A Level Maths Revision Notes

On this page you will find a complete set of lesson notes for the A Level Maths syllabus as taught from September 2017. These notes are lessons delivered by myself to my own students so if you have missed any lessons or just feel the need to brush up, please take a look.

Year	Strand	Topic	Link
1	Pure	Proof	Proof
1	Pure	Proof	Implication and Proof By Deduction
1	Pure	Proof	Sets and Interval Notation
1	Pure	Indices and Surds	Intro to Indices
1	Pure	Indices and Surds	Writing One Number as a Power of Another
1	Pure	Indices and Surds	Basic Surd Operations
1	Pure	Indices and Surds	Rationalising the Denominator
1	Pure	Quadratics	Factorising and Solving Quadratic Equations
1	Pure	Quadratics	Completing the Square
1	Pure	Quadratics	Simultaneous Equations
1	Pure	Quadratics	Linear Inequalities
1	Pure	Quadratics	Quadratic Inequalities
1	Pure	Quadratics	Stealth Quadratics
1	Pure	Polynomials	Polynomial Division and Factor Theorem
1	Pure	Graphs and Functions	Standard Graphs
1	Pure	Graphs and Functions	Sketching Cubic Graphs
1	Pure	Graphs and Functions	Sketching Quartic Graphs
1	Pure	Graphs and Functions	Transformations of Graphs and Functions
1	Pure	Straight Lines	Introduction to Straight Lines
1	Pure	Straight Lines	Parallel and Perpendicular Lines
1	Pure	Circles	Equations of Circles
1	Pure	Circles	Tangents and Normals To Circles
1	Pure	Exponentials and Logarithms	Intro to Logarithms
1	Pure	Exponentials and Logarithms	Laws of Logarithms
1	Pure	Exponentials and Logarithms	Solving Exponential Equations
1	Pure	Exponentials and Logarithms	Solving Logarithmic Equations
1	Pure	Exponentials and Logarithms	Logarithmic Graphs
1	Pure	Exponentials and Logarithms	Modelling with Exponentials
1	Pure	Exponentials and Logarithms	e and Natural Logarithms
1	Pure	Exponentials and Logarithms	Exponential Growth
1	Pure	Exponentials and Logarithms	Differential of exp(kx)
1	Pure	Binomial Expansion	Intro to Binomial Expansion
1	Pure	Binomial Expansion	Further Binomial Expansion
1	Pure	Trigonometry	Equations and Trig Identities
1	Pure	Trigonometry	Finding a Trigonometric Quantity Given Another
1	Pure	Trigonometry	Further Solving Trig Equations
1	Pure	Trigonometry	Solving Trig Equations
1	Pure	Vectors	Collinear Vectors
1	Pure	Vectors	Geometric Problems Using Vectors
1	Pure	Vectors	Magnitude and Direction of a Vector
1	Pure	Differentiation	Basic Differentiation of Powers of x
1	Pure	Differentiation	Differentiation (Tangents and Normals)
1	Pure	Differentiation	Differentiation from First Principles
1	Pure	Differentiation	Finding and Classifying Stationary Points
1	Pure	Differentiation	Further Differentiation from First Principles
1	Pure	Differentiation	Successive Approximatons in Differentiation
1	Pure	Differentiation	Modelling with Differentiation
1	Pure	Differentiation	Practical Differentiation Problems
1	Pure	Integration	Area Between a Curve and the x-Axis
1	Pure	Integration	Definite Integrals
1	Pure	Integration	Introduction to Integration
1	Pure	Integration	Solving Differential Equations
1	Mech	Kinematics	Variable Acceleration
1	Mech	Kinematics	S-T and V-T Graphs
1	Mech	Kinematics	Deriving SUVAT Equations
1	Mech	Kinematics	Intro to SUVAT
1	Mech	Kinematics	Motion Under Gravity
1	Mech	Forces and Motion	Newton’s Second Law (F=ma) in One and Two Dimensions
1	Mech	Forces and Motion	Resolving Perpendicular Forces
1	Mech	Connected Particles	Particles Over a Pulley
1	Mech	Connected Particles	Horizontally Connected Particles
1	Stats	Sampling	Sampling Techniques
1	Stats	Statistical Diagrams	Cumulative Frequency Diagrams
1	Stats	Statistical Diagrams	Histograms
1	Stats	Measures of Location and Spread	Outliers and Cleaning Data
1	Stats	Measures of Location and Spread	Averages and Spread
1	Stats	Correlation and Regression	Correlation and Regression
1	Stats	Discrete Random Variables	Discrete Random Variables
1	Stats	Discrete Random Variables	Calculating Binomial Probabilities
1	Stats	Discrete Random Variables	Cumulative Binomial Probabilities
