A Level Maths Revision Notes
Welcome to the complete library of A Level Maths revision notes from ALevelMathsRevision.com. These free lesson notes cover every topic in the A Level Maths syllabus across Year 1 and Year 2, spanning Pure, Statistics, and Mechanics. Each set of A Level Maths lesson notes has been handwritten by John Armstrong, an experienced A Level Maths tutor, and is designed as a clear, concise summary of the key ideas — ideal for quick revision before a test, catching up on a missed lesson, or consolidating your understanding of a topic.
Revision notes are part of Stage 3 of your A Level Maths journey — topic revision. Once you've learned a topic through the video lessons and practised it with worksheets, these notes help you consolidate the key ideas before moving on to past paper revision. The journey above shows how every resource on this site fits together.
Your A Level maths journey
We're with you every step of the way. Click here to find out more about the journey.
Only follow this arrow when you have covered the whole curriculum.
These notes follow the current A Level Maths specification and are suitable for students preparing for exams with any UK exam board, including AQA, Edexcel, OCR, and OCR MEI. Use the search bar or the filters below to find the notes you need by year, strand, or topic.
| Year | Strand | Topic | Lesson |
|---|---|---|---|
| Year 1 | Pure | Proof | Proof |
| Year 1 | Pure | Proof | Proof With Odds And Evens |
| Year 1 | Pure | Proof | Sets And Interval Notation |
| Year 1 | Pure | Indices | Fractional And Negative Indices |
| Year 1 | Pure | Indices | Writing One Number As A Power Of Another |
| Year 1 | Pure | Surds | Basic Surd Operations |
| Year 1 | Pure | Surds | Rationalising The Denominator |
| Year 1 | Pure | Quadratic Equations | Introduction To Completing The Square |
| Year 1 | Pure | Quadratic Equations | Completing The Square |
| Year 1 | Pure | Quadratic Equations | Applications Of Completing The Square |
| Year 1 | Pure | Quadratic Equations | Simultaneous Equations |
| Year 1 | Pure | Quadratic Equations | Stealth Quadratics |
| Year 1 | Pure | Quadratic Inequalities and The Discriminant | Quadratic Inequalities |
| Year 1 | Pure | Quadratic Inequalities and The Discriminant | Quadratic Inequalities And The Discriminant |
| Year 1 | Pure | Straight Line Geometry | Introduction To Straight Lines |
| Year 1 | Pure | Straight Line Geometry | Parallel And Perpendicular Lines |
| Year 1 | Pure | Circle Geometry | Equations Of Circles |
| Year 1 | Pure | Circle Geometry | Tangents And Normals To Circles |
| Year 1 | Pure | Polynomial Division And The Factor Theorem | Polynomial Division And The Factor Theorem |
| Year 1 | Pure | Polynomial Division And The Factor Theorem | Sketching Cubic Graphs |
| Year 1 | Pure | Polynomial Division And The Factor Theorem | Sketching Quartic Graphs |
| Year 1 | Pure | Transformations | Standard Graphs |
| Year 1 | Pure | Transformations | Transformations Of Graphs And Functions |
| Year 1 | Pure | Trigonometry | Trigonometric Identities |
| Year 1 | Pure | Trigonometry | Solving Trig Equations |
| Year 1 | Pure | Trigonometry | Sine And Cosine Rule |
| Year 1 | Pure | Trigonometry | Finding A Trigonometric Quantity Given Another |
| Year 1 | Pure | Binomial Expansion | Binomial Expansion |
| Year 1 | Pure | Binomial Expansion | Further Binomial Expansion |
| Year 1 | Pure | Exponentials and Logarithms | Introduction To Logarithms |
| Year 1 | Pure | Exponentials and Logarithms | The Number E And Natural Logarithms |
| Year 1 | Pure | Exponentials and Logarithms | Exponential Growth |
| Year 1 | Pure | Exponentials and Logarithms | Solving Logarithmic Equations |
| Year 1 | Pure | Exponentials and Logarithms | Solving Exponential Equations |
| Year 1 | Pure | Exponentials and Logarithms | Logarithmic And Exponential Graphs |
| Year 1 | Pure | Exponentials and Logarithms | Modelling With Exponentials |
| Year 1 | Pure | Differentiation | Differentiation From First Principles |
| Year 1 | Pure | Differentiation | Basic Differentiation Of Powers Of X |
| Year 1 | Pure | Differentiation | Tangents And Normals To Curves |
| Year 1 | Pure | Differentiation | Finding And Classifying Stationary Points |
