AQA A-Level

AQA A-Level Mathematics past papers, mark schemes & revision

Every AQA A-Level Mathematics past paper, mark scheme, examiner report, topic breakdown, worked example, and revision plan — all on one page.

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Specification · 7357

What you’ll sit

You will sit three papers, each 2 hours and worth 100 marks. Paper 1 is Pure Mathematics only. Paper 2 mixes Pure with Mechanics. Paper 3 mixes Pure with Statistics. Calculators (advanced scientific or graphical) are permitted on all three papers. The course covers approximately ⅔ Pure (algebra, calculus, trigonometry, vectors, proof) and ⅓ applied (½ Mechanics, ½ Statistics). Papers sit in May/June at the end of Year 13; the AS Maths qualification (7356) is a separate one-year option not required for the A-level.

Paper structure

Three papers · 100 marks each · 2 hours each · Paper 1 Pure Mathematics, Paper 2 Pure + Mechanics, Paper 3 Pure + Statistics · Calculator allowed on all papers

Awarded by

Assessment and Qualifications Alliance. Exam code 7357. Specification page: AQA A-Level Mathematics.

Past papers · AQA A-Level Mathematics

Every paper, every year, with mark schemes

Below is the official series of AQA A-Level Mathematics past papers from 2018 onward. Each paper, mark scheme, and examiner report is free to download from the AQA assessment-resources hub. Open the AQA hub →

Year	Paper	Tier	Duration	Marks	Notes	Download
2024	Paper 1	—	2h	100	Pure Mathematics	AQA hub →
	Paper 2	—	2h	100	Pure + Mechanics	AQA hub →
	Paper 3	—	2h	100	Pure + Statistics	AQA hub →
2023	Paper 1	—	2h	100	Pure Mathematics	AQA hub →
	Paper 2	—	2h	100	Pure + Mechanics	AQA hub →
	Paper 3	—	2h	100	Pure + Statistics	AQA hub →
2022	Paper 1	—	2h	100	Pure Mathematics	AQA hub →
	Paper 2	—	2h	100	Pure + Mechanics	AQA hub →
	Paper 3	—	2h	100	Pure + Statistics	AQA hub →
2021	Paper 1	—	2h	100	Centre-assessed; advance info issued	AQA hub →
	Paper 2	—	2h	100	Centre-assessed grades	AQA hub →
	Paper 3	—	2h	100	Centre-assessed grades	AQA hub →
2020	—	—	—	—	No exams (COVID-19 disruption). Centre-assessed grades.	AQA hub →
2019	Paper 1	—	2h	100	Pure Mathematics	AQA hub →
	Paper 2	—	2h	100	Pure + Mechanics	AQA hub →
	Paper 3	—	2h	100	Pure + Statistics	AQA hub →
2018	Paper 1	—	2h	100	Pure Mathematics — first new-spec exam	AQA hub →
	Paper 2	—	2h	100	Pure + Mechanics — first new-spec exam	AQA hub →
	Paper 3	—	2h	100	Pure + Statistics — first new-spec exam	AQA hub →

Mark schemes → Examiner reports → Grade boundaries →

Topics · full specification

Every topic in the AQA A-Level Mathematics specification

Each topic links to a deeper revision guide. The mark allocation column shows roughly how many marks per paper that topic typically attracts.

Proof

5% of Pure

Proof by deduction, exhaustion, counter-example, and contradiction. Disproving conjectures.

Proof by contradiction for √2 irrational
Counter-examples to false generalisations

Algebra and functions

15-20% of Pure

Polynomials, rational expressions, partial fractions, exponentials & logarithms, function composition & inverses, modulus functions, transformations.

Partial fractions decomposition
Solving exponential equations with logs
Composite & inverse functions

Coordinate geometry

5-10% of Pure

Straight lines, circles, parametric equations.

Tangent to a circle from external point
Parametric to Cartesian conversion

Sequences and series

5-10% of Pure

Arithmetic & geometric progressions, sigma notation, binomial expansion (for positive integer + rational n), increasing/decreasing/periodic sequences.

