AQA Higher Maths exam questions by topic
2,430 original practice questions across 54 modules, written by our maths tutors and organised into six free PDF practice books, one for each AQA content area. Every book includes GCSE-style mark allocations, formula and method banks, and full worked answers with marking guidance.
These are not past papers. Every question is independently written, so you can use them alongside real past papers without repeating questions you have already seen.
Free to download. No sign up, no email required. Independent resources aligned to AQA Mathematics 8300, not endorsed by or affiliated with AQA.
Which Higher topics can I practise?
All six AQA content areas at Higher tier: Number, Ratio and Proportion, Algebra, Geometry and Measures, Probability, and Statistics. Download each book free as a PDF and print what you need. Sitting Foundation instead? Use our Foundation exam questions library.
Number
Fractions and recurring decimals, factors, primes and counting, fractional indices, standard form, surds and exact values, estimation and upper and lower bounds.
Download the Number bookRatio, Proportion and Rates of Change
Sharing and changing ratios, similarity with area and volume scaling, direct and inverse proportion, reverse percentages, compound growth and decay, speed, density, pressure and gradients as rates of change.
Download the Ratio bookAlgebra
Algebraic proof and algebraic fractions, quadratic and simultaneous equations, inequalities, sequences, straight lines and circles, graphs, functions, composites, transformations and iteration.
Download the Algebra bookGeometry and Measures
Congruence, constructions and loci, circle theorems and geometric proof, sectors and frustums, Pythagoras and trigonometry including 3D problems, the sine and cosine rules, bearings, and vectors.
Download the Geometry bookProbability
Relative frequency and expectation, the product rule for counting, Venn diagrams and set notation, frequency trees, independent and dependent events, sampling without replacement and conditional probability.
Download the Probability bookStatistics
Sampling and bias, quartiles and outliers, grouped data and estimated means, time series, cumulative frequency and box plots, histograms and frequency density, scatter graphs and comparing distributions.
Download the Statistics bookHow is each book organised?
Every module follows the same four-stage sequence, moving from fluency to exam conditions to grade 7 to 9 reasoning. Answers, formulas and worked methods are collected at the end of each book, so students can mark their own work the way an examiner would.
The four stages in every module
- Fluency Check: 8 short questions confirming the prerequisites are accurate before the demand rises
- Standard Higher: 12 questions applying each skill at Higher tier, with the governing rule and exact working shown
- Multi-step Higher: 15 original exam-style questions connecting several stages, using GCSE-style contexts and mark allocations
- Grade 7 to 9 Challenge: 10 extended reasoning problems, including proof, targeting the marks that separate the top grades
What else is inside
- a formula and method bank for every module, stating when to use each method
- full answers and worked methods at the end of each book, with method marks credited only when the setup is shown
- AQA specification references on every module, from N1 to S6
- a contents and study plan page with score boxes, so weak modules get flagged for a second attempt
- an error-coding routine covering knowledge, method, arithmetic, reading, calculator and presentation errors, with a retest step after 2 to 7 days
- exact values expected throughout: fractions, surds and powers stay exact unless a question requests rounding
What do the 54 modules cover?
Each book numbers its modules from 1, and every module states its AQA specification references, so you can cross-check coverage against the syllabus or a school scheme of work.
| Book | Modules | Questions | AQA specification references |
|---|---|---|---|
| Number | 1 to 7 | 315 | N1 to N16 |
| Ratio, Proportion and Rates of Change | 1 to 7 | 315 | R1 to R16 |
| Algebra | 1 to 10 | 450 | A1 to A25 |
| Geometry and Measures | 1 to 10 | 450 | G1 to G25 |
| Probability | 1 to 10 | 450 | P1 to P9 |
| Statistics | 1 to 10 | 450 | S1 to S6 |
The questions were written against the AQA 8300 Higher specification and the recurring structures in the seven publicly available summer series, 2017, 2018, 2019, 2022, 2023, 2024 and 2025, across Papers 1H, 2H and 3H, without copying wording or values. Summer exams were cancelled in 2020 and 2021.
How should a student use these?
Work one module at a time in the four-stage order, mark against the worked answers, code each error, and retest anything weak after 2 to 7 days. Paper 1 is non-calculator, so practise some modules without one and keep values exact.
If the exam is months away
Follow each book in order, one or two modules a week. The retest step is the point: a correction only counts as secure when it can be reproduced from a blank page a few days later, without support.
If the exam is weeks away
Skip to the Multi-step Higher and Grade 7 to 9 Challenge sections of your weakest topics. Algebra carries the heaviest topic weighting on Higher papers, so prioritise the Algebra book if time is short.
If you are aiming for grade 8 or 9
Start each module at the Grade 7 to 9 Challenge to find your ceiling fast, then drop back only where marks are lost. The proof questions matter most: they are where top-grade candidates are separated.
Guide: revising GCSE Maths
How to structure Maths revision so practice actually moves the grade, rather than re-reading notes.
Read the revision guideGuide: official past papers
Where to find the real AQA past papers and mark schemes to sit alongside these books.
Find past papersGuide: last-minute revision
What to do with the final weeks when there is no time left to cover everything.
Read the last-minute guidePractice book questions
The short version: the books are free for personal use, they include full worked answers, and they are written for the AQA Higher tier, grades 4 to 9.
Are these real AQA past paper questions?
No. Every question is original and independently written. The authors reviewed the AQA 8300 Higher specification and the seven publicly available summer series, 2017, 2018, 2019, 2022, 2023, 2024 and 2025, to match the recurring question structures, contexts and mark demands, without copying wording or values. That means you can use these books and official past papers together without overlap.
Do the books include answers?
Yes. Every book collects full answers, formulas and worked methods at the end, and the marking guidance credits a method only when its mathematical setup is shown, mirroring how real Higher papers are marked. Students also code each error as knowledge, method, arithmetic, reading, calculator or presentation, to see what actually keeps going wrong.
Are they free? What is the licence?
The Free Website Edition is free for personal and household educational use. Tutors and schools must obtain the appropriate licence before copying for learners, and resale, paid redistribution and third-party uploading are prohibited.
Do they cover grade 8 and 9 content?
Yes. Every module ends with a Grade 7 to 9 Challenge section of extended reasoning problems, and the Higher-only material is all here: surds, algebraic proof, functions and iteration, circle theorems, vectors, 3D trigonometry, histograms and conditional probability among it.
How are these different from your Foundation books?
The Foundation books cover grades 1 to 5 with 1,440 questions across 32 modules. The Higher books rebuild every content area for grades 4 to 9, with 2,430 questions across 54 modules, a heavier weighting toward multi-step and proof questions, and exact-value working expected throughout. If a student is sitting Foundation, use the Foundation library instead.
Is there a non-calculator paper I should practise for?
Yes. AQA Higher is assessed by three papers of equal weight and paper 1 is non-calculator. Practise at least some of each module without a calculator, keeping fractions, surds and powers exact rather than reaching for a decimal.
My child keeps scoring low on the same module. What next?
Repeating the same questions rarely fixes it, because the problem is usually the method rather than the practice. If a module scores low after two honest attempts, that is the point to get the method retaught, whether by a teacher at school or a tutor. Fifteen of our tutors teach GCSE Maths and the first 30 minutes are free.
Practice finds the gaps. A tutor closes them
Fifteen of our tutors teach GCSE Maths, including three qualified teachers. Lessons are one to one on Zoom, £30 each with no premium for Higher tier, and the first 30 minutes are free with no card details. If a module keeps scoring low after two attempts, that is usually the sign to get help with the method rather than repeat the questions.