| Year 1 | Pure | Differentiation | Increasing And Decreasing Functions |
| Year 1 | Pure | Differentiation | Practical Applications Of Differentiation |
| Year 1 | Pure | Differentiation | Modelling With Differentiation |
| Year 1 | Pure | Integration | Introduction To Integration |
| Year 1 | Pure | Integration | Indefinite Integrals |
| Year 1 | Pure | Integration | Definite Integrals |
| Year 1 | Pure | Integration | Area Between A Curve And The X Axis |
| Year 1 | Pure | Integration | Solving Differential Equations |
| Year 1 | Pure | Vectors | Vectors |
| Year 1 | Pure | Vectors | Geometric Problems Using Vectors |
| Year 1 | Stats | Statistical Sampling | Sampling Techniques |
| Year 1 | Stats | Graphical Representation of Data | Histograms |
| Year 1 | Stats | Graphical Representation of Data | Cumulative Frequency Diagrams |
| Year 1 | Stats | Averages and Spread | Averages and Spread |
| Year 1 | Stats | Averages and Spread | Mean and Standard Deviation from Grouped Data |
| Year 1 | Stats | Averages and Spread | Interpolation |
| Year 1 | Stats | Averages and Spread | Intro to Standard Deviation |
| Year 1 | Stats | Averages and Spread | Outliers and Cleaning Data |
| Year 1 | Stats | Correlation and Regression | Correlation and Regression |
| Year 1 | Stats | Discrete Distributions (inc. Binomial Distribution) | Discrete Random Variables |
| Year 1 | Stats | Probability | Mutually Exclusive and Independent Events |
| Year 1 | Stats | Discrete Distributions (inc. Binomial Distribution) | Calculating Binomial Probabilities |
| Year 1 | Stats | Discrete Distributions (inc. Binomial Distribution) | Cumulative Binomial Probabilities |
| Year 1 | Stats | Binomial Hypothesis Testing | Intro to Hypothesis Tests |
| Year 1 | Stats | Binomial Hypothesis Testing | Hypothesis Testing – Finding Critical Regions |
| Year 1 | Stats | Binomial Hypothesis Testing | One Tail Binomial Hypothesis Testing |
| Year 1 | Stats | Binomial Hypothesis Testing | Two Tail Binomial Hypothesis Testing |
| Year 1 | Stats | Binomial Hypothesis Testing | Exam Questions Involving Trial and Improvement |
| Year 1 | Mech | Displacement-Time and Velocity-Time Graphs | S-T and V-T Graphs |
| Year 1 | Mech | Kinematics: Constant Acceleration (SUVAT) | Deriving SUVAT Equations |
| Year 1 | Mech | Kinematics: Constant Acceleration (SUVAT) | Intro to SUVAT |
| Year 1 | Mech | Kinematics: Constant Acceleration (SUVAT) | Free Motion Under Gravity |
| Year 1 | Mech | Kinematics: Variable Acceleration | Introduction to Kinematics |
| Year 1 | Mech | Kinematics: Variable Acceleration | Differentiation and Integration in Kinematics |
| Year 1 | Mech | Resolving Forces and Newton's Second Law (F = ma) | Resolving Perpendicular Forces |
| Year 1 | Mech | Resolving Forces and Newton's Second Law (F = ma) | Newton's Second Law in One and Two Dimensions |
| Year 1 | Mech | Resolving Forces and Newton's Second Law (F = ma) | Forces in 2d with Vectors |
| Year 1 | Mech | Newton's Third Law (Objects in Contact and Connected Particles) | Horizontally Connected Particles |
| Year 1 | Mech | Newton's Third Law (Objects in Contact and Connected Particles) | Particles Over a Pulley |
| Year 2 | Pure | Sequences and Series | Arithmetic Sequences |
| Year 2 | Pure | Sequences and Series | Geometric Sequences |
| Year 2 | Pure | Sequences and Series | Inductive Sequences |
| Year 2 | Pure | Sequences and Series | Sigma Notation and Mixed Sequence Problems |
| Year 2 | Pure | Rational Expressions | Simplifying Algebraic Fractions |
| Year 2 | Pure | Rational Expressions | Higher Order Polynomial Division |
| Year 2 | Pure | Rational Expressions | Partial Fractions |
| Year 2 | Pure | General Binomial Expansion | General Binomial Expansion |
| Year 2 | Pure | Functions | Mappings |
| Year 2 | Pure | Functions | Domain and Range |
| Year 2 | Pure | Functions | Inverse of a Function |
| Year 2 | Pure | Functions | Composite Functions |
| Year 2 | Pure | Functions | Multiple Transformations of Functions |
| Year 2 | Pure | The Modulus Function | Solving Equations Involving Moduli |
| Year 2 | Pure | The Modulus Function | Further Sketching Modulus Functions |
| Year 2 | Pure | The Modulus Function | Modulus Inequalities |
| Year 2 | Pure | Trigonometry: Radians, Circle Sectors and Triangles | Radians and Circle Sectors |