Sum to infinity of a geometric series
Binomial expansion of (1+x)ⁿ for rational n

Trigonometry

15% of Pure

Radians, exact values, identities (sin²x + cos²x = 1, double-angle, R-formulae, addition formulae), small-angle approximations.

R sin(x + α) form
Solving trig equations in a given interval
Double-angle identities for integration

Calculus (differentiation)

15% of Pure

First principles, polynomial differentiation, product rule, quotient rule, chain rule, implicit differentiation, parametric differentiation, second derivatives & stationary points.

Chain rule on composite functions
Implicit differentiation of x²+y² = 1 type equations
Connected rates of change

Calculus (integration)

15% of Pure

Polynomial integration, definite integrals, area under a curve, integration by substitution, integration by parts, partial fractions in integration, solving differential equations by separation.

Integration by parts (LIATE)
Substitution to simplify roots
Separable first-order ODEs

Vectors

5% of Pure

2D and 3D vectors, magnitude & direction, position vectors, vector equations of lines, scalar product (dot product) — Pure only at A-level.

Vector equation of a line
Angle between vectors via dot product

Mechanics

~17% of total A-level

Kinematics (SUVAT, variable acceleration), forces & Newton's laws, friction, projectiles, moments.

Variable acceleration with calculus
Connected particles (string over pulley)
Projectile motion with components

Statistics

~17% of total A-level

Sampling, presentation of data (histograms, cumulative frequency, box plots), measures of location & spread, correlation & regression, probability (Venn, tree diagrams, conditional), discrete & continuous random variables (binomial & normal distributions), hypothesis testing (binomial & for correlation).

Binomial hypothesis testing
Normal distribution probabilities
Conditional probability

Assessment objectives

How your marks are awarded

Examiners award marks against three Assessment Objectives. Knowing the split helps you target practice — most students under-prepare for AO3.

AO1 50%

Use and apply standard techniques

Recall facts, select and use methods, perform routine calculations.

AO2 25%

Reason, interpret and communicate mathematically

Construct rigorous arguments, identify errors, present solutions clearly.

AO3 25%

Solve problems within mathematics and in other contexts

Translate real-world situations into mathematical processes, interpret results, evaluate models.

Worked examples · step by step

How to actually answer these questions

Each worked example shows the full mark-scheme path. Steps map to where examiners typically award method (M) and accuracy (A) marks.

Integration by parts — ∫x·sin(x) dx

Question. Find ∫ x sin(x) dx.

1. Choose u and dv/dx. Let u = x (so du/dx = 1) and dv/dx = sin(x) (so v = −cos(x)).
2. Apply ∫u(dv/dx) dx = uv − ∫v(du/dx) dx. ∫x·sin(x) dx = x·(−cos x) − ∫(−cos x)·1 dx = −x cos(x) + ∫cos(x) dx.
3. Integrate ∫cos(x) dx. ∫cos(x) dx = sin(x) + C.
4. Combine. ∫x sin(x) dx = −x cos(x) + sin(x) + C.

Answer ∫ x sin(x) dx = −x cos(x) + sin(x) + C

Examiner tip. The LIATE rule helps you pick u: Logarithm, Inverse-trig, Algebraic, Trigonometric, Exponential. Earlier in the list = better as u. Here, x (algebraic) beats sin x (trig).

Connected-particles mechanics (Paper 2)

Question. Particles A (mass 4 kg) and B (mass 2 kg) are connected by a light inextensible string passing over a smooth pulley. The system is released from rest. Find the acceleration of A and the tension in the string. Take g = 9.8 m s⁻².

1. Forces on A (heavier, descends). 4g − T = 4a ⟹ 39.2 − T = 4a.
2. Forces on B (lighter, ascends). T − 2g = 2a ⟹ T − 19.6 = 2a.
3. Add equations to eliminate T. 39.2 − 19.6 = 4a + 2a ⟹ 19.6 = 6a.
4. Solve for a. a = 19.6 / 6 ≈ 3.27 m s⁻².
5. Substitute back for T. T = 2a + 19.6 = 2(3.27) + 19.6 ≈ 26.13 N.

