Number
15–20% of totalPlace value, integers, fractions, decimals, percentages, surds, indices, standard form, rounding & estimation, error intervals.
- Surds simplification
- Standard form arithmetic
- Reverse percentages
- Bounds calculations
AQA GCSE
AQA GCSE Mathematics past papers, mark schemes & revision
Every AQA GCSE Mathematics past paper, mark scheme, examiner report, topic breakdown, worked example, and revision plan — all on one page.
Specification · 8300
What you’ll sit
You will sit three papers, each 1 hour 30 minutes and worth 80 marks. Paper 1 is non-calculator — every question is solvable without one, but expect to manipulate fractions, percentages, surds, and standard form by hand. Papers 2 and 3 are calculator-allowed, with longer multi-step questions on geometry, statistics, and ratio/proportion. You sit either the Higher tier (grades 4–9, all topics) or the Foundation tier (grades 1–5, narrower topic list with more accessible questions). Schools enter you based on your year-10 mock data. The papers are typically sat in May and June, with results released in late August.
Paper structure
Three papers · 80 marks each · 1h 30m each · Paper 1 non-calculator, Papers 2 & 3 calculator allowed · Available at Higher (grades 4-9) and Foundation (grades 1-5) tiers
Awarded by
Assessment and Qualifications Alliance. Exam code 8300. Specification page: AQA GCSE Mathematics.
Past papers · AQA GCSE Mathematics
Every paper, every year, with mark schemes
Below is the official series of AQA GCSE 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 | Download |
|---|---|---|---|---|---|
| 2024 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 1 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 2 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Foundation | 1h 30m | 80 | AQA hub → | |
| 2023 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 1 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 2 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Foundation | 1h 30m | 80 | AQA hub → | |
| 2022 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 1 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 2 | Foundation | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Foundation | 1h 30m | 80 | AQA hub → | |
| 2021 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → | |
| 2020 | — | — | — | — | AQA hub → |
| 2019 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → | |
| 2018 | Paper 1 | Higher | 1h 30m | 80 | AQA hub → |
| Paper 2 | Higher | 1h 30m | 80 | AQA hub → | |
| Paper 3 | Higher | 1h 30m | 80 | AQA hub → |
Topics · full specification
Every topic in the AQA GCSE 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.
Algebra
25–30% of totalExpressions, equations, inequalities, sequences (linear, quadratic, geometric, Fibonacci), graphs of linear & quadratic & cubic & exponential functions, simultaneous equations, completing the square, function notation.
- Quadratic formula
- Completing the square
- Solving by factorisation
- Solving simultaneous linear-quadratic
- Drawing & interpreting cubic graphs
Ratio, proportion & rates of change
15–20% of totalDirect & inverse proportion, compound measures (speed, density, pressure), best-buy problems, percentage change & growth/decay, exchange rates, gradient as rate.
- Setting up proportionality equations (y = kx, y = k/x)
- Multi-stage percentage compound change
- Density & pressure word problems
Geometry & measures
20–25% of totalProperties of shapes, angles in parallel lines, polygons, circle theorems, congruence & similarity, area & volume, transformations (translation, rotation, reflection, enlargement), Pythagoras, trigonometry (SOHCAHTOA & sine/cosine rules), vectors.
- Sine rule / cosine rule
- Circle theorems (alternate segment, tangent-radius, cyclic quadrilateral)
- Vector geometry proofs
- 3D Pythagoras and trigonometry
Probability
5–10% of totalListing outcomes, probability scales, mutually exclusive events, tree diagrams, Venn diagrams, conditional probability (Higher only), expected frequency, relative frequency vs theoretical.
- Tree diagrams with replacement / without replacement
- Venn diagrams with set notation (A∩B, A∪B, A')
- Conditional probability via tree diagrams
Statistics
5–10% of totalAverages (mean, median, mode), spread (range, IQR), data representation (pie charts, bar charts, frequency tables, histograms, cumulative-frequency curves, box plots), correlation & line of best fit, scatter graphs, sampling.
