • Introduction
  • Harder Equations
  • Collecting Like Terms Review
  • Harder Equations Example 1
  • Harder Equations Example 2
  • Harder Equations Example 3
  • Harder Equations Example 4
  • Basic Inequalities
  • Introduction to Inequalities
  • Introduction to Inequalities
  • Solving Simple Inequalities
  • Solving Simple Inequalities Example 1
  • Solving Simple Inequalities Example 2
  • Solving Simple Inequalities Example 3
  • Solving Simple Inequalities Example 4
  • Solving Simple Inequalities Example 5
  • Basic Formulae
  • Words and Symbols
  • Finding a Formula Example 1
  • Finding a Formula Example 2
  • Finding a Formula Example 3
  • Finding a Formula Example 4
  • Substitution
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Numbers into Formulae Example 5
  • Directed Numbers Review Example 1
  • Directed Numbers Review Example 2
  • Substituting with Directed Numbers Example 1
  • Substituting with Directed Numbers Example 2
  • Algebraic Products
  • Single Bracket
  • Expanding with a Single Bracket Example 1
  • Expanding with a Single Bracket Example 2
  • Expand and Simplify
  • Expanding Brackets Extension Example
  • Pair of Brackets
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Squaring a Bracket
  • Expanding (x + a)(x - a)
  • Pair of Brackets Extension Example
  • Expand and Simplify Extension Example
  • Factorising into a Single Bracket
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising into a Pair of Brackets
  • Factorising into a Pair of Brackets Example 1
  • Factorising into a Pair of Brackets Example 2
  • Factorising into a Pair of Brackets Example 3
  • Factorising into a Pair of Brackets Example 4
  • Factorising into a Pair of Brackets Example 5
  • Factorising into a Pair of Brackets Example 6
  • Factorising into a Pair of Brackets Example 7
  • Factorising into a Pair of Brackets Example 8
  • Factorising into a Pair of Brackets Example 9
  • Factorising into a Pair of Brackets Example 10
  • The Difference of 2 Squares
  • The Difference of 2 Squares Example 1
  • The Difference of 2 Squares Example 2
  • The Difference of 2 Squares Example 3
  • The Difference of 2 Squares Extension Example
  • Formulae with Brackets
  • Expanding Brackets Review
  • Expanding Brackets Review Example 1
  • Expanding Brackets Review Example 2
  • Expanding Brackets Review Example 3
  • Formulae with Brackets
  • Formulae with Brackets Example 1
  • Formulae with Brackets Example 2
  • Formulae with Brackets Example 3
  • Further Equations
  • Equations with Brackets
  • Solving Equations with Brackets Example 1
  • Solving Equations with Brackets Example 2
  • Further Inequalities
  • Inequalities with Brackets
  • Solving Inequalities with Brackets Example 1
  • Solving Inequalities with Brackets Example 2
  • Simultaneous Equations
  • Algebraic Solution
  • Simultaneous Equations Algebraic Solution Example 1
  • Simultaneous Equations Algebraic Solution Example 2
  • Simultaneous Equations Algebraic Solution Example 3
  • Simultaneous Equations Algebraic Solution Example 4
  • Simultaneous Equations Algebraic Solution Example 5
  • Simultaneous Equations Algebraic Solution Example 6
  • Simultaneous Equations Algebraic Solution Example 7
  • Simultaneous Equations Algebraic Solution Example 8
  • More Formulae
  • Deriving Formulae
  • Deriving Formulae Example 1
  • Deriving Formulae Example 2
  • Deriving Formulae Example 3
  • Deriving Formulae Example 4
  • Substitution into Formulae
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Expressions into Formulae
  • Rearranging Formulae
  • Rearranging Formulae Example 1
  • Rearranging Formulae Example 2
  • Rearranging Formulae Example 3
  • Rearranging Formulae Example 4
  • nth Terms for Sequences
  • Finding nth Terms Example 1
  • Finding nth Terms Example 2
  • Finding nth Terms Example 3
  • Finding nth Terms Example 4
  • Quadratic Equations
  • Solving Quadratic Equations
  • Introduction to Quadratic Equations Part 1
  • Introduction to Quadratic Equations Part 2
  • Introduction to Quadratic Equations Part 3
  • Solving Quadratic Equations by Factorising Example 1
  • Solving Quadratic Equations by Factorising Example 2
  • Solving Quadratic Equations by Factorising Example 3
  • Solving Quadratic Equations by Factorising Example 4
  • Solving Quadratic Equations by Factorising Example 5
  • Solving Quadratic Equations by Factorising Example 6
  • Solving Quadratic Equations by Factorising Example 7
  • Forming and Solving
  • Trial and Improvement
  • Solving Equations by Trial and Improvement Example 1
  • Solving Equations by Trial and Improvement Example 2
  • Solving Equations by Trial and Improvement Example 3
  • Indices
  • Indices with Algebra
  • The First Index Law
  • The Second Index Law
  • Using the Index Laws Example 1
  • Negative Indices
  • Ratio and Proportion
  • Ratio Revision
  • Ratio Revision Example 1
  • Ratio Revision Example 2
  • Ratio Revision Example 3
  • Expressing a Ratio in the Form 1:n Example 1
  • Expressing a Ratio in the Form 1:n Example 2
  • Dividing in a Given Ratio Example 1
  • Dividing in a Given Ratio Example 2
  • Dividing in a Given Ratio Example 3
  • Direct Proportion
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Direct Proportion Example 4
  • Direct Proportion Example 5
  • Inverse Proportion
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Inverse Proportion Example 4
  • Inverse Proportion Example 5
  • Introduction to Area Example 1
  • Introduction to Area Example 2
  • Introduction to Area Example 3
  • Standard Shapes
  • Area of a Square
  • Area of a Rectangle Example 1
  • Area of a Rectangle Example 2
  • Finding a Length
  • Compound Shapes
  • Shapes Made from Squares and Rectangles Example 1
  • Shapes Made from Squares and Rectangles Example 2
  • Shapes Made from Squares and Rectangles Example 3
  • Converting Units
  • Converting Between Units of Area Example 1
  • Converting Between Units of Area Example 2
  • Converting Between Units of Area Example 3
  • Converting Between Units of Area Example 4
  • Basic Perimeter
  • Perimeter
  • Basic Perimeter Example 1
  • Basic Perimeter Example 2
  • Basic Perimeter Example 3
  • Introducing Geometry
  • The Meaning of Angle
  • Introduction to Angles
  • Introduction to Measuring Angles
  • Types of Angle
  • Measuring Angles
  • Using a Protractor to Measure Angles
  • Using a Protractor to Draw Angles
  • Angle Facts
  • Vertically Opposite Angles
  • Angles on a Straight Line
  • Angles at a Point
  • Mixed Example
  • Triangles and Quadrilaterals
  • Naming Sides and Angles
  • Naming Angles
  • Naming Sides
  • Angle Sum for a Triangle
  • The Angle Sum for a Triangle Intro
  • The Angle Sum for a Triangle Example 1
  • The Angle Sum for a Triangle Example 2
  • The Angle Sum for a Triangle Example 3
  • The Angle Sum for a Triangle Example 4
  • The Angle Sum for a Triangle Example 5
  • Constructions
  • Side and Two Angles
  • Two Sides and an Angle
  • Three Sides
  • Quadrilaterals
  • Introduction to Quadrilaterals
  • Angle Sum for a Quadrilateral Example 1
  • Angle Sum for a Quadrilateral Example 2
  • Angle Sum for a Quadrilateral Example 3
  • Basic Coordinates
  • Introduction
  • Introduction to Coordinate Systems
  • Coordinates
  • Basic Coordinates Example 1
  • Basic Coordinates Example 2
  • Basic Coordinates Example 3
  • Negative Coordinates
  • Negative Coordinates Example 1
  • Negative Coordinates Example 2
  • Solids
  • Drawing Solids
  • Drawing a Cuboid on Squared Paper
  • Drawing a Cuboid on Isometric Paper
  • Counting Cubes
  • Nets
  • Folding a Net (Demonstration)
  • Folding a Net
  • Drawing a Net Example 1
  • Drawing a Net Example 2
  • Volume
  • Volume of a Cuboid Example 1
  • Volume of a Cuboid Example 2
  • Volume of a Cuboid Example 3
  • Volume of a Cuboid Example 4
  • Volume of a Cuboid Example 5
  • Volume of a Cuboid Example 6
  • Unit Conversion
  • Converting Cubic Units Example 1
  • Converting Cubic Units Example 2
  • Converting Cubic Units Example 3
  • Capacity
  • The Meaning of Capacity
  • Capacity Example 1
  • Capacity Example 2
  • Surface Area
  • Surface Area of a Cuboid Example 1
  • Surface Area of a Cuboid Example 2
  • Imperial Units
  • Imperial Units of Volume
  • Parallel Lines
  • Introduction
  • Introduction to Parallel Lines
  • Corresponding Angles
  • Introduction to Corresponding Angles
  • Corresponding Angles Example 1
  • Corresponding Angles Example 2
  • Corresponding Angles Example 3
  • Corresponding Angles Example 4
  • Alternate Angles
  • Introduction to Alternate Angles
  • Alternate Angles Example 1
  • Alternate Angles Example 2
  • Alternate Angles Example 3
  • Interior Angles
  • Introduction to Interior Angles
  • Interior Angles Example 1
  • Mixed Questions
  • Parallel Lines Mixed Example 1
  • Parallel Lines Mixed Example 2
  • Polygons
  • Introduction to Polygons
  • Introduction to Polygons
  • Regular and Irregular Polygons
  • Regular and Irregular Polygons
  • Interior and Exterior Angles
  • Interior and Exterior Angles
  • Sum of Exterior Angles
  • Sum of Exterior Angles Example 1
  • Sum of Exterior Angles Example 2
  • Sum of Exterior Angles Example 3
  • Interior Angles
  • Interior Angles Example 1
  • Interior Angles Example 2
  • Interior Angles Example 3
  • Pythagoras' Theorem
  • Introduction
  • Introduction to Pythagoas' Theorem
  • Finding the Hypotenuse
  • Finding the Hypotenuse Example 1
  • Finding the Hypotenuse Example 2
  • Finding the Hypotenuse Example 3
  • Finding the Hypotenuse Calculator Guide
  • Finding a Shorter Side
  • Finding a Shorter Side Example 1
  • Finding a Shorter Side Example 2
  • Finding a Shorter Side Example 3
  • Finding a Shorter Side Calculator Guide
  • Harder Problems
  • Harder Problems Example
  • Three Dimensional Problems
  • Pythagoras in 3 Dimensions
  • More Length, Area and Volume
  • Area of a Triangle
  • Introduction to the Area of a Triangle
  • Area of a Triangle Example 1
  • Area of a Triangle Example 2
  • Area of a Triangle Example 3
  • Area of a Triangle Example 4
  • Area of a Parallelogram
  • Introduction to the Area of a Parallelogram
  • Area of a Parallelogram Example 1
  • Area of a Parallelogram Example 2
  • Area of a Parallelogram Example 3
  • Area of a Trapezium
  • Introduction to the Area of a Trapezium
  • Area of a Trapezium Example 1
  • Area and Circumference of a Circle
  • Terminology and Introduction to the Circle
  • Area and Circumference Example 1
  • Area and Circumference Calculator Guide 1
  • Area and Circumference Example 2
  • Area and Circumference Example 3
  • Area and Circumference Example 4
  • Area and Circumference Example 5
  • Area and Circumference Example 6
  • Sectors of Circles
  • More Terminology of Circles
  • Introduction to Area of Sector
  • Introduction to Arc Length
  • Area of Sector and Arc length Example 1
  • Area of Sector and Arc length Example 2
  • Area of Sector and Arc length Example 3
  • Volume of a Prism
  • What is a Prism?
  • Volume of a Prism Example 1
  • Volume of a Prism Example 2
  • Volume of a Prism Example 3
  • Volume of a Prism Example 4
  • Dimensions of a Formula
  • Dimensions Introduction Part 1
  • Dimensions Example 1
  • Dimensions Introduction Part 2
  • Dimensions Example 2
  • Dimensions Example 3
  • Trigonometry
  • Introduction
  • Introduction to Trigonometry
  • Collecting Like Terms Example 2
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Calculator Guide 1
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding a Side Calculator Guide 2
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Finding an Angle Calculator Guide
  • Harder Examples
  • Multi-Step Trig Problems Example 1
  • Multi-Step Trig Problems Example 2
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1
  • Three Dimensional Problems Example 2
  • Further Area and Volume
  • Upper and Lower Bounds
  • Upper and Lower Bounds Example 1
  • Upper and Lower Bounds Example 2
  • Upper and Lower Bounds and Trigonometry Example 1
  • Upper and Lower Bounds and Trigonometry Example 2
  • Pyramids
  • The Volume and Area of a Pyramid
  • Pyramid Example 1
  • Pyramid Example 2
  • Pyramid Example 3
  • Angle Between a Line and a Plane
  • definition of the Angle Between a Line and a Plane
  • Angle Between a Line and a Plane Example 1
  • Angle Between a Line and a Plane Example 2
  • Cylinders
  • The Volume and Area of a Cylinder
  • Cylinder Example 1
  • Cylinder Example 2
  • Cones
  • The Volume and Area of a Cone
  • Cone Example 1
  • Cone Example 2
  • Cone Example 3
  • Spheres
  • The Volume and Area of a Sphere
  • Sphere Example 1
  • Sphere Example 2
  • Sphere Example 3
  • Sphere Example 4
  • Sphere Example 5
  • Sphere Example 6
  • Sine and Cosine Rules
  • Introduction to Sine and Cosine Rules
  • Non Right-Angled Trigonometry
  • The Sine Rule
  • The Cosine Rule
  • Using The Sine Rule
  • Using The Sine Rule Example 1
  • Using The Sine Rule Example 2
  • Using the Cosine Rule
  • Using the Cosine Rule Example 1
  • Using the Cosine Rule Example 2
  • Miscellaneous Example
  • Finding All of the Unknowns in a Triangle
  • Extension - Ambiguity
  • The Ambiguous Case of the Sine Rule
  • Shape Space and Measure
  • Basic Area
  • Introduction
  • Introduction to Area Example 1
  • Introduction to Area Example 2
  • Introduction to Area Example 3
  • Standard Shapes
  • Area of a Square
  • Area of a Rectangle Example 1
  • Area of a Rectangle Example 2
  • Finding a Length
  • Compound Shapes
  • Shapes Made from Squares and Rectangles Example 1
  • Shapes Made from Squares and Rectangles Example 2
  • Shapes Made from Squares and Rectangles Example 3
  • Converting Units
  • Converting Between Units of Area Example 1
  • Converting Between Units of Area Example 2
  • Converting Between Units of Area Example 3
  • Converting Between Units of Area Example 4
  • Basic Perimeter
  • Perimeter
  • Basic Perimeter Example 1
  • Basic Perimeter Example 2
  • Basic Perimeter Example 3
  • Introducing Geometry
  • The Meaning of Angle
  • Introduction to Angles
  • Introduction to Measuring Angles
  • Types of Angle
  • Measuring Angles
  • Using a Protractor to Measure Angles
  • Using a Protractor to Draw Angles
  • Angle Facts
  • Vertically Opposite Angles
  • Angles on a Straight Line
  • Angles at a Point
  • Mixed Example
  • Triangles and Quadrilaterals
  • Naming Sides and Angles
  • Naming Angles
  • Naming Sides
  • Angle Sum for a Triangle
  • The Angle Sum for a Triangle Intro
  • The Angle Sum for a Triangle Example 1
  • The Angle Sum for a Triangle Example 2
  • The Angle Sum for a Triangle Example 3
  • The Angle Sum for a Triangle Example 4
  • The Angle Sum for a Triangle Example 5
  • Constructions
  • Side and Two Angles
  • Two Sides and an Angle
  • Three Sides
  • Quadrilaterals
  • Introduction to Quadrilaterals
  • Angle Sum for a Quadrilateral Example 1
  • Angle Sum for a Quadrilateral Example 2
  • Angle Sum for a Quadrilateral Example 3
  • Basic Coordinates
  • Introduction
  • Introduction to Coordinate Systems
  • Coordinates
  • Basic Coordinates Example 1
  • Basic Coordinates Example 2
  • Basic Coordinates Example 3
  • Negative Coordinates
  • Negative Coordinates Example 1
  • Negative Coordinates Example 2
  • Solids
  • Drawing Solids
  • Drawing a Cuboid on Squared Paper
  • Drawing a Cuboid on Isometric Paper
  • Counting Cubes
  • Nets
  • Folding a Net (Demonstration)
  • Folding a Net
  • Drawing a Net Example 1
  • Drawing a Net Example 2
  • Volume
  • Volume of a Cuboid Example 1
  • Volume of a Cuboid Example 2
  • Volume of a Cuboid Example 3
  • Volume of a Cuboid Example 4
  • Volume of a Cuboid Example 5
  • Volume of a Cuboid Example 6
  • Unit Conversion
  • Converting Cubic Units Example 1
  • Converting Cubic Units Example 2
  • Converting Cubic Units Example 3
  • Capacity
  • The Meaning of Capacity
  • Capacity Example 1
  • Capacity Example 2
  • Surface Area
  • Surface Area of a Cuboid Example 1
  • Surface Area of a Cuboid Example 2
  • Imperial Units
  • Imperial Units of Volume
  • Parallel Lines
  • Introduction
  • Introduction to Parallel Lines
  • Corresponding Angles
  • Introduction to Corresponding Angles
  • Corresponding Angles Example 1
  • Corresponding Angles Example 2
  • Corresponding Angles Example 3
  • Corresponding Angles Example 4
  • Alternate Angles
  • Introduction to Alternate Angles
  • Alternate Angles Example 1
  • Alternate Angles Example 2
  • Alternate Angles Example 3
  • Interior Angles
  • Introduction to Interior Angles
  • Interior Angles Example 1
  • Mixed Questions
  • Parallel Lines Mixed Example 1
  • Parallel Lines Mixed Example 2
  • Polygons
  • Introduction to Polygons
  • Introduction to Polygons
  • Regular and Irregular Polygons
  • Regular and Irregular Polygons
  • Interior and Exterior Angles
  • Interior and Exterior Angles
  • Sum of Exterior Angles
  • Sum of Exterior Angles Example 1
  • Sum of Exterior Angles Example 2
  • Sum of Exterior Angles Example 3
  • Interior Angles
  • Interior Angles Example 1
  • Interior Angles Example 2
  • Interior Angles Example 3
  • Pythagoras' Theorem
  • Introduction
  • Introduction to Pythagoas' Theorem
  • Finding the Hypotenuse
  • Finding the Hypotenuse Example 1
  • Finding the Hypotenuse Example 2
  • Finding the Hypotenuse Example 3
  • Finding the Hypotenuse Calculator Guide
  • Introduction to Recurring Decimals
  • Recurring Decimals
  • Fractions Involving BIDMAS Example 3
  • Fractions Involving BIDMAS Example 2
  • Fractions Involving BIDMAS Example 1
  • Fractions Involving BIDMAS
  • Working With Numbers Extension
  • Reviewing Fraction Work Example 2
  • Reviewing Fraction Work Example 1
  • Fraction Review
  • Reciprocals Introduction
  • Reciprocals
  • Range of Values for a Corrected Number Example 8
  • Range of Values for a Corrected Number Example 7
  • Range of Values for a Corrected Number Example 6
  • Range of Values for a Corrected Number Example 5
  • Range of Values for a Corrected Number Example 4
  • Range of Values for a Corrected Number Example 3
  • Range of Values for a Corrected Number Example 2
  • Range of Values for a Corrected Number Example 1
  • Range of Values for a Corrected Number
  • Working With Numbers
  • The Zero Index
  • The Meaning of the Zero Index
  • Introduction to Standard Form Example 6
  • Introduction to Standard Form Example 5
  • Introduction to Standard Form Example 4
  • Introduction to Standard Form Example 3
  • Introduction to Standard Form Example 2
  • Introduction to Standard Form Example 1
  • Introduction to Standard Form
  • Negative Indices Example 3
  • Negative Indices Example 2
  • Negative Indices Example 1
  • Negative Indices
  • Second Index Law Example 2
  • Second Index Law Example 1
  • The Second Index Law
  • First Index Law Example 2
  • First Index Law Example 1
  • The First Index Law
  • Introduction to Indices
  • Indices
  • Indices and Standard Form
  • Decreasing a Quantity by a Given Percentage
  • Increasing a Quantity by a Given Percentage
  • Finding One Quantity as a Percentage of Another Example 2
  • Finding One Quantity as a Percentage of Another Example 1
  • Finding a percentage of a Quantity Example 4
  • Finding a percentage of a Quantity Example 3
  • Finding a percentage of a Quantity Example 2
  • Finding a percentage of a Quantity Example 1
  • Percentage of a Quantity
  • Percentages, Fractions and Decimals Example 3
  • Percentages, Fractions and Decimals Example 2
  • Percentages, Fractions and Decimals Example 1
  • Percentages, Fractions and Decimals
  • Introduction to Fractions and Percentages Example 4
  • Introduction to Fractions and Percentages Example 3
  • Introduction to Fractions and Percentages Example 2
  • Percentages and Fractions
  • Introduction to Fractions and Percentages Example 1
  • Introduction to Decimals and Percentages Example 3
  • Introduction to Decimals and Percentages Example 2
  • Introduction to Decimals and Percentages Example 1
  • Percentages and Decimals
  • Introduction to Percentages
  • Introduction
  • Percentages
  • Mixed Operations on a Calculator Involving Decimals
  • Dividing Decimals on a Calculator
  • Multiplying Decimals on a Calculator
  • Subtracting Decimals on a Calculator
  • Adding Decimals on a Calculator
  • Calculator Guide
  • Rounding to Significant Figures
  • Rounding to Decimal Places Example 2
  • Rounding to Decimal Places Example 1
  • Rounding to the Nearest Whole Number
  • Rounding
  • Decimals and Directed Numbers
  • Directed Numbers
  • Dividing Decimals by Decimals Example 4
  • Dividing Decimals by Decimals Example 3
  • Dividing Decimals by Decimals Example 2
  • Dividing Decimals by Decimals Example 1
  • Dividing Decimals by Decimals Introduction
  • Dividing Decimals
  • Dividing Decimals by 10, 100 etc.
  • Multiplying Decimals by Decimals Example 3
  • Multiplying Decimals by Decimals Example 2
  • Multiplying Decimals by Decimals Example 1
  • Multiplying Decimals by an Integer
  • Multiplying Decimals
  • Multiplying Decimals by 10, 100 etc.
  • Subtraction of Decimals
  • Subtracting Decimals
  • Addition of Decimals
  • Adding Decimals
  • Putting Decimals Into Numerical Order
  • Ordering Decimals
  • Meaning of Decimals
  • Introduction to Decimal Fractions
  • Decimals
  • Dividing Mixed Numbers on the Calculator
  • Dividing Fractions on the Calculator
  • Multiplying Mixed Numbers on the Calculator
  • Multiplying Fractions on the Calculator
  • Subtracting Mixed Numbers on the Calculator
  • Subtracting Fractions on the Calculator
  • Adding Mixed Numbers on the Calculator
  • Adding Fractions on the Calculator
  • Calculator Guide
  • Fractions with Mixed Operations Example 4
  • Fractions with Mixed Operations Example 3
  • Fractions with Mixed Operations Example 2
  • Fractions with Mixed Operations Example 1
  • Using BIDMAS
  • Directed Numbers and Fractions
  • Directed Numbers
  • Dividing - Whole Number and Mixed Number
  • Dividing - Dealing with Whole Numbers
  • Dividing - Dealing with Mixed Numbers
  • Dividing Fractions Example 2
  • Dividing Fractions
  • Dividing Fractions Example 1
  • Miscellaneous Example
  • Multiplying - Whole Number and Mixed Number
  • Multiplying - Dealing with Whole Numbers
  • Multiplying - Dealing with Mixed Numbers
  • Multiplying Fractions Example 2
  • Multiplying Fractions
  • Multiplying Fractions Example 1
  • Mixed Add and Subtract Example 2
  • Mixed Add and Subtract Example 1
  • Mixed Add and Subtract
  • Subtracting - Dealing with Mixed Numbers Example 2
  • Subtracting - Dealing with Mixed Numbers Example 1
  • Subtracting Using a Common Denominator Example 2
  • Subtracting Using a Common Denominator Example 1
  • Subtracting Fractions with the Same Denominator Example 1
  • Subtracting Fractions
  • Adding - Dealing with Mixed Numbers
  • Adding Using a Common Denominator Example 2
  • Adding Using a Common Denominator Example 1
  • Adding Fractions with the Same Denominator Example 2
  • Adding Fractions with the Same Denominator Example 1
  • Adding Fractions
  • Equivalent Fractions Example 3
  • Equivalent Fractions Example 2
  • Equivalent Fractions Example 1
  • Equivalent Fractions
  • Introduction to Fractions
  • Introduction
  • Fractions
  • Lowest Common Multiple Example 3
  • Lowest Common Multiple Example 2
  • Lowest Common Multiple Example 1
  • Lowest Common Multiple
  • Highest Common Factor Example 2
  • Highest Common Factor Example 1
  • Highest Common Factor
  • Expressing a Number as a Product of Primes
  • Divisibility Tests for Integers
  • Introduction to Prime Numbers
  • Prime Numbers
  • Multiples of Integers
  • Factors of Integers
  • Factors and Multiples
  • Factors, Multiples, Prime Numbers
  • Directed Numbers on the Calculator
  • BIDMAS on the Calculator Example 2
  • BIDMAS on the Calculator Example 1
  • Dividing Integers on the Calculator
  • Multiplying Integers on the Calculator
  • Subtracting Integers on the Calculator
  • Adding Integers on the Calculator
  • Calculator Guide
  • Dividing Directed Numbers
  • Multiplying Directed Numbers
  • Subtracting Directed Numbers
  • Adding Directed Numbers
  • Introduction to Directed Numbers
  • Directed Numbers
  • Mixed Operations with Integers - BIDMAS Example 2
  • Mixed Operations
  • Mixed Operations with Integers - BIDMAS Example 1
  • Dividing Two Integers Example 4
  • Dividing
  • Integers - Extension
  • Dividing Two Integers Example 3
  • Dividing Two Integers Example 2
  • Dividing Two Integers Example 1
  • Dividing Integers by 10, 100 etc.
  • Dividing
  • Multiplying Two Integers Example 4 - Practical Example
  • Multiplying Two Integers Example 3
  • Multiplying Two Integers Example 2
  • Multiplying Two Integers Example 1
  • Multiplying Integers by 10, 100 etc.
  • Introduction to Multiplying Integers
  • Multiplying
  • Rounding Integers Example 3
  • Rounding Integers Example 2
  • Rounding Integers Example 1
  • Rounding
  • Mixed Example 1
  • Addition and Subtraction
  • Subtracting Integers Example 2
  • Borrowing Digits Explained
  • Subtraction
  • Subtracting Integers Example 1
  • Adding Integers Example 3
  • Carrying Figures Explained
  • Adding Integers Example 2
  • Adding Integers Example 1
  • Integers
  • Addition
  • GCSE-H
  • Number
  • Finding a Shorter Side
  • Finding a Shorter Side Example 1
  • Finding a Shorter Side Example 2
  • Finding a Shorter Side Example 3
  • Finding a Shorter Side Calculator Guide
  • Harder Problems
  • Harder Problems Example
  • Three Dimensional Problems
  • Pythagoras in 3 Dimensions
  • More Length, Area and Volume
  • Area of a Triangle
  • Introduction to the Area of a Triangle
  • Area of a Triangle Example 1
  • Area of a Triangle Example 2
  • Area of a Triangle Example 3
  • Area of a Triangle Example 4
  • Area of a Parallelogram
  • Introduction to the Area of a Parallelogram
  • Area of a Parallelogram Example 1
  • Area of a Parallelogram Example 2
  • Area of a Parallelogram Example 3
  • Area of a Trapezium
  • Introduction to the Area of a Trapezium
  • Area of a Trapezium Example 1
  • Area and Circumference of a Circle
  • Terminology and Introduction to the Circle
  • Area and Circumference Example 1
  • Area and Circumference Calculator Guide 1
  • Area and Circumference Example 2
  • Area and Circumference Example 3
  • Area and Circumference Example 4
  • Area and Circumference Example 5
  • Area and Circumference Example 6
  • Sectors of Circles
  • More Terminology of Circles
  • Introduction to Area of Sector
  • Introduction to Arc Length
  • Area of Sector and Arc length Example 1
  • Area of Sector and Arc length Example 2
  • Area of Sector and Arc length Example 3
  • Volume of a Prism
  • What is a Prism?
  • Volume of a Prism Example 1
  • Volume of a Prism Example 2
  • Volume of a Prism Example 3
  • Volume of a Prism Example 4
  • Dimensions of a Formula
  • Dimensions Introduction Part 1
  • Dimensions Example 1
  • Dimensions Introduction Part 2
  • Dimensions Example 2
  • Dimensions Example 3
  • Trigonometry
  • Introduction
  • Introduction to Trigonometry
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Calculator Guide 1
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding a Side Calculator Guide 2
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Finding an Angle Calculator Guide
  • Further Area and Volume
  • Cylinders
  • The Volume and Area of a Cylinder
  • Cylinder Example 1
  • Cylinder Example 2
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Factorising into a Single Bracket Example 3
  • Symmetry
  • Line Symmetry
  • Line Symmetry Example 1
  • Line Symmetry Example 2
  • Line Symmetry Example 3
  • Line Symmetry Example 4
  • Rotational Symmetry
  • Rotational Symmetry Example 1
  • Rotational Symmetry Example 2
  • Both Types of Symmetry
  • Both Types of Symmetry
  • Sections and Planes of Symmetry
  • Sections Example 1
  • Congruence
  • Planes of Symmetry
  • Loci
  • Introduction to Loci
  • Loci Introduction
  • Loci Examples
  • Loci Examples Example 1
  • Loci Examples Example 2
  • Loci Examples Example 3
  • Loci Examples Example 4
  • Symmetry
  • Line Symmetry
  • Line Symmetry Example 1
  • Line Symmetry Example 2
  • Line Symmetry Example 3
  • Line Symmetry Example 4
  • Rotational Symmetry
  • Rotational Symmetry Example 1
  • Rotational Symmetry Example 2
  • Both Types of Symmetry
  • Both Types of Symmetry
  • Sections and Planes of Symmetry
  • Sections Example 1
  • Congruence
  • Planes of Symmetry
  • Loci
  • Introduction to Loci
  • Loci Introduction
  • Loci Examples
  • Loci Examples Example 1
  • Loci Examples Example 2
  • Loci Examples Example 3
  • Loci Examples Example 4
  • IB-HL
  • Background
  • Algebra
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Designing Questionnaires
  • Questionnaires
  • Pros and Cons
  • The Stratified Sample Example 2
  • The Stratified Sample Example 1
  • The Systematic Sample
  • Introduction to Sampling
  • The Random Sample
  • Sampling
  • Intro to Two Way Tables Example 2
  • Intro to Two Way Tables Example 1
  • Intro to Two Way Tables
  • Two Way Tables
  • Other Uses of Cumulative Frequency Example 3
  • Other Uses of Cumulative Frequency Example 2
  • Other Uses
  • Other Uses of Cumulative Frequency Example 1
  • Using Cumulative Frequency to Find Median and Quartiles Example 2
  • Using Cumulative Frequency to Find Median and Quartiles Example 1
  • Median and Quartiles
  • Drawing a Cumulative Frequency Graph Example 2
  • Drawing a Cumulative Frequency Graph Example 1
  • Drawing a Cumulative Frequency Graph
  • Producing a Cumulative Frequency Example 2
  • Producing a Cumulative Frequency Example 1
  • Cumulative Frequency
  • Producing a Cumulative Frequency
  • Tree Diagrams Example 4
  • Tree Diagrams Example 3
  • Tree Diagrams Example 2
  • Tree Diagrams Example 1
  • Introduction to Tree Diagrams - Part 2
  • Tree Diagrams
  • Introduction to Tree Diagrams - Part 1
  • Probability 4
  • The Multiplication Rule Example 2
  • The Multiplication Rule Example 1
  • Multiplication Rule
  • The Addition Rule Example 1
  • Addition Rule
  • Mutuallly Exclusive or Independent?
  • Independent Events 2
  • Independent Events 1
  • Mutually Exclusive Events
  • Probability 3
  • Mutually Exclusive and Independent Events
  • A Note on Correlation
  • Correlation
  • Plotting and Using Scatter Diagrams
  • Plotting and Using
  • Scatter Diagrams Introduction
  • Scatter Diagrams Introduction
  • Scatter Diagrams
  • Expected Number of Occurrences Example 3
  • Expected Number of Occurrences Example 2
  • Expected Number of Occurrences
  • Expected Number of Occurrences Example 1
  • Possibility (Sample) Spaces Example 4
  • Possibility (Sample) Spaces Example 3
  • Possibility (Sample) Spaces Example 2
  • Possibility (Sample) Spaces
  • Possibility (Sample) Spaces Example 1
  • The Sum for All Possibilities Example 2
  • The Sum for All Possibilities Example 1
  • The Sum for All Possibilities
  • The probability of An Event Not Happening Example 3
  • The probability of An Event Not Happening Example 2
  • An Event Not Happening
  • The probability of An Event Not Happening Example 1
  • Probability 2
  • Experimental Probability Example 2
  • Experimental Probability
  • Experimental Probability Example 1
  • Basic Theoretical Probabilility Example 3
  • Basic Theoretical Probabilility Example 2
  • Basic Theoretical Probabilility Example 1
  • Theoretical Probabilility
  • Types of Probability
  • The Probability Scale
  • Probability 1
  • Introduction to Probability
  • Straight Lines
  • Straight Lines Example 1
  • Conversion Graphs Example 1
  • Conversion Graphs
  • Reading from Line Graphs
  • Reading from Line Graphs Example 1
  • Line Graphs
  • Stem and Leaf Diagrams Example 3
  • Stem and Leaf Diagrams Example 2
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams Example 1
  • Boxplots Example 3
  • Boxplots Example 2
  • Boxplots
  • Boxplots Example 1
  • Calculating the Interquartile Range Example 2
  • Calculating the Interquartile Range Example 1
  • The Interquartile Range
  • Finding Quartiles Example 2
  • Finding Quartiles Example 1
  • Quartiles
  • The Range for Grouped Data
  • The Mode for Grouped Data
  • The Median for Grouped Data
  • The Mean for Grouped Data
  • Grouped Data
  • Grouping Data
  • Calculating the Range
  • The Range
  • The Mean for a Frequency Distribution
  • The Mean for a Set of Numbers
  • The Median for a Frequency Distribution
  • The Median for a Set of Numbers
  • The Mode for a Frequency Distribution
  • The Mode for a Set of Numbers
  • Averages
  • Averages
  • Why Summarise Data?
