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 = a^x
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 a^x = 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 Ex2
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 = a^x
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 = a^x
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 a^x = 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 Ex2
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
Solving Trigonometric Equations Using Graphs
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 = a^x
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 a^x = 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 Ex2
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 = a^x
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 a^x = 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 Ex2
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