- Estimated mean from grouped data
- Reading cumulative frequency curves
- Histograms with frequency density
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 Higher: 40% · Foundation: 50%
Use and apply standard techniques
Recall facts and procedures, use mathematical notation, perform routine procedures (e.g. arithmetic, algebraic manipulation, solving standard equations).
AO2 Higher: 30% · Foundation: 25%
Reason, interpret and communicate mathematically
Make deductions and inferences, explain steps in a solution, interpret diagrams and information, present arguments clearly.
AO3 Higher: 30% · Foundation: 25%
Solve problems within mathematics and in other contexts
Translate problems into mathematical processes, interpret results in context, evaluate methods, identify assumptions.
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.
Solving a quadratic by completing the square (Higher)
Question. Solve x² − 6x + 2 = 0 by completing the square. Give your answer in surd form.
- 1. Half the coefficient of x. Half of −6 is −3. Square it: 9.
- 2. Rewrite the quadratic. x² − 6x + 2 = (x − 3)² − 9 + 2 = (x − 3)² − 7.
- 3. Set equal to zero and isolate. (x − 3)² − 7 = 0 ⟹ (x − 3)² = 7.
- 4. Take the square root. x − 3 = ±√7.
- 5. Solve for x. x = 3 + √7 or x = 3 − √7.
Answer x = 3 ± √7
Examiner tip. AQA mark schemes award an "M1" mark for correctly identifying the half-coefficient step and an "A1" for the surd form — don't convert to decimals.
Conditional probability via a tree diagram (Higher)
Question. A bag contains 5 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability that exactly one is red?
- 1. Identify the two outcomes. Exactly one red = (Red then Blue) OR (Blue then Red).
- 2. Probability of Red then Blue. P(R) × P(B | R) = 5/8 × 3/7 = 15/56.
- 3. Probability of Blue then Red. P(B) × P(R | B) = 3/8 × 5/7 = 15/56.
- 4. Add (mutually exclusive). 15/56 + 15/56 = 30/56 = 15/28.
Answer P(exactly one red) = 15/28
Examiner tip. Always check whether you should add or multiply: "and" means multiply along a branch, "or" means add between branches. Reduce fractions to lowest terms for the final mark.
Volume of a frustum (Higher)
Question. A cone of base radius 6 cm and height 12 cm has its top cut off parallel to the base at half its height. Find the volume of the frustum that remains. Leave your answer in terms of π.
- 1. Volume of original cone. V = ⅓πr²h = ⅓π × 36 × 12 = 144π cm³.
- 2. Find dimensions of the cone that was cut off. It is similar to the original with linear scale factor ½, so its radius is 3 cm and height is 6 cm.
- 3. Volume of the cut-off cone. V = ⅓π × 9 × 6 = 18π cm³.
- 4. Subtract. 144π − 18π = 126π cm³.
Answer Volume of frustum = 126π cm³
Examiner tip. The trap here is using the scale factor on the volume directly (½ of 144π) — but volume scales by the cube of the linear factor (½³ = ⅛). Either use the cube scaling or compute both cone volumes separately.
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 to rationalise denominators when simplifying surds (e.g. leaving 1/√2 instead of √2/2).
Fix. After every surd division, multiply numerator and denominator by the denominator surd.
Mistake 2
Using degrees instead of radians (or vice-versa) on calculator-allowed papers.
Fix. GCSE Maths uses degrees only — set your calculator to DEG mode before walking into the exam, every time.
Mistake 3
Solving 3x² = 27 by dividing by 3 first and getting x = ±3 only, missing x = ±√9 = ±3 correctly but assuming linear.
Fix. Always check whether an equation is quadratic before manipulating — quadratics give two solutions, equations of higher degree give more.
Mistake 4
Treating compound percentage decay as simple percentage decay over multiple years.
Fix. For "depreciates by 12% per year for 3 years" use multiplier × 0.88³, not subtract 36%.