  • Organising and Summarising Data
  • Summarising Data
  • Pie Charts Example 2
  • Data Handling
  • Basic Statistics
  • Frequency Tables
  • Creating a Frequency Table Example 1
  • Creating a Frequency Table Example 2
  • Observation Sheet
  • Collecting Data on an Observation Sheet
  • Bar Charts
  • Bar Chart Example 1
  • Bar Chart Example 2
  • Pictograms
  • Pictograms Example 1
  • Misleading Diagrams
  • Misleading Diagrams Example 1
  • Pie Charts
  • Pie Charts Example 1
  • Pie Charts Example 2
  • Organising and Summarising Data
  • Summarising Data
  • Why Summarise Data?
  • Averages
  • Averages
  • The Mode for a Set of Numbers
  • The Mode for a Frequency Distribution
  • The Median for a Set of Numbers
  • The Median for a Frequency Distribution
  • The Mean for a Set of Numbers
  • The Mean for a Frequency Distribution
  • The Range
  • Calculating the Range
  • Grouped Data
  • Grouping Data
  • The Mean for Grouped Data
  • The Median for Grouped Data
  • The Mode for Grouped Data
  • The Range for Grouped Data
  • Quartiles
  • Finding Quartiles Example 1
  • Finding Quartiles Example 2
  • The Interquartile Range
  • Calculating the Interquartile Range Example 1
  • Calculating the Interquartile Range Example 2
  • Boxplots
  • Boxplots Example 1
  • Boxplots Example 2
  • Boxplots Example 3
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams Example 1
  • Stem and Leaf Diagrams Example 2
  • Stem and Leaf Diagrams Example 3
  • Line Graphs
  • Reading from Line Graphs
  • Reading from Line Graphs Example 1
  • Conversion Graphs
  • Conversion Graphs Example 1
  • Straight Lines
  • Straight Lines Example 1
  • Probability 1
  • Introduction to Probability
  • The Probability Scale
  • Types of Probability
  • Theoretical Probabilility
  • Basic Theoretical Probabilility Example 1
  • Basic Theoretical Probabilility Example 2
  • Basic Theoretical Probabilility Example 3
  • Experimental Probability
  • Experimental Probability Example 1
  • Experimental Probability Example 2
  • Probability 2
  • An Event Not Happening
  • The probability of An Event Not Happening Example 1
  • The probability of An Event Not Happening Example 2
  • The probability of An Event Not Happening Example 3
  • The Sum for All Possibilities
  • The Sum for All Possibilities Example 1
  • The Sum for All Possibilities Example 2
  • Possibility (Sample) Spaces
  • Possibility (Sample) Spaces Example 1
  • Possibility (Sample) Spaces Example 2
  • Possibility (Sample) Spaces Example 3
  • Possibility (Sample) Spaces Example 4
  • Expected Number of Occurrences
  • Expected Number of Occurrences Example 1
  • Expected Number of Occurrences Example 2
  • Expected Number of Occurrences Example 3
  • Scatter Diagrams
  • Scatter Diagrams Introduction
  • Scatter Diagrams Introduction
  • Plotting and Using
  • Plotting and Using Scatter Diagrams
  • Correlation
  • A Note on Correlation
  • Probability 3
  • Mutually Exclusive and Independent Events
  • Mutually Exclusive Events
  • Independent Events 1
  • Independent Events 2
  • Mutuallly Exclusive or Independent?
  • Addition Rule
  • The Addition Rule Example 1
  • Multiplication Rule
  • The Multiplication Rule Example 1
  • The Multiplication Rule Example 2
  • Miscellaneous Probability Example
  • Miscellaneous Probability Example
  • Conditional Probability
  • Conditional Probability Example 1
  • Conditional Probability Example 2
  • Probability 4
  • Tree Diagrams
  • Introduction to Tree Diagrams - Part 1
  • Introduction to Tree Diagrams - Part 2
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Tree Diagrams Example 3
  • Tree Diagrams Example 4
  • Tree Diagrams Example 5
  • Tree Diagrams Example 6
  • Cumulative Frequency
  • Producing a Cumulative Frequency
  • Producing a Cumulative Frequency Example 1
  • Producing a Cumulative Frequency Example 2
  • Drawing a Cumulative Frequency Graph
  • Drawing a Cumulative Frequency Graph Example 1
  • Drawing a Cumulative Frequency Graph Example 2
  • Median and Quartiles
  • Using Cumulative Frequency to Find Median and Quartiles Example 1
  • Using Cumulative Frequency to Find Median and Quartiles Example 2
  • Other Uses
  • Other Uses of Cumulative Frequency Example 1
  • Other Uses of Cumulative Frequency Example 2
  • Other Uses of Cumulative Frequency Example 3
  • Histograms
  • Histograms and Their Use
  • Histograms Introduction
  • Histograms Example 1
  • Histograms Example 2
  • Two Way Tables
  • Intro to Two Way Tables
  • Intro to Two Way Tables Example 1
  • Intro to Two Way Tables Example 2
  • Sampling
  • Introduction to Sampling
  • The Random Sample
  • The Systematic Sample
  • The Stratified Sample Example 1
  • The Stratified Sample Example 2
  • Pros and Cons
  • Questionnaires
  • Designing Questionnaires
  • Moving Averages
  • Calculating and using Moving Averages
  • Calculating and using Moving Averages Example 1
  • Calculating and using Moving Averages Example 2
  • Calculating and using Moving Averages Example 3
  • Data Handling
  • Basic Statistics
  • Frequency Tables
  • Creating a Frequency Table Example 1
  • Creating a Frequency Table Example 2
  • Observation Sheet
  • Collecting Data on an Observation Sheet
  • Bar Charts
  • Bar Chart Example 1
  • Bar Chart Example 2
  • Pictograms
  • Pictograms Example 1
  • Misleading Diagrams
  • Misleading Diagrams Example 1
  • Pie Charts
  • Pie Charts Example 1
  • Working with Surds Example 1
  • Surd Introduction
  • Surds
  • Factorising Quadratic Expressions Example 6
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 1
  • Factorising into a Single Bracket Example 4
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 1
  • Factorising Expressions
  • Expanding a Pair of Brackets Example 4
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 1
  • Expanding a Single Bracket Example 4
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 1
  • Expanding Brackets
  • Collecting Like Terms Example 4
  • Collecting Like Terms Example 3
  • Working with Surds Example 7
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Pure
  • Differential Calculus
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Graphing & Transforming Functions
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • Quadratic Functions
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Counting and Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • Non Right Angled Triangle Trigonometry
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Periodic Phenomena
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Complex Numbers & Polynomials
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Linear Interpolation
  • Interval Bisection
  • Newton-Raphson
  • Summary of Numerical Methods
  • Exponents
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Statistics
  • Discrete Random Variables
  • Introduction
  • The Concept of a Discrete Random Variable
  • The Probability Function
  • Discrete Probability Distributions Example 1
  • Discrete Probability Distributions Example 2
  • The Cumulative Distribution Function
  • The Cumulative Distribution Function Example 1
  • The Cumulative Distribution Function Example 2
  • Expectation
  • The Expectation of a Discrete Random Variable Example 1
  • The Expectation of a Discrete Random Variable Example 2
  • The Expectation of a Discrete Random Variable Example 3
  • The Expectation of a Discrete Random Variable Example 4
  • The Expectation of a Discrete Random Variable Example 5
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Linear Functions of Probability Distributions
  • Linear Functions of Probability Distributions Example 1
  • Linear Functions of Probability Distributions Example 2
  • The Discrete Uniform Distribution
  • Introducing The Discrete Uniform Distribution
  • The Discrete Uniform Distribution Example 1
  • The Discrete Uniform Distribution Example 2
  • Probability
  • Venn Diagrams
  • Introduction to Venn Diagrams
  • Using Venn Diagrams for probability
  • Identifying Events
  • Using Venn Diagrams
  • Addition Rule
  • The Addition Rule
  • Using the Addition Rule
  • Dependent Events
  • Introduction to Dependent Probabilities
  • Using the Dependent Probability Formula Example 1
  • Using the Dependent Probability Formula Example 2
  • Independent Events
  • Introduction to Independent Events
  • Independent Events Example 1
  • Independent Events Example 2
  • Independent Events Example 3
  • Mutually Exclusive Events
  • Mutually Exclusive Events
  • Mutually Exclusive Events Example
  • Tree Diagrams
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Arrangements
  • Using Arrangements Example 1
  • Using Arrangements Example 2
  • The Normal Distribution
  • Introduction
  • The Concept of a Normal Distribution
  • Features of a Normal Distribution
  • The Normal Curve as a PDF and the Standard Normal
  • The Standard Normal
  • Using Standard Normal Tables Example 1
  • Using Standard Normal Tables Example 2
  • Using Standard Normal Tables Example 3
  • Using Standard Normal Tables Example 4
  • Using Standard Normal Tables Example 5
  • Using Standard Normal Tables Example 6
  • Transforming Normal Distributions to the Standard Normal
  • Working with General Normals
  • Working with General Normals Example 1
  • Working with General Normals Example 2
  • Working with General Normals Example 3
  • Working with General Normals Example 4
  • Applying The Normal Distribution
  • Problems Using The Normal Distribution Example 1
  • Problems Using The Normal Distribution Example 2
  • Problems Using The Normal Distribution Example 3
  • Problems Using The Normal Distribution Example 4
  • Problems Using The Normal Distribution Example 5
  • The Binomial and Poisson Distributions
  • The Binomial Distribution
  • Introduction to the Binomial Distribution
  • Binomial Examples - Example 1
  • Binomial Examples - Example 2
  • Binomial Examples - Example 3
  • Binomial Examples - Example 4
  • The Expecation and Variance for a Binomial Distribution
  • Expectation and Varaince Example 1
  • Expectation and Varaince Example 2
  • Expectation and Varaince Example 3
  • The Poisson Distribution
  • Introduction to the Poisson Distribution Part 1
  • Introduction to the Poisson Distribution Part 2
  • Poisson Examples - Example 1
  • Poisson Examples - Example 2
  • Poisson Examples - Example 3
  • Poisson Examples - Example 4
  • The Binomial and Poisson Distributions
  • Which Distribution?
  • The Poisson as an Approximation to the Binomial
  • Poisson as Approximation to Binomial Intro
  • Poisson as Approximation to Binomial Example
  • Continuous Distributions
  • The Continuous Uniform Distribution (Rectangular)
  • Introduction to the Rectangular Distribution
  • The Mean and Variance
  • Rectangular Distribution Example 1
  • Rectangular Distribution Example 2
  • Rectangular Distribution Example 3
  • Approximating Binomial Distribution Using the Normal Distribution
  • Approximating Binomial with Normal Intro
  • Approximating Binomial with Normal Example 1
  • Approximating Binomial with Normal Example 2
  • Approximating Poisson Distribution Using the Normal Distribution
  • Approximating Poisson with Normal Intro
  • Approximating Poisson with Normal Example
  • Continuous Random Variables
  • Introduction to Continuous Random Variables
  • Continuous Random Variables - Intro Part 1
  • Continuous Random Variables - Intro Part 2
  • Continuous Random Variables - Intro Part 3
  • Continuous Random Variables - Intro Part 4
  • Probability Density Functions
  • Probability Density Function - Example 1
  • Probability Density Function - Example 2
  • Probability Density Function - Example 3
  • Cumulative Distribution Functions
  • Cumulative Distribution Functions - Intro Part 1
  • Cumulative Distribution Functions - Intro Part 2
  • Cumulative Distribution Functions - Example 1
  • Cumulative Distribution Functions - Example 2
  • Cumulative Distribution Functions - Example 3
  • Cumulative Distribution Functions - Example 4
  • Expectation and Variance
  • Expectation and Variance Example 1
  • Expectation and Variance Example 2
  • Expectation and Variance Example 3
  • Expectation and Variance Example 4
  • Median and Quartiles Example 1
  • Median and Quartiles Example 2
  • Background
  • Introducing Statistical Models
  • Statistical Modelling Part 1
  • Statistical Modelling Part 2
  • Introduction
  • Types of Data
  • Why Do We Represent Data in Graphs and Charts?
  • Frequency Distributions
  • Frequency Distributions
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams
  • Grouped Frequency Distributions
  • Grouped Frequency Distributions
  • Class Limits and Boundaries
  • Cumulative Frequency
  • Cumulative Frequency Example 1
  • Cumulative Frequency Example 2
  • Histograms
  • Histograms Example 1
  • Histograms Example 2
  • The Relative Frequency Histogram
  • Why Summarise Data?
  • The Mode
  • Mode for Discrete Numbers
  • Mode for a Frequency Distribution
  • Mode for a Grouped Frequency Distribution
  • Advantages and Disadvantages of the Mode
  • The Median
  • Median for Discrete Numbers
  • Median for a Frequency Distribution
  • Median for a Grouped Frequency Distribution Example 1
  • Median for a Grouped Frequency Distribution Example 2
  • Median from a Cumulative Frequency Graph
  • Advantages and Disadvantages of the Median
  • Other Quantiles
  • Introducing Other Quantiles
  • Quantiles Example 1 - Discrete Data
  • Quantiles Example 2 - Discrete Data
  • Quantiles Example 3 - Discrete Data
  • Quantiles Example 4 - Frequency Distribution
  • Quantiles Example 5 - Grouped Frequency Distribution
  • Quantiles Example 6 - Grouped Frequency Distribution
  • Quantiles Example 7 - Cumulative Frequency Graph
  • Quantiles Example 8 - Stem and Leaf
  • The Boxplot
  • The Boxplot
  • The Mean
  • Mean Example 1 - Discrete data
  • Mean Example 2 - Frequency Distribution
  • Mean Example 3 - Grouped Frequency Distribution
  • Mean Example 4 - Grouped Frequency Distribution
  • Mean Example 5 - Advantages and Disadvantages
  • Coding
  • Mean Example with Coding
  • The Concept of Dispersion
  • Range
  • Range Example 1 - Discrete Data
  • Range Example 2 - Frequency Distribution
  • Range Example 3 - Grouped Frequency Distribution
  • Range Example 4 - Advantages and Disadvantages
  • Interquartile Range
  • IQR Example 1 - Discrete Data
  • IQR Example 2 - Frequency Distribution
  • IQR Example 3 - Grouped Frequency Distribution
  • IQR Example 4 - Cumulative Frequency Graph
  • IQR Example 5 - Stem and Leaf
  • IQR Example 6 - Advantages and Disadvantages
  • Boxplots
  • The Boxplot
  • Standard Deviation and Variance
  • The Concept of Variance
  • The Variance Formulae
  • Population SD and Variance Example 1
  • Population SD and Variance Example 2
  • Population SD and Variance Example 3
  • Sample SD and Variance Example 1
  • Sample SD and Variance Example 2
  • Sample SD and Variance Example 3
  • Advantages and Disadvantages of SD
  • SD Example with Coding
  • Interpretation
  • Interpretation Example 1
  • Interpretation Example 2
  • KS3
  • Number
  • Integers
  • Addition
  • Adding Integers Example 1
  • Adding Integers Example 2
  • Carrying Figures Explained
  • Adding Integers Example 3
  • Subtraction
  • Subtracting Integers Example 1
  • Borrowing Digits Explained
  • Subtracting Integers Example 2
  • Addition and Subtraction
  • Mixed Example 1
  • Rounding
  • Rounding Integers Example 1
  • Rounding Integers Example 2
  • Rounding Integers Example 3
  • Multiplying
  • Introduction to Multiplying Integers
  • Multiplying Integers by 10, 100 etc.
  • Multiplying Two Integers Example 1
  • Multiplying Two Integers Example 2
  • Multiplying Two Integers Example 3
  • Multiplying Two Integers Example 4 - Practical Example
  • Dividing
  • Dividing Integers by 10, 100 etc.
  • Dividing Two Integers Example 1
  • Dividing Two Integers Example 2
  • Dividing Two Integers Example 3
  • Integers - Extension
  • Dividing
  • Dividing Two Integers Example 4
  • Mixed Operations
  • Mixed Operations with Integers - BIDMAS Example 1
  • Mixed Operations with Integers - BIDMAS Example 2
  • Directed Numbers
  • Introduction to Directed Numbers
  • Adding Directed Numbers
  • Subtracting Directed Numbers
  • Multiplying Directed Numbers
  • Dividing Directed Numbers
  • Calculator Guide
  • Adding Integers on the Calculator
  • Subtracting Integers on the Calculator
  • Multiplying Integers on the Calculator
  • Dividing Integers on the Calculator
  • BIDMAS on the Calculator Example 1
  • BIDMAS on the Calculator Example 2
  • Directed Numbers on the Calculator
  • Factors, Multiples, Prime Numbers
  • Factors and Multiples
  • Factors of Integers
  • Multiples of Integers
  • Prime Numbers
  • Introduction to Prime Numbers
  • Divisibility Tests for Integers
  • Expressing a Number as a Product of Primes
  • Highest Common Factor
  • Highest Common Factor Example 1
  • Highest Common Factor Example 2
  • Lowest Common Multiple
  • Lowest Common Multiple Example 1
  • Lowest Common Multiple Example 2
  • Lowest Common Multiple Example 3
  • Fractions
  • Introduction
  • Introduction to Fractions
  • Equivalent Fractions
  • Equivalent Fractions Example 1
  • Equivalent Fractions Example 2
  • Equivalent Fractions Example 3
  • Adding Fractions
  • Adding Fractions with the Same Denominator Example 1
  • Adding Fractions with the Same Denominator Example 2
  • Adding Using a Common Denominator Example 1
  • Adding Using a Common Denominator Example 2
  • Adding - Dealing with Mixed Numbers
  • Subtracting Fractions
  • Subtracting Fractions with the Same Denominator Example 1
  • Subtracting Using a Common Denominator Example 1
  • Subtracting Using a Common Denominator Example 2
  • Subtracting - Dealing with Mixed Numbers Example 1
  • Subtracting - Dealing with Mixed Numbers Example 2
  • Mixed Add and Subtract
  • Mixed Add and Subtract Example 1
  • Mixed Add and Subtract Example 2
  • Multiplying Fractions
  • Multiplying Fractions Example 1
  • Multiplying Fractions Example 2
  • Multiplying - Dealing with Mixed Numbers
  • Multiplying - Dealing with Whole Numbers
  • Multiplying - Whole Number and Mixed Number
  • Miscellaneous Example
  • Dividing Fractions
  • Dividing Fractions Example 1
  • Dividing Fractions Example 2
  • Dividing - Dealing with Mixed Numbers
  • Dividing - Dealing with Whole Numbers
  • Dividing - Whole Number and Mixed Number
  • Directed Numbers
  • Directed Numbers and Fractions
  • Using BIDMAS
  • Fractions with Mixed Operations Example 1
  • Fractions with Mixed Operations Example 2
  • Fractions with Mixed Operations Example 3
  • Fractions with Mixed Operations Example 4
  • Calculator Guide
  • Adding Fractions on the Calculator
  • Adding Mixed Numbers on the Calculator
  • Subtracting Fractions on the Calculator
  • Subtracting Mixed Numbers on the Calculator
  • Multiplying Fractions on the Calculator
  • Multiplying Mixed Numbers on the Calculator
  • Dividing Fractions on the Calculator
  • Dividing Mixed Numbers on the Calculator
  • Decimals
  • Meaning of Decimals
  • Introduction to Decimal Fractions
  • Ordering Decimals
  • Putting Decimals Into Numerical Order
  • Adding Decimals
  • Addition of Decimals
  • Subtracting Decimals
  • Subtraction of Decimals
  • Multiplying Decimals
  • Multiplying Decimals by 10, 100 etc.
  • Multiplying Decimals by an Integer
  • Multiplying Decimals by Decimals Example 1
  • Multiplying Decimals by Decimals Example 2
  • Multiplying Decimals by Decimals Example 3
  • Dividing Decimals
  • Dividing Decimals by 10, 100 etc.
  • Dividing Decimals by Decimals Introduction
  • Dividing Decimals by Decimals Example 1
  • Dividing Decimals by Decimals Example 2
  • Dividing Decimals by Decimals Example 3
  • Dividing Decimals by Decimals Example 4
  • Directed Numbers
  • Decimals and Directed Numbers
  • Rounding
  • Rounding to the Nearest Whole Number
  • Rounding to Decimal Places Example 1
  • Rounding to Decimal Places Example 2
  • Rounding to Significant Figures
  • Calculator Guide
  • Adding Decimals on a Calculator
  • Subtracting Decimals on a Calculator
  • Multiplying Decimals on a Calculator
  • Dividing Decimals on a Calculator
  • Mixed Operations on a Calculator Involving Decimals
  • Percentages
  • Introduction
  • Introduction to Percentages
  • Percentages and Decimals
  • Introduction to Decimals and Percentages Example 1
  • Introduction to Decimals and Percentages Example 2
  • Introduction to Decimals and Percentages Example 3
  • Percentages and Fractions
  • Introduction to Fractions and Percentages Example 1
  • Introduction to Fractions and Percentages Example 2
  • Introduction to Fractions and Percentages Example 3
  • Introduction to Fractions and Percentages Example 4
  • Percentages, Fractions and Decimals
  • Percentages, Fractions and Decimals Example 1
  • Percentages, Fractions and Decimals Example 2
  • Percentages, Fractions and Decimals Example 3
  • Percentage of a Quantity
  • Finding a percentage of a Quantity Example 1
  • Finding a percentage of a Quantity Example 2
  • Finding a percentage of a Quantity Example 3
  • Finding a percentage of a Quantity Example 4
  • Finding One Quantity as a Percentage of Another Example 1
  • Finding One Quantity as a Percentage of Another Example 2
  • Increasing a Quantity by a Given Percentage
  • Decreasing a Quantity by a Given Percentage
  • Indices and Standard Form
  • Indices
  • Introduction to Indices
  • The First Index Law
  • First Index Law Example 1
  • First Index Law Example 2
  • The Second Index Law
  • Second Index Law Example 1
  • Second Index Law Example 2
  • Negative Indices
  • Negative Indices Example 1
  • Negative Indices Example 2
  • Negative Indices Example 3
  • Introduction to Standard Form
  • Introduction to Standard Form Example 1
  • Introduction to Standard Form Example 2
  • Introduction to Standard Form Example 3
  • Introduction to Standard Form Example 4
  • Introduction to Standard Form Example 5
  • Introduction to Standard Form Example 6
  • The Zero Index
  • The Meaning of the Zero Index
  • Working With Numbers
  • Range of Values for a Corrected Number
  • Range of Values for a Corrected Number Example 1
  • Range of Values for a Corrected Number Example 2
  • Range of Values for a Corrected Number Example 3
  • Range of Values for a Corrected Number Example 4
  • Range of Values for a Corrected Number Example 5
  • Range of Values for a Corrected Number Example 6
  • Range of Values for a Corrected Number Example 7
  • Range of Values for a Corrected Number Example 8
  • Reciprocals
  • Reciprocals Introduction
  • Fraction Review
  • Reviewing Fraction Work Example 1
  • Reviewing Fraction Work Example 2
  • Working With Numbers Extension
  • Fractions Involving BIDMAS
  • Fractions Involving BIDMAS Example 1
  • Fractions Involving BIDMAS Example 2
  • Fractions Involving BIDMAS Example 3
  • Recurring Decimals
  • Introduction to Recurring Decimals
  • Converting Between Decimals and Fractions (Advanced)
  • Converting Between Decimals and Fractions (Advanced) Example 1
  • Converting Between Decimals and Fractions (Advanced) Example 2
  • Converting Between Decimals and Fractions (Advanced) Example 3
  • Converting Between Decimals and Fractions (Advanced) Example 4
  • Converting Between Decimals and Fractions (Advanced) Example 5
  • Converting Between Decimals and Fractions (Advanced) Example 6
  • Standard Form Advanced
  • Advanced Standard Form Example 1
  • Advanced Standard Form Example 2
  • Advanced Standard Form Example 3
  • Advanced Standard Form Example 4
  • Advanced Standard Form Example 5
  • Advanced Standard Form Example 6
  • Advanced Standard Form Example 7
  • Number Sequences and Patterns
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms for Number Sequences
  • Finding the nth Term Example 1
  • Finding the nth Term Example 2
  • Finding the nth Term Example 3
  • Finding the nth Term Example 4
  • Number Sequences and Patterns Extension
  • nth Terms for Number Sequences
  • Number Sequence Extension Work Example 1
  • Number Sequence Extension Work Example 2
  • Number Sequence Extension Work Example 3
  • Number Sequence Extension Work Example 4
  • Percentages Advanced
  • Profit and Loss
  • Percentage Profit and Loss Example 1
  • Percentage Profit and Loss Example 2
  • Percentage Profit and Loss Example 3
  • Percentage Profit and Loss Example 4
  • Percentage Profit and Loss Example 5
  • Income Tax
  • Income Tax Calculations Example 1
  • Income Tax Calculations Example 2
  • Percentages Advanced Extension
  • Income Tax
  • Income Tax Calculations Example 3
  • Income Tax Calculations Example 4
  • Sale Reductions
  • Sale Reductions Example
  • Finding the Original Quantity
  • Finding the Original Quantity Example 1
  • Finding the Original Quantity Example 2
  • Finding the Original Quantity Example 3
  • Finding the Original Quantity Example 4
  • Interest
  • Interest Example 1
  • Interest Example 2
  • Interest Example 3
  • Interest Example 4 - Simple and Compound Interest
  • Interest Example 5 - Compound Interest
  • Extra Fraction Work
  • Fractions
  • Expressing one Quantity as a Fraction of Another
  • Finding a Fraction of a Quantity
  • Finding Whole Given Fraction Example 1
  • Finding Whole Given Fraction Example 2
  • Finding Whole Given Fraction Example 3
  • Percentages
  • Finding Whole Given Percentage Example 1
  • Finding Whole Given Percentage Example 2
  • Ratio
  • Introduction to Ratio
  • Simplifying Ratios Example 1
  • Simplifying Ratios Example 2
  • Simplifying Ratios Example 3
  • Simplifying Ratios Example 4
  • Simplifying Ratios Example 5
  • Ratio and Fraction
  • Ratio and Proportion
  • Ratio
  • Dividing in Given Ratio Example 1
  • Dividing in Given Ratio Example 2
  • Dividing in Given Ratio Example 3
  • Equivalent Ratios Introduction
  • Equivalent Ratios Example 1
  • Equivalent Ratios Example 2
  • Equivalent Ratios Example 3
  • Equivalent Ratios Example 4
  • The Form 1:n Example 1
  • The Form 1:n Example 2
  • The Form 1:n Example 3
  • Algebra
  • Algebra Basics
  • Introduction to Algebra
  • Introduction to Algebra
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Multiplying Algebraic Expressions Example 1
  • Multiplying Algebraic Expressions Example 2
  • Basic Equations
  • Forming Simple Equations
  • Forming Simple Equations From Information Given
  • Solving Simple Equations
  • Equation as a Balance
  • Solving Simple Equations Example 1
  • Solving Simple Equations Example 2
  • Solving Simple Equations Example 3
  • Solving Simple Equations Example 4
  • Harder Equations
  • Collecting Like Terms Review
  • Harder Equations Example 1
  • Harder Equations Example 2
  • Harder Equations Example 3
  • Harder Equations Example 4
  • Basic Inequalities
  • Introduction to Inequalities
  • Introduction to Inequalities
  • Solving Simple Inequalities
  • Solving Simple Inequalities Example 1
  • Solving Simple Inequalities Example 2
  • Solving Simple Inequalities Example 3
  • Solving Simple Inequalities Example 4
  • Solving Simple Inequalities Example 5
  • Basic Formulae
  • Words and Symbols
  • Finding a Formula Example 1
  • Finding a Formula Example 2
  • Finding a Formula Example 3
  • Finding a Formula Example 4
  • Substitution
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Numbers into Formulae Example 5
  • Directed Numbers Review Example 1
  • Directed Numbers Review Example 2
  • Substituting with Directed Numbers Example 1
  • Substituting with Directed Numbers Example 2
  • Algebraic Products
  • Single Bracket
  • Expanding with a Single Bracket Example 1
  • Expanding with a Single Bracket Example 2
  • Expand and Simplify
  • Expanding Brackets Extension Example
  • Pair of Brackets
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Squaring a Bracket
  • Expanding (x + a)(x - a)
  • Pair of Brackets Extension Example
  • Expand and Simplify Extension Example
  • Factorising into a Single Bracket
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising into a Pair of Brackets
  • Factorising into a Pair of Brackets Example 1
  • Factorising into a Pair of Brackets Example 2
  • Factorising into a Pair of Brackets Example 3
  • Factorising into a Pair of Brackets Example 4
  • Factorising into a Pair of Brackets Example 5
  • Factorising into a Pair of Brackets Example 6
  • Factorising into a Pair of Brackets Example 7
  • Factorising into a Pair of Brackets Example 8
  • Factorising into a Pair of Brackets Example 9
  • Factorising into a Pair of Brackets Example 10
  • Simultaneous Equations
  • Algebraic Solution
  • Simultaneous Equations Algebraic Solution Example 1
  • Simultaneous Equations Algebraic Solution Example 2
  • Simultaneous Equations Algebraic Solution Example 3
  • Simultaneous Equations Algebraic Solution Example 4
  • Simultaneous Equations Algebraic Solution Example 5
  • Simultaneous Equations Algebraic Solution Example 6
  • Simultaneous Equations Algebraic Solution Example 7
  • Simultaneous Equations Algebraic Solution Example 8
  • Graphical Solution
  • Simultaneous Equations Graphical Solution Example 1
  • Simultaneous Equations Graphical Solution Example 2
  • No Solutions or Infinite Solutions
  • No Solutions or Infinite Solutions
  • Problem Solving
  • Problem Solving Example 1
  • Problem Solving Example 2
  • More Formulae
  • Deriving Formulae
  • Deriving Formulae Example 1
  • Deriving Formulae Example 2
  • Deriving Formulae Example 3
  • Deriving Formulae Example 4
  • Substitution into Formulae
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Expressions into Formulae
  • Rearranging Formulae
  • Rearranging Formulae Example 1
  • Rearranging Formulae Example 2
  • Rearranging Formulae Example 3
  • Rearranging Formulae Example 4
  • nth Terms for Sequences
  • Finding nth Terms Example 1
  • Finding nth Terms Example 2
  • Finding nth Terms Example 3
  • Finding nth Terms Example 4
  • Quadratic Equations
  • Trial and Improvement
  • Solving Equations by Trial and Improvement Example 1
  • Solving Equations by Trial and Improvement Example 2
  • Solving Equations by Trial and Improvement Example 3
  • Indices
  • Indices with Algebra
  • The First Index Law
  • The Second Index Law
  • The Power mn
  • Using the Index Laws Example 1
  • Negative Indices
  • Fractional Indices
  • Ratio and Proportion
  • Ratio Revision
  • Ratio Revision Example 1
  • Ratio Revision Example 2
  • Ratio Revision Example 3
  • Expressing a Ratio in the Form 1:n Example 1
  • Expressing a Ratio in the Form 1:n Example 2
  • Dividing in a Given Ratio Example 1
  • Dividing in a Given Ratio Example 2
  • Dividing in a Given Ratio Example 3
  • Direct Proportion
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Direct Proportion Example 4
  • Direct Proportion Example 5
  • Inverse Proportion
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Inverse Proportion Example 4
  • Inverse Proportion Example 5
  • Algebraic Fractions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Advanced Formulae
  • Substitution
  • Substituting Numbers in Standard Form Example 1
  • Substituting Numbers in Standard Form Example 1 - Calculator Guide
  • Substituting Numbers in Standard Form Example 2
  • Substituting Numbers in Standard Form Example 2 - Calculator Guide
  • Substituting Numbers in Standard Form Example 3
  • Substituting Numbers in Standard Form Example 3 - Calculator Guide
  • Data Handling
  • Basic Statistics
  • Frequency Tables
  • Creating a Frequency Table Example 1
  • Creating a Frequency Table Example 2
  • Observation Sheet
  • Collecting Data on an Observation Sheet
  • Bar Charts
  • Bar Chart Example 1
  • Bar Chart Example 2
  • Pictograms
  • Pictograms Example 1
  • Misleading Diagrams
  • Misleading Diagrams Example 1
  • Pie Charts
  • Pie Charts Example 1
  • Pie Charts Example 2
  • Organising and Summarising Data
  • Summarising Data
  • Why Summarise Data?
