OCR Higher Maths exam questions by topic
Six free PDF books of original exam-style questions for OCR Higher, 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 7 to 9 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 Higher 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 Higher topics can I practise?
All six content areas at Higher 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 Foundation instead? Use our OCR Foundation exam questions.
Number
Indices and fractional powers, surds and exact values, standard form, recurring decimals, limits of accuracy and error intervals, repeated and reverse percentage change, the product rule for counting, and number reasoning.
Download the Number bookAlgebra
Quadratic expansion, factorisation and equations, completing the square, inequalities, simultaneous equations, algebraic fractions, functions and iteration, sequences, straight lines and non-linear graphs, and proof.
Download the Algebra bookRatio, Proportion and Rates of Change
Changing ratios, direct and inverse proportion with constants, similarity with area and volume scale factors, compound growth and decay, reverse percentages, speed, density and pressure, and rates of change on graphs.
Download the Ratio bookGeometry and Measures
Congruence and similarity, constructions and loci, circle theorems and proof, arcs, sectors and frustums, Pythagoras and trigonometry in two and three dimensions, the sine and cosine rules, bearings, transformations 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, tree diagrams with and 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 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 7 to 9 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, with exact values expected until a question asks for rounding
- the full Higher content, so grade 8 and 9 material is practised under the same chapter structure as the rest
- 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 | TBC | TBC |
| 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 Higher specification and the recurring assessment demands of the Higher 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 7 to 9 questions, and they show quickly whether a topic is secure or whether it needs the method retaught.
If you are aiming for grade 8 or 9
Start each chapter at question 9 to find your ceiling fast, then work back only where marks are lost. Treat the working on 5-mark questions as the point of the exercise: OCR Higher rewards a justified method, not a number that happens to be right.
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 Higher tier, grades 4 to 9.
Are these real OCR past paper questions?
No. Every question is original and independently written. The authors used the OCR J560 Higher specification and the recurring demands of the Higher 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.
Do they cover grade 8 and 9 content?
Yes. Questions 9 to 12 of every chapter are the grade 7 to 9 reasoning questions, and the Higher-only material is all here: surds, fractional and negative indices, algebraic proof, functions and iteration, circle theorems, vectors, 3D trigonometry, histograms and conditional probability among it.
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 with no premium for Higher tier, 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.