Answer Acceleration ≈ 3.27 m s⁻² (A descends), Tension ≈ 26.1 N

Examiner tip. The string is inextensible AND the pulley smooth — those two phrases tell you that (a) both masses share the same acceleration magnitude and (b) the tension is the same on both sides of the pulley. Always state these assumptions if asked.

Binomial hypothesis test (Paper 3)

Question. A coin is tossed 20 times. Let X be the number of heads. Test at the 5% significance level whether the coin is biased towards heads, given that X = 15 was observed.

1. State hypotheses. H₀: p = 0.5 (fair coin). H₁: p > 0.5 (biased towards heads). One-tailed test.
2. Assume H₀ true. Under H₀, X ~ B(20, 0.5).
3. Calculate P(X ≥ 15). P(X ≥ 15) = 1 − P(X ≤ 14) = 1 − 0.9793 = 0.0207 (from tables).
4. Compare with significance level. 0.0207 < 0.05.
5. Conclude. There is sufficient evidence at the 5% significance level to reject H₀. The coin appears to be biased towards heads.

Answer Reject H₀; sufficient evidence at the 5% level that the coin is biased towards heads.

Examiner tip. AQA examiners insist on the exact phrasing "sufficient/insufficient evidence at the X% level to reject H₀". A bare "yes the coin is biased" loses the conclusion mark.

Examiner-report distilled

The mistakes most candidates make

Pulled from AQA’s own examiner reports across recent series. Each one costs marks. Each one is fixable.

Mistake 1

Forgetting "+ C" on indefinite integrals.

Fix. Drill yourself: any integral without limits gets "+ C". AQA examiners deduct a mark every time.

Mistake 2

Switching radians and degrees mid-paper.

Fix. A-Level Maths is overwhelmingly in radians — work in radians by default and convert only when explicitly asked.

Mistake 3

Mixing up integration by parts as ∫u dv vs ∫u·v dx.

Fix. Memorise the formula ∫u(dv/dx) dx = uv − ∫v(du/dx) dx and recompute it on every problem.

Mistake 4

Treating a hypothesis test conclusion as "X = Y" instead of "evidence to reject H₀".

Fix. Always phrase the conclusion as "there is sufficient/insufficient evidence at the X% significance level to reject H₀" — AQA mark schemes are very specific about the wording.

Mistake 5

Dividing by sin x when solving sin x · f(x) = 0, losing the sin x = 0 solutions.

Fix. Factorise instead of dividing: sin x · f(x) = 0 means sin x = 0 OR f(x) = 0. Capture both branches.

Grade boundaries · most recent series

What it took to hit each grade

Indicative boundaries from the most recent published series. Boundaries shift slightly year to year. Open the grade-boundary calculator →

Grade	Marks	% of total
A*	234	78%
A	195	65%
B	156	52%
C	117	39%
D	78	26%
E	39	13%

Revision plan · 8 weeks to exam

An 8-week plan that actually works

A staged sequence designed by examiners, not motivational posters. Each block has a single focus and a single measurable outcome.

1

Sept–Dec (Y13)

Y12 review + new Pure (further integration, parametrics, polar/vectors). Lock down Y12 calculus while building Y13 layer.

Outcome. Strong Pure foundation by Christmas mocks.
2

Jan–Easter

Mechanics + Statistics deep dives. Hypothesis testing, projectile motion, connected particles.

Outcome. Applied topics solid; only Pure refinement remaining.
3

Easter–exam

Past papers under timed conditions (one per week minimum), examiner-report review.

Outcome. Exam-ready and aware of the trick traps your specific board uses.
4

Final 2 weeks

Targeted weakness practice based on past paper score breakdown. No new content.

Outcome. Calm, well-rested, ready.

Last reviewed 26 May 2026.

Related · explore the spec further

More on AQA A-Level Mathematics

All boards for Mathematics AQA across all subjects Grade-boundary calculator All past papers 2026 question-bank insights How to revise (study science) All revision guides AQA official →

About AQA A-Level Mathematics

AQA is the largest exam board in England, setting GCSE and A-Level exams taken by millions of students each year. Known for clear mark schemes and well-structured specifications across all major subjects.