  • Averages
  • Averages
  • The Mode for a Set of Numbers
  • The Mode for a Frequency Distribution
  • The Median for a Set of Numbers
  • The Median for a Frequency Distribution
  • The Mean for a Set of Numbers
  • The Mean for a Frequency Distribution
  • The Range
  • Calculating the Range
  • Grouped Data
  • Grouping Data
  • The Mean for Grouped Data
  • The Median for Grouped Data
  • The Mode for Grouped Data
  • The Range for Grouped Data
  • Quartiles
  • Finding Quartiles Example 1
  • Finding Quartiles Example 2
  • The Interquartile Range
  • Calculating the Interquartile Range Example 1
  • Calculating the Interquartile Range Example 2
  • Boxplots
  • Boxplots Example 1
  • Boxplots Example 2
  • Boxplots Example 3
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams Example 1
  • Stem and Leaf Diagrams Example 2
  • Stem and Leaf Diagrams Example 3
  • Line Graphs
  • Reading from Line Graphs
  • Reading from Line Graphs Example 1
  • Conversion Graphs
  • Conversion Graphs Example 1
  • Straight Lines
  • Straight Lines Example 1
  • Probability 1
  • Introduction to Probability
  • The Probability Scale
  • Types of Probability
  • Theoretical Probabilility
  • Basic Theoretical Probabilility Example 1
  • Basic Theoretical Probabilility Example 2
  • Basic Theoretical Probabilility Example 3
  • Experimental Probability
  • Experimental Probability Example 1
  • Experimental Probability Example 2
  • Probability 2
  • An Event Not Happening
  • The probability of An Event Not Happening Example 1
  • The probability of An Event Not Happening Example 2
  • The probability of An Event Not Happening Example 3
  • The Sum for All Possibilities
  • The Sum for All Possibilities Example 1
  • The Sum for All Possibilities Example 2
  • Possibility (Sample) Spaces
  • Possibility (Sample) Spaces Example 1
  • Possibility (Sample) Spaces Example 2
  • Possibility (Sample) Spaces Example 3
  • Possibility (Sample) Spaces Example 4
  • Expected Number of Occurrences
  • Expected Number of Occurrences Example 1
  • Expected Number of Occurrences Example 2
  • Expected Number of Occurrences Example 3
  • Scatter Diagrams
  • Scatter Diagrams Introduction
  • Scatter Diagrams Introduction
  • Plotting and Using
  • Plotting and Using Scatter Diagrams
  • Correlation
  • A Note on Correlation
  • Probability 3
  • Mutually Exclusive and Independent Events
  • Mutually Exclusive Events
  • Independent Events 1
  • Independent Events 2
  • Mutuallly Exclusive or Independent?
  • Addition Rule
  • The Addition Rule Example 1
  • Multiplication Rule
  • The Multiplication Rule Example 1
  • The Multiplication Rule Example 2
  • Miscellaneous Probability Example
  • Miscellaneous Probability Example
  • Conditional Probability
  • Conditional Probability Example 1
  • Conditional Probability Example 2
  • Probability 4
  • Tree Diagrams
  • Introduction to Tree Diagrams - Part 1
  • Introduction to Tree Diagrams - Part 2
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Tree Diagrams Example 3
  • Tree Diagrams Example 4
  • Tree Diagrams Example 5
  • Tree Diagrams Example 6
  • Cumulative Frequency
  • Producing a Cumulative Frequency
  • Producing a Cumulative Frequency Example 1
  • Producing a Cumulative Frequency Example 2
  • Drawing a Cumulative Frequency Graph
  • Drawing a Cumulative Frequency Graph Example 1
  • Drawing a Cumulative Frequency Graph Example 2
  • Median and Quartiles
  • Using Cumulative Frequency to Find Median and Quartiles Example 1
  • Using Cumulative Frequency to Find Median and Quartiles Example 2
  • Other Uses
  • Other Uses of Cumulative Frequency Example 1
  • Other Uses of Cumulative Frequency Example 2
  • Other Uses of Cumulative Frequency Example 3
  • Histograms
  • Histograms and Their Use
  • Histograms Introduction
  • Histograms Example 1
  • Histograms Example 2
  • Two Way Tables
  • Intro to Two Way Tables
  • Intro to Two Way Tables Example 1
  • Intro to Two Way Tables Example 2
  • Transformations
  • Reflection
  • Reflection in Horizontal and Vertical Lines
  • Reflection in Diagonal Lines
  • Rotation
  • Rotation About a Fixed Point
  • Enlargement
  • Enlargements with Positive Scale Factors
  • Enlargements with Negative Scale Factors
  • Translation
  • Translation of Shape
  • Describing Transformations
  • Fully Describing a Given Transformation
  • Metric Units
  • Length
  • Metric Units of Length
  • Length Example 1
  • Length Example 2
  • Mass
  • Metric Units of Mass
  • Mass Example 1
  • Adding Metric Quantities
  • Adding Metric Quantities Example 1
  • Adding Metric Quantities Example 2
  • Adding Metric Quantities Example 3
  • Money
  • Money Example 1
  • Money Example 2
  • Transformations
  • Reflection
  • Reflection in Horizontal and Vertical Lines
  • Reflection in Diagonal Lines
  • Rotation
  • Rotation About a Fixed Point
  • Enlargement
  • Enlargements with Positive Scale Factors
  • Translation
  • Translation of Shape
  • Describing Transformations
  • Fully Describing a Given Transformation
  • Metric Units
  • Length
  • Metric Units of Length
  • Length Example 1
  • Length Example 2
  • Mass
  • Metric Units of Mass
  • Mass Example 1
  • Adding Metric Quantities
  • Adding Metric Quantities Example 1
  • Adding Metric Quantities Example 2
  • Adding Metric Quantities Example 3
  • Money
  • Money Example 1
  • Money Example 2
  • Circle Theorems
  • Angle Subtended By Arc
  • Angle Subtended By Arc
  • Angle Subtended at Centre
  • Angle Subtended at Centre
  • Angle in Semicircle
  • Angle in Semicircle
  • Mixed Examples
  • Mixed Examples
  • Cyclic Quadrilaterals
  • Cyclic Quadrilaterals
  • Tangent Properties
  • Tangent Properties
  • The Alternate Segment Theorem
  • The Alternate Segment Theorem
  • Circle Theorems
  • Nomenclature
  • Circle Nomenclature
  • Angle Subtended By Arc
  • Angle Subtended By Arc
  • Angle Subtended at Centre
  • Angle Subtended at Centre
  • Angle in Semicircle
  • Angle in Semicircle
  • Mixed Examples
  • Mixed Examples
  • Cyclic Quadrilaterals
  • Cyclic Quadrilaterals
  • Constructions
  • Ruler and Compass Constructions
  • The Right Angle
  • Bisecting an Angle
  • The Sixty Degree Angle
  • Thirty Degrees and Forty Five Degrees
  • Constructions
  • Ruler and Compass Constructions
  • Constructing a Perpendicular Bisector
  • The Right Angle
  • Bisecting an Angle
  • The Sixty Degree Angle
  • Thirty Degrees and Forty Five Degrees
  • Inequalities and Graphs
  • Introduction to Graphical Inequalities
  • An Introduction to Graphical Inequalities
  • Vertical Lines
  • Vertical Lines Example 1
  • Vertical Lines Example 2
  • Vertical Lines Example 3
  • Horizontal Lines
  • Horizontal Lines Example 1
  • Horizontal Lines Example 2
  • Horizontal Lines Example 3
  • Mixed Horizontal and Vertical Lines
  • Mixed Horizontal and Vertical Example 1
  • Mixed Horizontal and Vertical Example 2
  • Mixed Horizontal and Vertical Example 3
  • Inequalities Involving Both x and y
  • Inequalities Involving Both x and y Example 1
  • A Note on Point Testing
  • Integer-Valued Coordinates
  • Inequalities Involving Both x and y Example 2
  • Inequalities Involving Both x and y Example 3
  • Inequalities Involving Both x and y Example 4
  • Inequalities Involving Both x and y Example 5
  • Inequalities Involving Both x and y Example 6
  • A Practical Problem
  • Practical Example
  • Inequalities and Graphs
  • Introduction to Graphical Inequalities
  • An Introduction to Graphical Inequalities
  • Vertical Lines
  • Vertical Lines Example 1
  • Vertical Lines Example 2
  • Vertical Lines Example 3
  • Horizontal Lines
  • Horizontal Lines Example 1
  • Horizontal Lines Example 2
  • Horizontal Lines Example 3
  • Mixed Horizontal and Vertical Lines
  • Mixed Horizontal and Vertical Example 1
  • Mixed Horizontal and Vertical Example 2
  • Mixed Horizontal and Vertical Example 3
  • Inequalities and Graphs
  • Introduction to Graphical Inequalities
  • An Introduction to Graphical Inequalities
  • Vertical Lines
  • Vertical Lines Example 1
  • Vertical Lines Example 2
  • Vertical Lines Example 3
  • Horizontal Lines
  • Horizontal Lines Example 1
  • Horizontal Lines Example 2
  • Horizontal Lines Example 3
  • Mixed Horizontal and Vertical Lines
  • Mixed Horizontal and Vertical Example 1
  • Mixed Horizontal and Vertical Example 2
  • Mixed Horizontal and Vertical Example 3
  • Plans and Elevations
  • Drawing Plans and Elevations for Solid Objects
  • Plans and Elevations Example 1
  • Plans and Elevations Example 2
  • Plans and Elevations Example 3
  • Scale Drawing
  • Drawing Accurate Scale Drawings
  • Scale Drawing Example 1
  • Scale Drawing Example 2
  • Scale Drawing Example 3
  • Plans and Elevations
  • Drawing Plans and Elevations for Solid Objects
  • Plans and Elevations Example 1
  • Plans and Elevations Example 2
  • Plans and Elevations Example 3
  • Scale Drawing
  • Drawing Accurate Scale Drawings
  • Scale Drawing Example 1
  • Scale Drawing Example 2
  • Scale Drawing Example 3
  • Shape Space and Measure
  • Plans and Elevations
  • Drawing Plans and Elevations for Solid Objects
  • Plans and Elevations Example 1
  • Plans and Elevations Example 2
  • Plans and Elevations Example 3
  • Scale Drawing
  • Drawing Accurate Scale Drawings
  • Scale Drawing Example 1
  • Scale Drawing Example 2
  • Scale Drawing Example 3
  • OCR Add Math
  • Algebra
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • SSM
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • Coordinate Geometry
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • Index Laws
  • First Index Law
  • Second Index Law
  • Third Index Law
  • Raising a Number to the Power Zero
  • Fourth Index Law Example 1
  • Fourth Index Law Example 2
  • Fourth Index Law Example 3
  • Fifth Index Law Example 1
  • Fifth Index Law Example 2
  • Sixth Index Law Example 1
  • Sixth Index Law Example 2
  • Using Index Laws Example 1
  • Using Index Laws Example 2
  • Surds
  • Surd Introduction
  • Working with Surds Example 1
  • Working with Surds Example 2
  • Working with Surds Example 3
  • Working with Surds Example 4
  • Working with Surds Example 5
  • Working with Surds Example 6
  • Working with Surds Example 7
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Basic Area
  • Introduction
  • Introduction to Area Example 1
  • Introduction to Area Example 2
  • Introduction to Area Example 3
  • Standard Shapes
  • Area of a Square
  • Area of a Rectangle Example 1
  • Area of a Rectangle Example 2
  • Finding a Length
  • Compound Shapes
  • Shapes Made from Squares and Rectangles Example 1
  • Shapes Made from Squares and Rectangles Example 2
  • Shapes Made from Squares and Rectangles Example 3
  • Converting Units
  • Converting Between Units of Area Example 1
  • Converting Between Units of Area Example 2
  • Converting Between Units of Area Example 3
  • Converting Between Units of Area Example 4
  • Basic Perimeter
  • Perimeter
  • Basic Perimeter Example 1
  • Basic Perimeter Example 2
  • Basic Perimeter Example 3
  • Introducing Geometry
  • The Meaning of Angle
  • Introduction to Angles
  • Introduction to Measuring Angles
  • Types of Angle
  • Measuring Angles
  • Using a Protractor to Measure Angles
  • Using a Protractor to Draw Angles
  • Angle Facts
  • Vertically Opposite Angles
  • Angles on a Straight Line
  • Angles at a Point
  • Mixed Example
  • Triangles and Quadrilaterals
  • Naming Sides and Angles
  • Naming Angles
  • Naming Sides
  • Angle Sum for a Triangle
  • The Angle Sum for a Triangle Intro
  • The Angle Sum for a Triangle Example 1
  • The Angle Sum for a Triangle Example 2
  • The Angle Sum for a Triangle Example 3
  • The Angle Sum for a Triangle Example 4
  • The Angle Sum for a Triangle Example 5
  • Constructions
  • Side and Two Angles
  • Two Sides and an Angle
  • Three Sides
  • Quadrilaterals
  • Introduction to Quadrilaterals
  • Angle Sum for a Quadrilateral Example 1
  • Angle Sum for a Quadrilateral Example 2
  • Angle Sum for a Quadrilateral Example 3
  • Basic Coordinates
  • Introduction
  • Introduction to Coordinate Systems
  • Coordinates
  • Basic Coordinates Example 1
  • Basic Coordinates Example 2
  • Basic Coordinates Example 3
  • Negative Coordinates
  • Negative Coordinates Example 1
  • Negative Coordinates Example 2
  • Solids
  • Drawing Solids
  • Drawing a Cuboid on Squared Paper
  • Drawing a Cuboid on Isometric Paper
  • Counting Cubes
  • Nets
  • Folding a Net (Demonstration)
  • Folding a Net
  • Drawing a Net Example 1
  • Drawing a Net Example 2
  • Volume
  • Volume of a Cuboid Example 1
  • Volume of a Cuboid Example 2
  • Volume of a Cuboid Example 3
  • Volume of a Cuboid Example 4
  • Volume of a Cuboid Example 5
  • Volume of a Cuboid Example 6
  • Unit Conversion
  • Converting Cubic Units Example 1
  • Converting Cubic Units Example 2
  • Converting Cubic Units Example 3
  • Capacity
  • The Meaning of Capacity
  • Capacity Example 1
  • Capacity Example 2
  • Surface Area
  • Surface Area of a Cuboid Example 1
  • Surface Area of a Cuboid Example 2
  • Imperial Units
  • Imperial Units of Volume
  • Parallel Lines
  • Introduction
  • Introduction to Parallel Lines
  • Corresponding Angles
  • Introduction to Corresponding Angles
  • Corresponding Angles Example 1
  • Corresponding Angles Example 2
  • Corresponding Angles Example 3
  • Corresponding Angles Example 4
  • Alternate Angles
  • Introduction to Alternate Angles
  • Alternate Angles Example 1
  • Alternate Angles Example 2
  • Alternate Angles Example 3
  • Interior Angles
  • Introduction to Interior Angles
  • Interior Angles Example 1
  • Mixed Questions
  • Parallel Lines Mixed Example 1
  • Parallel Lines Mixed Example 2
  • Polygons
  • Introduction to Polygons
  • Introduction to Polygons
  • Regular and Irregular Polygons
  • Regular and Irregular Polygons
  • Interior and Exterior Angles
  • Interior and Exterior Angles
  • Sum of Exterior Angles
  • Sum of Exterior Angles Example 1
  • Sum of Exterior Angles Example 2
  • Sum of Exterior Angles Example 3
  • Interior Angles
  • Interior Angles Example 1
  • Interior Angles Example 2
  • Interior Angles Example 3
  • Pythagoras' Theorem
  • Introduction
  • Introduction to Pythagoas' Theorem
  • Finding the Hypotenuse
  • Finding the Hypotenuse Example 1
  • Finding the Hypotenuse Example 2
  • Finding the Hypotenuse Example 3
  • Finding the Hypotenuse Calculator Guide
  • Finding a Shorter Side
  • Finding a Shorter Side Example 1
  • Finding a Shorter Side Example 2
  • Finding a Shorter Side Example 3
  • Finding a Shorter Side Calculator Guide
  • Harder Problems
  • Harder Problems Example
  • Three Dimensional Problems
  • Pythagoras in 3 Dimensions
  • More Length, Area and Volume
  • Area of a Triangle
  • Introduction to the Area of a Triangle
  • Area of a Triangle Example 1
  • Area of a Triangle Example 2
  • Area of a Triangle Example 3
  • Area of a Triangle Example 4
  • Area of a Parallelogram
  • Introduction to the Area of a Parallelogram
  • Area of a Parallelogram Example 1
  • Area of a Parallelogram Example 2
  • Area of a Parallelogram Example 3
  • Area of a Trapezium
  • Introduction to the Area of a Trapezium
  • Area of a Trapezium Example 1
  • Area and Circumference of a Circle
  • Terminology and Introduction to the Circle
  • Area and Circumference Example 1
  • Area and Circumference Calculator Guide 1
  • Area and Circumference Example 2
  • Area and Circumference Example 3
  • Area and Circumference Example 4
  • Area and Circumference Example 5
  • Area and Circumference Example 6
  • Sectors of Circles
  • More Terminology of Circles
  • Introduction to Area of Sector
  • Introduction to Arc Length
  • Area of Sector and Arc length Example 1
  • Area of Sector and Arc length Example 2
  • Area of Sector and Arc length Example 3
  • Volume of a Prism
  • What is a Prism?
  • Volume of a Prism Example 1
  • Volume of a Prism Example 2
  • Volume of a Prism Example 3
  • Volume of a Prism Example 4
  • Trigonometry (Yr 9 only)
  • Introduction
  • Introduction to Trigonometry
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Calculator Guide 1
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding a Side Calculator Guide 2
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Finding an Angle Calculator Guide
  • Harder Examples
  • Multi-Step Trig Problems Example 1
  • Multi-Step Trig Problems Example 2
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1
  • Three Dimensional Problems Example 2
  • Further Area and Volume
  • Upper and Lower Bounds
  • Upper and Lower Bounds Example 1
  • Upper and Lower Bounds Example 2
  • Upper and Lower Bounds and Trigonometry Example 1
  • Upper and Lower Bounds and Trigonometry Example 2
  • Symmetry
  • Line Symmetry
  • Line Symmetry Example 1
  • Line Symmetry Example 2
  • Line Symmetry Example 3
  • Line Symmetry Example 4
  • Rotational Symmetry
  • Rotational Symmetry Example 1
  • Rotational Symmetry Example 2
  • Both Types of Symmetry
  • Both Types of Symmetry
  • Sections and Planes of Symmetry
  • Sections Example 1
  • Congruence
  • Planes of Symmetry
  • Loci
  • Introduction to Loci
  • Loci Introduction
  • Loci Examples
  • Loci Examples Example 1
  • Loci Examples Example 2
  • Loci Examples Example 3
  • Loci Examples Example 4
  • Transformations
  • Reflection
  • Reflection in Horizontal and Vertical Lines
  • Reflection in Diagonal Lines
  • Rotation
  • Rotation About a Fixed Point
  • Enlargement
  • Enlargements with Positive Scale Factors
  • Enlargements with Negative Scale Factors
  • Translation
  • Translation of Shape
  • Describing Transformations
  • Fully Describing a Given Transformation
  • Metric Units
  • Length
  • Metric Units of Length
  • Length Example 1
  • Length Example 2
  • Mass
  • Metric Units of Mass
  • Mass Example 1
  • Adding Metric Quantities
  • Adding Metric Quantities Example 1
  • Adding Metric Quantities Example 2
  • Adding Metric Quantities Example 3
  • Money
  • Money Example 1
  • Money Example 2
  • Constructions
  • Ruler and Compass Constructions
  • Constructing a Perpendicular Bisector
  • The Right Angle
  • Bisecting an Angle
  • The Sixty Degree Angle
  • Thirty Degrees and Forty Five Degrees
  • Imperial Units
  • Imperial Units of Length
  • Imperial Units of Length Intro
  • Imperial Units of Length Example 1
  • Imperial Units of Length Example 2
  • Imperial Units of Mass
  • Imperial Units of Mass Intro
  • Imperial Units of Mass Example 1
  • Imperial Units of Mass Example 2
  • Conversion Between Imperial and Metric
  • Conversion Between Imperial and Metric Intro
  • Conversion Between Imperial and Metric Example 1
  • Conversion Between Imperial and Metric Example 2
  • Quadrilateral Properties
  • Properties of Quadrilaterals and their Diagonals
  • Properties of the Square
  • Properties of the Rectangle
  • Properties of the Parallelogram
  • Properties of the Rhombus
  • Properties of the Kite
  • Properties of the Trapezium
  • Travel Graphs
  • Speed, Distance, Time
  • Speed, Distance, Time Example 1
  • Speed, Distance, Time Example 2
  • Using a Travel Graph
  • Travel Graphs Example 1
  • Travel Graphs Example 2
  • Similar Figures and Triangles
  • Similar Figures
  • Similar Figures Introduction
  • Areas of Similar Figures Intro
  • Areas of Similar Figures Example 1
  • Areas of Similar Figures Example 2
  • Volumes of Similar Solids Intro
  • Volumes of Similar Solids Example 1
  • Volumes of Similar Solids Example 2
  • Similar Triangles
  • Similar Triangles Intro
  • Similar TrianglesExample 1
  • Similar TrianglesExample 2
  • Similar TrianglesExample 3
  • Imperial Units
  • Imperial Units of Length
  • Imperial Units of Length Intro
  • Imperial Units of Length Example 1
  • Imperial Units of Length Example 2
  • Imperial Units of Mass
  • Imperial Units of Mass Intro
  • Imperial Units of Mass Example 1
  • Imperial Units of Mass Example 2
  • Conversion Between Imperial and Metric
  • Conversion Between Imperial and Metric Intro
  • Conversion Between Imperial and Metric Example 1
  • Conversion Between Imperial and Metric Example 2
  • Quadrilateral Properties
  • Properties of Quadrilaterals and their Diagonals
  • Properties of the Square
  • Properties of the Rectangle
  • Properties of the Parallelogram
  • Properties of the Rhombus
  • Properties of the Kite
  • Properties of the Trapezium
  • Congruent Triangles
  • Properties of Congruent Triangles
  • Congruent Triangles Intro Part 1
  • Congruent Triangles Intro Part 2
  • Congruent Triangles Example 1
  • Congruent Triangles Example 2
  • Congruent Triangles Example 3
  • Congruent Triangles Example 4
  • Tangents to Curves
  • Drawing a Tangent to a Curve
  • Drawing a Tangent to a Curve
  • Travel Graphs
  • Speed, Distance, Time
  • Speed, Distance, Time Example 1
  • Speed, Distance, Time Example 2
  • Using a Travel Graph
  • Travel Graphs Example 1
  • Travel Graphs Example 2
  • Imperial Units
  • Imperial Units of Length
  • Imperial Units of Length Intro
  • Imperial Units of Length Example 1
  • Imperial Units of Length Example 2
  • Imperial Units of Mass
  • Imperial Units of Mass Intro
  • Imperial Units of Mass Example 1
  • Imperial Units of Mass Example 2
  • Conversion Between Imperial and Metric
  • Conversion Between Imperial and Metric Intro
  • Conversion Between Imperial and Metric Example 1
  • Conversion Between Imperial and Metric Example 2
  • Quadrilateral Properties
  • Properties of Quadrilaterals and their Diagonals
  • Properties of the Square
  • Properties of the Rectangle
  • Properties of the Parallelogram
  • Properties of the Rhombus
  • Properties of the Kite
  • Properties of the Trapezium
  • Congruent Triangles
  • Properties of Congruent Triangles
  • Congruent Triangles Intro Part 1
  • Congruent Triangles Intro Part 2
  • Congruent Triangles Example 1
  • Congruent Triangles Example 2
  • Congruent Triangles Example 3
  • Congruent Triangles Example 4
  • Tangents to Curves
  • Drawing a Tangent to a Curve
  • Drawing a Tangent to a Curve
  • Travel Graphs
  • Speed, Distance, Time
  • Speed, Distance, Time Example 1
  • Speed, Distance, Time Example 2
  • Using a Travel Graph
  • Travel Graphs Example 1
  • Travel Graphs Example 2
  • M3
  • Vectors
  • Vector Representation
  • Representing Vectors
  • Vector Diagrams
  • Adding and Subtracting Vectors
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Column Vectors
  • Translation Vectors
  • Adding and Subtracting Column Vectors
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • Orthogonal Matrices
  • Orthogonal Matrices Example 1
  • Orthogonal Matrices Example 2
  • Orthogonal Matrices Example 3
  • Diagonalising a Symmetric Matrix
  • Diagonalising a Symmetric Matrix Example 1
  • Diagonalising a Symmetric Matrix Example 2
  • Diagonalising a Symmetric Matrix Example 3
  • FP1
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • Orthogonal Matrices
  • Orthogonal Matrices Example 1
  • Orthogonal Matrices Example 2
  • Orthogonal Matrices Example 3
  • Diagonalising a Symmetric Matrix
  • Diagonalising a Symmetric Matrix Example 1
  • Diagonalising a Symmetric Matrix Example 2
  • Diagonalising a Symmetric Matrix Example 3
  • FP1
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • FP4
  • Matrices
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • Orthogonal Matrices
  • Orthogonal Matrices Example 1
  • Orthogonal Matrices Example 2
  • Orthogonal Matrices Example 3
  • Diagonalising a Symmetric Matrix
  • Diagonalising a Symmetric Matrix Example 1
  • Diagonalising a Symmetric Matrix Example 2
  • Diagonalising a Symmetric Matrix Example 3
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • FP2
  • Matrices
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • FP1
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • FP1
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Alg1
  • Indices and Standard Form
  • Indices
  • Introduction to Indices
  • The First Index Law
  • First Index Law Example 1
  • First Index Law Example 2
  • The Second Index Law
  • Second Index Law Example 1
  • Second Index Law Example 2
  • Negative Indices
  • Negative Indices Example 1
  • Negative Indices Example 2
  • Negative Indices Example 3
  • The Zero Index
  • The Meaning of the Zero Index
  • Working With Numbers
  • Reciprocals
  • Reciprocals Introduction
  • Basic Equations
  • Solving Simple Equations
  • Equation as a Balance
  • Solving Simple Equations Example 1
  • Solving Simple Equations Example 2
  • Solving Simple Equations Example 3
  • Solving Simple Equations Example 4
  • Harder Equations
  • Collecting Like Terms Review
  • Harder Equations Example 1
  • Harder Equations Example 2
  • Harder Equations Example 3
  • Harder Equations Example 4
  • Basic Formulae
  • Substitution
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Numbers into Formulae Example 5
  • Directed Numbers Review Example 1
  • Directed Numbers Review Example 2
  • Substituting with Directed Numbers Example 1
  • Substituting with Directed Numbers Example 2
  • Algebraic Products
  • Single Bracket
  • Expanding with a Single Bracket Example 1
  • Expanding with a Single Bracket Example 2
  • Expand and Simplify
  • Expanding Brackets Extension Example
  • Pair of Brackets
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Squaring a Bracket
  • Expanding (x + a)(x - a)
  • Pair of Brackets Extension Example
  • Expand and Simplify Extension Example
  • Factorising into a Single Bracket
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising into a Pair of Brackets
  • Factorising into a Pair of Brackets Example 1
  • Factorising into a Pair of Brackets Example 2
  • Factorising into a Pair of Brackets Example 3
  • Factorising into a Pair of Brackets Example 4
  • Factorising into a Pair of Brackets Example 5
  • Factorising into a Pair of Brackets Example 6
  • Factorising into a Pair of Brackets Example 7
  • Factorising into a Pair of Brackets Example 8
  • Factorising into a Pair of Brackets Example 9
  • Factorising into a Pair of Brackets Example 10
  • The Difference of 2 Squares
  • The Difference of 2 Squares Example 1
  • The Difference of 2 Squares Example 2
  • The Difference of 2 Squares Example 3
  • The Difference of 2 Squares Extension Example
  • Formulae with Brackets
  • Expanding Brackets Review
  • Expanding Brackets Review Example 1
  • Expanding Brackets Review Example 2
  • Expanding Brackets Review Example 3
  • Formulae with Brackets
  • Formulae with Brackets Example 1
  • Formulae with Brackets Example 2
  • Formulae with Brackets Example 3
  • Further Equations
  • Equations with Brackets
  • Solving Equations with Brackets Example 1
  • Solving Equations with Brackets Example 2
  • Simultaneous Equations
  • Algebraic Solution
  • Simultaneous Equations Algebraic Solution Example 1
  • Simultaneous Equations Algebraic Solution Example 2
  • Simultaneous Equations Algebraic Solution Example 3
  • Simultaneous Equations Algebraic Solution Example 4
  • Simultaneous Equations Algebraic Solution Example 5
  • Simultaneous Equations Algebraic Solution Example 6
  • Simultaneous Equations Algebraic Solution Example 7
  • Simultaneous Equations Algebraic Solution Example 8
  • Graphical Solution
  • Simultaneous Equations Graphical Solution Example 1
  • Simultaneous Equations Graphical Solution Example 2
  • No Solutions or Infinite Solutions
  • No Solutions or Infinite Solutions
  • Problem Solving
  • Problem Solving Example 1
  • Problem Solving Example 2
  • Quadratic Equations
  • Solving Quadratic Equations
  • Introduction to Quadratic Equations Part 1
  • Introduction to Quadratic Equations Part 2
  • Introduction to Quadratic Equations Part 3
  • Solving Quadratic Equations by Factorising Example 1
  • Solving Quadratic Equations by Factorising Example 2
  • Solving Quadratic Equations by Factorising Example 3
  • Solving Quadratic Equations by Factorising Example 4
  • Solving Quadratic Equations by Factorising Example 5
  • Solving Quadratic Equations by Factorising Example 6
  • Solving Quadratic Equations by Factorising Example 7
  • Forming and Solving
  • The Quadratic Formula
  • Solving Quadratic Equations Using The Formula Example 1
  • Solving Quadratic Equations Using The Formula Example 2
  • Solving Quadratic Equations Using The Formula Example 3
  • Solving Quadratic Equations Using The Formula Example 4
  • Completing the Square
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • The Meaning of Completed Square Form
  • Solving Quadratics by Completing the Square
  • Quadratic Equations Extension
  • Completing the Square
  • Deriving the Quadratic Formula
  • Simultaneous Equations Linear and Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 4
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 5
  • Alg2
  • Basic Inequalities
  • Introduction to Inequalities
  • Introduction to Inequalities
  • Solving Simple Inequalities
  • Solving Simple Inequalities Example 1
  • Solving Simple Inequalities Example 2
  • Solving Simple Inequalities Example 3
  • Solving Simple Inequalities Example 4
  • Solving Simple Inequalities Example 5
  • Further Inequalities
  • Inequalities with Brackets
  • Solving Inequalities with Brackets Example 1
  • Solving Inequalities with Brackets Example 2
  • Algebraic Fractions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Multiplying and Dividing
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Lowest Common Multiples
  • Lowest Common Multiples (Algebraic) Example 1
  • Lowest Common Multiples (Algebraic) Example 2
  • Lowest Common Multiples (Algebraic) Example 3
  • Lowest Common Multiples (Algebraic) Example 4
  • Adding and Subtracting
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Adding and Subtracting Algebraic Fractions Example 7
  • Equations
  • Solving Equations Involving Fractions Example 1
  • Solving Equations Involving Fractions Example 2
  • Solving Equations Involving Fractions Example 3
  • Advanced Formulae
  • Substitution
  • Substituting Numbers in Standard Form Example 1
  • Substituting Numbers in Standard Form Example 1 - Calculator Guide
  • Substituting Numbers in Standard Form Example 2
  • Substituting Numbers in Standard Form Example 2 - Calculator Guide
  • Substituting Numbers in Standard Form Example 3
  • Substituting Numbers in Standard Form Example 3 - Calculator Guide
  • Rearranging Formulae
  • Rearranging Formulae (Advanced) Example 1
  • Rearranging Formulae (Advanced) Example 2
  • Rearranging Formulae (Advanced) Example 3
  • Rearranging Formulae (Advanced) Example 4
  • Rearranging Formulae (Advanced) Example 5
  • Rearranging Formulae (Advanced) Example 6
  • Rearranging Formulae (Advanced) Example 7
  • Miscelaneous Example
  • Miscellaneous Example
  • Advanced Inequalities
  • Quadratic Inequalities
  • Solving Quadratic Inequalities Example 1
  • Solving Quadratic Inequalities Example 2
  • Solving Quadratic Inequalities Example 3
  • Solving Quadratic Inequalities Example 4
  • Algebra and Functions
  • Simplifying Algebraic Fractions
  • Algebraic Fractions Example 1
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 6
  • Alg3
  • Algebra and Functions
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Alg4
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Basics
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers Introduction
  • Surds
  • Surd Introduction
  • Simplifying Surds Example 1
  • Simplifying Surds Example 2
  • Simplifying Surds Example 3
  • Rationalising Denominators
  • General Problems
  • Irrational Miscellaneous Example 1
  • Irrational Miscellaneous Example 2
  • Rational and Irrational Numbers Extension
  • An Infinite Number!
  • How Many Irrational Numbers Are There?
