OCR Foundation Maths exam questions by topic
Six free PDF books of original exam-style questions for OCR Foundation, one for each content area, written by our maths tutors. Every chapter has 12 curated questions that climb from 1-mark fluency to 5-mark grade 4 to 5 reasoning, with complete worked solutions and a completion record so a student can track what needs a second attempt.
These are not past papers. Every question is independently written, so you can use these books alongside real OCR past papers without repeating questions you have already seen. If a topic has never been taught properly, start with our OCR Foundation lesson notebooks and come back here to practise.
Free to download. No sign up, no email required. Independent resources aligned to OCR GCSE (9-1) Mathematics J560, not produced, approved or endorsed by OCR or Cambridge University Press & Assessment.
Which Foundation topics can I practise?
All six content areas at Foundation tier, in the order Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measures, Probability, and Statistics. Download each book free as a PDF and print what you need. Sitting Higher instead? Use our OCR Higher exam questions.
Number
Place value and ordering, four operations and directed numbers, order of operations, factors, multiples and primes, prime factors, powers and roots, fractions, decimals and percentages, calculator methods, standard form, and rounding, estimation and bounds.
Download the Number bookAlgebra
Notation and simplifying, expanding and factorising, substitution and formulae, linear equations and inequalities, sequences and the nth term, simultaneous equations and simple quadratics.
Download the Algebra bookRatio, Proportion and Rates of Change
Simplifying and sharing ratios, unit and currency conversion, scale drawings, percentage change and reverse percentages, direct and inverse proportion, speed, density and pressure, and compound interest.
Download the Ratio bookGeometry and Measures
Angles and polygons, constructions, loci and bearings, transformations, congruence and similarity, perimeter, area and circles, volume and surface area, Pythagoras, trigonometry and vectors.
Download the Geometry bookProbability
The probability scale, listing outcomes and sample spaces, frequency trees, Venn diagrams, relative frequency and expectation, and tree diagrams for combined events.
Download the Probability bookStatistics
Data collection and sampling, tables, bar charts and pictograms, pie charts, averages and spread, grouped frequency tables, scatter graphs and time series.
Download the Statistics bookHow is each book organised?
Every chapter follows the same pattern: a focus page stating what the chapter covers and how the demand rises, 12 curated questions marked from 1 to 5, complete worked solutions with a marking note, and a completion record. Chapters are curated rather than padded: each one prioritises distinct tasks, accurate tier boundaries and visible reasoning.
The four parts of every chapter
- Chapter focus: one line stating the skills covered, and an assessment progression note explaining how questions 1 to 12 build in demand
- Questions 1 to 4: secure fluency, 1 or 2 marks each, confirming the basic procedure is accurate before the demand rises
- Questions 5 to 8: connected methods, 2 marks each, applying the skill in a short context or a two-step calculation, then questions 9 to 12: grade 4 to 5 reasoning, 3 to 5 marks, with working required on every 5-mark question
- Worked solutions and a completion record: every question is solved in full with a marking note, then a table records the score, a repair target and a retest date for each of the 12 questions
What else is inside
- a contents page and publication statement at the front of every book, listing every chapter
- GCSE-style mark allocations on every question, stated as an independent teaching allocation rather than an official OCR mark scheme
- worked solutions for every question, directly after each chapter, with a marking note stating what earns the method marks and what the final mark is reserved for
- a completion record per chapter with a score box, repair target and retest date for each question
- You must show your working printed on every 5-mark question, matching how the real papers are worded
- Foundation-tier content only, so a student is never practising material that will not be examined
- a rights notice on every completion record, so the licence terms travel with any page that gets printed
What do the six books cover?
Each book is divided into chapters of 12 questions, and every chapter opens with a focus line stating the skills it covers, so you can cross-check coverage against the OCR J560 specification or a school scheme of work.
| Book | Unit | Chapters | Questions |
|---|---|---|---|
| Number | 1 | 16 | 192 |
| Algebra | 2 | TBC | TBC |
| Ratio, Proportion and Rates of Change | 3 | TBC | TBC |
| Geometry and Measures | 4 | TBC | TBC |
| Probability | 5 | TBC | TBC |
| Statistics | 6 | TBC | TBC |
The questions were written against the OCR J560 Foundation specification and the recurring assessment demands of the Foundation papers, without reproducing any past-paper wording, diagrams or numerical data. Specification references identify curriculum alignment only; every question, solution and marking note is independently authored. Marks indicate an independent teaching allocation, not an official OCR mark scheme.
How should a student use these?
Work one chapter at a time, all 12 questions in order, mark against the worked solutions, and fill in the completion record honestly. Anything under about 70 percent goes back on the list for a retest a week later. OCR GCSE Maths is assessed by three papers at each tier and one of them is sat without a calculator, so practise some chapters without one. Assessment arrangements and the OCR formula sheet can change, so check the current details on the OCR website.
If the exam is months away
Follow the books in order, two or three chapters a week. Use the completion record as it is designed: a repair target for each wrong question and a retest date, so the same mistake is not made twice.
If the exam is weeks away
Skip to questions 9 to 12 of each chapter in your weakest topics. Those are the grade 4 to 5 questions, and they show quickly whether a topic is secure or whether it needs the method retaught. Number and Ratio carry heavy weight on Foundation papers, so prioritise those two books if time is short.
If you are resitting
Start with questions 9 to 12 to find gaps fast, then drop back to questions 1 to 8 only where you lose marks. Our resit tutoring page covers November entry and one to one support.
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 OCR 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 guideExam question book questions
The short version: the books are free for personal use, they include complete worked solutions, and they are written for the OCR Foundation tier, grades 1 to 5.
Are these real OCR past paper questions?
No. Every question is original and independently written. The authors used the OCR J560 Foundation specification and the recurring demands of the Foundation papers to decide coverage and mark weighting, without reproducing any past-paper wording, diagrams or numerical data. That means you can use these books and official past papers together without overlap.
What does curated mean?
Each chapter has been edited down to 12 distinct tasks rather than a long list of near-identical drills. The 12 questions are chosen so that questions 1 to 4 confirm fluency, 5 to 8 connect methods, and 9 to 12 demand the reasoning the top grades of the tier require, with the marks rising from 1 to 5 as the demand rises.
Do the books include answers?
Yes. Every chapter is followed by complete worked solutions, and each solution carries a marking note stating that a correct method and accurate progress earn credit while the final mark is reserved for the required answer, justification or conclusion. That mirrors how real papers are marked and shows where partial credit is earned even when the final answer is 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.
Are they only for Foundation tier?
They are written for the OCR J560 Foundation tier, grades 1 to 5. Much of the material overlaps with AQA and Edexcel Foundation because the national curriculum content is shared, but the chapter structure follows OCR. We also publish separate AQA and Edexcel practice books in our resources library.
Is there a non-calculator paper I should practise for?
Yes. OCR GCSE Maths is assessed by three papers at each tier and one of them is sat without a calculator, so practise at least some chapters without one, especially in Number and Ratio. Assessment arrangements and the OCR formula sheet can change, so check the current details on the OCR website.
My child keeps scoring low on the same chapter. What next?
Repeating the same questions rarely fixes it, because the problem is usually the method rather than the practice. If a chapter 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, and the first 30 minutes are free with no card details. If a chapter keeps scoring low after two attempts, that is usually the sign to get help with the method rather than repeat the questions.