AQA · A-level7357 A-level Mathematics
3 components21 topics21 with lessons
Source: AQA 7357 specification · Confirm the syllabus year with your school.
Exam infoExam structure, syllabus and formula booklet2 official documents
First teaching 2017
| Paper | Time | Marks | Weighting |
|---|
| Paper 1 Pure | 2 h | 100 | 33⅓% |
| Paper 2 Pure and Mechanics | 2 h | 100 | 33⅓% |
| Paper 3 Pure and Statistics | 2 h | 100 | 33⅓% |
- A calculator is needed in every paper. It must do iteration, summary statistics, distribution probabilities and the inverse normal.
- A formulae booklet is provided. The formulae in Appendix B of the specification are not in it and must be learnt.
Summarised from the official specification, checked 16 Oct 2026. The board's document is the final word.
PDFVersion 1.3 (31 January 2018)
A-level Mathematics 7357 — specification
Three 2-hour, 100-mark papers, each worth a third. Paper 1 is pure; Paper 2 is pure and mechanics; Paper 3 is pure and statistics. A calculator is needed in every paper: it must do iteration, summary statistics, distribution probabilities and the inverse normal.
PDFv1.2
Formulae for A-level Mathematics
The formulae booklet used in AS (7356) and A-level (7357) Mathematics exams. Appendix B of the specification lists the formulae you must learn because they are not in the booklet.
All AQA documents: exam rules, key dates and grade thresholds →
Paper 1Pure10 topics
- Proof
Deduction, exhaustion and counterexample · Proof by contradiction2 lessons - Algebra and functions
Includes quadratic functions and completing the square
Completing the square and the vertex · Modulus graphs and equations · Solving quadratic equations · Modulus inequalities · The discriminant and the nature of roots · Polynomials: division, factor and remainder theorems · Partial fractions · Linear and quadratic inequalities · Simultaneous equations and lines meeting curves9 lessons - Coordinate geometry
Gradient, length, midpoint and equations of lines · Parallel and perpendicular lines · The equation of a circle · Tangents, chords and intersections4 lessons - Sequences and series
Binomial expansion · Arithmetic progressions · Geometric progressions · Sum to infinity · Binomial expansion for any rational n5 lessons - Trigonometry
Radians · Exact values and the unit circle · Reciprocal functions and their identities · Arc length and sector area · Compound-angle formulae · Graphs and transformations · Inverse trigonometric functions · Double-angle formulae · Segments, chords and composite shapes · Trigonometric identities · The R-form (harmonic form) · Solving trigonometric equations12 lessons - Exponentials and logarithms
Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms5 lessons - Differentiation
Derivatives of eˣ, ln x and trigonometric functions · Gradients and the power rule · The chain rule · The product and quotient rules · Tangents and normals · Implicit differentiation · Stationary points and increasing functions · Parametric differentiation · Stationary points and tangents · Optimisation and rates of change10 lessons - Integration
Integrating eˣ, 1/x and trigonometric functions · Indefinite integration · Integration using trigonometric identities · Integrating (ax + b)ⁿ · Definite integrals · Exact definite integrals and logarithms · Areas under and between curves · Integration by substitution · Integration by parts · Forming differential equations · Separating the variables · Particular solutions with harder integrals · Modelling with differential equations13 lessons - Numerical methods
Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs · The trapezium rule · Newton–Raphson, bisection and interpolation5 lessons - Vectors
2D and 3D vectors; vector equations of lines are in Further Mathematics
Position vectors, magnitude and unit vectors1 lessons
Paper 2Pure and Mechanics5 topics
- Pure content (sections A–J)
Completing the square and the vertex · Solving quadratic equations · The discriminant and the nature of roots · Linear and quadratic inequalities · Simultaneous equations and lines meeting curves · Gradient, length, midpoint and equations of lines · Parallel and perpendicular lines · The equation of a circle · Tangents, chords and intersections · Radians · Arc length and sector area · Segments, chords and composite shapes · Exact values and the unit circle · Graphs and transformations · Inverse trigonometric functions · Trigonometric identities · Solving trigonometric equations · Binomial expansion · Arithmetic progressions · Geometric progressions · Sum to infinity · Gradients and the power rule · The chain rule · Tangents and normals · Stationary points and increasing functions · Optimisation and rates of change · Indefinite integration · Integrating (ax + b)ⁿ · Definite integrals · Areas under and between curves · Modulus graphs and equations · Modulus inequalities · Polynomials: division, factor and remainder theorems · Partial fractions · Binomial expansion for any rational n · Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms · Reciprocal functions and their identities · Derivatives of eˣ, ln x and trigonometric functions · The product and quotient rules · Implicit differentiation · Parametric differentiation · Stationary points and tangents · Integrating eˣ, 1/x and trigonometric functions · Integration using trigonometric identities · Exact definite integrals and logarithms · The trapezium rule · Integration by substitution · Integration by parts · Compound-angle formulae · Double-angle formulae · The R-form (harmonic form) · Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs · Newton–Raphson, bisection and interpolation · Forming differential equations · Separating the variables · Particular solutions with harder integrals · Modelling with differential equations · Position vectors, magnitude and unit vectors · Deduction, exhaustion and counterexample · Proof by contradiction66 lessons - Quantities and units in mechanics
Modelling assumptions and their meaning · Quantities, units and evaluating models2 lessons - Kinematics
Constant acceleration (suvat) · Motion graphs · Vertical motion under gravity · Variable acceleration · Position, velocity and acceleration vectors5 lessons - Forces and Newton's laws
Forces, components and resultants · Equilibrium of a particle · Newton’s laws and F = ma · Connected particles and pulleys · Lifts and vertical motion · Friction · Inclined planes · Motion on inclined planes8 lessons - Moments
Moments and beams on supports · Tilting and non-uniform rods2 lessons
Paper 3Pure and Statistics6 topics
- Pure content (sections A–J)
Completing the square and the vertex · Solving quadratic equations · The discriminant and the nature of roots · Linear and quadratic inequalities · Simultaneous equations and lines meeting curves · Gradient, length, midpoint and equations of lines · Parallel and perpendicular lines · The equation of a circle · Tangents, chords and intersections · Radians · Arc length and sector area · Segments, chords and composite shapes · Exact values and the unit circle · Graphs and transformations · Inverse trigonometric functions · Trigonometric identities · Solving trigonometric equations · Binomial expansion · Arithmetic progressions · Geometric progressions · Sum to infinity · Gradients and the power rule · The chain rule · Tangents and normals · Stationary points and increasing functions · Optimisation and rates of change · Indefinite integration · Integrating (ax + b)ⁿ · Definite integrals · Areas under and between curves · Modulus graphs and equations · Modulus inequalities · Polynomials: division, factor and remainder theorems · Partial fractions · Binomial expansion for any rational n · Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms · Reciprocal functions and their identities · Derivatives of eˣ, ln x and trigonometric functions · The product and quotient rules · Implicit differentiation · Parametric differentiation · Stationary points and tangents · Integrating eˣ, 1/x and trigonometric functions · Integration using trigonometric identities · Exact definite integrals and logarithms · The trapezium rule · Integration by substitution · Integration by parts · Compound-angle formulae · Double-angle formulae · The R-form (harmonic form) · Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs · Newton–Raphson, bisection and interpolation · Forming differential equations · Separating the variables · Particular solutions with harder integrals · Modelling with differential equations · Position vectors, magnitude and unit vectors · Deduction, exhaustion and counterexample · Proof by contradiction66 lessons - Statistical sampling
Populations and sampling methods1 lessons - Data presentation and interpretation
Stem-and-leaf diagrams and box plots · Histograms and cumulative frequency · Mean and standard deviation · Coded and combined data · Summary statistics and the PMCC · The least squares regression line6 lessons - Probability
Combined events and Venn diagrams · Tree diagrams and conditional probability · Independent and mutually exclusive events3 lessons - Statistical distributions
Probability distributions · The binomial distribution · Standardising and normal probabilities · Inverse normal and finding μ and σ · Normal approximation to the binomial5 lessons - Statistical hypothesis testing
Binomial and Poisson tests · Tests for a population mean · Type I and Type II errors3 lessons