  • Indices Advanced
  • Review
  • Review of Indices so Far
  • The Power mn
  • The Power mn Example 1
  • The Power mn Example 2
  • Fractional Indices
  • Introduction to the Fractional Index 1/n
  • Fractional Indices Example 1
  • Fractional Indices Example 2
  • Introduction to the Fractional Index m/n
  • Fractional Indices Example 3
  • Fractional Indices Example 4
  • Fractional Indices Example 5
  • Fractional Indices Example 6
  • Indices
  • Indices with Algebra
  • The First Index Law
  • The Second Index Law
  • The Power mn
  • Using the Index Laws Example 1
  • Negative Indices
  • Fractional Indices
  • Pythagoras' Theorem
  • Introduction
  • Introduction to Pythagoas' Theorem
  • Finding the Hypotenuse
  • Finding the Hypotenuse Example 1
  • Finding the Hypotenuse Example 2
  • Finding the Hypotenuse Example 3
  • Finding the Hypotenuse Calculator Guide
  • Finding a Shorter Side
  • Finding a Shorter Side Example 1
  • Finding a Shorter Side Example 2
  • Finding a Shorter Side Example 3
  • Finding a Shorter Side Calculator Guide
  • Harder Problems
  • Harder Problems Example
  • More Length, Area and Volume
  • Area of a Triangle
  • Introduction to the Area of a Triangle
  • Area of a Triangle Example 1
  • Area of a Triangle Example 2
  • Area of a Triangle Example 3
  • Calc1
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Calc2
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • Calc3
  • Constant Acceleration
  • SUVAT
  • The SUVAT Quantities
  • The SUVAT Equations
  • Using the Constant Acceleration Formulae
  • Using the Constant Acceleration Formulae Example 1
  • Using the Constant Acceleration Formulae Example 2
  • Using the Constant Acceleration Formulae Example 3
  • Using the Constant Acceleration Formulae Example 4
  • Using the Constant Acceleration Formulae Example 5
  • CG1
  • Graphs of Straight Lines
  • Vertical Lines
  • Equations of ines Parallel to the Y-Axis
  • Horizontal Lines
  • Equations of ines Parallel to the X-Axis
  • The Line y = x
  • The Line y = x
  • Plotting Lines from Equations
  • Plotting Lines Example 1
  • Plotting Lines Example 2
  • Plotting Lines Example 3
  • The Equation of a Straight Line
  • Equations of Straight Lines Introduction
  • Equations of Straight Lines Example 1
  • Equations of Straight Lines Example 2
  • Intersection
  • The Interection of Two Lines
  • The Interection of Two Lines Example 1
  • Parallel Lines
  • Parallel Lines Introduction
  • The Equations of Parallel Lines Example 1
  • The Equations of Parallel Lines Example 2
  • Perpendicular Lines
  • Perpendicular Lines Introduction
  • Gradients of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 2
  • Coordinate Geometry
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • CG2
  • Linear Programming
  • Graphical Solution
  • Formulating a Linear programming Problem
  • Representing a LP Problem Graphically
  • Using the Graph to Solve a Linear Programming Problem
  • Trig1
  • Trigonometry
  • Introduction
  • Introduction to Trigonometry
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Calculator Guide 1
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding a Side Calculator Guide 2
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Finding an Angle Calculator Guide
  • Harder Examples
  • Multi-Step Trig Problems Example 1
  • Multi-Step Trig Problems Example 2
  • Sine and Cosine Rules
  • Introduction to Sine and Cosine Rules
  • Non Right-Angled Trigonometry
  • The Sine Rule
  • The Cosine Rule
  • Using The Sine Rule
  • Using The Sine Rule Example 1
  • Using The Sine Rule Example 2
  • Using the Cosine Rule
  • Using the Cosine Rule Example 1
  • Using the Cosine Rule Example 2
  • Miscellaneous Example
  • Finding All of the Unknowns in a Triangle
  • Extension - Ambiguity
  • The Ambiguous Case of the Sine Rule
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2θ + Cos2θ = 1
  • Introducing the Identity Sin2θ + Cos2θ
  • The Identity tanθ = sinθ/cosθ
  • Introducing the Identity tanθ = sinθ/cosθ
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Trig2
  • Pythagoras' Theorem
  • Three Dimensional Problems
  • Pythagoras in 3 Dimensions
  • Trigonometry
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1
  • Three Dimensional Problems Example 2
  • Further Area and Volume
  • Angle Between a Line and a Plane
  • definition of the Angle Between a Line and a Plane
  • Angle Between a Line and a Plane Example 1
  • Angle Between a Line and a Plane Example 2
  • Further Kinematics
  • Acceleration as a Function of Time
  • Acceleration as a Function of Time Intro
  • Acceleration as a Function of Time Example 1
  • Acceleration as a Function of Time Example 2
  • Acceleration as a Function of Time Example 3
  • Acceleration as a Function of Time Example 4
  • Acceleration as a Function of Time Example 5
  • Acceleration as a Function of Displacement
  • Acceleration as a Function of Displacement Intro
  • Acceleration as a Function of Displacement Example 1
  • Acceleration as a Function of Displacement Example 2
  • Acceleration as a Function of Displacement Example 3
  • Elastic Strings
  • Introduction to Elastic Strings
  • Introduction to Elastic Strings Part 1
  • Introduction to Elastic Strings Part 2
  • Basic Examples
  • Basic Examples 1
  • Basic Examples 2
  • Basic Examples 3
  • Equilibrium
  • Equilibrium Example 1
  • Equilibrium Example 2
  • Equilibrium Example 3
  • Equilibrium Example 4
  • Equilibrium Example 5
  • Elastic Potential Energy
  • Elastic Potential Energy Introduction
  • Elastic Potential Energy Example 1
  • Elastic Potential Energy Example 2
  • Conservation of Energy
  • Conservation of Energy Example 1
  • Conservation of Energy Example 2
  • Conservation of Energy Example 3
  • Circular Motion
  • Constant Angular Velocity
  • Constant Angular Velocity Introduction
  • Constant Angular Velocity Basic Examples 1
  • Constant Angular Velocity Basic Examples 2
  • Constant Angular Velocity Basic Examples 3
  • Constant Angular Velocity Basic Examples 4
  • Constant Angular Velocity Basic Examples 5
  • Constant Angular Velocity Basic Examples 6
  • Horizontal Circles
  • Motion in Horizontal Circles Example 1
  • Motion in Horizontal Circles Example 2
  • Motion in Horizontal Circles Example 3
  • Motion in Horizontal Circles Example 4
  • The Conical Pendulum
  • Conical Pendulum Introduction
  • Conical pendulum Examples 1
  • Conical pendulum Examples 2
  • Banked Tracks
  • Motion on a Banked Track Example 1
  • Motion on a Banked Track Example 2
  • Motion on a Banked Track Example 3
  • Motion on a Banked Track Example 4
  • Vertical Circles
  • Vertical Circles Introduction
  • Fixed Vertical Circles Example 1
  • Fixed Vertical Circles Example 2
  • Fixed Vertical Circles Example 3
  • Vertical Circles Which Are Not Fixed
  • General Vertical Circles Example 1
  • General Vertical Circles Example 2
  • General Vertical Circles Example 3
  • Further Dynamics
  • Force as a Function of Time or Displacement
  • Force as Function of Time Intro
  • Force as Function of Displacement Intro
  • Force as Function of Time Example
  • Force as Function of Displacement Example
  • Work and Impulse
  • Impulse for a Variable Force
  • Work Done by a Variable Force
  • Impulse for a Variable Force Example
  • Work Done by a Variable Force Example
  • Miscellaneous Example on Variable Force
  • Newton's Law of Gravitation
  • Newton's Law of Gravitation Intro
  • Newton's Law of Gravitation Example 1
  • Newton's Law of Gravitation Example 2
  • Newton's Law of Gravitation Example 3
  • Newton's Law of Gravitation Example 4
  • Newton's Law of Gravitation Example 5
  • Newton's Law of Gravitation Example 6
  • Simple Harmonic Motion
  • Introduction to SHM and the Equations
  • SHM Example 1
  • SHM Example 2
  • SHM Example 3
  • SHM Example 4
  • SHM Example 5
  • SHM Example 6
  • SHM Example 7
  • Hyperbolic Functions
  • Introducing the Hyperbolic Functions
  • The Hyperbolic Functions
  • The Inverse Hyperbolic Functions
  • Hyperbolic Identities
  • Hyperbolic Functions Examples
  • Hyperbolic Functions Example 1
  • Hyperbolic Functions Example 2
  • Hyperbolic Functions Example 3
  • Differentiation
  • Hyperbolic Functions
  • Differentiating Hyperbolic Functions
  • Differentiating Inverse Hyperbolic Functions
  • Trigonometric Functions
  • Differentiating Inverse Trigonometric Functions
  • HCF and LCM
  • My Class' favourite Method
  • HCF and LCM
  • My Class' favourite Method
  • HCF and LCM
  • My Class' favourite Method
  • Integration
  • Using Standard Integrals
  • Using Standard Integrals and Reversing Differentiation
  • Using Identities
  • Using Identities in Integration
  • Miscellaneous Examples
  • Miscellaneous Integration Examples 1
  • Miscellaneous Integration Examples 2
  • Using Completing the Square
  • Completing the Square Examples
  • Integrating Inverse Functions
  • Inverse Trigonometric and Hyperbolic Functions
  • Reduction Formulae
  • Introduction to Reduction Formulae
  • Reduction Formulae Example 1
  • Reduction Formulae Example 2
  • Reduction Formulae Example 3
  • Reduction Formulae Example 4
  • Length of a Curve
  • Length of a Curve Intro
  • Length of a Curve Example 1
  • Length of a Curve Example 2
  • Length of a Curve Example 3
  • Area of a Surface
  • Area of a Surface Intro
  • Area of a Surface Example 1
  • Area of a Surface Example 2
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Differentiating Functions Involving Powers of x
  • dy/dx as The Gradient Function
  • Finding the Equation of a Tangent
  • Finding the Equation of a Normal
  • Increasing and Decreasing Functions
  • Turning Points
  • Problem Solving
  • Revision
  • Simpson's Rule
  • Simpson's Rule
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Distance Between Two Points
  • Midpoint of a Line
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Distance Between Two Points
  • Midpoint of a Line
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Distance Between Two Points
  • Midpoint of a Line
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Distance Between Two Points
  • Midpoint of a Line
  • Revision
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Revision
  • Distance Between Two Points
  • Midpoint of a Line
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Revision
  • The Equation of a Straight Line
  • Gradient of a Straight Line Given Two Points
  • Finding the Equation from a Point and the Gradient
  • Finding the Equation from Two Given Points
  • Parallel Lines
  • Perpendicular Lines
  • Distance Between Two Points
  • Midpoint of a Line
  • Revision
  • Equation of a Circle
  • Intersection of a Line and a Circle
  • Use of Circle Theorems 1
  • Use of Circle Theorems 2
  • Use of Circle Theorems 3
  • Using Arrangements Example 3
  • Using Arrangements Example 3
  • Revision
  • Integration as Antidifferentiation
  • Revision
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Revision
  • Integration as Antidifferentiation
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Revision
  • Integration as Antidifferentiation
  • Revision
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Revision
  • Integration as Antidifferentiation
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Revision
  • Integration as Antidifferentiation
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Revision
  • Integration as Antidifferentiation
  • Using Indices
  • Finding C
  • Definite Integrals
  • Area
  • Compound Areas
  • Graphs
  • Graphs of Rational Functions
  • Graphs of Rational Functions Example 1
  • Graphs of Rational Functions Example 2
  • Graphs of Rational Functions Example 3
  • Graphs of Rational Functions Example 4
  • Statics
  • Centre of Mass of Lamina
  • Centre of Mass of Lamina Example 1
  • Centre of Mass of Lamina Example 2
  • Centre of Mass of Lamina Example 3
  • Centre of Mass of Lamina Example 4
  • Centre of Mass of Lamina Example 5
  • Arcs
  • Centre of Mass of Arc Example 1
  • Centre of Mass of Arc Example 2
  • Solids
  • Centre of Mass of a Solid Example 1
  • Centre of Mass of a Solid Example 2
  • Shells
  • Centre of Mass of a Shell Example 1
  • Centre of Mass of a Shell Example 2
  • Composite Shapes
  • Composite Shapes Example 1
  • Composite Shapes Example 2
  • Composite Shapes Example 3
  • Composite Shapes Example 4
  • Equilibrium
  • Equilibrium Example Part a
  • Equilibrium Example Part b
  • Equilibrium Example Part c
  • Equilibrium Example Part d
  • Equilibrium Example Part e
  • Equation of Circle Example 10
  • Rates of Change
  • Rates of Change
  • Rates of Change Example 1
  • Rates of Change Example 2
  • Rates of Change Example 3
  • Rates of Change Example 4
  • Rates of Change
  • Rates of Change
  • Rates of Change Example 1
  • Rates of Change Example 2
  • Rates of Change Example 3
  • Rates of Change Example 4
  • M4
  • Collisions
  • Oblique Impact With Smooth Surfaces
  • Impact of Sphere with Smooth Surface Intro
  • Impact of Sphere with Smooth Surface Example 1
  • Impact of Sphere with Smooth Surface Example 2
  • Impact of Sphere with Smooth Surface Example 3
  • Impact of Sphere with Smooth Surface Example 4
  • Oblique Impact Between Smooth Spheres
  • Impact Between Two Smooth Spheres Intro
  • Impact Between Two Smooth Spheres Example 1
  • Impact Between Two Smooth Spheres Example 2
  • Impact Between Two Smooth Spheres Example 3
  • Maclaurin and Taylor
  • Higher Derivatives
  • Higher Derivatives
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • Taylor's Expansion
  • The Taylor Expansion
  • Taylor's Expansion Example 1
  • Taylor's Expansion Example 2
  • Differential Equations
  • Power Series Solutions to Differential Equations Example 1
  • Power Series Solutions to Differential Equations Example 2
  • Power Series Solutions to Differential Equations Example 3
  • Approximations to Definite Integrals
  • Approximations to Definite Integrals
  • M3
  • Dimensions
  • Dimensions of a Formula
  • Dimensions Intro
  • Other Quantities
  • Dimensional Consistency
  • Elastic Strings
  • Introduction to Elastic Strings
  • Introduction to Elastic Strings Part 1
  • Introduction to Elastic Strings Part 2
  • Introduction to Elastic Strings Part 3
  • Basic Examples
  • Basic Examples 1
  • Basic Examples 2
  • Basic Examples 3
  • Equilibrium
  • Equilibrium Example 1
  • Equilibrium Example 2
  • Equilibrium Example 3
  • Equilibrium Example 4
  • Equilibrium Example 5
  • Elastic Potential Energy
  • Elastic Potential Energy Introduction
  • Elastic Potential Energy Example 1
  • Elastic Potential Energy Example 2
  • Conservation of Energy
  • Conservation of Energy Example 1
  • Conservation of Energy Example 2
  • Conservation of Energy Example 3
  • Circular Motion
  • Constant Angular Velocity
  • Constant Angular Velocity Introduction
  • Constant Angular Velocity Basic Examples 1
  • Constant Angular Velocity Basic Examples 2
  • Constant Angular Velocity Basic Examples 3
  • Constant Angular Velocity Basic Examples 4
  • Constant Angular Velocity Basic Examples 5
  • Constant Angular Velocity Basic Examples 6
  • Horizontal Circles
  • Motion in Horizontal Circles Example 1
  • Motion in Horizontal Circles Example 2
  • Motion in Horizontal Circles Example 3
  • Motion in Horizontal Circles Example 4
  • The Conical Pendulum
  • Conical Pendulum Introduction
  • Conical pendulum Examples 1
  • Conical pendulum Examples 2
  • Banked Tracks
  • Motion on a Banked Track Example 1
  • Motion on a Banked Track Example 2
  • Motion on a Banked Track Example 3
  • Motion on a Banked Track Example 4
  • Vertical Circles
  • Vertical Circles Introduction
  • Fixed Vertical Circles Example 1
  • Fixed Vertical Circles Example 2
  • Fixed Vertical Circles Example 3
  • Vertical Circles Which Are Not Fixed
  • General Vertical Circles Example 1
  • General Vertical Circles Example 2
  • General Vertical Circles Example 3
  • Further Dynamics
  • Force as a Function of Time or Displacement
  • Force as Function of Time Intro
  • Force as Function of Displacement Intro
  • Force as Function of Time Example
  • Force as Function of Displacement Example
  • Simple Harmonic Motion
  • Introduction to SHM and the Equations
  • SHM Example 1
  • SHM Example 2
  • SHM Example 3
  • SHM Example 4
  • SHM Example 5
  • SHM Example 6
  • SHM Example 7
  • Statics
  • Centre of Mass of Lamina
  • Centre of Mass of Lamina Example 1
  • Centre of Mass of Lamina Example 2
  • Centre of Mass of Lamina Example 3
  • Centre of Mass of Lamina Example 4
  • Centre of Mass of Lamina Example 5
  • Arcs
  • Centre of Mass of Arc Example 1
  • Centre of Mass of Arc Example 2
  • Solids
  • Centre of Mass of a Solid Example 1
  • Centre of Mass of a Solid Example 2
  • Shells
  • Centre of Mass of a Shell Example 1
  • Centre of Mass of a Shell Example 2
  • Composite Shapes
  • Composite Shapes Example 1
  • Composite Shapes Example 2
  • Composite Shapes Example 3
  • Composite Shapes Example 4
  • Equilibrium
  • Equilibrium Example Part a
  • Equilibrium Example Part b
  • Equilibrium Example Part c
  • Equilibrium Example Part d
  • Equilibrium Example Part e
  • Dimension Example
  • Simple Harmonic Motion
  • Simple Harmonic Motion
  • SHM Intro
  • Start Positions
  • Centre of Mass
  • Centre of Mass Intro
  • Proof
  • Proof by Induction
  • Proof by Induction Intro
  • Proof by Induction Example 1
  • Proof by Induction Example 2
  • Proof by Induction Example 3
  • The Exponential Form
  • Exponential Form Intro
  • Exponential Form Example 1
  • Exponential Form Example 2
  • Hyperbolic Functions
  • Relationships with Hyperbolic Functions
  • Hyperbolic Identities - Osborn's Rule Explained
  • Multiplying and Dividing
  • Multiplying and Dividing Intro
  • Multiplying and Dividing Example 1
  • Multiplying and Dividing Example 2
  • Multiplying and Dividing Consequences
  • Miscellaneous Examples
  • Miscellaneous Example 1
  • Miscellaneous Example 2
  • De Moivre's Theorem
  • De Moivre's Theorem Intro
  • De Moivre's Theorem Example 1
  • De Moivre's Theorem Example 2
  • De Moivre's Theorem Example 3
  • nth Roots of Complex Numbers
  • nth Roots of Unity
  • nth Roots for a General Complex Number
  • Loci in the Complex Plane
  • Basic Circles
  • Half Lines
  • More Complex Loci 1
  • More Complex Loci 2
  • More Complex Loci 3
  • Moments of a Force
  • Introducing Moments
  • The Turning Effect of a Force
  • Basic Moments Example 1
  • Basic Moments Example 2
  • Basic Moments Example 3
  • Basic Moments Example 4
  • Basic Moments Example 5
  • Basic Moments Example 6
  • Basic Moments Example 7
  • Moments and Equilibrium
  • Moment Problems Involving Equilibrium Example 1
  • Moment Problems Involving Equilibrium Example 2
  • Moment Problems Involving Equilibrium Example 3
  • Equilibrium Revision
  • Revision Example 1
  • Revision Example 2
  • More Complex Equilibrium Problems Involving Rigid Bodies
  • Equilibrium Problems Involving Rigid Bodies Example 1
  • Equilibrium Problems Involving Rigid Bodies Example 2
  • Equilibrium Problems Involving Rigid Bodies Example 3
  • Ladder Problems
  • Ladder Problems Example 1
  • Ladder Problems Example 2 Part a
  • Ladder Problems Example 2 Part b
  • Vectors
  • The Vector Product
  • Vector Product Intro
  • Vector Product Example 1
  • Vector Product Example 2
  • Using The Vector Product
  • Area of a Triangle
  • Area of a Parallelogram
  • Volume of a Parallelepiped (Scalar Triple Product)
  • Volume of a Tetrahedron
  • Vector Equations of Lines and Planes
  • Vector Equation of a Line
  • Parametric Equation of a Plane
  • Scalar Product Equation of a Plane
  • Cartesian Equation of a Plane
  • Converting Between Forms
  • Geometric Properties of Lines and Planes
  • Distance of a Plane from the Origin
  • Distance Between Two Planes
  • Distance of a Point from a Plane
  • Angle Between a Line and a Plane
  • The Angle Between Two Planes
  • The Line of Intersection of Two Planes
  • The Shortest Distance Between Two Skew Lines
  • Equation of Circle Example 10
  • Equation of Circle Example 10
  • Equation of Circle Example 10
  • Equation of Circle Example 10
  • Equation of Circle Example 10
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Sine and Cosine Rule Including Bearings Example 2
  • Numerical Methods
  • Step-By-Step Solution of Differential Equations
  • First Order First Method - Geometrical Derivation
  • First Order First Method - Formal Derivation
  • First Order First Method - Example
  • First Order Second Method - Geometrical Derivation
  • First Order Second Method - Formal Derivation
  • First Order Second Method - Example
  • Second Order Method - Derivation
  • Second Order Method - Example 1
  • Second Order Method - Example 2
  • D2
  • Critical Path Analysis
  • Introduction
  • Introduction to CPA
  • Drawing a Network
  • Drawing a Network Example 1
  • Drawing a Network Example 2
  • Drawing a Network Example 3
  • Analysis of a Network
  • Time Analysis Example 1
  • Time Analysis Example 2
  • Time Analysis Example 3
  • Cascade (Gantt) Charts
  • Cascade Example 1
  • Cascade Example 2
  • Scheduling
  • Scheduling Example 1
  • Scheduling Example 2
  • D1
  • Trees
  • Minimum Spanning Trees
  • Introduction
  • Kruskal's Algorithm Example 1
  • Kruskal's Algorithm Example 2
  • Prim's Algorithm Example 1
  • Prim's Algorithm Example 2
  • Prim's Algorithm in a table
  • Route Inspection
  • The Route Inspection Algorithm
  • Introduction
  • Route Inspection Example
  • Shortest Path
  • Dijkstra's Algorithm
  • Dijkstra Example
  • Linear Programming
  • Graphical Solution
  • Formulating a Linear programming Problem
  • Representing a LP Problem Graphically
  • Using the Graph to Solve a Linear Programming Problem
  • The Simplex
  • Forming an Initial Tableau
  • Solving a Simplex Tableau
  • The Simplex Explained
  • D2
  • Critical Path Analysis
  • Introduction
  • Introduction to CPA
  • Drawing a Network
  • Drawing a Network Example 1
  • Drawing a Network Example 2
  • Drawing a Network Example 3
  • Analysis of a Network
  • Time Analysis Example 1
  • Time Analysis Example 2
  • Time Analysis Example 3
  • Cascade (Gantt) Charts
  • Cascade Example 1
  • Cascade Example 2
  • Scheduling
  • Scheduling Example 1
  • Scheduling Example 2
  • D1
  • Trees
  • Minimum Spanning Trees
  • Introduction
  • Kruskal's Algorithm Example 1
  • Kruskal's Algorithm Example 2
  • Prim's Algorithm Example 1
  • Prim's Algorithm Example 2
  • Prim's Algorithm in a table
  • Route Inspection
  • The Route Inspection Algorithm
  • Introduction
  • Route Inspection Example
  • Shortest Path
  • Dijkstra's Algorithm
  • Dijkstra Example
  • Linear Programming
  • Graphical Solution
  • Formulating a Linear programming Problem
  • Representing a LP Problem Graphically
  • Using the Graph to Solve a Linear Programming Problem
  • The Simplex
  • Forming an Initial Tableau
  • Solving a Simplex Tableau
  • The Simplex Explained
  • Permutations and Combinations
  • Arrangements
  • Arrangements Intro
  • Arrangements Example 1
  • Arrangements Example 2
  • Combinations
  • Combinations Intro
  • Combinations Example 1
  • Combinations Example 2
  • Permutations
  • Permutations Intro
  • Miscellaneous Examples
  • Miscellaneous Examples 1
  • Miscellaneous Examples 2
  • Miscellaneous Examples 3
  • Miscellaneous Examples 4
  • Permutations and Combinations
  • Arrangements
  • Arrangements Intro
  • Arrangements Example 1
  • Arrangements Example 2
  • Combinations
  • Combinations Intro
  • Combinations Example 1
  • Combinations Example 2
  • Permutations
  • Permutations Intro
  • Miscellaneous Examples
  • Miscellaneous Examples 1
  • Miscellaneous Examples 2
  • Miscellaneous Examples 3
  • Miscellaneous Examples 4
  • Permutations and Combinations
  • Arrangements
  • Arrangements Intro
  • Arrangements Example 1
  • Arrangements Example 2
  • Combinations
  • Combinations Intro
  • Combinations Example 1
  • Combinations Example 2
  • Permutations
  • Permutations Intro
  • Miscellaneous Examples
  • Miscellaneous Examples 1
  • Miscellaneous Examples 2
  • Miscellaneous Examples 3
  • Miscellaneous Examples 4
  • Matchings
  • Modelling the Situation
  • Nomenclature and the Bipartite Graph
  • Alternating Paths
  • Alternating Paths
  • Examples
  • Worked Example
  • Matchings
  • Modelling the Situation
  • Nomenclature and the Bipartite Graph
  • Alternating Paths
  • Alternating Paths
  • Examples
  • Worked Example
  • Matchings
  • Modelling the Situation
  • Nomenclature and the Bipartite Graph
  • Alternating Paths
  • Alternating Paths
  • Examples
  • Worked Example
  • General Algorithms
  • Introduction
  • Introduction to Algorithms
  • Applying a Given Algorithm
  • Sorting
  • The Bubble Sort
  • The Quick Sort
  • Bin Packing
  • Bin-Packing Intro
  • The First-Fit Algorithm
  • The First-Fit Decreasing Algorithm
  • Full-Bin Combinations
  • Searching Algorithms
  • The Binary Search Algorithm
  • General Algorithms
  • Introduction
  • Introduction to Algorithms
  • Applying a Given Algorithm
  • Sorting
  • The Bubble Sort
  • The Quick Sort
  • The Selection with Interchange Sort
  • The Shuttle Sort
  • The Insertion Sort
  • Bin Packing
  • Bin-Packing Intro
  • The First-Fit Algorithm
  • The First-Fit Decreasing Algorithm
  • Full-Bin Combinations
  • Searching Algorithms
  • The Linear Search Algorithm
  • The Indexed Sequential Search Algorithm
  • The Binary Search Algorithm
  • Simulation
  • Introduction
  • Introduction to Simulation
  • Worked Example
  • Simulation Example
  • A Simulation
  • A Computer Simulation Example
  • Note
  • An Important Note
  • Flows
  • Feasibility and Conservation
  • Flow, Feasibility and Conservation
  • Flow Along Paths
  • Flow Along Paths
  • Finding Maximal Flow
  • The Labelling Procedure
  • Backflow
  • Cuts
  • Proving Flow is Maximal
  • Supersources and Supersinks
  • Problems Involving Multiple Sources and Sinks
  • Travelling Salesman
  • Introduction
  • Introduction and Definitions
  • Lower Bounds
  • Producing Lower Bounds
  • A Note on Lower Bounds
  • Upper Bounds Part 1
  • Upper Bounds 1
  • Nearest Neighbour
  • The Nearest Neighbour Algorithm Part 1
  • The Nearest Neighbour Algorithm Part 2
  • The Nearest Neighbour Algorithm Part 3
  • Upper Bounds Part 2
  • Upper Bounds Using Nearest Neighbour Part 1
  • Upper Bounds Using Nearest Neighbour Part 2
  • D2
  • Travelling Salesman
  • Introduction
  • Introduction and Definitions
  • Lower Bounds
  • Producing Lower Bounds
  • A Note on Lower Bounds
  • Upper Bounds Part 1
  • Upper Bounds 1
  • Nearest Neighbour
  • The Nearest Neighbour Algorithm Part 1
  • The Nearest Neighbour Algorithm Part 2
  • The Nearest Neighbour Algorithm Part 3
  • Upper Bounds Part 2
  • Upper Bounds Using Nearest Neighbour Part 1
  • Upper Bounds Using Nearest Neighbour Part 2
  • D2
  • Travelling Salesman
  • Introduction
  • Introduction and Definitions
  • Lower Bounds
  • Producing Lower Bounds
  • A Note on Lower Bounds
  • Upper Bounds Part 1
  • Upper Bounds 1
  • Nearest Neighbour
  • The Nearest Neighbour Algorithm Part 1
  • The Nearest Neighbour Algorithm Part 2
  • The Nearest Neighbour Algorithm Part 3
  • Upper Bounds Part 2
  • Upper Bounds Using Nearest Neighbour Part 1
  • Upper Bounds Using Nearest Neighbour Part 2
  • Floyd's Algorithm
  • Floyd's Algorithm
  • Introduction to Floyd's Algorithm
  • Floyd's Algorithm Example
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Sketching Curves
  • Graph Transformations
  • Transformations Introduction
  • The Transformation f(x) + a
  • The Transformation f(x - a)
  • The Transformation af(x) Example 1
  • The Transformation af(x) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 3
  • The Effect of Transformations on a Point Example 1
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 3
  • Cubic Curves
  • The Graph y = x3 Example 1
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 6
  • The General Cubic Curve Introduction
  • The General Cubic Curve Example 1
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 5
  • Reciprocal Curves
  • The Reciprocal Function Example 1
  • The Reciprocal Function Example 2
  • The Intersection of Two Curves
  • Sketching Two Curves to Find the Number of Points of Intersection
  • The Sine and Cosine Rules
  • Overview
  • Introducing the Sine and Cosine Rules
  • The Sine Rule
  • Sine Rule Example 1
  • Sine Rule Example 2
  • Sine Rule Example 3
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 3
  • The Cosine Rule
  • Introduction to the Cosine Rule Part 1
  • Introduction to the Cosine Rule Part 2
  • Cosine Rule Example 1
  • Cosine Rule Example 2
  • Area
  • Area Formula
  • Area Example
  • Bearings Example
  • Sine and Cosine Rule Including Bearings
  • P1
  • Algebra and Functions
  • Collecting Like Terms
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 4
  • Expanding Brackets
  • Expanding a Single Bracket Example 1
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 4
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 4
  • Factorising Expressions
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising Quadratic Expressions Example 1
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 6
  • An Introduction to Trigonometric Identities and Equations
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2? + Cos2? = 1
  • Introducing the Identity Sin2? + Cos2?
  • The Identity tan? = sin?/cos?
  • Introducing the Identity tan? = sin?/cos?
