A Level · AQA 7357

A Level Maths

Three papers, nineteen specification sections, one examiner writing the resources. Everything on this page maps directly to the AQA 7357 specification — Pure Mathematics (A–J), Statistics (K–O) and Mechanics (P–S) — with original questions built from what the mark scheme actually rewards.

Three papers · 2 hours each Papers 1 & 2 Pure · Paper 3 Statistics & Mechanics 100 marks per paper Strand owner: Mr Poore

Pure Mathematics — Sections A to J

The core of the course. Half the exam. All of it covered.

Pure Mathematics underpins Papers 1 and 2 in full and bleeds into every Statistics and Mechanics method. These ten sections are the spine of the qualification.

A — Proof

Deductive reasoning, proof by exhaustion, proof by contradiction and disproof by counterexample. The mathematical language and rigour the whole course is written in.

Planned

B — Algebra and Functions

Laws of indices, surds and rationalising denominators, quadratics (discriminant, completing the square), simultaneous equations, linear and quadratic inequalities, polynomials, factor theorem, algebraic division, partial fractions, modulus function, composite and inverse functions, graph transformations.

In production

C — Coordinate Geometry

Straight lines: gradient, mid-point, distance, parallel and perpendicular conditions. Circles in Cartesian and completed-square form, tangents and normals. Parametric equations: sketching curves, converting to Cartesian form, gradients and areas.

Planned

D — Sequences and Series

Arithmetic and geometric progressions, nth term and sum formulae, sum to infinity (|r| < 1), sigma notation, recurrence relations, binomial expansion for positive integer n and for rational and negative n.

Planned

E — Trigonometry

Sine rule, cosine rule, area formula. Radian measure, arc length and sector area. Small angle approximations. Reciprocal functions (sec, cosec, cot). Pythagorean and reciprocal identities. Addition and double-angle formulae. R sin(θ ± α) form. Inverse trigonometric functions and their graphs.

Planned

F — Exponentials and Logarithms

The functions e^x and ln x, laws of logarithms, solving equations of the form a^x = b, exponential growth and decay models, using logarithms to linearise data for statistical analysis.

Planned

G — Differentiation

Definition as a gradient function and from first principles (xⁿ, sin x). Chain, product and quotient rules. Differentiation of trig functions, e^kx and ln x. Parametric and implicit differentiation. Connected rates of change. Stationary points, second derivatives, concavity and optimisation.

In production

H — Integration

Integration as the reverse of differentiation. Definite integrals, areas under and between curves. Integrating trig functions, e^kx and 1/x. Integration by substitution, by parts and using partial fractions. Trapezium rule. Separable differential equations and modelling.

In production

I — Numerical Methods

Locating roots by change of sign and graphical methods. Fixed-point iteration x_n+1 = g(x_n), staircase and cobweb diagram analysis. The Newton–Raphson method. Issues of convergence and failure.

Planned

J — Vectors

2D and 3D column vectors and i, j, k notation, magnitude and direction, position vectors. The scalar (dot) product and the angle between two vectors. Vector equation of a straight line in 2D and 3D.

Planned

Statistics — Sections K to O

Five sections. Rooted in data, built for interpretation.

Statistics occupies roughly half of Paper 3. It rewards students who can read context, interpret outputs and reason about uncertainty — not just calculate. The AQA Large Data Set runs through Section K and L and appears in Paper 3 every year.

K — Statistical Sampling

Populations, samples and the need for sampling. Simple random, systematic, stratified, quota and opportunity sampling: methods, advantages and limitations. The AQA Large Data Set — working with real data in context and critiquing sampling decisions.

Planned

L — Data Presentation and Interpretation

Histograms with unequal class widths (frequency density), cumulative frequency diagrams and box plots. Mean, median, mode, variance, standard deviation, IQR, outliers and coding. Scatter diagrams, the product-moment correlation coefficient, and linear regression (y on x).

Planned

M — Probability

Mutually exclusive and independent events, addition and multiplication laws, conditional probability using P(A|B) = P(A ∩ B) / P(B). Venn diagrams, two-way tables and probability tree diagrams. Discrete and continuous probability distributions.

Planned

N — Statistical Distributions

Discrete probability distributions: mean and variance from a table. Binomial distribution B(n, p): conditions, probabilities and cumulative values. Normal distribution N(μ, σ²): properties, standardising to Z, and the normal approximation to the binomial with continuity correction.

In production

O — Statistical Hypothesis Testing

Null and alternative hypotheses, significance levels and critical regions. One-tailed and two-tailed tests. Hypothesis test for a population proportion (binomial) and for a population mean (normal, known variance). Testing the product-moment correlation coefficient.

Planned

Mechanics — Sections P to S

Four sections. The applied half of Paper 3.

A Level Mechanics is about modelling the physical world with enough mathematical rigour to require calculus, vectors and careful reasoning about assumptions. These four sections cover the full content of the AQA Mechanics strand.

P — Quantities and Units

SI units of length, mass, time and force. The definitions of velocity, acceleration, the newton and derived units. Scalar versus vector quantities in a mechanics context — the foundation every other section builds on.

Planned

Q — Kinematics

Displacement, velocity, speed and acceleration. The five SUVAT equations and their derivation. Velocity–time and displacement–time graphs. Vertical motion under gravity. Projectile motion (horizontal and vertical components). Variable acceleration using differentiation and integration.

In production

R — Forces and Newton’s Laws

Newton’s First, Second and Third Laws. Resolving forces in two perpendicular directions. Weight, tension, normal reaction and friction. The coefficient of friction F ≤ μR. Connected particles: pulleys, lifts and tow-bar problems. Inclined plane problems.

Planned

S — Moments

The moment of a force about a point. Equilibrium conditions for a rigid body: sum of forces and sum of moments both zero. Problems involving rods, beams, pivots and supports. Analysis of when a body will slide versus topple.

Planned

Papers and packs

What’s coming, and when.

Every resource is original — written from the specification and past-paper patterns, never recycled exam questions — and comes with a full mark scheme that shows how the marks are actually awarded.

Resource	Includes	Status
Pure Mathematics topic packsSections A–J · Papers 1 and 2 content	Topic-by-topic packs covering every Pure section with original questions and full mark schemes — built for the algebra and calculus the exam rewards most	In production
Statistics topic packsSections K–O · Paper 3 Statistics strand	Full coverage of all five Statistics sections including AQA Large Data Set context questions and hypothesis testing with worked examples	Planned
Mechanics topic packsSections P–S · Paper 3 Mechanics strand	All four Mechanics sections with diagrams, worked examples and exam-standard questions on SUVAT, forces, connected particles and moments	Planned
Predicted papers — summer 2027Papers 1, 2 and 3 · built from past-paper gap analysis	Full predicted set for all three papers with mark schemes, plus rapid Paper 3 best-guess updates between the real exams	Coming spring 2027

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