AQA A-Level Mathematics comprises three equally-weighted papers, each worth 96 marks and lasting 2 hours, giving you a total of 192 marks across the qualification. You'll face a balanced assessment of Pure Mathematics, Statistics, and Mechanics, with AQA's distinctive approach emphasising rigorous proof and mathematical reasoning throughout. Unlike some exam boards, AQA integrates applied mathematics seamlessly within their specification, requiring you to demonstrate competence across theoretical and practical applications. Their mark schemes are renowned for clarity and consistency, rewarding method marks generously even when final answers are incorrect—a hallmark of AQA's fair assessment philosophy that benefits prepared candidates.

Topics in AQA A-Level Mathematics

1 Pure Mathematics

2 Algebra & Functions

3 Calculus

4 Trigonometry

5 Vectors

6 Statistics

7 Mechanics

8 Proof

9 Sequences & Series

10 Numerical Methods

Study Tips for AQA Mathematics

AQA weights all three papers equally at 96 marks each, so dedicate proportional revision time to Pure Mathematics, Statistics, and Mechanics. Don't over-focus on Pure—allocate roughly one-third of your time to Statistics and Mechanics combined, as many students neglect applied content and lose marks unnecessarily.

AQA's mark schemes heavily reward 'show your working' questions. Practice writing out every algebraic step, even when you could calculate mentally. This mirrors AQA's assessment style where method marks constitute 60-70% of available marks on most questions.

Familiarise yourself with AQA's specific command words: 'prove', 'show that', 'verify', and 'solve' appear frequently in their papers. AQA distinguishes rigorously between these—'prove' demands complete logical justification, whilst 'solve' permits less detailed working if you arrive at the correct answer.

Use AQA's published specimen papers and past papers from their question bank as your primary revision resource. AQA's question style is remarkably consistent year-on-year, so practising their genuine papers is more valuable than generic textbook questions for predicting what you'll encounter.

Exam Tips for AQA Mathematics

Allocate your 2-hour paper time strategically: spend roughly 25 minutes on the first 30-40 mark section, 45 minutes on the middle 50-60 mark section, and 50 minutes on the final complex questions. AQA front-loads easier marks, so securing these quickly builds confidence and leaves maximum time for challenging proof and mechanics questions.

When you encounter AQA's 'show that' questions, write your working as a continuous logical narrative rather than isolated calculations. AQA examiners expect to follow your reasoning step-by-step; unjustified leaps cost marks even if your final line is correct, because AQA prioritises demonstrating understanding over mere answers.

For AQA's Statistics and Mechanics sections, always state your probability distributions, assumptions, or force diagrams explicitly. AQA's marking scheme allocates dedicated marks for 'stating assumptions' or 'defining variables'—omitting these costs 1-2 easy marks per question, so make these statements routine practice before exam day.

Frequently Asked Questions

How many papers are in AQA A-Level Mathematics?

AQA A-Level Mathematics comprises three papers, each lasting 2 hours and worth 96 marks. Paper 1 covers Pure Mathematics only; Paper 2 covers Pure Mathematics and Statistics; Paper 3 covers Pure Mathematics and Mechanics. This structure means Pure Mathematics content appears across all three papers, whilst Statistics and Mechanics each appear on just one dedicated paper.

What topics does AQA A-Level Mathematics cover?

AQA's specification includes Pure Mathematics (proof, algebra, functions, sequences, series, trigonometry, calculus, numerical methods, and vectors), Statistics (hypothesis testing, correlation, probability distributions, sampling), and Mechanics (force, motion, energy, momentum). The specification emphasises mathematical reasoning and proof throughout, with applied contexts integrated rather than separated.

Is AQA A-Level Mathematics hard?

AQA's Mathematics is pitched at a standard comparable to other major boards, but its reputation for rigour and detailed mark schemes makes it accessible if you prepare systematically. AQA rewards method marks generously—you can achieve 70%+ by demonstrating solid technique even with occasional errors. The difficulty lies in mastering proof and mechanics reasoning, not in unfair question design.