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities
  • Coordinate Geometry
  • Introduction to the Equation of a Straight Line
  • Equation of a Straight Line Example 1
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 5
  • Finding the Gradient of a Straight Line
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 5
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Equations and Inequalities
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Inequalities
  • Linear Inequalities Example 1
  • Linear Inequalities Example 2
  • Quadratic Inequalities Example 1
  • Quadratic Inequalities Example 2
  • Quadratic Inequalities Example 3
  • Quadratic Inequalities Example 4
  • Quadratic Inequalities Example 5
  • Exponentials and Logarithms
  • Introduction
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Functions
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Geometric Sequences and Series
  • Introduction
  • Introduction to Geometric Sequences
  • The nth Term
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • The Sum of the First n Terms
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Sum to Infinity
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • Graphs of Trigonometric Functions
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 1
  • The Formula for the Equation of a Circle
  • The Equation of a Circle
  • Coordinate Geometry
  • Adding and Subtracting Algebraic Fractions Example 6
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 5
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 1
  • Algebraic Fractions Example 6
  • Algebraic Fractions Example 5
  • Algebraic Fractions Example 4
  • Algebraic Fractions Example 3
  • Algebraic Fractions Example 2
  • Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions
  • Working with Surds Example 7
  • Working with Surds Example 6
  • Working with Surds Example 5
  • Working with Surds Example 4
  • Working with Surds Example 3
  • Working with Surds Example 2
  • Working with Surds Example 1
  • Surd Introduction
  • Surds
  • Using Index Laws Example 2
  • Using Index Laws Example 1
  • Sixth Index Law Example 2
  • Sixth Index Law Example 1
  • Fifth Index Law Example 2
  • Fifth Index Law Example 1
  • Fourth Index Law Example 3
  • Fourth Index Law Example 2
  • Fourth Index Law Example 1
  • Raising a Number to the Power Zero
  • Third Index Law
  • Second Index Law
  • First Index Law
  • Index Laws
  • Algebra and Functions
  • Basics
  • Cam-Int A Level Maths
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Quadratic Functions
  • Plotting Quadratic Graphs
  • Plotting a Quadratic Graph Example 1
  • Plotting a Quadratic Graph Example 2
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • Completing The Square
  • Completing the Square Introduction
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • Completing the Square Example 4
  • Completing the Square Example 5
  • What Completed Square Form Shows Example 1
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 4
  • Solving by Completing the Square Example 1
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 4
  • Derivation of the Quadratic Formula
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Sketching Quadratics
  • Sketching a Quadratic Example 1
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 4
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Radian Measure
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Sequences and Series
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • P2
  • Algebra and Functions
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Differentiation Techniques
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Exponentials and Logarithms
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Further Trigonometry
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • Integration
  • The Trapezium Rule
  • Introducing the Trapezium Rule Part 1
  • Introducing the Trapezium Rule Part 2
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Parametric Equations
  • Using Parametric Equations Example 1
  • Using Parametric Equations Example 2
  • Using Parametric Equations Example 3
  • Using Parametric Equations Example 4
  • Differential Equations
  • Differential Equations Example 1
  • Differential Equations Example 2
  • Differential Equations Example 3
  • Differential Equations Example 4
  • Numerical Methods
  • Introduction
  • Why Solve Equations Numerically
  • Graphical Solutions
  • Rearrange to Give f(x) = 0
  • Useful Background Revision
  • Locating Roots of Equations
  • Showing That a Root of an Equation Lies in a Given Interval -Example 1
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Parametric and Implicit Equations
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Implicit Functions
  • Differentiating Functions Given Implicitly Example 1
  • Differentiating Functions Given Implicitly Example 2
  • Differentiating Functions Given Implicitly Example 3
  • Differentiating Functions Given Implicitly Example 4
  • Differentiating Functions Given Implicitly Example 5
  • Differentiating Functions Given Implicitly Example 6
  • Transformations of Graphs
  • The Modulus Function
  • Introduction to The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Solving Equations and Inequalities Involving Moduli
  • Solving Equations and Inequalities Involving Moduli Example 1
  • Solving Equations and Inequalities Involving Moduli Example 2
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Combinations of Transformations Example 5
  • Combinations of Transformations Example 6
  • Trigonometry
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • P3
  • Algebra and Functions
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type II - Quadratic Factor in Denominator Example 1
  • Type II - Quadratic Factor in Denominator Example 2
  • Type II - Quadratic Factor in Denominator Example 3
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Type IV - Improper Fractions Example 1 (Leads to Type I)
  • Type IV - Improper Fractions Example 2 (Leads to Type III)
  • Type IV - Improper Fractions Example 3 (Leads to Type II)
  • Complex Numbers
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • The Binomial Expansion
  • The Binomial Expansion for Any Rational Index
  • Binomial Expansion for Any Rational Index Example 1
  • Binomial Expansion for Any Rational Index Example 2
  • Binomial Expansion for Any Rational Index Example 3
  • Binomial Expansion for Any Rational Index Example 4
  • Binomial Expansion for Any Rational Index Example 5
  • Binomial Expansion for Any Rational Index Example 6
  • Binomial Expansion for Any Rational Index Example 7
  • Binomial Expansion for Any Rational Index Example 8
  • Binomial Expansion for Any Rational Index Example 9
  • Binomial Expansion for Any Rational Index Example 10
  • Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • The Binomial Expansion
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • Vectors
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • Distributions
  • Geometric Distribution
  • Geometric Distribution Introduction
  • Geometric Distribution Expectation and Variance
  • Geometric Distribution Example 1
  • Complex Numbers
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Proof
  • Proof by Induction
  • Introduction to Proof by Induction
  • Induction Example 1
  • Induction Example 2
  • Induction Example 3
  • Induction Example 4
  • Induction Example 5
  • Proof by Induction Intro
  • Proof by Induction Example 1
  • Proof by Induction Example 2
  • Proof by Induction Example 3
  • Series
  • Summation by Method of Differences
  • Differences Example 1
  • Differences Example 2
  • Differences Example 3
  • Using Standard Results
  • Standard Results Example
  • FP2
  • Polar Coordinates
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Areas of Regions for Polar Curves
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Tangents Parallel to and Perpendicular to the Intitial Line
  • Introduction
  • Example
  • Hyperbolic Functions
  • Introducing the Hyperbolic Functions
  • The Hyperbolic Functions
  • The Inverse Hyperbolic Functions
  • Hyperbolic Identities
  • Hyperbolic Functions Examples
  • Hyperbolic Functions Example 1
  • Hyperbolic Functions Example 2
  • Hyperbolic Functions Example 3
  • Differentiation & Integration
  • Hyperbolic Functions
  • Differentiating Hyperbolic Functions
  • Differentiating Inverse Hyperbolic Functions
  • Trigonometric Functions
  • Differentiating Inverse Trigonometric Functions
  • Using Standard Integrals
  • Using Standard Integrals and Reversing Differentiation
  • Using Identities
  • Using Identities in Integration
  • Miscellaneous Examples
  • Miscellaneous Integration Examples 1
  • Miscellaneous Integration Examples 2
  • Using Completing the Square
  • Completing the Square Examples
  • Integrating Inverse Functions
  • Inverse Trigonometric and Hyperbolic Functions
  • Reduction Formulae
  • Introduction to Reduction Formulae
  • Reduction Formulae Example 1
  • Reduction Formulae Example 2
  • Reduction Formulae Example 3
  • Reduction Formulae Example 4
  • Higher Derivatives
  • Higher Derivatives
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • Numerical Methods
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Newton-Raphson
  • FP3
  • Complex Numbers
  • The Exponential Form
  • Exponential Form Intro
  • Exponential Form Example 1
  • Exponential Form Example 2
  • Hyperbolic Functions
  • Relationships with Hyperbolic Functions
  • Hyperbolic Identities - Osborn's Rule Explained
  • Multiplying and Dividing
  • Multiplying and Dividing Intro
  • Multiplying and Dividing Example 1
  • Multiplying and Dividing Example 2
  • Multiplying and Dividing Consequences
  • Miscellaneous Examples
  • Miscellaneous Example 1
  • Miscellaneous Example 2
  • De Moivre's Theorem
  • De Moivre's Theorem Intro
  • De Moivre's Theorem Example 1
  • De Moivre's Theorem Example 2
  • De Moivre's Theorem Example 3
  • nth Roots of Complex Numbers
  • nth Roots of Unity
  • nth Roots for a General Complex Number
  • Loci in the Complex Plane
  • Basic Circles
  • Half Lines
  • More Complex Loci 1
  • More Complex Loci 2
  • More Complex Loci 3
  • Differential Equations
  • Separable Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Family of Solution Curves
  • Example 1
  • Example 2
  • Exact Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • General First Order Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • 2nd Order Differential Equations with Constant Coeeficients
  • Introduction to 2nd Order Differential Equations
  • Real Distinct Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Complex Roots to the Auxiliary Equation
  • Complimentary Function and Particular Integral
  • CF & PI Example 1
  • CF & PI Example 2
  • CF & PI Example 3
  • CF & PI Example 4
  • CF & PI Example 5
  • CF & PI Example 6
  • CF & PI Example 7
  • Using Substitutions to Solve Differential equations
  • Using Substitutions Example 1
  • Using Substitutions Example 2
  • Using Substitutions Example 3
  • Step-By-Step Solution of Differential Equations
  • First Order First Method - Geometrical Derivation
  • First Order First Method - Formal Derivation
  • First Order First Method - Example
  • First Order Second Method - Geometrical Derivation
  • First Order Second Method - Formal Derivation
  • First Order Second Method - Example
  • Second Order Method - Derivation
  • Second Order Method - Example 1
  • Second Order Method - Example 2
  • Vectors
  • The Vector Product
  • Vector Product Intro
  • Vector Product Example 1
  • Vector Product Example 2
  • Using The Vector Product
  • Area of a Triangle
  • Area of a Parallelogram
  • Volume of a Parallelepiped (Scalar Triple Product)
  • Volume of a Tetrahedron
  • Vector Equations of Lines and Planes
  • Vector Equation of a Line
  • Parametric Equation of a Plane
  • Scalar Product Equation of a Plane
  • Cartesian Equation of a Plane
  • Converting Between Forms
  • Geometric Properties of Lines and Planes
  • Distance of a Plane from the Origin
  • Distance Between Two Planes
  • Distance of a Point from a Plane
  • Angle Between a Line and a Plane
  • The Angle Between Two Planes
  • The Line of Intersection of Two Planes
  • The Shortest Distance Between Two Skew Lines
  • M3
  • Circular Motion
  • Vertical Circles
  • Vertical Circles Introduction
  • Fixed Vertical Circles Example 1
  • Fixed Vertical Circles Example 2
  • Fixed Vertical Circles Example 3
  • Vertical Circles Which Are Not Fixed
  • General Vertical Circles Example 1
  • General Vertical Circles Example 2
  • General Vertical Circles Example 3
  • Elastic Strings
  • Introduction to Elastic Strings
  • Introduction to Elastic Strings Part 1
  • Introduction to Elastic Strings Part 2
  • Basic Examples
  • Basic Examples 1
  • Basic Examples 2
  • Basic Examples 3
  • Equilibrium
  • Equilibrium Example 1
  • Equilibrium Example 2
  • Equilibrium Example 3
  • Equilibrium Example 4
  • Equilibrium Example 5
  • Elastic Potential Energy
  • Elastic Potential Energy Introduction
  • Elastic Potential Energy Example 1
  • Elastic Potential Energy Example 2
  • Conservation of Energy
  • Conservation of Energy Example 1
  • Conservation of Energy Example 2
  • Conservation of Energy Example 3
  • Equilibrium
  • More Complex Equilibrium Problems Involving Rigid Bodies
  • Equilibrium Problems Involving Rigid Bodies Example 1
  • Equilibrium Problems Involving Rigid Bodies Example 2
  • Equilibrium Problems Involving Rigid Bodies Example 3
  • Simple Harmonic Motion
  • Simple Harmonic Motion
  • Introduction to SHM and the Equations
  • SHM Example 1
  • SHM Example 2
  • SHM Example 3
  • SHM Example 4
  • SHM Example 5
  • SHM Example 6
  • SHM Example 7
  • Variable Force
  • Acceleration as a Function of Time
  • Acceleration as a Function of Time Intro
  • Acceleration as a Function of Time Example 1
  • Acceleration as a Function of Time Example 2
  • Acceleration as a Function of Time Example 3
  • Acceleration as a Function of Time Example 4
  • Acceleration as a Function of Time Example 5
  • Acceleration as a Function of Displacement
  • Acceleration as a Function of Displacement Intro
  • Acceleration as a Function of Displacement Example 1
  • Acceleration as a Function of Displacement Example 2
  • Acceleration as a Function of Displacement Example 3
  • Num
  • CCEAAdd
  • Complex Numbers
  • The Exponential Form
  • Exponential Form Intro
  • Exponential Form Example 1
  • Exponential Form Example 2
  • Hyperbolic Functions
  • Relationships with Hyperbolic Functions
  • Hyperbolic Identities - Osborn's Rule Explained
  • Multiplying and Dividing
  • Multiplying and Dividing Intro
  • Multiplying and Dividing Example 1
  • Multiplying and Dividing Example 2
  • Multiplying and Dividing Consequences
  • Miscellaneous Examples
  • Miscellaneous Example 1
  • Miscellaneous Example 2
  • De Moivre's Theorem
  • De Moivre's Theorem Intro
  • De Moivre's Theorem Example 1
  • De Moivre's Theorem Example 2
  • De Moivre's Theorem Example 3
  • nth Roots of Complex Numbers
  • nth Roots of Unity
  • nth Roots for a General Complex Number
  • Loci in the Complex Plane
  • Basic Circles
  • Half Lines
  • More Complex Loci 1
  • More Complex Loci 2
  • More Complex Loci 3
  • Tranformations of the Complex Plane
  • Complex Number Transformations Introduction
  • Transformation Examples
  • Complex Number Transformations Example 1
  • Complex Number Transformations Example 2
  • Complex Number Transformations Example 3
  • Complex Number Transformations Example 4
  • Complex Number Transformations Example 5
  • Invariant Points
  • Invariant Points Example
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Calculus
  • Hyperbolic Functions
  • Differentiating Hyperbolic Functions
  • Differentiating Inverse Hyperbolic Functions
  • Trigonometric Functions
  • Differentiating Inverse Trigonometric Functions
  • Hyperbolic Functions
  • Introducing the Hyperbolic Functions
  • The Hyperbolic Functions
  • The Inverse Hyperbolic Functions
  • Hyperbolic Identities
  • Hyperbolic Functions Examples
  • Hyperbolic Functions Example 1
  • Hyperbolic Functions Example 2
  • Hyperbolic Functions Example 3
  • Maclaurin and Taylor
  • Higher Derivatives
  • Higher Derivatives
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • Taylor's Expansion
  • The Taylor Expansion
  • Taylor's Expansion Example 1
  • Taylor's Expansion Example 2
  • Differential Equations
  • Power Series Solutions to Differential Equations Example 1
  • Power Series Solutions to Differential Equations Example 2
  • Power Series Solutions to Differential Equations Example 3
  • Approximations to Definite Integrals
  • Approximations to Definite Integrals
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • Orthogonal Matrices
  • Orthogonal Matrices Example 1
  • Orthogonal Matrices Example 2
  • Orthogonal Matrices Example 3
  • Diagonalising a Symmetric Matrix
  • Diagonalising a Symmetric Matrix Example 1
  • Diagonalising a Symmetric Matrix Example 2
  • Diagonalising a Symmetric Matrix Example 3
  • Polar Coordinates
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Areas of Regions for Polar Curves
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Tangents Parallel to and Perpendicular to the Intitial Line
  • Introduction
  • Example
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Cartesian Equations of Lines
  • Groups
  • Introduction
  • Definitions
  • Introduction Example 1
  • Introduction Example 2
  • Introduction Example 3
  • Introduction Example 4
  • Order and Subgroups
  • Order and Subgroups Intro
  • Isomorphism
  • Isomorphism Intro
  • Group Structure
  • Order 1 and 2
  • Order 3
  • Order 4
  • Order 5
  • Order 6
  • Definitions
  • Graph Definitions
  • Definitions
  • Definitions
  • Graph Definitions
  • Definitions
  • Definitions
  • Graph Definitions
  • Definitions
  • Complex Numbers
  • FP1 - New (for those in L6 or sitting the course in a single year)
  • FP1 - Old (for those in U6)
  • Proof by Induction Prologue
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Numerical Methods
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Linear Interpolation
  • Interval Bisection
  • Newton-Raphson
  • Summary of Numerical Methods
  • Coordinate Geometry
  • The Parabola
  • Introduction to The parabola
  • Tangents and Normals
  • Parabola Examples 1
  • Parabola Examples 2
  • Parabola Examples 3
  • Parabola Examples 4
  • Parabola Examples 5
  • Parabola Examples 6
  • Parabola Examples 7
  • The Hyperbola
  • Introduction to the Hyperbola Part 1
  • Introduction to the Hyperbola Part 2
  • The Rectangular Hyperbola
  • Tangents and Normals Part 1
  • Tangents and Normals Part 2
  • Hyperbola Examples 1
  • Hyperbola Examples 2
  • Hyperbola Examples 3
  • Hyperbola Examples 4
  • Hyperbola Examples 5
  • Hyperbola Examples 6
  • Matrices
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Series
  • Using Standard Results
  • Standard Results Example
  • Proof
  • Proof by Induction
  • Proof by Induction Intro
  • Proof by Induction Example 1
  • Proof by Induction Example 2
  • Proof by Induction Example 3
  • FP2 - Old (for those in U6)
  • FP2 - New (for those in L6 or sitting the course in a single year)
  • Using Substitutions Example 1
  • Using Substitutions to Solve Differential equations
  • CF & PI Example 7
  • CF & PI Example 6
  • CF & PI Example 5
  • CF & PI Example 4
  • CF & PI Example 3
  • CF & PI Example 2
  • CF & PI Example 1
  • Complimentary Function and Particular Integral
  • Complex Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Real Distinct Roots to the Auxiliary Equation
  • Introduction to 2nd Order Differential Equations
  • 2nd Order Differential Equations
  • 2nd Order Differential Equations with Constant Coeeficients
  • Example 3
  • Example 2
  • Example 1
  • General First Order Equations
  • Introduction
  • Example 3
  • Example 2
  • Example 1
  • Introduction
  • Exact Equations
  • Example 2
  • Example 1
  • Example 3
  • Family of Solution Curves
  • Example 2
  • Example 1
  • Introduction
  • Separable Equations
  • First Order Differential Equations
  • Invariant Points Example
  • Invariant Points
  • Complex Number Transformations Example 5
  • Complex Number Transformations Example 4
  • Complex Number Transformations Example 3
  • Complex Number Transformations Example 2
  • Complex Number Transformations Example 1
  • Transformation Examples
  • Complex Number Transformations Introduction
  • Tranformations of the Complex Plane
  • More Complex Loci 3
  • More Complex Loci 2
  • More Complex Loci 1
  • Half Lines
  • Basic Circles
  • Loci in the Complex Plane
  • nth Roots for a General Complex Number
  • nth Roots of Unity
  • nth Roots of Complex Numbers
  • De Moivre's Theorem Example 3
  • De Moivre's Theorem Example 2
  • De Moivre's Theorem Example 1
  • De Moivre's Theorem Intro
  • De Moivre's Theorem
  • Miscellaneous Example 2
  • Miscellaneous Example 1
  • Miscellaneous Examples
  • Multiplying and Dividing Consequences
  • Multiplying and Dividing Example 2
  • Multiplying and Dividing Example 1
  • Multiplying and Dividing Intro
  • Multiplying and Dividing
  • Hyperbolic Identities - Osborn's Rule Explained
  • Relationships with Hyperbolic Functions
  • Hyperbolic Functions
  • Exponential Form Example 2
  • Exponential Form Example 1
  • Exponential Form Intro
  • The Exponential Form
  • Complex Numbers
  • Differences Example 3
  • Differences Example 2
  • Differences Example 1
  • Summation by Method of Differences
  • Series
  • Inequalities Example 6
  • Inequalities Example 5
  • Solving Inequalities Involving Modulus
  • Inequalities Example 4
  • Inequalities Example 3
  • Inequalities Example 2
  • Inequalities Example 1
  • Introduction
  • Solving Inequalities
  • Inequalities
  • Using Substitutions Example 2
  • Using Substitutions Example 3
  • Maclaurin and Taylor
  • Higher Derivatives
  • Higher Derivatives
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • Taylor's Expansion
  • The Taylor Expansion
  • Taylor's Expansion Example 1
  • Taylor's Expansion Example 2
  • Differential Equations
  • Power Series Solutions to Differential Equations Example 1
  • Power Series Solutions to Differential Equations Example 2
  • Power Series Solutions to Differential Equations Example 3
  • Approximations to Definite Integrals
  • Approximations to Definite Integrals
  • Polar Coordinates
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Areas of Regions for Polar Curves
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Tangents Parallel to and Perpendicular to the Intitial Line
  • Introduction
  • Example
  • FP3 - Old (for those in U6)
  • FP3 - New (for those in L6 or sitting the course in a single year)
  • Hyperbolic Functions
  • Introducing the Hyperbolic Functions
  • The Hyperbolic Functions
  • The Inverse Hyperbolic Functions
  • Hyperbolic Identities
  • Hyperbolic Functions Examples
  • Hyperbolic Functions Example 1
  • Hyperbolic Functions Example 2
  • Hyperbolic Functions Example 3
  • Coordinate Geometry
  • The Ellipse
  • Introduction to the Ellipse Part 1
  • Introduction to the Ellipse Part 2
  • Tangents and Normals
  • Ellipse Examples 1
  • Ellipse Examples 2
  • Ellipse Examples 3
  • Ellipse Examples 4
  • Ellipse Examples 5
  • Ellipse Examples 6
  • Ellipse Examples 7
  • Differentiation
  • Hyperbolic Functions
  • Differentiating Hyperbolic Functions
  • Differentiating Inverse Hyperbolic Functions
  • Trigonometric Functions
  • Differentiating Inverse Trigonometric Functions
  • Integration
  • Using Standard Integrals
  • Using Standard Integrals and Reversing Differentiation
  • Using Identities
  • Using Identities in Integration
  • Miscellaneous Examples
  • Miscellaneous Integration Examples 1
  • Miscellaneous Integration Examples 2
  • Using Completing the Square
  • Completing the Square Examples
  • Integrating Inverse Functions
  • Inverse Trigonometric and Hyperbolic Functions
  • Reduction Formulae
  • Introduction to Reduction Formulae
  • Reduction Formulae Example 1
  • Reduction Formulae Example 2
  • Reduction Formulae Example 3
  • Reduction Formulae Example 4
  • Length of a Curve
  • Length of a Curve Intro
  • Length of a Curve Example 1
  • Length of a Curve Example 2
  • Length of a Curve Example 3
  • Area of a Surface
  • Area of a Surface Intro
  • Area of a Surface Example 1
  • Area of a Surface Example 2
  • Vectors
  • The Vector Product
  • Vector Product Intro
  • Vector Product Example 1
  • Vector Product Example 2
  • Using The Vector Product
  • Area of a Triangle
  • Area of a Parallelogram
  • Volume of a Parallelepiped (Scalar Triple Product)
  • Volume of a Tetrahedron
  • Vector Equations of Lines and Planes
  • Vector Equation of a Line
  • Parametric Equation of a Plane
  • Scalar Product Equation of a Plane
  • Cartesian Equation of a Plane
  • Converting Between Forms
  • Geometric Properties of Lines and Planes
  • Distance of a Plane from the Origin
  • Distance Between Two Planes
  • Distance of a Point from a Plane
  • Angle Between a Line and a Plane
  • The Angle Between Two Planes
  • The Line of Intersection of Two Planes
  • The Shortest Distance Between Two Skew Lines
  • Matrices
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Advanced Transformations
  • Advanced Transformations Example 1
  • Advanced Transformations Example 2
  • Advanced Transformations Example 3
  • Advanced Transformations Example 4
  • Combinations of Transformations
  • Combinations of Transformations Example 1
  • Combinations of Transformations Example 2
  • Combinations of Transformations Example 3
  • Combinations of Transformations Example 4
  • Transpose Matrices
  • Transpose Matrices Example
  • Eigenvectors and Eigenvalues
  • Eigenvectors and Eigenvalues Intro 1
  • Eigenvectors and Eigenvalues Intro 2
  • Eigenvectors and Eigenvalues Example 1
  • Eigenvectors and Eigenvalues Example 2
  • Eigenvectors and Eigenvalues Example 3
  • Normalising Eigenvectors Example 1
  • Normalising Eigenvectors Example 2
  • Orthogonal Eigenvectors
  • Orthogonal Matrices
  • Orthogonal Matrices Example 1
  • Orthogonal Matrices Example 2
  • Orthogonal Matrices Example 3
  • Diagonalising a Symmetric Matrix
  • Diagonalising a Symmetric Matrix Example 1
  • Diagonalising a Symmetric Matrix Example 2
  • Diagonalising a Symmetric Matrix Example 3
  • FP3
  • Vectors
  • The Vector Product
  • Vector Product Intro
  • Vector Product Example 1
  • Vector Product Example 2
  • Using The Vector Product
  • Area of a Triangle
  • Area of a Parallelogram
  • Volume of a Parallelepiped (Scalar Triple Product)
  • Volume of a Tetrahedron (Scalar Triple Product)
  • Cyclic Permutation of Vectors
  • Handedness
  • Vector Equations of Lines and Planes
  • Parametric Equation of a Plane
  • Scalar Product Equation of a Plane
  • Cartesian Equation of a Plane
  • Converting Between Forms
  • Geometric Properties of Lines and Planes
  • Distance of a Plane from the Origin
  • Distance Between Two Planes
  • Distance of a Point from a Plane
  • The Line of Intersection of Two Planes
  • The Shortest Distance Between Two Skew Lines
  • The Shortest Distance Between Two Skew Lines eg2
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Testing Whether 4 Points are Coplanar
  • Multivariable Calculus
  • Implicit Functions
  • Intro - Revision of Implicit Functions
  • Surfaces and Sections
  • Building a Surface
  • Sections Part 1 - Introduction
  • Sections Part 2
  • Partial Differentiation
  • Partial Derivatives
  • Tangent Planes
  • Tangent Planes Part 1
  • Tangent Planes Part 2
  • Directional Derivatives
  • The Vector Grad f
  • Stationary Points
  • Stationary Points Introduction
  • Stationary Points Example 1
  • Stationary Points Example 2
  • Stationary Points Example 3
  • Approximations and Errors
  • Approximations and Errors - Intro
  • Approximations and Errors - Example 1
  • Approximations and Errors - Example 2
  • The surface g(x, y, z) = k
  • The Vector Grad g
  • Intro to the Surface g(x, y, z) = k
  • Finding a Tangent Plane to g(x, y, z) = k
  • Differential Geometry
  • Intrinsic Coordinates
  • Introduction to Intrinsic Coordinates
  • Intrinsic Coordinates Example 1
  • Intrinsic Coordinates Example 2
  • Intrinsic Coordinates Example 3
  • Evnvelopes
  • Envelopes Intro
  • Envelopes Example 1
  • Envelopes Example 2
  • Radius of Curvature
  • Introduction to Radius of Curvature
  • Radius of Curvature Example 1
  • Radius of Curvature Example 2
  • Centre of Curvature
  • Centre of Curvature Intro
  • Centre of Curvature Example 1
  • Centre of Curvature Example 2
  • Length of a Curve
  • Length of a Curve Intro
  • Length of a Curve Example 1
  • Length of a Curve Example 2
  • Length of a Curve Example 3
  • Area of a Surface
  • Area of a Surface Intro
  • Area of a Surface Example 1
  • Area of a Surface Example 2
  • The Evolute of a Curve
  • Evolute of a Curve Intro
  • Evolute of a Curve Example 1
  • Evolute of a Curve Example 2
  • Order and Subgroups Example
  • Groups
  • Introduction
  • Definitions
  • Introduction Example 1
  • Introduction Example 2
  • Introduction Example 3
  • Introduction Example 4
  • Order and Subgroups
  • Order and Subgroups Intro
  • Isomorphism
  • Isomorphism Intro
  • Group Structure
  • Order 1 and 2
  • Order 3
  • Order 4
  • Order 5
  • Order 6
  • Finding the Gradient from Two Points Example 5
  • Finding the Gradient from Two Points Example 4
  • Finding the Gradient from Two Points Example 3
  • Finding the Gradient from Two Points Example 2
  • Finding the Gradient from Two Points Example 1
  • Finding the Gradient of a Straight Line
  • Equation of a Straight Line Example 5
  • Equation of a Straight Line Example 4
  • Equation of a Straight Line Example 3
  • Equation of a Straight Line Example 2
  • Equation of a Straight Line Example 1
  • Introduction to the Equation of a Straight Line
  • Properties of a Straight Line
  • Derivation of the Quadratic Formula
  • Solving by Completing the Square Example 4
  • Solving by Completing the Square Example 3
  • Solving by Completing the Square Example 2
  • Solving by Completing the Square Example 1
  • What Completed Square Form Shows Example 4
  • What Completed Square Form Shows Example 3
  • What Completed Square Form Shows Example 2
  • What Completed Square Form Shows Example 1
  • Completing the Square Example 5
  • Completing the Square Example 4
  • Completing the Square Example 3
  • Completing the Square Example 2
  • Completing the Square Example 1
  • Completing the Square Introduction
  • Completing The Square
  • Functions & Graphs
  • M1(H)
  • Sine and Cosine Rule Including Bearings
  • Bearings Example
  • Area Example
  • Area Formula
  • Area
  • Cosine Rule Example 2
  • Cosine Rule Example 1
  • Introduction to the Cosine Rule Part 2
  • Introduction to the Cosine Rule Part 1
  • The Cosine Rule
  • Sine Rule - The Ambiguous Case Example 3
  • Sine Rule - The Ambiguous Case Example 2
  • Sine Rule - The Ambiguous Case Example 1
  • Sine Rule Example 3
  • Sine Rule Example 2
  • Sine Rule Example 1
  • The Sine Rule
  • Introducing the Sine and Cosine Rules
  • Overview
  • The Sine and Cosine Rules
  • Sketching Two Curves to Find the Number of Points of Intersection
  • The Intersection of Two Curves
  • The Reciprocal Function Example 2
  • The Reciprocal Function Example 1
  • Reciprocal Curves
  • The General Cubic Curve Example 5
  • The General Cubic Curve Example 4
  • The General Cubic Curve Example 3
  • The General Cubic Curve Example 2
  • The General Cubic Curve Example 1
  • The General Cubic Curve Introduction
  • The Graph y = x3 Example 6
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 1
  • Cubic Curves
  • The Effect of Transformations on a Point Example 3
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 1
  • The Transformation f(ax) Example 3
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation af(x) Example 2
  • The Transformation af(x) Example 1
  • The Transformation f(x - a)
  • The Transformation f(x) + a
  • Transformations Introduction
  • Sketching Curves
  • Graph Transformations
  • Sketching a Quadratic Example 4
  • Sketching a Quadratic Example 3
  • Sketching a Quadratic Example 2
  • Sketching a Quadratic Example 1
  • Sketching Quadratics
  • Plotting a Quadratic Graph Example 2
  • Plotting a Quadratic Graph Example 1
  • Plotting Quadratic Graphs
  • Quadratic Functions
  • Working with Surds Example 7
  • Working with Surds Example 6
  • Working with Surds Example 5
  • Working with Surds Example 4
  • Working with Surds Example 3
  • Working with Surds Example 2
  • Working with Surds Example 1
  • Surd Introduction
  • Surds
  • Using Index Laws Example 2
  • Using Index Laws Example 1
  • Sixth Index Law Example 2
  • Sixth Index Law Example 1
  • Fifth Index Law Example 2
  • Fifth Index Law Example 1
  • Fourth Index Law Example 3
  • Fourth Index Law Example 2
  • Fourth Index Law Example 1
  • Raising a Number to the Power Zero
  • Third Index Law
  • Second Index Law
  • Index Laws
  • First Index Law
  • Factorising Quadratic Expressions Example 6
  • Factorising Quadratic Expressions Example 5
  • Factorising Quadratic Expressions Example 4
  • Factorising Quadratic Expressions Example 3
  • Factorising Quadratic Expressions Example 2
  • Factorising Quadratic Expressions Example 1
  • Factorising into a Single Bracket Example 4
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 1
  • Factorising Expressions
  • Expanding a Pair of Brackets Example 4
  • Expanding a Pair of Brackets Example 3
  • Expanding a Pair of Brackets Example 2
  • Expanding a Pair of Brackets Example 1
  • Expanding a Single Bracket Example 4
  • Expanding a Single Bracket Example 3
  • Expanding a Single Bracket Example 2
  • Expanding a Single Bracket Example 1
  • Expanding Brackets
  • Collecting Like Terms Example 4
  • Collecting Like Terms Example 3
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 1
  • Collecting Like Terms
  • Algebra and Functions
  • Basics
  • Scottish Highers Maths
  • Finding the Equation of a Straight Line
  • Equation of a Straight Line given Gradient and a Point on the Line Example 1
  • Equation of a Straight Line given Gradient and a Point on the Line Example 2
  • Equation of a Straight Line given Gradient and a Point on the Line Example 3
  • Equation of a Straight Line from Two Points Example 1
  • Equation of a Straight Line from Two Points Example 2
  • Perpendicular Lines
  • Perpendicular Lines Example 1
  • Perpendicular Lines Example 2
  • Perpendicular Lines Example 3
  • Finding the Mid-Point of a Line
  • Calculating the Midpoint of a Line Example 1
  • Calculating the Midpoint of a Line Example 2
  • Deriving the Formula for the Midpoint of a Line
  • Using the Midpoint Formula Example 1
  • Using the Midpoint Formula Example 2
  • Using the Midpoint Formula Example 3
  • Using the Midpoint Formula Example 4
  • Finding the Length of a Line
  • Finding the Distance Between 2 Points Example 1
  • Finding the Distance Between 2 Points Example 2
  • The Formula for the Distance Between 2 Points
  • Using the Distance Formula Example 1
  • Using the Distance Formula Example 2
  • Introduction to Radians
  • Radians and Degrees
  • Length of an Arc
  • Length of an Arc, Angle In Degrees
  • The Formula for an Arc Length, Angle in Radians
  • Arc Length Example 1
  • Arc Length Example 2
  • Area of a Sector
  • Area of a Sector, Angle in Degrees
  • The formula for the Area of a Sector, Angle in Radians
  • Area of Sector Example 1
  • Area of Sector Example 2
  • Compound Shapes
  • Area and Perimeter of Compound Shapes Ex1
  • Area and Perimeter of Compound Shapes Ex 2
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • The Graphs of the Three Trigonometric Ratios
  • The Graphs of the 3 Trigonometric Functions
  • Transformations of Graphs
  • Review of Graph Transformations
  • Graph Transformations Applied to Trig Graphs
  • Introduction
  • Introduction to Functions
  • Domain and Range
  • Domain and Range Example 1
  • Domain and Range Example 2
  • Domain and Range Example 3
  • Domain and Range Example 4
  • Domain and Range Example 5
  • Types of Function
  • Types of Function Example 1
  • Types of Function Example 2
  • Types of Function Example 3
  • Types of Function Example 4
  • Compound Functions
  • Compound Function Example 1
  • Compound Function Example 2
  • Compound Function Example 3
  • Compound Function Example 4
  • Compound Function Example 5
  • Inverse Functions
  • Inverse Functions Example 1
  • Inverse Functions Example 2
  • Inverse Functions Example 3
  • Inverse Functions Example 4
  • Inverse Functions Example 5
  • Inverse Functions Example 6
  • Introduction to the Exponential Function and Natural Log Part 1
  • Introduction to the Exponential Function and Natural Log Part 2
  • The Natural Logarithm
  • The Natural Logarithm
  • Graph Transformations
  • Graph Transformations Example 1
  • Graph Transformations Example 2
  • Graph Transformations Example 3
  • Graph Transformations Example 4
  • Graph Transformations Example 5
  • Graph Transformations Example 6
  • An Exponential Problem
  • An Exponential Problem
  • Exponential Equations
  • Exponential and Log Equations Example 1
  • Exponential and Log Equations Example 2
  • Exponential and Log Equations Example 3
  • Recurrence Relations
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms of Sequences
  • nth Terms of Sequences Example 1
  • nth Terms of Sequences Example 2
  • nth Terms of Sequences Example 3
  • nth Terms of Sequences Example 4
  • Recurrence Relations
  • Recurrence Relations Example 1
  • Recurrence Relations Example 2
  • Recurrence Relations Example 3
  • Recurrence Relations Example 4
  • Basic Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Using the Differentiation Formula
  • Differentiation Example 1
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Tangents and Normals
  • Finding the Equation of a Tangent and Normal to a Curve Example 1
  • Finding the Equation of a Tangent and Normal to a Curve Example 2
  • Successive Differentials
  • Successive Differentials Example 1
  • Successive Differentials Example 2
  • Rates of Change
  • The Differential as a Rate of Change Example 1
  • The Differential as a Rate of Change Example 2
  • Differentiation Revision
  • Revision Example 1
  • Revision Example 2
  • Revision Example 3
  • Revision Example 4
  • Revision Example 5
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • M2(H)
  • Factor/Remainder and Quadratic Theory
  • Solving a Quadratic Equation by Factorising
  • Solving a Quadratic by Factorising Example 1
  • Solving a Quadratic by Factorising Example 2
  • Solving a Quadratic by Factorising Example 3
  • Solving a Quadratic by Factorising Example 4
  • Solving a Quadratic by Factorising Example 5
  • Solving a Quadratic by Factorising Example 6
  • The Quadratic Formula
  • Using the Quadratic Formula Example 1
  • Using the Quadratic Formula Example 2
  • Using the Quadratic Formula Example 3
  • Simultaneous Equations
  • Solving Simultaneous Equations by Elimination Example 1
  • Solving Simultaneous Equations by Elimination Example 2
  • Solving Simultaneous Equations by Elimination Example 3
  • Solving Simultaneous Equations by Elimination Example 4
  • Solving Simultaneous Equations by Graph
  • Solving Simultaneous Equations by Substitution Example 1
  • Solving Simultaneous Equations by Substitution Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Discriminant Problems
  • Discriminant Problems Example 1
  • Discriminant Problems Example 2
  • Polynomial Division
  • Dividing a Polynomial by a Linear Factor Example 1
  • Dividing a Polynomial by a Linear Factor Example 2
  • Dividing a Polynomial by a Linear Factor Example 3
  • Dividing a Polynomial by a Linear Factor Example 4
  • Dividing a Polynomial by a Linear Factor Example 5
  • Dividing a Polynomial by a Linear Factor Example 6
  • The Factor Theorem
  • Explaining the Factor Theorem
  • Using the Factor Theorem Example 1
  • Using the Factor Theorem Example 2
  • Using the Factor Theorem Example 3
  • Using the Factor Theorem Example 4
  • The Remainder Theorem
  • Explaining the Remainder Theorem
  • Using the Remainder Theorem Example 1
  • Using the Remainder Theorem Example 2
  • Using the Remainder Theorem Example 3
  • Using the Remainder Theorem Example 4
  • Locating Roots of Equations
  • Explanation of How Change of Sign Implies a Root
  • Showing That a Root of an Equation Lies in a Given Interval -Example 2
  • Showing That a Root of an Equation Lies in a Given Interval -Example 3
  • Trigonometric Formulae
  • Reciprocal Trigonometric Functions
  • Introducing the Reciprocal Trigonometric Functions
  • The Reciprocal Trigonometric Equations and CAST
  • Exact Values Part 1
  • Exact Values Part 2
  • Using the Calculator
  • Graphs of Reciprocal Trigonometric Functions - The Sec
  • Graphs of Reciprocal Trigonometric Functions - The Cosec
  • Graphs of Reciprocal Trigonometric Functions - The Cot
  • Graphs of Reciprocal Trigonometric Functions - Transformations 1
  • Graphs of Reciprocal Trigonometric Functions - Transformations 2
  • Solving a Basic Equation
  • Trigonometric Identities
  • Trigonometric Identities Example 1
  • The Pythagorean Identities
  • Using the Pythagorean Identities to Simplify an Expression
  • Proving an Identity
  • Solving an Equation
  • Exact Values
  • Eliminating a Parameter
  • Inverse Trigonometric Functions
  • Definitions of arcsin, arccos and arctan
  • Solving a Problem
  • The Compound Angle Formulae
  • The Compound Angle (Addition) Formulae
  • Proving sin(A-B) from sin (A+B)
  • Proving tan(A+B) using sin(A+B) and cos(A+B)
  • Finding an Exact value for a Compound Angle
  • Solving an Equation using Compound Angle Formulae
  • The Double Angle Formulae
  • Introducing the Double Angle Formulae
  • Finding an Exact Value for a Double Angle
  • Proving an Identity
  • Solving an Equation Example 1
  • Solving an Equation Example 2
  • Basic Integration
  • Introduction
  • Integration as the Reverse of Differentiation Part 1
  • Integration as the Reverse of Differentiation Part 2
  • Integration Examples
  • Integration Using the Formula Example 1
  • Integration Using the Formula Example 2
  • Integration Using the Formula Example 3
  • Integration Using the Formula Example 4
  • Integration Using the Formula Example 5
  • Finding C
  • Using Extra Information to Find C
  • Equation of a Circle
  • The Equation of a Circle
  • The Formula for the Equation of a Circle
  • Equation of Circle Example 1
  • Equation of Circle Example 2
  • Equation of Circle Example 3
  • Equation of Circle Example 4
  • Equation of Circle Example 5
  • Equation of Circle Example 6
  • Equation of Circle Example 7
  • Equation of Circle Example 8
  • Equation of Circle Example 9
  • Finding the Equation of a Tangent to a Circle
  • Finding the Equation of a Tangent to a Circle
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • The Identity Sin2? + Cos2? = 1
  • Introducing the Identity Sin2? + Cos2?
