AFFORDABLE MATHS TUITION

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

Learn at your own pace, when you want # 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