Mistake 5
Drawing a tree diagram and forgetting that "without replacement" changes the denominator of the second pick.
Fix. Write the new totals on each branch as you draw it — don't do it in your head.
Mistake 6
Using the cosine rule when the sine rule is faster, and getting bogged down in arithmetic.
Fix. If you have two angles and a side (or two sides and an opposite angle), use the sine rule. Reach for cosine only when you have three sides or two sides + included angle.
Formulae · memorise or know-where-to-find
Key formulae for AQA GCSE Mathematics
Some are on the equation sheet; some are not. Highlighted ones are the ones examiners report as most often forgotten in exam pressure.
| Name | Expression | When to use |
|---|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | Solving any quadratic ax² + bx + c = 0 that doesn't factor neatly. |
| Pythagoras' theorem | a² + b² = c² | Finding the third side of a right-angled triangle. |
| Sine rule | a / sin A = b / sin B = c / sin C | Non-right triangle: have two angles + one side, or two sides + non-included angle. |
| Cosine rule | a² = b² + c² − 2bc·cos A | Non-right triangle: have three sides (to find an angle) or two sides + included angle (to find third side). |
| Area of triangle (non-right) | Area = ½ab·sin C | When you have two sides and the included angle. |
| Volume of cone | V = ⅓πr²h | Cone or frustum problems. |
| Volume of sphere | V = ⁴⁄₃πr³ | Anywhere a sphere appears (radius given). |
| Compound interest | A = P(1 + r/100)ⁿ | Multi-year percentage growth / decay (use r negative for decay). |
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 →
| Tier | Grade | Marks | % of total |
|---|---|---|---|
| Higher | 9 | 198 | 82.5% |
| Higher | 7 | 138 | 57.5% |
| Higher | 4 | 50 | 20.8% |
| Foundation | 5 | 156 | 65% |
| Foundation | 4 | 124 | 51.7% |
| Foundation | 1 | 22 | 9.2% |
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
Weeks 8–6 before paper 1
Number + Algebra fundamentals — surds, indices, standard form, expanding & factorising, solving linear & quadratic.
Outcome. Confidence on the first 60% of Paper 1 marks.
- 2
Weeks 6–4
Geometry + Trigonometry — angles, Pythagoras, SOHCAHTOA, sine/cosine rules, 3D problems.
Outcome. Comfortable with any triangle-based question.
- 3
Weeks 4–2
Statistics + Probability — tree diagrams, Venn diagrams, cumulative frequency, histograms.
Outcome. Solid on the predictable stats topics across Papers 2 and 3.
- 4
Final 2 weeks
Past papers under timed conditions, one per session, marked and corrected the same day.
Outcome. Exam-ready: knows the question style, pacing, and own weak spots.
Last reviewed 26 May 2026.
Related · explore the spec further
More on AQA GCSE Mathematics
About AQA GCSE 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 GCSE Mathematics comprises three papers, each worth 96 marks and lasting 1 hour 30 minutes, totalling 288 marks across the qualification. You'll sit Paper 1 (non-calculator), Paper 2 (calculator), and Paper 3 (calculator), with all papers containing a mix of question types from straightforward procedural questions to multi-step problem-solving tasks. AQA's specification is known for its clarity and logical progression through Number, Algebra, Ratio & Proportion, Geometry & Measures, Probability, Statistics, Trigonometry, Graphs, Sequences, and Vectors. Their mark schemes reward method marks generously, meaning you can earn significant credit even if your final answer is incorrect, provided your working demonstrates mathematical reasoning. This approach makes AQA particularly accessible for students who show their working clearly.
Topics in AQA GCSE Mathematics
1 Number
2 Algebra
3 Ratio & Proportion
4 Geometry & Measures
5 Probability
6 Statistics
7 Trigonometry
8 Graphs
9 Sequences
10 Vectors
Study Tips for AQA Mathematics
1
Familiarise yourself with AQA's three-paper structure by practising papers under timed conditions. Since Papers 2 and 3 allow calculators while Paper 1 doesn't, dedicate specific revision sessions to non-calculator techniques like mental arithmetic, fraction manipulation, and algebraic simplification to build confidence without technology.