  • The Identity tan? = sin?/cos?
  • Introducing the Identity tan? = sin?/cos?
  • Using Identities to Solve Trigonometric Equations
  • Using Identities to Solve Trigonometric Equations Example 1
  • Using Identities to Solve Trigonometric Equations Example 2
  • Using Identities to Solve Trigonometric Equations Example 3
  • Using Identities to Solve Trigonometric Equations Example 4
  • Using Trigonometric Identities
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 1
  • Finding Exact Values for Ratios Given the Exact Value for Another Example 2
  • Using Identities for Simplifying Expressions and Proving Identities Example 6
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Areas Under Curves
  • Introduction to Finding Area By Integration
  • Finding Area by Integration Example 1
  • Areas Below the x-axis
  • Finding Area by Integration Example 2
  • Finding Area by Integration Example 3
  • Compound Areas
  • Compound Areas Example 1
  • Compound Areas Example 2
  • M3(H)
  • Further Trigonometric Relationships
  • The Form asinx + bcosx
  • Expressing asinx + bcosx in the Form Rsin(x + a)
  • Maximum and Minimum Values for asinx + bcosx
  • Equation Example 1
  • Equation Example 2
  • The Sum and Product Formulae
  • Derivation of the Sum and Product Formulae
  • Finding an Exact Value
  • Solving an Equation
  • Proving an Identity
  • Logarithmic & Exponential Functions
  • The graph of y = ax
  • An Introduction to Exponential Graphs Part 1
  • An Introduction to Exponential Graphs Part 2
  • An Introduction to Exponential Graphs Part 3
  • The Definition of Logarithms
  • The Definition of the Logarithm
  • Using the Definition of the Logarithm Example 1
  • Using the Definition of the Logarithm Example 2
  • Use of Calculator
  • Using the Calculator to Evaluate Logarithms
  • Laws of Logarithms
  • Introduction to Laws of Logarithms
  • Using Log Laws Example 1
  • Using Log Laws Example 2
  • Using Log Laws Example 3
  • Solving equations of the form ax = b
  • Solving Exponential Equations Example 1
  • Solving Exponential Equations Example 2
  • Changing the Base of a Logarithm
  • The Change of Base Formula
  • Using the Change of Base Formula Example 1
  • Using the Change of Base Formula Example 2
  • Using the Change of Base Formula Example 3
  • Graph Problems
  • Problems Involving the Use Of Graphs Example 1
  • Problems Involving the Use Of Graphs Example 2
  • Problems Involving the Use Of Graphs Example 3
  • Problems Involving the Use Of Graphs Example 4
  • Problems Involving the Use Of Graphs Example 5
  • Problems Involving the Use Of Graphs Example 6
  • Problems Involving the Use Of Graphs Example 7
  • Further Differentiation & Integration
  • The Chain Rule
  • Introducing the Chain Rule - Part 1
  • Introducing the Chain Rule - Part 2
  • The Chain Rule Example 1
  • The Chain Rule Example 2
  • The Chain Rule Example 3
  • The Chain Rule Example 4
  • The Chain Rule Example 5
  • The Chain Rule Example 6
  • The Chain Rule Example 7
  • Trigonometric Functions
  • Differentiating sinx from First Principles
  • The 'Cycle' for Trigonometric Differentiation
  • Differentiating Trigonometric Functions Example 1
  • Differentiating Trigonometric Functions Example 2
  • Differentiating Trigonometric Functions Example 3
  • Differentiating Trigonometric Functions Example 4
  • Differentiating Trigonometric Functions Example 5
  • Differentiating Trigonometric Functions Example 6
  • Differentiating Trigonometric Functions Example 7
  • Differentiating Trigonometric Functions Example 8
  • Differentiating Trigonometric Functions Example 9
  • Differentiating Trigonometric Functions Example 10
  • Differentiating Trigonometric Functions Example 11
  • Differentiating Trigonometric Functions Example 12
  • Differentiating Trigonometric Functions Example 13
  • Vectors in 3 Dimensions
  • Vector Introduction
  • Introduction to Vectors Part 1
  • Introduction to Vectors Part 2
  • Introduction to Vectors Part 3
  • Vector Journeys
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Vector Journeys Example 3
  • Parallel Vectors
  • Parallel Vectors Example 1
  • Parallel Vectors Example 2
  • Vector Problems
  • A Detailed problem Involving Vectors
  • Position Vectors
  • Position Vectors
  • Unit Vectors
  • Base Unit Vectors
  • Unit Vectors
  • Introducing 3-D
  • Using Base Unit Vectors Example 1 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 2 - Unit Vector in Given Direction
  • The Distance Between 2 Points in 3D Space
  • Using Base Unit Vectors Example 3 - Unit Vector in Given Direction
  • Using Base Unit Vectors Example 4
  • Distance Between Two Points
  • Distance Between 2 Points Example 1
  • Distance Between 2 Points Example 2
  • Distance Between 2 Points Example 3
  • The Scalar product
  • Introducing the Scalar Product
  • Consequences of the Scalar Product
  • Finding the Angle Between Two vectors
  • Simplifying Expressions
  • Finding a Vector Perpendicular to Two Given Vectors
  • The Vector Equation of a Straight Line
  • Introducing the Vector Equation of a Straight Line
  • Finding a Straight Line Given a Point and a Direction
  • Finding the Distance Between Two Points on a Line
  • The Vector Equation of a Straight Line Between Two Given Points
  • Finding the Point of Intersection of Two Lines
  • Showing That Two Lines Are Skew
  • Finding the Angle Between Two Lines
  • Standard Integrals
  • Introducing Some Standard Integrals
  • Using Standard Integrals Example 1
  • Using Standard Integrals Example 2
  • Using Standard Integrals Example 3
  • Using the Chain Rule
  • Using the Chain Rule Example 1
  • Using the Chain Rule Example 2
  • Using the Chain Rule Example 3
  • Using the Chain Rule Example 4
  • Using the Chain Rule Example 5
  • Using the Chain Rule Example 6
  • Using the Chain Rule Example 7
  • Using the Chain Rule Example 8
  • M1(AH)
  • Properties of Function
  • The Modulus Function
  • The Graph of the Modulus Function
  • Sketching Functions of the Form y = |f(x)| Example 1
  • Sketching Functions of the Form y = |f(x)| Example 2
  • Sketching Functions of the Form y = |f(x)| Example 3
  • Sketching Functions of the Form y = |f(x)| Example 4
  • Sketching Functions of the Form y = f(|x|) Example 1
  • Sketching Functions of the Form y = f(|x|) Example 2
  • Sketching Functions of the Form y = f(|x|) Example 3
  • Transformations Involving the Modulus Function
  • Transformations Involving the Modulus Function Example 1
  • Transformations Involving the Modulus Function Example 2
  • Transformations Involving the Modulus Function Example 3
  • Transformations Involving the Modulus Function Example 4
  • Transformations Involving the Modulus Function Example 5
  • Systems of Linear Equations
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • Simultaneous Equations
  • Simultaneous Equations Example 1
  • Simultaneous Equations Example 2
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • Invariant Points and Lines
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 3
  • Three by Three Determinant
  • Three by Three Determinant Example 1
  • Three by Three Determinant Example 2
  • Three by Three Inverse
  • Three by Three Inverse Example 1
  • Three by Three Inverse Example 2
  • Algebra
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Simplifying Algebraic Fractions Example 4
  • Simplifying Algebraic Fractions Example 5
  • Multiplying and Dividing Algebraic Fractions
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Multiplying and Dividing Algebraic Fractions Example 4
  • Multiplying and Dividing Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Algebraic Division
  • Algebraic Division Revision Example 1
  • Algebraic Division Revision Example 2
  • Algebraic Division - Division by Quadratic Example 1
  • Algebraic Division - Division by Quadratic Example 2
  • Algebraic Division - Division by Quadratic Example 3
  • Algebraic Division - Division by Quadratic Example 4
  • Introduction to The Modulus Function
  • Differentiation
  • The Product Rule
  • The Product Rule Example 1
  • The Product Rule Example 2
  • The Product Rule Example 3
  • The Product Rule Example 4
  • The Product Rule Example 5
  • The Quotient Rule
  • The Quotient Rule Example 1
  • The Quotient Rule Example 2
  • The Quotient Rule Example 3
  • Exponential Functions
  • Differentiating Exponential Functions Example 1
  • Differentiating Exponential Functions Example 2
  • Differentiating Exponential Functions Example 3
  • Differentiating Exponential Functions Example 4
  • Differentiating Exponential Functions Example 5
  • Differentiating Exponential Functions Example 6
  • Logarithmic Functions
  • Differentiating Logarithmic Functions Example 1
  • Differentiating Logarithmic Functions Example 2
  • Differentiating Logarithmic Functions Example 3
  • Differentiating Logarithmic Functions Example 4
  • Differentiating Logarithmic Functions Example 5
  • Differentiating Logarithmic Functions Example 6
  • Differentiating Logarithmic Functions Example 7
  • Partial Fractions
  • Introduction
  • Type I - Linear Factors Only in Denominator Example 1
  • Type I - Linear Factors Only in Denominator Example 2
  • Type I - Linear Factors Only in Denominator Example 3
  • Type I - Linear Factors Only in Denominator Example 4
  • Type II - Quadratic Factor in Denominator Example 1
  • Type II - Quadratic Factor in Denominator Example 2
  • Type II - Quadratic Factor in Denominator Example 3
  • Type III - Quadratic Factor in Denominator Example 1
  • Type III - Quadratic Factor in Denominator Example 2
  • Type III - Quadratic Factor in Denominator Example 3
  • Type IV - Improper Fractions Example 1 (Leads to Type I)
  • Type IV - Improper Fractions Example 2 (Leads to Type III)
  • Type IV - Improper Fractions Example 3 (Leads to Type II)
  • Integration
  • Using Identities
  • Using Identities Example 1
  • Using Identities Example 2
  • Using Identities Example 3
  • Using Partial Fractions
  • Using Partial Fractions Example 1
  • Using Partial Fractions Example 2
  • Integration by Substitution
  • Integration by Substitution Example 1
  • Integration by Substitution Example 2
  • Integration by Substitution Example 3
  • Integration by Substitution Example 4
  • Integration by Substitution Example 5
  • Integration by Substitution Example 6 - With Limits
  • Integration by Substitution Example 7 - With Limits
  • Integration by Substitution Example 8 - With Limits
  • Areas and Volumes of Revolution
  • Area and Volume of Revolution Example 1
  • Area and Volume of Revolution Example 2
  • Area and Volume of Revolution Example 3
  • Area and Volume of Revolution Example 4
  • Area and Volume of Revolution Example 5
  • Pascal's Triangle
  • Introducing Pascal's Triangle
  • Pascal's Triangle as Coefficients for Binomial Expansions
  • Investigating the Patterns within a Binomial Expansion
  • Using Pascal's Triangle to Expand (a + b)n
  • Using Pascal's Triangle for Binomial Expansion Ex 1
  • Using Pascal's Triangle for Binomial Expansion Ex 2
  • Using Pascal's Triangle for Binomial Expansion Ex 3
  • Using Pascal's Triangle for Binomial Expansion Ex 4
  • Using Pascal's Triangle for Binomial Expansion Ex 5
  • Using Pascal's Triangle for Binomial Expansion Ex 6
  • Using Pascal's Triangle for Binomial Expansion Ex 7
  • Factorials and Combinations
  • Introduction to the nCr Function Part 1
  • Introduction to the nCr Function Part 2
  • Introduction to the nCr Function Part 3
  • Using Combinations to Expand (a + b)n
  • Using the nCr Function to Expand Binomials Example 1
  • Using the nCr Function to Expand Binomials Example 2
  • Using the nCr Function to Expand Binomials Example 3
  • Using the nCr Function to Expand Binomials Example 4
  • Using the nCr Function to Expand Binomials Example 5
  • Using the nCr Function to Expand Binomials Example 6
  • M2(AH)
  • Complex Numbers
  • Introduction to Complex Numbers
  • Imaginary Numbers and Complex Numbers
  • Real and Imaginary Parts
  • Working with Complex Numbers Example 1
  • Working with Complex Numbers Example 2
  • Working with Complex Numbers Example 3
  • Working with Complex Numbers Example 4
  • Working with Complex Numbers Example 5
  • Working with Complex Numbers Example 6
  • Working with Complex Numbers Example 7
  • Quadratics with Complex Roots Example 1
  • Quadratics with Complex Roots Example 2
  • Quadratics with Complex Roots Example 3
  • The Argand Diagram
  • Introduction to the Argand Diagram
  • Modulus and Argument
  • Modulus and Argument Example 1
  • Modulus and Argument Example 2
  • Modulus and Argument Example 3
  • Modulus and Argument Example 4
  • Mod-Arg Form
  • Mod-Arg Form Example 1
  • Mod-Arg Form Example 2
  • Mod-Arg Form Example 3
  • Mod-Arg Form Example 4
  • Mod-Arg Form Example 5
  • Equations Involving Complex Numbers
  • Equations Involving Complex Numbers Example 1
  • Equations Involving Complex Numbers Example 2
  • Square Roots
  • Finding Square Roots of Complex Numbers Example 1
  • Finding Square Roots of Complex Numbers Example 2
  • Further Integration
  • Separable Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Family of Solution Curves
  • Example 1
  • Example 2
  • Exact Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • General First Order Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Further Differentiation
  • Parametric Equations
  • Forming a Cartesian Equation from Parametric Equations Example 1
  • Forming a Cartesian Equation from Parametric Equations Example 2
  • Differentiating with Parametric Equations
  • Differentiating with Parametric Equations Example 1
  • Differentiating with Parametric Equations Example 2
  • Integration by Parts
  • Integration by Parts - Introduction
  • Integration by Parts Example 1
  • Integration by Parts Example 2
  • Integration by Parts Example 3
  • Integration by Parts Example 4
  • Integration by Parts Example 5
  • Integration by Parts Example 6 - With Limits
  • Integration by Parts Example 7 - With Limits
  • Sequences and Series
  • Arithmetic Sequences
  • Introduction to Arithmetic Sequences Part 1
  • Introduction to Arithmetic Sequences Part 2
  • nth Term of an Arithmetic Sequence Example 1
  • nth Term of an Arithmetic Sequence Example 2
  • nth Term of an Arithmetic Sequence Example 3
  • nth Term of an Arithmetic Sequence Example 4
  • Sum of an Arithmetic Series Example 1
  • Sum of an Arithmetic Series Example 2
  • Sum of an Arithmetic Series Example 3
  • Sum of an Arithmetic Series Example 4
  • Sigma Notation
  • Introduction to Sigma Notation Example 1
  • Introduction to Sigma Notation Example 2
  • Introduction to Sigma Notation Example 3
  • Geometric Sequences
  • Introduction to Geometric Sequences
  • Derivation of the nth Term Formula
  • nth Term Example 1
  • nth Term Example 2
  • nth Term Example 3
  • nth Term Example 4
  • Derivation of the Sum of n Terms Formula
  • The Sum of n Terms Example 1
  • The Sum of n Terms Example 2
  • The Sum of n Terms Example 3
  • The Sum of n Terms Example 4
  • The Sum of n Terms Example 5
  • The Sum of n Terms Example 6
  • The Concept of a Sum to Infinity
  • The Sum to Infinity Example 1
  • The Sum to Infinity Example 2
  • The Sum to Infinity Example 3
  • M3(AH)
  • Further Ordinary Differential Equations
  • Separable Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Family of Solution Curves
  • Example 1
  • Example 2
  • Exact Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • General First Order Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Further Sequences & Series
  • x = g(x)
  • The form x = g(x) Example 1
  • The form x = g(x) Example 2
  • Iteration
  • Iteration Example 1
  • Iteration Example 2
  • Iteration Example 3
  • Analysis of the Technique
  • Different Arrangements
  • Cobweb Success
  • Cobweb Failure
  • Staircase Success
  • Complex Behaviour
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Linear Interpolation
  • Interval Bisection
  • Newton-Raphson
  • Summary of Numerical Methods
  • 2nd Order Differential Equations with Constant Coeeficients
  • Introduction to 2nd Order Differential Equations
  • Real Distinct Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Complex Roots to the Auxiliary Equation
  • Complimentary Function and Particular Integral
  • CF & PI Example 1
  • CF & PI Example 2
  • CF & PI Example 3
  • CF & PI Example 4
  • CF & PI Example 5
  • CF & PI Example 6
  • CF & PI Example 7
  • Using Substitutions to Solve Differential equations
  • Using Substitutions Example 1
  • Using Substitutions Example 2
  • Using Substitutions Example 3
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Problem Solving
  • Using Differentiation in Problem Solving Example 1
  • Using Differentiation in Problem Solving Example 2
  • Using Differentiation in Problem Solving Example 3
  • Using Identities for Simplifying Expressions and Proving Identities Example 1
  • Using Identities for Simplifying Expressions and Proving Identities Example 2
  • Using Identities for Simplifying Expressions and Proving Identities Example 3
  • Using Identities for Simplifying Expressions and Proving Identities Example 4
  • Using Identities for Simplifying Expressions and Proving Identities Example 5
  • Algebraic Factors
  • Algebraic Factors
  • Algebraic Factors
  • Algebraic Factors
  • Friction
  • Problems Involving Friction
  • Introduction to Friction
  • Finding the Frictional Force Example1
  • Finding the Frictional Force Example2
  • Finding the Frictional Force Example3
  • Introducing the Coefficient of Friction
  • Problems Involving the Coefficient of Friction Example 1
  • Problems Involving the Coefficient of Friction Example 2
  • Problems Involving the Coefficient of Friction Example 3
  • Problems Involving the Coefficient of Friction Example 4
  • Problems Involving the Coefficient of Friction Example 5
  • Problems Involving the Coefficient of Friction Example 6
  • Problems Involving the Coefficient of Friction Example 7
  • Newton's Second Law - Applying F = ma
  • Applying Newton's Second Law Example 1
  • Applying Newton's Second Law Example 2
  • Connected Bodies
  • The Motion of Connected Bodies Example 1
  • The Motion of Connected Bodies Example 2
  • The Motion of Connected Bodies Example 3 Part 1
  • The Motion of Connected Bodies Example 3 Part 2
  • Frameworks
  • Finding Forces in Frameworks
  • Frameworks Example 1
  • Frameworks Example 2
  • Frameworks Example 3
  • The Quotient Rule Example 4
  • The Quotient Rule Example 5
  • Graphs of Rational Functions Example 1
  • Graphs of Rational Functions
  • Algebra and Graphs
  • Binomial Examples - Example 5
  • Graphs of Rational Functions Example 2
  • Graphs of Rational Functions Example 3
  • Graphs of Rational Functions Example 4
  • Complex Numbers
  • Introduction
  • Introduction to Complex Numbers
  • Simplifying Expressions
  • Adding and Subtracting
  • Multiplying
  • Quadratics
  • Solving a Quadratic with Complex Roots
  • Real and Imaginary Parts
  • Real Parts, Imaginary Parts and Conjugates
  • Realising the Denominator
  • Multiplying Through By Conjugate
  • Solving Equations
  • Equating Real and Imaginary Parts
  • Finding Z
  • Series
  • Using Standard Results
  • Standard Results Example
  • Differentiation
  • The Gradient of a Curve
  • Introduction to Gradients of Curves Part 1
  • Introduction to Gradients of Curves Part 2
  • Introduction to Gradients of Curves Part 3
  • Differentiation from First Principles
  • Differentiation of y = x2 from First Principles
  • Integration
  • The Definite Integral
  • Definite Integration Example 1
  • Definite Integration Example 2
  • Definite Integration Example 3
  • Definite Integration Example 4
  • Definite Integration Example 5
  • Definite Integration Example 6
  • Numerical Methods
  • Numerical Techniques for Finding Roots of Equations
  • Introduction to Numerical Techniques for Finding Roots
  • Linear Interpolation
  • Interval Bisection
  • Newton-Raphson
  • Summary of Numerical Methods
  • Trigonometry
  • Positive and Negative Angles
  • An Introduction to Angles Beyond 90 degrees
  • Extending the Definition of Sin, Cos and Tan for Angles > 90°
  • Sin, Cos and Tan for any Angle Part 1
  • Sin, Cos and Tan for any Angle Part 2
  • Sin, Cos and Tan for any Angle Part 3
  • Sin, Cos and Tan for any Angle Part 4
  • Sin, Cos and Tan for any Angle Part 5
  • Sin, Cos and Tan for any Angle Part 6
  • Some Special Angles
  • Exact Values for Special Angles Part 1
  • Exact Values for Special Angles Part 2
  • Exact Values for Special Angles Part 3
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 1
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 2
  • Finding Exact Values for the Sin, Cos and Tan of Any Angle Example 3
  • Solving Basic Trigonometric Equations in a Given Range
  • Solving Basic Trigonometric Equations Example 1
  • Solving Basic Trigonometric Equations Example 2
  • Solving Basic Trigonometric Equations Example 3
  • Solving Basic Trigonometric Equations Example 4
  • Solving Basic Trigonometric Equations Example 5
  • Solving Basic Trigonometric Equations Example 6
  • Solving Basic Trigonometric Equations Example 7
  • Solving Basic Trigonometric Equations Example 8
  • Solving Basic Trigonometric Equations Example 9
  • Solving Basic Trigonometric Equations Example 10
  • Solving Basic Trigonometric Equations Example 11
  • Comparing Graph and CAST
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • De Moivre's Theorem Example 2
  • De Moivre's Theorem Example 1
  • De Moivre's Theorem Intro
  • De Moivre's Theorem
  • Miscellaneous Example 2
  • Miscellaneous Example 1
  • Miscellaneous Examples
  • Multiplying and Dividing Consequences
  • Multiplying and Dividing Example 2
  • Multiplying and Dividing Example 1
  • Multiplying and Dividing Intro
  • Multiplying and Dividing
  • Hyperbolic Identities - Osborn's Rule Explained
  • Relationships with Hyperbolic Functions
  • Hyperbolic Functions
  • Exponential Form Example 2
  • Exponential Form Example 1
  • Exponential Form Intro
  • The Exponential Form
  • De Moivre's Theorem
  • Roots of Polynomials Example
  • Roots of Polynomials
  • Roots of Polynomials
  • More Complex Loci 3
  • More Complex Loci 2
  • More Complex Loci 1
  • Half Lines
  • Basic Circles
  • Loci in the Complex Plane
  • Modulus and Argument Example 5
  • Modulus and Argument Example 4
  • Modulus and Argument Example 3
  • Modulus and Argument Example 2
  • Modulus and Argument Example 1
  • Modulus and Argument Intro
  • Modulus and Locus Example 2
  • Modulus and Locus Example 1
  • Argand Example 1
  • The Argand Diagram
  • FP2
  • Complex Numbers
  • Differentiation of y = x2 from First Principles
  • Invariant Points and Lines Example 3
  • Invariant Points and Lines Example 2
  • Invariant Points and Lines Example 1
  • Invariant Points and Lines
  • Transformations and Inverses
  • De Moivre's Theorem Example 3
  • nth Roots of Complex Numbers
  • nth Roots of Unity
  • nth Roots for a General Complex Number
  • Series
  • Summation by Method of Differences
  • Differences Example 1
  • Differences Example 2
  • Differences Example 3
  • Proof by Induction
  • Introduction to Proof by Induction
  • Induction Example 1
  • Induction Example 2
  • Induction Example 3
  • Induction Example 4
  • Induction Example 5
  • Hyperbolic Functions
  • Introducing the Hyperbolic Functions
  • The Hyperbolic Functions
  • The Inverse Hyperbolic Functions
  • Hyperbolic Identities
  • Hyperbolic Functions Examples
  • Hyperbolic Functions Example 1
  • Hyperbolic Functions Example 2
  • Hyperbolic Functions Example 3
  • Differentiation
  • Hyperbolic Functions
  • Differentiating Hyperbolic Functions
  • Differentiating Inverse Hyperbolic Functions
  • Trigonometric Functions
  • Differentiating Inverse Trigonometric Functions
  • Integration
  • Length of a Curve
  • Length of a Curve Intro
  • Length of a Curve Example 1
  • Length of a Curve Example 2
  • Length of a Curve Example 3
  • Area of a Surface
  • Area of a Surface Intro
  • Area of a Surface Example 1
  • Area of a Surface Example 2
  • FP3
  • Maclaurin
  • Higher Derivatives
  • Higher Derivatives
  • Maclaurin's Expansion
  • The Maclaurin Expansion
  • Maclaurin's Expansion Example 1
  • Maclaurin's Expansion Example 2
  • Maclaurin's Expansion Example 3
  • Validity
  • Approximations Intro
  • Approximations Example 1
  • Approximations Example 2
  • Approximations Example 3
  • Polar Coordinates
  • Introducing Polar Coordinates
  • Introduction
  • Sketching Graphs in Polar Form
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Converting Equations from One Form to the Other
  • Example 1
  • Example 2
  • Example 3
  • Areas of Regions for Polar Curves
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • First Order Differential Equations
  • Separable Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • Family of Solution Curves
  • Example 1
  • Example 2
  • Exact Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • General First Order Equations
  • Introduction
  • Example 1
  • Example 2
  • Example 3
  • 2nd Order Differential Equations
  • 2nd Order Differential Equations with Constant Coeeficients
  • Introduction to 2nd Order Differential Equations
  • Real Distinct Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Complex Roots to the Auxiliary Equation
  • Complimentary Function and Particular Integral
  • CF & PI Example 1
  • CF & PI Example 2
  • CF & PI Example 3
  • CF & PI Example 4
  • CF & PI Example 5
  • CF & PI Example 6
  • CF & PI Example 7
  • Using Substitutions to Solve Differential equations
  • Using Substitutions Example 1
  • Using Substitutions Example 2
  • Using Substitutions Example 3
  • Vectors
  • The Vector Product
  • Vector Product Intro
  • Vector Product Example 1
  • Vector Product Example 2
  • Using The Vector Product
  • Area of a Triangle
  • Area of a Parallelogram
  • Volume of a Parallelepiped (Scalar Triple Product)
  • Volume of a Tetrahedron
  • Vector Equations of Lines and Planes
  • Vector Equation of a Line
  • Parametric Equation of a Plane
  • Scalar Product Equation of a Plane
  • Cartesian Equation of a Plane
  • Converting Between Forms
  • Geometric Properties of Lines and Planes
  • Distance of a Plane from the Origin
  • Distance Between Two Planes
  • Distance of a Point from a Plane
  • Angle Between a Line and a Plane
  • The Angle Between Two Planes
  • The Line of Intersection of Two Planes
  • The Shortest Distance Between Two Skew Lines
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Basic Transformations
  • Position Vectors
  • Applying a Tranformation Matrix Example 1
  • Applying a Tranformation Matrix Example 2
  • Applying a Tranformation Matrix Example 3
  • Finding a Transformation Matrix Example 1
  • Finding a Transformation Matrix Example 2
  • Transformations and Inverses
  • IGCSE-H
  • Algebra
  • Inequalities and Graphs
  • Introduction to Graphical Inequalities
  • An Introduction to Graphical Inequalities
  • Vertical Lines
  • Vertical Lines Example 1
  • Vertical Lines Example 2
  • Vertical Lines Example 3
  • Horizontal Lines
  • Horizontal Lines Example 1
  • Horizontal Lines Example 2
  • Horizontal Lines Example 3
  • Mixed Horizontal and Vertical Lines
  • Mixed Horizontal and Vertical Example 1
  • Mixed Horizontal and Vertical Example 2
  • Mixed Horizontal and Vertical Example 3
  • Inequalities Involving Both x and y
  • Inequalities Involving Both x and y Example 1
  • A Note on Point Testing
  • Integer-Valued Coordinates
  • Inequalities Involving Both x and y Example 2
  • Inequalities Involving Both x and y Example 3
  • Inequalities Involving Both x and y Example 4
  • Inequalities Involving Both x and y Example 5
  • Inequalities Involving Both x and y Example 6
  • A Practical Problem
  • Practical Example
  • Algebra Basics
  • Introduction to Algebra
  • Introduction to Algebra
  • Collecting Like Terms Example 1
  • Collecting Like Terms Example 2
  • Collecting Like Terms Example 3
  • Multiplying Algebraic Expressions Example 1
  • Multiplying Algebraic Expressions Example 2
  • Basic Equations
  • Forming Simple Equations
  • Forming Simple Equations From Information Given
  • Solving Simple Equations
  • Equation as a Balance
  • Solving Simple Equations Example 1
  • Solving Simple Equations Example 2
  • Solving Simple Equations Example 3
  • Solving Simple Equations Example 4
  • Harder Equations
  • Collecting Like Terms Review
  • Harder Equations Example 1
  • Harder Equations Example 2
  • Harder Equations Example 3
  • Harder Equations Example 4
  • Basic Inequalities
  • Introduction to Inequalities
  • Introduction to Inequalities
  • Solving Simple Inequalities
  • Solving Simple Inequalities Example 1
  • Solving Simple Inequalities Example 2
  • Solving Simple Inequalities Example 3
  • Solving Simple Inequalities Example 4
  • Solving Simple Inequalities Example 5
  • Basic Formulae
  • Words and Symbols
  • Finding a Formula Example 1
  • Finding a Formula Example 2
  • Finding a Formula Example 3
  • Finding a Formula Example 4
  • Substitution
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Numbers into Formulae Example 5
  • Directed Numbers Review Example 1
  • Directed Numbers Review Example 2
  • Substituting with Directed Numbers Example 1
  • Substituting with Directed Numbers Example 2
  • Algebraic Products
  • Single Bracket
  • Expanding with a Single Bracket Example 1
  • Expanding with a Single Bracket Example 2
  • Expand and Simplify
  • Expanding Brackets Extension Example
  • Pair of Brackets
  • Expanding a Pair of Brackets Example 1
  • Expanding a Pair of Brackets Example 2
  • Squaring a Bracket
  • Expanding (x + a)(x - a)
  • Pair of Brackets Extension Example
  • Expand and Simplify Extension Example
  • Factorising into a Single Bracket
  • Factorising into a Single Bracket Example 1
  • Factorising into a Single Bracket Example 2
  • Factorising into a Single Bracket Example 3
  • Factorising into a Single Bracket Example 4
  • Factorising into a Pair of Brackets
  • Factorising into a Pair of Brackets Example 1
  • Factorising into a Pair of Brackets Example 2
  • Factorising into a Pair of Brackets Example 3
  • Factorising into a Pair of Brackets Example 4
  • Factorising into a Pair of Brackets Example 5
  • Factorising into a Pair of Brackets Example 6
  • Factorising into a Pair of Brackets Example 7
  • Factorising into a Pair of Brackets Example 8
  • Factorising into a Pair of Brackets Example 9
  • Factorising into a Pair of Brackets Example 10
  • The Difference of 2 Squares
  • The Difference of 2 Squares Example 1
  • The Difference of 2 Squares Example 2
  • The Difference of 2 Squares Example 3
  • The Difference of 2 Squares Extension Example
  • Formulae with Brackets
  • Expanding Brackets Review
  • Expanding Brackets Review Example 1
  • Expanding Brackets Review Example 2
  • Expanding Brackets Review Example 3
  • Formulae with Brackets
  • Formulae with Brackets Example 1
  • Formulae with Brackets Example 2
  • Formulae with Brackets Example 3
  • Further Equations
  • Equations with Brackets
  • Solving Equations with Brackets Example 1
  • Solving Equations with Brackets Example 2
  • Further Inequalities
  • Inequalities with Brackets
  • Solving Inequalities with Brackets Example 1
  • Solving Inequalities with Brackets Example 2
  • Simultaneous Equations
  • Algebraic Solution
  • Simultaneous Equations Algebraic Solution Example 1
  • Simultaneous Equations Algebraic Solution Example 2
  • Simultaneous Equations Algebraic Solution Example 3
  • Simultaneous Equations Algebraic Solution Example 4
  • Simultaneous Equations Algebraic Solution Example 5
  • Simultaneous Equations Algebraic Solution Example 6
  • Simultaneous Equations Algebraic Solution Example 7
  • Simultaneous Equations Algebraic Solution Example 8
  • Graphical Solution
  • Simultaneous Equations Graphical Solution Example 1
  • Simultaneous Equations Graphical Solution Example 2
  • No Solutions or Infinite Solutions
  • No Solutions or Infinite Solutions
  • Problem Solving
  • Problem Solving Example 1
  • Problem Solving Example 2
  • More Formulae
  • Deriving Formulae
  • Deriving Formulae Example 1
  • Deriving Formulae Example 2
  • Deriving Formulae Example 3
  • Deriving Formulae Example 4
  • Substitution into Formulae
  • Substituting Numbers into Formulae Example 1
  • Substituting Numbers into Formulae Example 2
  • Substituting Numbers into Formulae Example 3
  • Substituting Numbers into Formulae Example 4
  • Substituting Expressions into Formulae
  • Rearranging Formulae
  • Rearranging Formulae Example 1
  • Rearranging Formulae Example 2
  • Rearranging Formulae Example 3
  • Rearranging Formulae Example 4
  • nth Terms for Sequences
  • Finding nth Terms Example 1
  • Finding nth Terms Example 2
  • Finding nth Terms Example 3
  • Finding nth Terms Example 4
  • Graphs of Straight Lines
  • Vertical Lines
  • Equations of ines Parallel to the Y-Axis
  • Horizontal Lines
  • Equations of ines Parallel to the X-Axis
  • The Line y = x
  • The Line y = x
  • Plotting Lines from Equations
  • Plotting Lines Example 1
  • Plotting Lines Example 2
  • Plotting Lines Example 3
  • The Equation of a Straight Line
  • Equations of Straight Lines Introduction
  • Equations of Straight Lines Example 1
  • Equations of Straight Lines Example 2
  • Intersection
  • The Interection of Two Lines
  • The Interection of Two Lines Example 1
  • Parallel Lines
  • Parallel Lines Introduction
  • The Equations of Parallel Lines Example 1
  • The Equations of Parallel Lines Example 2
  • Perpendicular Lines
  • Perpendicular Lines Introduction
  • Gradients of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 1
  • Equations of Perpendicular Lines Example 2
  • Quadratic Equations
  • Solving Quadratic Equations
  • Introduction to Quadratic Equations Part 1
  • Introduction to Quadratic Equations Part 2
  • Introduction to Quadratic Equations Part 3
  • Solving Quadratic Equations by Factorising Example 1
  • Solving Quadratic Equations by Factorising Example 2
  • Solving Quadratic Equations by Factorising Example 3
  • Solving Quadratic Equations by Factorising Example 4
  • Solving Quadratic Equations by Factorising Example 5
  • Solving Quadratic Equations by Factorising Example 6
  • Solving Quadratic Equations by Factorising Example 7
  • Forming and Solving
  • Trial and Improvement
  • Solving Equations by Trial and Improvement Example 1
  • Solving Equations by Trial and Improvement Example 2
  • Solving Equations by Trial and Improvement Example 3
  • The Quadratic Formula
  • Solving Quadratic Equations Using The Formula Example 1
  • Solving Quadratic Equations Using The Formula Example 2
  • Solving Quadratic Equations Using The Formula Example 3
  • Solving Quadratic Equations Using The Formula Example 4
  • Completing the Square
  • Completing the Square Example 1
  • Completing the Square Example 2
  • Completing the Square Example 3
  • The Meaning of Completed Square Form
  • Solving Quadratics by Completing the Square
  • Quadratic Equations Extension
  • Completing the Square
  • Deriving the Quadratic Formula
  • Quadratic Graphs
  • Plotting Quadratic Graphs
  • Plotting Quadratic Graphs Example 1
  • Plotting Quadratic Graphs Example 2
  • The Shape of a Quadratic
  • Happy or Sad?