| Year 2 | Pure | Trigonometry: Compound and Double Angle Formulae | Compound Angle Formulae |
| Year 2 | Pure | Trigonometry: Compound and Double Angle Formulae | Double Angle Formulae |
| Year 2 | Pure | Trigonometry: Compound and Double Angle Formulae | Rcos(x+a) and Rsin(x+a) |
| Year 2 | Pure | Trigonometry: Secant, Cosecant and Cotangent | Reciprocal Trig Functions |
| Year 2 | Pure | Trigonometry: Secant, Cosecant and Cotangent | Further Reciprocal Trig Functions and Proofs |
| Year 2 | Pure | Trigonometry: Secant, Cosecant and Cotangent | Solving Equations With Reciprocal Trig Functions |
| Year 2 | Pure | Trigonometry: Small Angle Approximations and Inverse Trig Functions | Small Angle Approximations |
| Year 2 | Pure | Trigonometry: Small Angle Approximations and Inverse Trig Functions | Inverse Trig Functions |
| Year 2 | Pure | Further Differentiation | Chain Rule |
| Year 2 | Pure | Further Differentiation | Product Rule |
| Year 2 | Pure | Further Differentiation | Quotient Rule |
| Year 2 | Pure | Further Differentiation | Differentiating Trig Functions |
| Year 2 | Pure | Further Differentiation | Differentiating Inverse Functions |
| Year 2 | Pure | Further Differentiation | Implicit Differentiation |
| Year 2 | Pure | Concave and Convex Curves and Points of Inflection | Convexity, Concavity and Points of Inflection |
| Year 2 | Pure | Further Integration | Standard Integrals |
| Year 2 | Pure | Further Integration | Methods for Trig Integration |
| Year 2 | Pure | Further Integration | Further Integration With Partial Fractions |
| Year 2 | Pure | Further Integration | Integration by Parts |
| Year 2 | Pure | Further Integration | Integration – Choosing the Correct Method |
| Year 2 | Pure | Integration By Substitution | Integration by Substitution |
| Year 2 | Pure | Parametric Equations | Intro to Parametric Equations |
| Year 2 | Pure | Parametric Equations | Parametric Differentiation |
| Year 2 | Pure | Parametric Equations | Parametric Integration |
| Year 2 | Pure | Connected Rates of Change | Connected Rates of Change |
| Year 2 | Pure | Differential Equations | Differential Equations – Separating the Variables |
| Year 2 | Pure | Proof By Contradiction | Proof By Contradiction |
| Year 2 | Pure | Numerical Methods | Locating Roots with a Change of Sign |
| Year 2 | Pure | Numerical Methods | Fixed Point Iteration |
| Year 2 | Pure | Numerical Methods | Newton-Raphson Method |
| Year 2 | Pure | Numerical Methods | Approximating Integrals with Rectangles |
| Year 2 | Pure | Numerical Methods | Trapezium Rule and Numerical Integration |
| Year 2 | Pure | Vectors in 3-d | Vectors in 3d |
| Year 2 | Stats | Conditional Probability | Probabilities and Venn Diagrams |
| Year 2 | Stats | Conditional Probability | Conditional Probabilities on Venn Diagrams |
| Year 2 | Stats | Conditional Probability | Conditional Probability on Tree Diagrams |
| Year 2 | Stats | Conditional Probability | Further Conditional Probability |
| Year 2 | Stats | The Normal Distribution | Normal Distribution – Calculating Probabilities |
| Year 2 | Stats | The Normal Distribution | Inverse Normal Distribution |
| Year 2 | Stats | The Normal Distribution | Normal Distribution – Calculating Unknown Mean and Variance |
| Year 2 | Stats | The Normal Distribution | Hypothesis Test for Sample Mean |
| Year 2 | Stats | The Normal Distribution | Normal Approximations to a Binomial Distribution |
| Year 2 | Stats | Further Correlation and Regression | Hypothesis Tests for Correlation |
| Year 2 | Mech | Resolving Non-Perpendicular Forces | Resolving Non-Perpendicular Forces |
| Year 2 | Mech | Resolving Non-Perpendicular Forces | Static Bodies in 2d |
| Year 2 | Mech | Vector Mechanics | Constant Acceleration in 2d |
| Year 2 | Mech | Vector Mechanics | Constant Acceleration in 2d Worked Examples |
| Year 2 | Mech | Vector Mechanics | Variable Acceleration in 2d |
| Year 2 | Mech | Projectiles | Projectiles |
| Year 2 | Mech | Projectiles | Vectors and Trajectory of a Projectile |
| Year 2 | Mech | Coefficient Of Friction | Forces on a Slope with Friction |
| Year 2 | Mech | Moments | Intro to Moments |
| Year 2 | Mech | Moments | Moments in 2d |
| Year 2 | Mech | Moments | Non-Uniform Rods |