2
Use AQA's detailed mark schemes during revision—they explicitly show how marks are allocated for method and accuracy. When you attempt past papers, mark them using AQA's scheme to understand their marking philosophy; this reveals that showing working is crucial since method marks can constitute 60-70% of total marks on complex questions.
3
Study AQA's command word usage across their papers. Terms like 'show that', 'explain', 'prove', and 'find' appear frequently and require different response types. AQA's 'show that' questions especially demand rigorous working, so practise presenting mathematical arguments clearly and concisely as AQA examiners expect.
4
Organise your revision around AQA's specification topic blocks rather than mixing topics randomly. AQA groups related content logically, so revising Algebra comprehensively before moving to Graphs helps you see connections. Use AQA's published specification document as your roadmap to ensure you cover all content weightings accurately.
Exam Tips for AQA Mathematics
1
In Paper 1 (non-calculator), allocate extra time to questions worth 4-5 marks as these typically require multi-step solutions without calculator support. AQA's mark allocation means a 5-mark question might need three separate calculations; write out each step clearly to capture all method marks even if you make a computational error mid-question.
2
Manage your time across all three papers by spending roughly 3 minutes per mark available. Since each AQA paper is 96 marks across 90 minutes, this gives you approximately 1 minute 52 seconds per mark. Prioritise questions you find straightforward to secure baseline marks, then return to challenging questions where AQA's generous method marking can still earn you credit.
3
Pay close attention to AQA's question phrasing—they frequently use 'justify your answer' and 'explain your reasoning' which require you to demonstrate understanding beyond calculation. These questions often carry higher marks on AQA papers, so invest time in writing brief explanations rather than rushing through to the next question.
Frequently Asked Questions
How many papers are in AQA GCSE Mathematics?
AQA GCSE Mathematics consists of three equally-weighted papers. Paper 1 is non-calculator (1 hour 30 minutes, 96 marks), while Papers 2 and 3 are calculator papers (each 1 hour 30 minutes, 96 marks each). Total assessment is 288 marks, with your final grade determined by combined performance across all three papers.
What topics does AQA GCSE Mathematics cover?
AQA's Mathematics specification encompasses ten main topic areas: Number (including integers, decimals, fractions, percentages, powers, roots), Algebra (expressions, equations, inequalities, sequences), Ratio & Proportion, Geometry & Measures (angles, polygons, circles, 3D shapes, transformations), Probability, Statistics (data collection, averages, distributions), Trigonometry, Graphs (linear, quadratic, cubic, reciprocal functions), Sequences (arithmetic and geometric), and Vectors. Each topic appears across all three papers.
Is AQA GCSE Mathematics hard?
AQA's Mathematics papers are considered moderately challenging but fair. The difficulty lies not in obscure content but in requiring deep understanding and multi-step problem-solving. However, AQA's marking approach is student-friendly—method marks are awarded generously, so you can earn substantial credit for demonstrating correct mathematical reasoning even with arithmetic errors. This accessibility through clear mark schemes makes AQA popular among schools.
AQA GCSE Mathematics Study Guides
GCSE Maths Algebra: From Basics to Complex Problem Solving
Complete GCSE Maths algebra revision from simplifying expressions to solving quadratics. Clear worked examples and practice questions for every topic.
GCSE Maths Geometry and Measures: Essential Revision Guide
Master GCSE Maths geometry and measures. Cover angles, shapes, transformations, and trigonometry with clear explanations and worked examples.
GCSE Maths Number: Fractions, Percentages, and Ratios Guide
Master GCSE Maths Number topics including fractions, percentages, ratios, and standard form. Clear explanations with worked examples at every level.
GCSE Maths Statistics and Probability: Complete Revision Guide
Master GCSE Maths statistics and probability. Cover averages, charts, probability trees, and Venn diagrams with clear worked examples for your exam.
Useful Resources
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