  • Other Tables
  • Other Tables Example 1
  • Other Tables Example 2
  • Indices
  • Indices with Algebra
  • The First Index Law
  • The Second Index Law
  • The Power mn
  • Using the Index Laws Example 1
  • Negative Indices
  • Fractional Indices
  • Ratio and Proportion
  • Ratio Revision
  • Ratio Revision Example 1
  • Ratio Revision Example 2
  • Ratio Revision Example 3
  • Expressing a Ratio in the Form 1:n Example 1
  • Expressing a Ratio in the Form 1:n Example 2
  • Dividing in a Given Ratio Example 1
  • Dividing in a Given Ratio Example 2
  • Dividing in a Given Ratio Example 3
  • Direct Proportion
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Direct Proportion Example 4
  • Direct Proportion Example 5
  • Inverse Proportion
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Inverse Proportion Example 4
  • Inverse Proportion Example 5
  • Algebraic Fractions
  • Simplifying Algebraic Fractions
  • Simplifying Algebraic Fractions Example 1
  • Simplifying Algebraic Fractions Example 2
  • Simplifying Algebraic Fractions Example 3
  • Multiplying and Dividing
  • Multiplying and Dividing Algebraic Fractions Example 1
  • Multiplying and Dividing Algebraic Fractions Example 2
  • Multiplying and Dividing Algebraic Fractions Example 3
  • Lowest Common Multiples
  • Lowest Common Multiples (Algebraic) Example 1
  • Lowest Common Multiples (Algebraic) Example 2
  • Lowest Common Multiples (Algebraic) Example 3
  • Lowest Common Multiples (Algebraic) Example 4
  • Adding and Subtracting
  • Adding and Subtracting Algebraic Fractions Example 1
  • Adding and Subtracting Algebraic Fractions Example 2
  • Adding and Subtracting Algebraic Fractions Example 3
  • Adding and Subtracting Algebraic Fractions Example 4
  • Adding and Subtracting Algebraic Fractions Example 5
  • Adding and Subtracting Algebraic Fractions Example 6
  • Adding and Subtracting Algebraic Fractions Example 7
  • Equations
  • Solving Equations Involving Fractions Example 1
  • Solving Equations Involving Fractions Example 2
  • Solving Equations Involving Fractions Example 3
  • Advanced Formulae
  • Substitution
  • Substituting Numbers in Standard Form Example 1
  • Substituting Numbers in Standard Form Example 1 - Calculator Guide
  • Substituting Numbers in Standard Form Example 2
  • Substituting Numbers in Standard Form Example 2 - Calculator Guide
  • Substituting Numbers in Standard Form Example 3
  • Substituting Numbers in Standard Form Example 3 - Calculator Guide
  • Rearranging Formulae
  • Rearranging Formulae (Advanced) Example 1
  • Rearranging Formulae (Advanced) Example 2
  • Rearranging Formulae (Advanced) Example 3
  • Rearranging Formulae (Advanced) Example 4
  • Rearranging Formulae (Advanced) Example 5
  • Rearranging Formulae (Advanced) Example 6
  • Rearranging Formulae (Advanced) Example 7
  • Miscelaneous Example
  • Miscellaneous Example
  • Advanced Inequalities
  • Quadratic Inequalities
  • Solving Quadratic Inequalities Example 1
  • Solving Quadratic Inequalities Example 2
  • Solving Quadratic Inequalities Example 3
  • Solving Quadratic Inequalities Example 4
  • Advanced Graphs
  • Using a Quadratic Graph
  • Using a Quadratic Graph to Solve Quadratic Equations
  • Cubic Graphs
  • Cubic Graphs Example 1
  • Cubic Graphs Example 2
  • Cubic Graphs Example 3
  • Cubic Graphs Example 4
  • Reciprocal Graphs
  • Introducation to Reciprocal Graphs
  • Reciprocal Graphs Example 1
  • Reciprocal Graphs Example 2
  • Shapes of Graphs
  • Shapes of Graphs Introducation
  • Shapes of Graphs Example 1
  • Shapes of Graphs Example 2
  • Using General Graphs
  • Using General Graphs Example 1
  • Using General Graphs Example 2
  • Using General Graphs Example 3
  • Using Gradients of Graphs
  • Using Gradients of Graphs Introduction
  • Using Gradients of Graphs Example 1
  • Using Gradients of Graphs Example 2
  • Using Gradients of Graphs Example 3
  • Algebraic Proof
  • Proving Statements Using Algebra
  • Proof Example 1
  • Proof Example 2
  • Proof Example 3
  • Proof Example 4
  • Simultaneous Equations Linear and Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 1
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 2
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 3
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 4
  • Solving Simultaneous Equations 1 Linear 1 Quadratic Example 5
  • Data Handling
  • Basic Statistics
  • Frequency Tables
  • Creating a Frequency Table Example 1
  • Creating a Frequency Table Example 2
  • Observation Sheet
  • Collecting Data on an Observation Sheet
  • Bar Charts
  • Bar Chart Example 1
  • Bar Chart Example 2
  • Pictograms
  • Pictograms Example 1
  • Misleading Diagrams
  • Misleading Diagrams Example 1
  • Pie Charts
  • Pie Charts Example 1
  • Pie Charts Example 2
  • Organising and Summarising Data
  • Summarising Data
  • Why Summarise Data?
  • Averages
  • Averages
  • The Mode for a Set of Numbers
  • The Mode for a Frequency Distribution
  • The Median for a Set of Numbers
  • The Median for a Frequency Distribution
  • The Mean for a Set of Numbers
  • The Mean for a Frequency Distribution
  • The Range
  • Calculating the Range
  • Grouped Data
  • Grouping Data
  • The Mean for Grouped Data
  • The Median for Grouped Data
  • The Mode for Grouped Data
  • The Range for Grouped Data
  • Quartiles
  • Finding Quartiles Example 1
  • Finding Quartiles Example 2
  • The Interquartile Range
  • Calculating the Interquartile Range Example 1
  • Calculating the Interquartile Range Example 2
  • Boxplots
  • Boxplots Example 1
  • Boxplots Example 2
  • Boxplots Example 3
  • Stem and Leaf Diagrams
  • Stem and Leaf Diagrams Example 1
  • Stem and Leaf Diagrams Example 2
  • Stem and Leaf Diagrams Example 3
  • Line Graphs
  • Reading from Line Graphs
  • Reading from Line Graphs Example 1
  • Conversion Graphs
  • Conversion Graphs Example 1
  • Straight Lines
  • Straight Lines Example 1
  • Probability 1
  • Introduction to Probability
  • The Probability Scale
  • Types of Probability
  • Theoretical Probabilility
  • Basic Theoretical Probabilility Example 1
  • Basic Theoretical Probabilility Example 2
  • Basic Theoretical Probabilility Example 3
  • Experimental Probability
  • Experimental Probability Example 1
  • Experimental Probability Example 2
  • Probability 2
  • An Event Not Happening
  • The probability of An Event Not Happening Example 1
  • The probability of An Event Not Happening Example 2
  • The probability of An Event Not Happening Example 3
  • The Sum for All Possibilities
  • The Sum for All Possibilities Example 1
  • The Sum for All Possibilities Example 2
  • Possibility (Sample) Spaces
  • Possibility (Sample) Spaces Example 1
  • Possibility (Sample) Spaces Example 2
  • Possibility (Sample) Spaces Example 3
  • Possibility (Sample) Spaces Example 4
  • Expected Number of Occurences
  • Expected Number of Occurences Example 1
  • Expected Number of Occurences Example 2
  • Expected Number of Occurences Example 3
  • Scatter Diagrams
  • Scatter Diagrams Introduction
  • Scatter Diagrams Introduction
  • Plotting and Using
  • Plotting and Using Scatter Diagrams
  • Correlation
  • A Note on Correlation
  • Probability 3
  • Mutually Exclusive and Independent Events
  • Mutually Exclusive Events
  • Independent Events 1
  • Independent Events 2
  • Mutuallly Exclusive or Independent?
  • Addition Rule
  • The Addition Rule Example 1
  • Multiplication Rule
  • The Multiplication Rule Example 1
  • The Multiplication Rule Example 2
  • Miscellaneous Probability Example
  • Miscellaneous Probability Example
  • Conditional Probability
  • Conditional Probability Example 1
  • Conditional Probability Example 2
  • Probability 4
  • Tree Diagrams
  • Introduction to Tree Diagrams - Part 1
  • Introduction to Tree Diagrams - Part 2
  • Tree Diagrams Example 1
  • Tree Diagrams Example 2
  • Tree Diagrams Example 3
  • Tree Diagrams Example 4
  • Tree Diagrams Example 5
  • Tree Diagrams Example 6
  • Cumulative Frequency
  • Producing a Cumulative Frequency
  • Producing a Cumulative Frequency Example 1
  • Producing a Cumulative Frequency Example 2
  • Drawing a Cumulative Frequency Graph
  • Drawing a Cumulative Frequency Graph Example 1
  • Drawing a Cumulative Frequency Graph Example 2
  • Median and Quartiles
  • Using Cumulative Frequency to Find Median and Quartiles Example 1
  • Using Cumulative Frequency to Find Median and Quartiles Example 2
  • Other Uses
  • Other Uses of Cumulative Frequency Example 1
  • Other Uses of Cumulative Frequency Example 2
  • Other Uses of Cumulative Frequency Example 3
  • Histograms
  • Histograms and Their Use
  • Histograms Introduction
  • Histograms Example 1
  • Histograms Example 2
  • Two Way Tables
  • Intro to Two Way Tables
  • Intro to Two Way Tables Example 1
  • Intro to Two Way Tables Example 2
  • Sampling
  • Introduction to Sampling
  • The Random Sample
  • The Systematic Sample
  • The Stratified Sample Example 1
  • The Stratified Sample Example 2
  • Pros and Cons
  • Questionnaires
  • Designing Questionnaires
  • Moving Averages
  • Calculating and using Moving Averages
  • Calculating and using Moving Averages Example 1
  • Calculating and using Moving Averages Example 2
  • Calculating and using Moving Averages Example 3
  • Number
  • Integers
  • Addition
  • Adding Integers Example 1
  • Adding Integers Example 2
  • Carrying Figures Explained
  • Adding Integers Example 3
  • Subtraction
  • Subtracting Integers Example 1
  • Borrowing Digits Explained
  • Subtracting Integers Example 2
  • Addition and Subtraction
  • Mixed Example 1
  • Rounding
  • Rounding Integers Example 1
  • Rounding Integers Example 2
  • Rounding Integers Example 3
  • Multiplying
  • Introduction to Multiplying Integers
  • Multiplying Integers by 10, 100 etc.
  • Multiplying Two Integers Example 1
  • Multiplying Two Integers Example 2
  • Multiplying Two Integers Example 3
  • Multiplying Two Integers Example 4 - Practical Example
  • Dividing
  • Dividing Integers by 10, 100 etc.
  • Dividing Two Integers Example 1
  • Dividing Two Integers Example 2
  • Dividing Two Integers Example 3
  • Integers - Extension
  • Dividing
  • Dividing Two Integers Example 4
  • Mixed Operations
  • Mixed Operations with Integers - BIDMAS Example 1
  • Mixed Operations with Integers - BIDMAS Example 2
  • Directed Numbers
  • Introduction to Directed Numbers
  • Adding Directed Numbers
  • Subtracting Directed Numbers
  • Multiplying Directed Numbers
  • Dividing Directed Numbers
  • Calculator Guide
  • Adding Integers on the Calculator
  • Subtracting Integers on the Calculator
  • Multiplying Integers on the Calculator
  • Dividing Integers on the Calculator
  • BIDMAS on the Calculator Example 1
  • BIDMAS on the Calculator Example 2
  • Directed Numbers on the Calculator
  • Factors, Multiples, Prime Numbers
  • Factors and Multiples
  • Factors of Integers
  • Multiples of Integers
  • Prime Numbers
  • Introduction to Prime Numbers
  • Divisibility Tests for Integers
  • Expressing a Number as a Product of Primes
  • Highest Common Factor
  • Highest Common Factor Example 1
  • Highest Common Factor Example 2
  • Lowest Common Multiple
  • Lowest Common Multiple Example 1
  • Lowest Common Multiple Example 2
  • Lowest Common Multiple Example 3
  • Fractions
  • Introduction
  • Introduction to Fractions
  • Equivalent Fractions
  • Equivalent Fractions Example 1
  • Equivalent Fractions Example 2
  • Equivalent Fractions Example 3
  • Adding Fractions
  • Adding Fractions with the Same Denominator Example 1
  • Adding Fractions with the Same Denominator Example 2
  • Adding Using a Common Denominator Example 1
  • Adding Using a Common Denominator Example 2
  • Adding - Dealing with Mixed Numbers
  • Subtracting Fractions
  • Subtracting Fractions with the Same Denominator Example 1
  • Subtracting Using a Common Denominator Example 1
  • Subtracting Using a Common Denominator Example 2
  • Subtracting - Dealing with Mixed Numbers Example 1
  • Subtracting - Dealing with Mixed Numbers Example 2
  • Mixed Add and Subtract
  • Mixed Add and Subtract Example 1
  • Mixed Add and Subtract Example 2
  • Multiplying Fractions
  • Multiplying Fractions Example 1
  • Multiplying Fractions Example 2
  • Multiplying - Dealing with Mixed Numbers
  • Multiplying - Dealing with Whole Numbers
  • Multiplying - Whole Number and Mixed Number
  • Miscellaneous Example
  • Dividing Fractions
  • Dividing Fractions Example 1
  • Dividing Fractions Example 2
  • Dividing - Dealing with Mixed Numbers
  • Dividing - Dealing with Whole Numbers
  • Dividing - Whole Number and Mixed Number
  • Directed Numbers
  • Directed Numbers and Fractions
  • Using BIDMAS
  • Fractions with Mixed Operations Example 1
  • Fractions with Mixed Operations Example 2
  • Fractions with Mixed Operations Example 3
  • Fractions with Mixed Operations Example 4
  • Calculator Guide
  • Adding Fractions on the Calculator
  • Adding Mixed Numbers on the Calculator
  • Subtracting Fractions on the Calculator
  • Subtracting Mixed Numbers on the Calculator
  • Multiplying Fractions on the Calculator
  • Multiplying Mixed Numbers on the Calculator
  • Dividing Fractions on the Calculator
  • Dividing Mixed Numbers on the Calculator
  • Decimals
  • Meaning of Decimals
  • Introduction to Decimal Fractions
  • Ordering Decimals
  • Putting Decimals Into Numerical Order
  • Adding Decimals
  • Addition of Decimals
  • Subtracting Decimals
  • Subtraction of Decimals
  • Multiplying Decimals
  • Multiplying Decimals by 10, 100 etc.
  • Multiplying Decimals by an Integer
  • Multiplying Decimals by Decimals Example 1
  • Multiplying Decimals by Decimals Example 2
  • Multiplying Decimals by Decimals Example 3
  • Dividing Decimals
  • Dividing Decimals by 10, 100 etc.
  • Dividing Decimals by Decimals Introduction
  • Dividing Decimals by Decimals Example 1
  • Dividing Decimals by Decimals Example 2
  • Dividing Decimals by Decimals Example 3
  • Dividing Decimals by Decimals Example 4
  • Directed Numbers
  • Decimals and Directed Numbers
  • Rounding
  • Rounding to the Nearest Whole Number
  • Rounding to Decimal Places Example 1
  • Rounding to Decimal Places Example 2
  • Rounding to Significant Figures
  • Calculator Guide
  • Adding Decimals on a Calculator
  • Subtracting Decimals on a Calculator
  • Multiplying Decimals on a Calculator
  • Dividing Decimals on a Calculator
  • Mixed Operations on a Calculator Involving Decimals
  • Percentages
  • Introduction
  • Introduction to Percentages
  • Percentages and Decimals
  • Introduction to Decimals and Percentages Example 1
  • Introduction to Decimals and Percentages Example 2
  • Introduction to Decimals and Percentages Example 3
  • Percentages and Fractions
  • Introduction to Fractions and Percentages Example 1
  • Introduction to Fractions and Percentages Example 2
  • Introduction to Fractions and Percentages Example 3
  • Introduction to Fractions and Percentages Example 4
  • Percentages, Fractions and Decimals
  • Percentages, Fractions and Decimals Example 1
  • Percentages, Fractions and Decimals Example 2
  • Percentages, Fractions and Decimals Example 3
  • Percentage of a Quantity
  • Finding a percentage of a Quantity Example 1
  • Finding a percentage of a Quantity Example 2
  • Finding a percentage of a Quantity Example 3
  • Finding a percentage of a Quantity Example 4
  • Finding One Quantity as a Percentage of Another Example 1
  • Finding One Quantity as a Percentage of Another Example 2
  • Increasing a Quantity by a Given Percentage
  • Decreasing a Quantity by a Given Percentage
  • Indices and Standard Form
  • Indices
  • Introduction to Indices
  • The First Index Law
  • First Index Law Example 1
  • First Index Law Example 2
  • The Second Index Law
  • Second Index Law Example 1
  • Second Index Law Example 2
  • Negative Indices
  • Negative Indices Example 1
  • Negative Indices Example 2
  • Negative Indices Example 3
  • Introduction to Standard Form
  • Introduction to Standard Form Example 1
  • Introduction to Standard Form Example 2
  • Introduction to Standard Form Example 3
  • Introduction to Standard Form Example 4
  • Introduction to Standard Form Example 5
  • Introduction to Standard Form Example 6
  • The Zero Index
  • The Meaning of the Zero Index
  • Working With Numbers
  • Range of Values for a Corrected Number
  • Range of Values for a Corrected Number Example 1
  • Range of Values for a Corrected Number Example 2
  • Range of Values for a Corrected Number Example 3
  • Range of Values for a Corrected Number Example 4
  • Range of Values for a Corrected Number Example 5
  • Range of Values for a Corrected Number Example 6
  • Range of Values for a Corrected Number Example 7
  • Range of Values for a Corrected Number Example 8
  • Reciprocals
  • Reciprocals Introduction
  • Fraction Review
  • Reviewing Fraction Work Example 1
  • Reviewing Fraction Work Example 2
  • Working With Numbers Extension
  • Fractions Involving BIDMAS
  • Fractions Involving BIDMAS Example 1
  • Fractions Involving BIDMAS Example 2
  • Fractions Involving BIDMAS Example 3
  • Recurring Decimals
  • Introduction to Recurring Decimals
  • Converting Between Decimals and Fractions (Advanced)
  • Converting Between Decimals and Fractions (Advanced) Example 1
  • Converting Between Decimals and Fractions (Advanced) Example 2
  • Converting Between Decimals and Fractions (Advanced) Example 3
  • Converting Between Decimals and Fractions (Advanced) Example 4
  • Converting Between Decimals and Fractions (Advanced) Example 5
  • Converting Between Decimals and Fractions (Advanced) Example 6
  • Standard Form Advanced
  • Advanced Standard Form Example 1
  • Advanced Standard Form Example 2
  • Advanced Standard Form Example 3
  • Advanced Standard Form Example 4
  • Advanced Standard Form Example 5
  • Advanced Standard Form Example 6
  • Advanced Standard Form Example 7
  • Number Sequences and Patterns
  • Continuing a Sequence
  • Continuing a Sequence Example 1
  • Continuing a Sequence Example 2
  • Continuing a Sequence Example 3
  • nth Terms for Number Sequences
  • Finding the nth Term Example 1
  • Finding the nth Term Example 2
  • Finding the nth Term Example 3
  • Finding the nth Term Example 4
  • Number Sequences and Patterns Extension
  • nth Terms for Number Sequences
  • Number Sequence Extension Work Example 1
  • Number Sequence Extension Work Example 2
  • Number Sequence Extension Work Example 3
  • Number Sequence Extension Work Example 4
  • Percentages Advanced
  • Profit and Loss
  • Percentage Profit and Loss Example 1
  • Percentage Profit and Loss Example 2
  • Percentage Profit and Loss Example 3
  • Percentage Profit and Loss Example 4
  • Percentage Profit and Loss Example 5
  • Income Tax
  • Income Tax Claculations Example 1
  • Income Tax Claculations Example 2
  • Percentages Advanced Extension
  • Income Tax
  • Income Tax Claculations Example 3
  • Income Tax Claculations Example 4
  • Sale Reductions
  • Sale Reductions Example
  • Finding the Original Quantity
  • Finding the Original Quantity Example 1
  • Finding the Original Quantity Example 2
  • Finding the Original Quantity Example 3
  • Finding the Original Quantity Example 4
  • Interest
  • Interest Example 1
  • Interest Example 2
  • Interest Example 3
  • Interest Example 4 - Simple and Compound Interest
  • Interest Example 5 - Compound Interest
  • Extra Fraction Work
  • Fractions
  • Expressing one Quantity as a Fraction of Another
  • Finding a Fraction of a Quantity
  • Finding Whole Given Fraction Example 1
  • Finding Whole Given Fraction Example 2
  • Finding Whole Given Fraction Example 3
  • Percentages
  • Finding Whole Given Percentage Example 1
  • Finding Whole Given Percentage Example 2
  • Ratio
  • Introduction to Ratio
  • Simplifying Ratios Example 1
  • Simplifying Ratios Example 2
  • Simplifying Ratios Example 3
  • Simplifying Ratios Example 4
  • Simplifying Ratios Example 5
  • Ratio and Fraction
  • Ratio and Proportion
  • Ratio
  • Dividing in Given Ratio Example 1
  • Dividing in Given Ratio Example 2
  • Dividing in Given Ratio Example 3
  • Equivalent Ratios Introduction
  • Equivalent Ratios Example 1
  • Equivalent Ratios Example 2
  • Equivalent Ratios Example 3
  • Equivalent Ratios Example 4
  • The Form 1:n Example 1
  • The Form 1:n Example 2
  • The Form 1:n Example 3
  • Direct Proportion
  • Direct Proportion Introduction
  • Direct Proportion Example 1
  • Direct Proportion Example 2
  • Direct Proportion Example 3
  • Inverse Proportion
  • Inverse Proportion Introduction
  • Inverse Proportion Example 1
  • Inverse Proportion Example 2
  • Inverse Proportion Example 3
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers
  • Rational and Irrational Numbers Introduction
  • Surds
  • Surd Introduction
  • Simplifying Surds Example 1
  • Simplifying Surds Example 2
  • Simplifying Surds Example 3
  • Rationalising Denominators
  • General Problems
  • Irrational Miscellaneous Example 1
  • Irrational Miscellaneous Example 2
  • Rational and Irrational Numbers Extension
  • An Infinite Number!
  • How Many Irrational Numbers Are There?
  • Indices Advanced
  • Review
  • Review of Indices so Far
  • The Power mn
  • The Power mn Example 1
  • The Power mn Example 2
  • Fractional Indices
  • Introduction to the Fractional Index 1/n
  • Fractional Indices Example 1
  • Fractional Indices Example 2
  • Introduction to the Fractional Index m/n
  • Fractional Indices Example 3
  • Fractional Indices Example 4
  • Fractional Indices Example 5
  • Fractional Indices Example 6
  • HCF and LCM
  • My Class' favourite Method
  • Shape Space and Measure
  • Transformations
  • Reflection
  • Reflection in Horizontal and Vertical Lines
  • Reflection in Diagonal Lines
  • Rotation
  • Rotation About a Fixed Point
  • Enlargement
  • Enlargements with Positive Scale Factors
  • Enlargements with Negative Scale Factors
  • Translation
  • Translation of Shape
  • Describing Transformations
  • Fully Describing a Given Transformation
  • Metric Units
  • Length
  • Metric Units of Length
  • Length Example 1
  • Length Example 2
  • Mass
  • Metric Units of Mass
  • Mass Example 1
  • Adding Metric Quantities
  • Adding Metric Quantities Example 1
  • Adding Metric Quantities Example 2
  • Adding Metric Quantities Example 3
  • Money
  • Money Example 1
  • Money Example 2
  • Circle Theorems
  • Nomenclature
  • Circle Nomenclature
  • Angle Subtended By Arc
  • Angle Subtended By Arc
  • Angle Subtended at Centre
  • Angle Subtended at Centre
  • Angle in Semicircle
  • Angle in Semicircle
  • Mixed Examples
  • Mixed Examples
  • Cyclic Quadrilaterals
  • Cyclic Quadrilaterals
  • Tangent Properties
  • Tangent Properties
  • The Alternate Segment Theorem
  • The Alternate Segment Theorem
  • Constructions
  • Ruler and Compass Constructions
  • Constructing a Perpendicular Bisector
  • The Right Angle
  • Bisecting an Angle
  • The Sixty Degree Angle
  • Thirty Degrees and Forty Five Degrees
  • Plans and Elevations
  • Drawing Plans and Elevations for Solid Objects
  • Plans and Elevations Example 1
  • Plans and Elevations Example 2
  • Plans and Elevations Example 3
  • Scale Drawing
  • Drawing Accurate Scale Drawings
  • Scale Drawing Example 1
  • Scale Drawing Example 2
  • Scale Drawing Example 3
  • Similar Figures and Triangles
  • Similar Figures
  • Similar Figures Introduction
  • Areas of Similar Figures Intro
  • Areas of Similar Figures Example 1
  • Areas of Similar Figures Example 2
  • Volumes of Similar Solids Intro
  • Volumes of Similar Solids Example 1
  • Volumes of Similar Solids Example 2
  • Similar Triangles
  • Similar Triangles Intro
  • Similar TrianglesExample 1
  • Similar TrianglesExample 2
  • Similar TrianglesExample 3
  • Imperial Units
  • Imperial Units of Length
  • Imperial Units of Length Intro
  • Imperial Units of Length Example 1
  • Imperial Units of Length Example 2
  • Imperial Units of Mass
  • Imperial Units of Mass Intro
  • Imperial Units of Mass Example 1
  • Imperial Units of Mass Example 2
  • Conversion Between Imperial and Metric
  • Conversion Between Imperial and Metric Intro
  • Conversion Between Imperial and Metric Example 1
  • Conversion Between Imperial and Metric Example 2
  • Quadrilateral Properties
  • Properties of Quadrilaterals and their Diagonals
  • Properties of the Square
  • Properties of the Rectangle
  • Properties of the Parallelogram
  • Properties of the Rhombus
  • Properties of the Kite
  • Properties of the Trapezium
  • Congruent Triangles
  • Properties of Congruent Triangles
  • Congruent Triangles Intro Part 1
  • Congruent Triangles Intro Part 2
  • Congruent Triangles Example 1
  • Congruent Triangles Example 2
  • Congruent Triangles Example 3
  • Congruent Triangles Example 4
  • Tangents to Curves
  • Drawing a Tangent to a Curve
  • Drawing a Tangent to a Curve
  • Travel Graphs
  • Speed, Distance, Time
  • Speed, Distance, Time Example 1
  • Speed, Distance, Time Example 2
  • Using a Travel Graph
  • Travel Graphs Example 1
  • Travel Graphs Example 2
  • Symmetry
  • Line Symmetry
  • Line Symmetry Example 1
  • Line Symmetry Example 2
  • Line Symmetry Example 3
  • Line Symmetry Example 4
  • Rotational Symmetry
  • Rotational Symmetry Example 1
  • Rotational Symmetry Example 2
  • Both Types of Symmetry
  • Both Types of Symmetry
  • Sections and Planes of Symmetry
  • Sections Example 1
  • Congruence
  • Planes of Symmetry
  • Loci
  • Introduction to Loci
  • Loci Introduction
  • Loci Examples
  • Loci Examples Example 1
  • Loci Examples Example 2
  • Loci Examples Example 3
  • Loci Examples Example 4
  • Basic Area
  • Introduction
  • Introduction to Area Example 1
  • Introduction to Area Example 2
  • Introduction to Area Example 3
  • Standard Shapes
  • Area of a Square
  • Area of a Rectangle Example 1
  • Area of a Rectangle Example 2
  • Finding a Length
  • Compound Shapes
  • Shapes Made from Squares and Rectangles Example 1
  • Shapes Made from Squares and Rectangles Example 2
  • Shapes Made from Squares and Rectangles Example 3
  • Converting Units
  • Converting Between Units of Area Example 1
  • Converting Between Units of Area Example 2
  • Converting Between Units of Area Example 3
  • Converting Between Units of Area Example 4
  • Basic Perimeter
  • Perimeter
  • Basic Perimeter Example 1
  • Basic Perimeter Example 2
  • Basic Perimeter Example 3
  • Introducing Geometry
  • The Meaning of Angle
  • Introduction to Angles
  • Introduction to Measuring Angles
  • Types of Angle
  • Measuring Angles
  • Using a Protractor to Measure Angles
  • Using a Protractor to Draw Angles
  • Angle Facts
  • Vertically Opposite Angles
  • Angles on a Straight Line
  • Angles at a Point
  • Mixed Example
  • Triangles and Quadrilaterals
  • Naming Sides and Angles
  • Naming Angles
  • Naming Sides
  • Angle Sum for a Triangle
  • The Angle Sum for a Triangle Intro
  • The Angle Sum for a Triangle Example 1
  • The Angle Sum for a Triangle Example 2
  • The Angle Sum for a Triangle Example 3
  • The Angle Sum for a Triangle Example 4
  • The Angle Sum for a Triangle Example 5
  • Constructions
  • Side and Two Angles
  • Two Sides and an Angle
  • Three Sides
  • Quadrilaterals
  • Introduction to Quadrilaterals
  • Angle Sum for a Quadrilateral Example 1
  • Angle Sum for a Quadrilateral Example 2
  • Angle Sum for a Quadrilateral Example 3
  • Basic Coordinates
  • Introduction
  • Introduction to Coordinate Systems
  • Coordinates
  • Basic Coordinates Example 1
  • Basic Coordinates Example 2
  • Basic Coordinates Example 3
  • Negative Coordinates
  • Negative Coordinates Example 1
  • Negative Coordinates Example 2
  • Solids
  • Drawing Solids
  • Drawing a Cuboid on Squared Paper
  • Drawing a Cuboid on Isometric Paper
  • Counting Cubes
  • Nets
  • Folding a Net (Demonstration)
  • Folding a Net
  • Drawing a Net Example 1
  • Drawing a Net Example 2
  • Volume
  • Volume of a Cuboid Example 1
  • Volume of a Cuboid Example 2
  • Volume of a Cuboid Example 3
  • Volume of a Cuboid Example 4
  • Volume of a Cuboid Example 5
  • Volume of a Cuboid Example 6
  • Unit Conversion
  • Converting Cubic Units Example 1
  • Converting Cubic Units Example 2
  • Converting Cubic Units Example 3
  • Capacity
  • The Meaning of Capacity
  • Capacity Example 1
  • Capacity Example 2
  • Surface Area
  • Surface Area of a Cuboid Example 1
  • Surface Area of a Cuboid Example 2
  • Imperial Units
  • Imperial Units of Volume
  • Parallel Lines
  • Introduction
  • Introduction to Parallel Lines
  • Corresponding Angles
  • Introduction to Corresponding Angles
  • Corresponding Angles Example 1
  • Corresponding Angles Example 2
  • Corresponding Angles Example 3
  • Corresponding Angles Example 4
  • Alternate Angles
  • Introduction to Alternate Angles
  • Alternate Angles Example 1
  • Alternate Angles Example 2
  • Alternate Angles Example 3
  • Interior Angles
  • Introduction to Interior Angles
  • Interior Angles Example 1
  • Mixed Questions
  • Parallel Lines Mixed Example 1
  • Parallel Lines Mixed Example 2
  • Polygons
  • Introduction to Polygons
  • Introduction to Polygons
  • Regular and Irregular Polygons
  • Regular and Irregular Polygons
  • Interior and Exterior Angles
  • Interior and Exterior Angles
  • Sum of Exterior Angles
  • Sum of Exterior Angles Example 1
  • Sum of Exterior Angles Example 2
  • Sum of Exterior Angles Example 3
  • Interior Angles
  • Interior Angles Example 1
  • Interior Angles Example 2
  • Interior Angles Example 3
  • Pythagoras' Theorem
  • Introduction
  • Introduction to Pythagoas' Theorem
  • Finding the Hypotenuse
  • Finding the Hypotenuse Example 1
  • Finding the Hypotenuse Example 2
  • Finding the Hypotenuse Example 3
  • Finding the Hypotenuse Calculator Guide
  • Finding a Shorter Side
  • Finding a Shorter Side Example 1
  • Finding a Shorter Side Example 2
  • Finding a Shorter Side Example 3
  • Finding a Shorter Side Calculator Guide
  • Harder Problems
  • Harder Problems Example
  • Three Dimensional Problems
  • Pythagoras in 3 Dimensions
  • More Length, Area and Volume
  • Area of a Triangle
  • Introduction to the Area of a Triangle
  • Area of a Triangle Example 1
  • Area of a Triangle Example 2
  • Area of a Triangle Example 3
  • Area of a Triangle Example 4
  • Area of a Parallelogram
  • Introduction to the Area of a Parallelogram
  • Area of a Parallelogram Example 1
  • Area of a Parallelogram Example 2
  • Area of a Parallelogram Example 3
  • Area of a Trapezium
  • Introduction to the Area of a Trapezium
  • Area of a Trapezium Example 1
  • Area and Circumference of a Circle
  • Terminology and Introduction to the Circle
  • Area and Circumference Example 1
  • Area and Circumference Calculator Guide 1
  • Area and Circumference Example 2
  • Area and Circumference Example 3
  • Area and Circumference Example 4
  • Area and Circumference Example 5
  • Area and Circumference Example 6
  • Sectors of Circles
  • More Terminology of Circles
  • Introduction to Area of Sector
  • Introduction to Arc Length
  • Area of Sector and Arc length Example 1
  • Area of Sector and Arc length Example 2
  • Area of Sector and Arc length Example 3
  • Volume of a Prism
  • What is a Prism?