1	Stats	Hypothesis Testing	One Tail Binomial Hypothesis Testing
1	Stats	Hypothesis Testing	Two Tail Binomial Hypothesis Testing
1	Stats	Hypothesis Testing	Critical Regions in Hypothesis Testing
1	Stats	Hypothesis Testing	Exam Questions Involving Trial and Improvement
2	Pure	Sequences and Series	Arithmetic Sequences
2	Pure	Sequences and Series	Geometric Sequences
2	Pure	Sequences and Series	Sum To Infinity of Geometric Sequences
2	Pure	Sequences and Series	Inductive Sequences
2	Pure	Rational Functions and Partial Fractions	Further Polynomial Division
2	Pure	Rational Functions and Partial Fractions	Rational Functions
2	Pure	Rational Functions and Partial Fractions	Partial Fractions
2	Pure	General Binomial Expansion	General Binomial Expansion
2	Pure	Functions	Composite Functions
2	Pure	Functions	Domain and Range
2	Pure	Functions	Mappings
2	Pure	Functions	Inverse of a Function
2	Pure	Functions	Multiple Transformations of Functions
2	Pure	Functions	Sketching Modulus Functions
2	Pure	Functions	Modulus Inequalities
2	Pure	Trigonometry	Radians, Circle Sectors and Triangles
2	Pure	Trigonometry	Inverse Trig Functions
2	Pure	Trigonometry	Compound Angle Formulae
2	Pure	Trigonometry	Double Angle Formulae
2	Pure	Trigonometry	Rcos(x+a) and Rsin(x+a)
2	Pure	Trigonometry	Small Angle Approximations
2	Pure	Trigonometry	Solving Equations With Reciprocal Trig Functions
2	Pure	Trigonometry	Further Reciprocal Trig Functions and Proofs
2	Pure	Differentiation	Chain Rule
2	Pure	Differentiation	Product Rule
2	Pure	Differentiation	Quotient Rule
2	Pure	Differentiation	Differentiating Trig Functions
2	Pure	Differentiation	Chain Rule
2	Pure	Differentiation	Implicit Differentiation
2	Pure	Integration	Standard Integrals
2	Pure	Integration	Methods for Trig Integration
2	Pure	Integration	Integration by Substitution
2	Pure	Integration	Integration by Parts
2	Pure	Integration	Integration Using Partial Fractions
2	Pure	Integration	Further Integration With Partial Fractions
2	Pure	Integration	Standard Integrals
2	Pure	Integration	Integration – Choosing the Correct Method
2	Pure	Integration	Area Between a Curve and the y-Axis
2	Pure	Integration	Area Between Two Curves
2	Pure	Proof	Proof By Contradiction
2	Pure	Differentiation	Convexity, Concavity and Points of Inflection
2	Pure	Parametric Equations	Intro to Parametric Equations
2	Pure	Parametric Equations	Parametric Differentiation
2	Pure	Parametric Equations	Parametric Integration
2	Pure	Differentiation	Connected Rates of Change
2	Pure	Integration	Further Integration and Area
2	Pure	Integration	Differential Equations – Separating the Variables
2	Pure	Numerical Methods	Fixed Point Iteration
2	Pure	Numerical Methods	Locating Roots with a Change of Sign
2	Pure	Numerical Methods	Newton Raphson Method
2	Pure	Numerical Methods	Trapezium Rule and Numerical Integration
2	Pure	Vectors	Vectors in 3d
2	Mech	Kinematics	Constant Acceleration in 2d
2	Mech	Kinematics	Variable Acceleration in 2d
2	Mech	Kinematics	Particles Projected Horizontally
2	Mech	Kinematics	Trajectory of a Projectile
2	Mech	Forces and Motion	Vectors in 3d
2	Mech	Forces and Motion	Resolving Non-Perpendicular Forces
2	Mech	Forces and Motion	Static Bodies in 2d
2	Mech	Forces and Motion	Forces on a Slope with Friction
2	Mech	Moments	Intro to Moments
2	Mech	Moments	Non-Uniform Rods
2	Mech	Moments	Moments in 2d
2	Stats	Conditional Probability	Probabilities and Venn Diagrams
2	Stats	Conditional Probability	Conditional Probabilities on Venn Diagrams
2	Stats	Conditional Probability	Conditional Probability on Tree Diagrams
2	Stats	Conditional Probability	Further Conditional Probability
2	Stats	Normal Distribution	Normal Distribution – Calculating Probabilities
2	Stats	Normal Distribution	Normal Distribution – Calculating Unknown Mean and Variance
2	Stats	Normal Distribution	Inverse Normal Distribution
2	Stats	Normal Distribution	Hypothesis Test for Sample Mean
2	Stats	Normal Distribution	Normal Approximation to Binomial Distribution
2	Stats	Correlation and Regression	Hypothesis Tests for Correlation