  • Volume of a Prism Example 1
  • Volume of a Prism Example 2
  • Volume of a Prism Example 3
  • Volume of a Prism Example 4
  • Dimensions of a Formula
  • Dimensions Introduction Part 1
  • Dimensions Example 1
  • Dimensions Introduction Part 2
  • Dimensions Example 2
  • Dimensions Example 3
  • Trigonometry
  • Introduction
  • Introduction to Trigonometry
  • Trigonometry 9, 10, 11
  • Finding a Side
  • Finding a Side Example 1
  • Finding a Side Example 2
  • Finding a Side Example 3
  • Finding a Side Calculator Guide 1
  • Finding a Side Example 4
  • Finding a Side Example 5
  • Finding a Side Example 6
  • Finding a Side Calculator Guide 2
  • Finding an Angle
  • Finding an Angle Example 1
  • Finding an Angle Example 2
  • Finding an Angle Example 3
  • Finding an Angle Calculator Guide
  • Harder Examples
  • Multi-Step Trig Problems Example 1
  • Multi-Step Trig Problems Example 2
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1
  • Three Dimensional Problems Example 2
  • Further Area and Volume
  • Upper and Lower Bounds
  • Upper and Lower Bounds Example 1
  • Upper and Lower Bounds Example 2
  • Upper and Lower Bounds and Trigonometry Example 1
  • Upper and Lower Bounds and Trigonometry Example 2
  • Pyramids
  • The Volume and Area of a Pyramid
  • Pyramid Example 1
  • Pyramid Example 2
  • Pyramid Example 3
  • Angle Between a Line and a Plane
  • definition of the Angle Between a Line and a Plane
  • Angle Between a Line and a Plane Example 1
  • Angle Between a Line and a Plane Example 2
  • Cylinders
  • The Volume and Area of a Cylinder
  • Cylinder Example 1
  • Cylinder Example 2
  • Cones
  • The Volume and Area of a Cone
  • Cone Example 1
  • Cone Example 2
  • Cone Example 3
  • Spheres
  • The Volume and Area of a Sphere
  • Sphere Example 1
  • Sphere Example 2
  • Sphere Example 3
  • Sphere Example 4
  • Sphere Example 5
  • Sphere Example 6
  • Sine and Cosine Rules
  • Introduction to Sine and Cosine Rules
  • Non Right-Angled Trigonometry
  • The Sine Rule
  • The Cosine Rule
  • Using The Sine Rule
  • Using The Sine Rule Example 1
  • Using The Sine Rule Example 2
  • Using the Cosine Rule
  • Using the Cosine Rule Example 1
  • Using the Cosine Rule Example 2
  • Miscellaneous Example
  • Finding All of the Unknowns in a Triangle
  • Extension - Ambiguity
  • The Ambiguous Case of the Sine Rule
  • Vectors
  • Vectors and Scalars
  • Vector Introduction
  • Vector Representation
  • Representing Vectors
  • Vector Diagrams
  • Adding and Subtracting Vectors
  • Vector Journeys Example 1
  • Vector Journeys Example 2
  • Column Vectors
  • Translation Vectors
  • Adding and Subtracting Column Vectors
  • Trigonometry - Right Angle Triangles
  • Introduction
  • Introduction to Trigonometry (9, 10, 11)
  • Finding a Side
  • Finding a Side Example 1 (9, 10, 11)
  • Finding a Side Example 2 (9, 10, 11)
  • Finding a Side Example 3 (9, 10, 11)
  • Finding a Side Example 4 (9, 10, 11)
  • Finding a Side Example 5 (9, 10, 11)
  • Finding a Side Example 6 (9, 10, 11)
  • Finding an Angle
  • Finding an Angle Example 1 (9, 10, 11)
  • Finding an Angle Example 2 (9, 10, 11)
  • Finding an Angle Example 3 (9, 10, 11)
  • Harder Examples
  • Multi-Step Trig Problems Example 1 (9, 10, 11)
  • Multi-Step Trig Problems Example 2 (9, 10, 11)
  • Three Dimensional Problems
  • Three Dimensional Problems Example 1 (9, 10, 11)
  • Three Dimensional Problems Example 2 (9, 10, 11)
  • Differentiation
  • Using the Differentiation Formula
  • Differentiation Example 2
  • Differentiation Example 3
  • Differentiation Example 4
  • Differentiation Example 5
  • Differentiation Example 6
  • Expressions with Multiple Terms
  • Dealing with More Complex Expressions Example 1
  • Dealing with More Complex Expressions Example 2
  • Dealing with More Complex Expressions Example 3
  • Dealing with More Complex Expressions Example 4
  • Finding Gradients
  • Using Differentiation to Find the Gradient at a Point Example 1
  • Using Differentiation to Find the Gradient at a Point Example 2
  • Finding The Equation of a Tangent
  • Finding The Equation of a Tangent Intro
  • Finding The Equation of a Tangent Example 1
  • Finding The Equation of a Tangent Example 2
  • Increasing and Decreasing Functions
  • The Concept of Increasing and Decreasing Functions
  • Increasing and Decreasing Functions Example 1
  • Turning Points
  • An Introduction to Turning Points Part 1
  • An Introduction to Turning Points Part 2
  • An Introduction to Turning Points Part 3
  • An Introduction to Turning Points Part 4
  • An Introduction to Turning Points Part 5
  • Finding Turning Points Example 1
  • Finding Turning Points Example 2
  • Finding Turning Points Example 3
  • Kinematics
  • Kinematics Intro
  • Kinematics Example
  • Functions
  • Introduction to Functions
  • Function Intro
  • Basic Notation
  • Domain and Range
  • Introduction to Domain and Range
  • Finding the Range
  • Values Which Cannot Be in the Domain
  • Composite Functions
  • Composite Functions Intro
  • Composite Functions Example
  • Inverse Functions
  • Inverse Functions Intro
  • Inverse Functions Example
  • Sets
  • Introduction to Sets
  • What is a Set?
  • Writing a Set as a List
  • The Venn Diagram
  • Venn Diagram, Intersection and Union
  • Subsets
  • The Compliment of a Set
  • Probem Solving Example 1
  • Probem Solving Example 2
  • Identifying Sets in a Venn Diagram
  • Sets
  • The Number Sets
  • Set-Builder Notation
  • Rearranging Formulae
  • Rearranging Formulae Example 1
  • Rearranging Formulae Example 2
  • Rearranging Formulae Example 3
  • Rearranging Formulae Example 4
  • Rearranging Formulae Example 5
  • Rearranging Formulae Example 6
  • Linear Combinations of Random Variables
  • Linear Combinations of Normal Random Variables
  • Combining Random Variables
  • Normal Random Variables
  • Normal Random variables Example
  • Planes
  • The Vector Equation of a Plane
  • The Vector Equation of a Plane Example 1
  • The Vector Equation of a Plane Example 2
  • The Distance of a Point from a Plane
  • The Distance of a Point from a Plane Example
  • Tests For Correlation Coefficients
  • Test for PMCC Example
  • Test for SRCC Example
  • Inverse Functions Example 7
  • Allocation Problems
  • Transportation Problems
  • Setting Up
  • Introducing the Problem
  • Linear Programming
  • The Transportation Tableau
  • Solving the Problem
  • Method Overview
  • Developing Initial Solutions Example 1
  • Developing Initial Solutions Example 2
  • Developing Initial Solutions Example 3
  • Testing For Optimality Example 1
  • Testing For Optimality Example 2
  • Improving Solutions - Forming Loops
  • Stepping-Stone Method Example 1
  • Stepping-Stone Method Example 2
  • Unbalanced Problems
  • Unbalanced Problems Example 1
  • Unbalanced Problems Example 2
  • Degeneracy
  • Degeneracy Example 1
  • Degeneracy Example 2
  • Introduction
  • Introduction
  • Formulation as a Linear Programming Problem
  • Solving Allocation Problems
  • Overview of the Hungarian Algorithm
  • The Opportunity Cost Matrix
  • Forming the Opportunity Cost Matrix Example 1
  • Forming the Opportunity Cost Matrix Example 2
  • Forming the Opportunity Cost Matrix Example 3
  • Optimality Testing
  • Testing for Optimality Example 1
  • Testing for Optimality Example 2
  • Testing for Optimality Example 3
  • Modifying a Matrix
  • Modifying a Matrix Example 1
  • Modifying a Matrix Example 2
  • Final Assignment
  • Final Assignment Example 1
  • Final Assignment Example 2
  • Unbalanced Problems
  • Unbalanced Problems Example
  • Maximisation Problems
  • Maximisation Example
  • Game Theory
  • Introduction
  • Introduction to Game Theory
  • Two Person Zero-Sum Games
  • Pure Strategy Games
  • Pure Strategy Games
  • Pure Strategy Games Example 1
  • Pure Strategy Games Example 2
  • Mixed Strategy Games
  • Mixed Strategy Games 2 by 2 Example 1
  • Mixed Strategy Games 2 by 2 Example 2
  • A 2 by 3 Example
  • A 3 by 2 Example
  • Use of Linear Programming
  • 3 by 3 Example 1 - Formulation
  • 3 by 3 Example 2 - Formulation
  • 3 by 3 Example 1 - Solution
  • Dominance
  • Dominance
  • Dynamic Programming
  • Introduction
  • Introduction to Dynamic Programming
  • Shortest Route
  • Shortest Route Method 1
  • Shortest Route Method 2
  • Other Uses
  • Longest Route
  • Minimax Route
  • Maximin Route
  • Miscellaneous Examples
  • Miscellaneous Example 1
  • Miscellaneous Example 2
  • Approximating Functions
  • Approximating Using Newton's Interpolating Formula
  • Differences
  • Newton's Interpolating Polynomial
  • How Many Points?
  • Our Quartic Approximation
  • Our Quadratic Approximation
  • Choosing the Appropriate Function
  • DE
  • Tangent Fields
  • Building a Tangent Field
  • Tangent Field Example 1
  • Tangent Field Example 2
  • Isoclines
  • Variables Separable
  • Differential Equations with Variables Separable
  • Introduction to Separating Variables
  • Separating Variables Example 1
  • Separating Variables Example 2
  • Separating Variables Example 3
  • Separating Variables Example 4
  • Comparing with Tangent Field
  • Solution Compared to Tangent Field Example 1
  • Solution Compared to Tangent Field Example 2
  • First Order Linear Differential Equations
  • Introduction
  • First Order Equations Intro
  • Exact Equations
  • Exact Equations Intro
  • Exact Equations Example 1
  • Exact Equations Example 2
  • Exact Equations Example 3
  • Exact Equations Example 4
  • Exact Equations Example 5
  • Exact Equations Example 6
  • Exact Equations Example 7
  • Exact Equations Example 8
  • Exact Equations Example 9
  • Integrating Factors
  • Integrating Factors Intro
  • Integrating Factors Example 1
  • Integrating Factors Example 2
  • Integrating Factors Example 3
  • Integrating Factors Example 4
  • Integrating Factors Example 5
  • Integrating Factors Example 6
  • Integrating Factors Example 7
  • Integrating Factors Example 8
  • Integrating Factors Example 9
  • Numerical Derivatives
  • Differentiatiating From First Principles
  • Forward Difference
  • Central Difference
  • Calculating Numerical Derivatives
  • First Differential
  • Second Differential
  • Extra Examples
  • Trig Identities Example 1
  • Trig Identities Example 2
  • Extra Example 1
  • Extra Example 2
  • Extra Examples
  • Extra Example 1
  • Extra Example 2
  • Extra Examples
  • Extra Example 1
  • Extra Example 2
  • Extra Examples
  • Extra Example 1
  • Extra Example 2
  • Extra Examples
  • Extra Example 1
  • Extra Example 2
  • Coordinate Geometry
  • The Curve y2 = f(x)
  • Introduction
  • Sketching Example 1
  • Sketching Example 2
  • The Substitution t equals tan(x/2)
  • The Identities
  • Integration Example 1
  • Integration Example 2
  • Integration Example 3
  • Integration Example 4
  • Lami's Theorem
  • Introducing Lami's Theorem
  • Lami's Theorem Example 1
  • Lami's Theorem Example 2
  • Dispersion
  • Outliers
  • Outliers Example 1
  • Outliers Example 2
  • Skewness
  • Skewness
  • Dispersion
  • Outliers
  • Outliers Example 1
  • Outliers Example 2
  • Skewness
  • Skewness
  • Dispersion
  • Outliers
  • Outliers Example 1
  • Outliers Example 2
  • Skewness
  • Skewness
  • Dispersion
  • Outliers
  • Outliers Example 1
  • Outliers Example 2
  • Skewness
  • Skewness
  • Dispersion
  • Outliers
  • Outliers Example 1
  • Outliers Example 2
  • Skewness
  • Skewness
  • Coursework
  • Type I and Type II Errors
  • Introduction to Type I and Type II Errors
  • Type I and Type II Errors Example 1
  • Type I and Type II Errors Example 2
  • Type I and Type II Errors Example 3
  • Introduction to Numerical Solutions of Equations
  • Introduction to Numerical Solutions of Equations
  • Terminology for Numerical Solutions of Equations
  • Coursework Outline for Numerical Solutions of Equations
  • Change of Sign
  • Decimal Search
  • Setting Up in Excel
  • Some Tips
  • Failure
  • Rearrangement
  • Rearrangement Part 1
  • Setting Up in Excel
  • Rearrangement Part 2
  • Success or Failure
  • Different Arrangements
  • Newton-Raphson
  • Introduction
  • Newton-Raphson Success
  • Setting Up in Excel
  • Possible Problems
  • Certain Failure
  • Comparison of Methods
  • Comparison of Methods
  • Finding Functions
  • Finding Functions
  • Numerical Solution of Equations
  • Numerical Solution of Equations Introduction
  • Why Use a Numerical Technique?
  • Bisection Method
  • Interval Bisection
  • Method of False Position
  • Linear Interpolation
  • Rearrangement (Fixed Point)
  • Fixed Point Iteration Part 1
  • Fixed Point Iteration Part 2
  • Success or Failure
  • Different Arrangements
  • Newton-Raphson
  • Newton-Raphson Introduction
  • Newton-Raphson Success
  • Newton-Raphson Possible Problems
  • Certain Failure Cases
  • Secant Method
  • The Secant Method
  • Errors
  • Introduction
  • Introducing Errors
  • Bisection Method
  • Fixed Point and Floating Point
  • Method of False Position
  • Rounding Errors
  • Rearrangement (Fixed Point)
  • Propagation of Errors - Addition and Subtraction
  • Propagation of Errors - Multiplying and Dividing
  • Propagation of Errors - Subtracting Nearly Equal Values
  • Ill-Conditioned Problems
  • Numerical Integration
  • Midpoint Rule
  • The Midpoint Rule
  • Trapezium Rule
  • The Trapezium Rule Formula
  • Overestimates and Underestimates
  • Trapezium Rule Example 1
  • Trapezium Rule Example 2
  • Trapezium Rule and Errors
  • Simpson's Rule
  • Simpson's Rule Example 1
  • Simpson's Rule and Errors
  • Simpson's Rule in Terms of Other Formulae
  • Matrices (CIE ONLY)
  • 2nd Order Differential Equations
  • 2nd Order Differential Equations with Constant Coeeficients
  • Introduction to 2nd Order Differential Equations
  • Real Distinct Roots to the Auxiliary Equation
  • Real Coincident Roots to the Auxiliary Equation
  • Pure Imaginary Roots to the Auxiliary Equation
  • Complex Roots to the Auxiliary Equation
  • Complimentary Function and Particular Integral
  • CF & PI Example 1
  • CF & PI Example 2
  • CF & PI Example 3
  • CF & PI Example 4
  • CF & PI Example 5
  • CF & PI Example 6
  • CF & PI Example 7
  • Oscillations
  • Simple Harmonic Motion
  • Introduction to SHM and the Equations
  • SHM Example 1
  • SHM Example 2
  • SHM Example 3
  • SHM Example 4
  • SHM Example 5
  • SHM Example 6
  • SHM Example 7
  • Damped Oscillations
  • Damped Oscillations Example
  • Systems of Equations
  • Simultaneous Differential Equations
  • Systems of Differential Equations Introduction
  • Systems of Differential Equations Example 1
  • Systems of Differential Equations Example 2
  • Systems of Differential Equations Example 3
  • Finding the Constants
  • Equilibrium Points
  • Solution Curves
  • Basic Work With Matrices
  • The Order of a Matrix
  • Adding Matrices
  • Subtracting Matrices
  • Multiplying by Scalar
  • Mixed Operations
  • Matrix Multiplication
  • Multiplying Matrices Example 1
  • Multiplying Matrices Example 2
  • Multiplying Matrices Example 3
  • Multiplying Matrices Example 4
  • Multiplying Matrices Example 5
  • Two by Two Determinant
  • The Determinant of a Two by Two Matrix
  • Two by Two Inverse
  • Two by Two Inverse Example 1
  • Two by Two Inverse Example 2
  • KS2
  • Data Handling
  • 3 - Figure Bearings
  • Sorting Diagrams
  • Venn Diagrams
  • Carroll Diagrams
  • Tree Diagrams
  • Data and Tables
  • Data and Tables Example 1
  • Data and Tables Example 2
  • Graphs and Charts
  • Bar Charts
  • Pictograms
  • Line Graphs
  • Pie Charts
  • Mean, Median and Mode
  • Mean
  • Mode
  • Median
  • Probabilities
  • Probabilities
  • Number
  • Bearings
  • Place Value
  • Numbers to 100
  • Numbers to 1000
  • Ordering Numbers
  • Large Numbers
  • Number Sequences
  • Continuing a Sequence
  • Adding and Subtracting Small Whole Numbers
  • Adding Numbers by Counting On
  • Subtracting Numbers by Counting On
  • Problems Involving Adding and Subtracting 1
  • Problems Involving Adding and Subtracting 2
  • Multiplication
  • Times Table for 2, 3, 4, 5, 10
  • Odd and Even Numbers
  • Odd and Even Numbers
  • Doubling and Halving
  • Doubling and Halving
  • Division
  • The Idea of Sharing
  • Rounding
  • Rounding Numbers to the Nearest 10
  • Rounding Numbers to the Nearest 100
  • Negative Numbers
  • Introducing Negative Numbers
  • Sequences Involving Negative Numbers
  • Decimals
  • Multiplying and Dividing Decimals by 10
  • Tenths
  • Hundredths
  • Decimals and Fractions
  • Ordering Decimals
  • Adding Larger Numbers
  • Long Addition of Whole Numbers
  • Ratio
  • Ratio
  • Factors and Multiples
  • Factors
  • Multiples
  • Adding Decimals
  • Adding Decimals
  • Equations
  • Missing Numbers
  • Equations
  • Fractions
  • What is a Fraction?
  • Comparing Fractions
  • Fractions of Amounts
  • Functions and Patterns
  • Functions and Patterns
  • Long Division
  • Single Digit Numbers
  • Two Digit Numbers
  • Short Division
  • Division Problems
  • Mental Maths
  • Introduction to Mental Maths
  • Multiplying and Dividing by 10
  • Order of Calculations
  • Adding by Counting On
  • Subtracting Mentally
  • Some Examples
  • Money Problems
  • Adding Money
  • Subtracting Money
  • Multiplying Amounts of Money
  • Dividing Amounts of Money
  • Value for Money
  • Multiplying by 10 and 100
  • Multiplying by a Single Digit Number
  • Multiplying by a Two Digit Number
  • Multiplying Decimals
  • Percentages
  • What is a Percentage?
  • Percentage of an Amount
  • Price Reductions
  • Problem Solving
  • Problem Solving
  • Nearest Whole Number
  • Rounding to 1 Decimal Place
  • Rounding to 2 Decimal Places
  • Subtracting Decimals
  • Subtracting Whole Numbers
  • Subtracting Decimals
  • Subtracting Money
  • Shape Space Measure
  • 2 - D shapes
  • Introducing Some 2-D Shapes
  • 3D Solids
  • Prisms and Pyramids
  • Measuring Length
  • Using a Ruler
  • Measuring Mass
  • Using Scales
  • Money
  • Coins
  • Capacity
  • Measuring Capacity
  • 3 - D Shapes
  • Introducing Some 23 - D Shapes
  • Faces, Edges and Vertices
  • Nets
  • Angles
  • Angles
  • Angles in a Triangle
  • Measuring Angles
  • Compass Points
  • Areas of Triangles
  • Areas of Triangles
  • Grids
  • Grids
  • Coordinates
  • Translations
  • Lines and Polygons
  • Parallel Lines
  • Types of Triangle
  • Quadrilaterals
  • Other Polygons
  • Diagonals
  • Area and Perimeter of Rectangles
  • Radius and Diameter of Circles
  • Measures
  • Imperial Measures
  • Metric Measures
  • Conversion
  • Symmetry
  • Line Symmetry
  • Rotational Symmetry
  • Time
  • The Calendar
  • Basic Facts
  • Minutes Past
  • Minutes To
  • Counting On (Easier Examples)
  • Digital Clocks and 24-Hour Clocks
  • Counting On (Harder Examples)
  • Timetables
  • School Timetables
  • Transformations
  • Translation
  • Reflection
  • Rotation
  • Introduction to Bearings
  • Bearings Example 1
  • Bearings Example 2
  • Bearings Example 3
  • Direct Proof
  • Bearings
  • 3 - Figure Bearings
  • Introduction to Bearings
  • Bearings Example 1
  • Bearings Example 2
  • Bearings Example 3
  • Proof
  • Bearings
  • 3 - Figure Bearings
  • Introduction to Bearings
  • Bearings Example 1
  • Bearings Example 2
  • Bearings Example 3
  • Direct Proof Example 1
  • Direct Proof Example 2
  • Direct Proof Example 3
  • Proof by Exhaustion
  • Proof by Exhaustion
  • Proof by Contradiction
  • Proof by Contradiction Example 1
  • Proof by Contradiction Example 2
  • Disproof by Counter-Example
  • Disproof by Counter-Example eg1
  • Disproof by Counter-Example eg2
  • Disproof by Counter-Example eg3
  • Disproof by Direct Argument
  • Disproof by Direct Argument Example 1
  • Disproof by Direct Argument Example 2
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Odd, Even and Periodic Functions
  • Roots and Coefficients
  • Quadratic Equations
  • Relationship Between Roots and Coeffs
  • Quadratic Example 1
  • Quadratic Example 2
  • Quadratic Example 3
  • Quadratic Example 4
  • Cubic Equations
  • Relationship Between Roots and Coeffs for Cubics
  • Cubic Example 1 - Symmetric Functions
  • Cubic Example 2
  • Cubic Example 3
  • Cubic Example 4
  • Quartic Equations
  • Relationship Between Roots and Coeffs for Quartics
  • Quartic Example 1
  • Roots and Coefficients
  • Quadratic Equations
  • Relationship Between Roots and Coeffs
  • Quadratic Example 1
  • Quadratic Example 2
  • Quadratic Example 3
  • Quadratic Example 4
  • Cubic Equations
  • Relationship Between Roots and Coeffs for Cubics
  • Cubic Example 1 - Symmetric Functions
  • Cubic Example 2
  • Cubic Example 3
  • Cubic Example 4
  • Quartic Equations
  • Relationship Between Roots and Coeffs for Quartics
  • Quartic Example 1
  • The Binomial Distribution
  • Introduction to the Binomial Distribution
  • Binomial Examples - Example 1
  • Binomial Examples - Example 2
  • Binomial Examples - Example 3
  • Binomial Examples - Example 4
  • The Expecation and Variance for a Binomial Distribution
  • Expectation and Varaince Example 1
  • Expectation and Varaince Example 2
  • Expectation and Varaince Example 3
  • Binomial Examples - Example 5
  • Spearman's Rank
  • Introduction to Spearman's Rank
  • Spearman's Rank Example 1
  • Spearman's Rank Example 2
  • Spearman's Rank Example 3
  • Meaning of Correlation Coefficient
  • Coordinate Systems
  • The Parabola
  • Introduction to the Parabola
  • Tangents and Normals to Parabolas
  • Tangents and Normals to Parabolas
  • Parabola Examples
  • Parabola Example 1
  • Parabola Example 2
  • Parabola Example 3
  • The Rectangular Hyperbola
  • Introduction to the Rectangular Hyperbola
  • Tangents and Normals to Rectangular Hyperbolas
  • Tangents and Normals to the Rectangular Hyperbola
  • Rectangular Hyperbola Examples
  • Rectangular Hyperbola Example 1
  • Rectangular Hyperbola Example 2
  • Rectangular Hyperbola Example 3
  • Chi-Square Tests
  • Motion in 1-D
  • Relationships Between a, v and x
  • Introduction to Motion in 1-D
  • Motion in 1-D Example 1
  • Motion in 1-D Example 2
  • Vertical Motion
  • Vertical Motion Introduction
  • Vertical Motion Example 1
  • Vertical Motion Example 2
  • Vertical Motion Example 3
  • Vertical Motion Example 4
  • Resisted Motion
  • Introduction to Resisted Motion
  • Resisted Motion Example
  • Chi-Square Test for Relationship Between Variables
  • Chi-Square Example 1
  • Chi-Square Example 2
  • Chi-Square Example 3
  • Chi-Square Tests
  • Chi-Square Test for Relationship Between Variables
  • Chi-Square Example 1
  • Chi-Square Example 2
  • Chi-Square Example 3
  • Chi-Square Tests
  • Chi-Square Test for Relationship Between Variables
  • Chi-Square Example 1
  • Chi-Square Example 2
  • Chi-Square Example 3
  • S3
  • Chi-Square Tests
  • Chi-Square Test for Relationship Between Variables
  • Chi-Square Example 1
  • Chi-Square Example 2
  • Chi-Square Example 3
  • Conics
  • The Parabola
  • Introducing the Parabola
  • Intersection of Parabola and Line
  • Translation of the Parabola
  • Stretching the Parabola Parallel to the x-axis
  • Stretching the Parabola Parallel to the y-axis
  • Reflecting the Parabola in the Line y = x
  • The Ellipse
  • Introducing the Ellipse
  • Intersection of an Ellipse and a Line
  • Translation of the Ellipse
  • Stretching the Ellipse Parallel to Coordinate Axes
  • Reflecting the Ellipse in the Line y = x
  • General Ellipse Example
  • The Hyperbola
  • Introducing the Hyperbola
  • Intersection of an Hyperbola and a Line
  • Translation of the Hyperbola
  • Stretching the Hyperbola Parallel to Coordinate Axes
  • Reflecting the Hyperbola in the Line y = x
  • The Rectangular Hyperbola
  • Introducing the Rectangular Hyperbola
  • Translation of the Rectangular Hyperbola
  • Stretching the Rectangular Hyperbola Parallel to Coordinate Axes
  • General Rectangular Hyperbola Example
  • Review of Graph Transformations
  • Transformations of the Sine Graph
  • Trig Graphs Example
  • Uses of Sine and Cosine Graphs
  • Introducing Trig Graphs
  • Sine and Cosine Graphs
  • The Graph y = x3 Example 6
  • The Graph y = x3 Example 5
  • The Graph y = x3 Example 4
  • The Graph y = x3 Example 3
  • The Graph y = x3 Example 2
  • The Graph y = x3 Example 1
  • Graph Transformations and Cubic Curves
  • The Effect of Transformations on a Point Example 3
  • The Effect of Transformations on a Point Example 2
  • The Effect of Transformations on a Point Example 1
  • The Transformation f(ax) Example 3
  • The Transformation f(ax) Example 2
  • The Transformation f(ax) Example 1
  • The Transformation af(x) Example 2
  • The Transformation af(x) Example 1
  • The Transformation f(x - a)
  • The Transformation f(x) + a
  • Transformations Introduction
  • Graph Transformations
  • Graph Transformations
  • Transformations Applied to the Sine Curve
  • Differentiating Functions Given Implicitly Example 7
  • Differentiating Functions Given Implicitly Example 7
  • Differentiating Functions Given Implicitly Example 7
  • Differentiating Functions Given Implicitly Example 7
  • Differentiating Functions Given Implicitly Example 7
  • Allocation
  • Hungarian Algorithm
  • Introducing the Hungarian Algorithm
  • Hungarian Algorithm Example 1
  • Hungarian Algorithm Example 2
  • Hungarian Algorithm Example 3
  • Dynamic Programming
  • Minimum Paths by Dynamic Programming
  • Labelling
  • Dynamic Programming Example 1
  • Dynamic Programming Example 2
  • Dynamic Programming Example 3
  • Game Theory
  • Introduction
  • Two-Person Zero-Sum Games
  • Play-Safe Strategies and Stable Solutions
  • Dominance
  • Playing the Game
  • Mixed Strategies - 2 x 2 Games
  • 2 x n Games
  • Games with a Stable Solution
  • n x 2 Games
  • Example with Dominance Present
  • Use of Simplex Example 1
  • Use of Simplex Example 2
  • 3D Coordinates
  • Introduction
  • Introduction to 3D Coordinates
  • Examples
  • 3D Coordinate Examples
  • The Distance Between 2 Points
  • The Distance Between 2 Points
  • The Mid-Ordinate Rule
  • The Mid-Ordinate Rule
  • Simpson's Rule
  • Simpson's Rule
  • Confidence Intervals and Hypothesis Tests
  • Confidence Intervals
  • Introducing Confidence Intervals
  • Confidence Intervals Example 1
  • Confidence Intervals Example 2
  • Test for Mean of Normal Variable
  • Testing for Mean of a Normal Distribution
  • Testing for Mean Example 1
  • Testing for Mean Example 2
  • Test for Difference Between Means
  • Testing for the Difference Between Two Means
  • Difference Between Means Example 1
  • Final Note
  • Large Samples