OCR Higher Maths lesson notebooks by topic
Nine free PDF notebooks that teach every OCR Higher topic from scratch, one notebook for each content area of the J560 specification. Each chapter explains the idea, shows the method with worked examples, connects it to real contexts and common mistakes, then sets independent practice with answers and method cues at the back.
These are teaching resources, not question banks. Use them when a topic has never clicked, or when a student needs the method explained again before more practice will help. When the method is secure, move on to our OCR Higher exam questions.
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 learn?
All nine OCR content areas at Higher tier, in specification order: Number, Ratio, Proportion and Rates of Change, Algebra, Graphs, Basic Geometry, Congruence and Similarity, Mensuration, Probability, and Statistics. Download each notebook free as a PDF and print what you need. Sitting Foundation instead? Use our OCR Foundation lesson notebooks.
Number
Fractional and negative indices, surds and rationalising denominators, standard form calculations, recurring decimals as fractions, the product rule for counting, and upper and lower bounds with error intervals.
Download the Number notebookRatio, Proportion and Rates of Change
Ratio with algebra, compound measures, repeated and reverse percentage change, direct and inverse proportion equations and graphs, exponential growth and decay, and gradients as rates of change.
Download the Ratio notebookAlgebra
Quadratics by factorising, the formula and completing the square, simultaneous linear and quadratic equations, inequalities, algebraic fractions, functions and inverses, iteration, quadratic and geometric sequences, and algebraic proof.
Download the Algebra notebookGraphs
Parallel and perpendicular lines, quadratic, cubic, reciprocal, exponential and trigonometric graphs, transformations of graphs, the equation of a circle and its tangents, and gradients and areas under curves.
Download the Graphs notebookBasic Geometry
Angle reasoning and geometric proof, circle theorems, constructions and loci, bearings, negative and fractional enlargement, and combinations of transformations.
Download the Geometry notebookCongruence and Similarity
Congruence proofs, similarity in length, area and volume, Pythagoras and trigonometry in two and three dimensions, the sine and cosine rules, the area of a triangle, and vector geometry proofs.
Download the Congruence notebookMensuration
Arcs, sectors and segments, volume and surface area of pyramids, cones, spheres and frustums, compound solids, and converting between units of area and volume.
Download the Mensuration notebookProbability
Set notation and Venn diagrams, tree diagrams with and without replacement, conditional probability, independent and mutually exclusive events, and probability from tables and algebra.
Download the Probability notebookStatistics
Sampling methods and bias, cumulative frequency and box plots, histograms with unequal class widths, quartiles and interquartile range, scatter graphs and interpretation, and comparing distributions.
Download the Statistics notebookHow is each chapter organised?
Every chapter runs to exactly four pages in the same order, so a student always knows what comes next: understand the idea, learn the method, apply and reason, then practise independently. Meaning comes first, method second and practice third. Answers with method cues are collected at the end of each notebook.
The four pages in every chapter
- Understand the idea: key vocabulary, an original diagram, why the method works, and a check question before moving on
- Method and examples: a reliable method stated in one or two lines, two fully worked examples, and a self-check question
- Apply and reason: where the maths appears in real life, three common misconceptions and how to repair them, a guided try, a reasoning prompt and exam communication tips
- Independent practice: 8 questions with mark allocations and a reflection line, secure, almost or reteach, with answers and method cues at the back
What else is inside
- a five-pass routine on every notebook: read, cover and reproduce, practise, mark and repair, retest after 2 to 7 days
- a specification coverage map giving the OCR J560 reference for every chapter, so coverage can be checked against a school scheme of work
- a fast-reference method bank at the front of each notebook, stating the key relationships in one line each
- an error-labelling routine, so a student can tell a concept error from an arithmetic, calculator-entry, accuracy, unit or interpretation error and fix the right thing
- practice answers with a method cue for every question, so a wrong answer can be repaired rather than copied
- Higher-assessable content only, including every Higher-only topic, with the reasoning and proof demands of the top grades built in
- an editorial sign-off page in every notebook stating what was checked before release
What do the nine notebooks cover?
The notebooks follow the twelve content sections of the OCR J560 specification, with sections 1 to 4 combined in the Number notebook and one notebook for each of sections 5 to 12. Every chapter states its OCR reference, so you can cross-check coverage against the specification.
| Notebook | Unit | Chapters | OCR J560 content |
|---|---|---|---|
| Number | 1 | TBC | Sections 1 to 4 |
| Ratio, Proportion and Rates of Change | 2 | TBC | Section 5 |
| Algebra | 3 | TBC | Section 6 |
| Graphs | 4 | TBC | Section 7 |
| Basic Geometry | 5 | TBC | Section 8 |
| Congruence and Similarity | 6 | TBC | Section 9 |
| Mensuration | 7 | TBC | Section 10 |
| Probability | 8 | TBC | Section 11 |
| Statistics | 9 | TBC | Section 12 |
The notebooks are organised around the skills represented by the OCR J560 content references. Every explanation, example, question, diagram and solution is independently written, and the notebooks do not reproduce OCR question papers, mark schemes, examiner reports, textbook pages or specification text. Specification references identify curriculum alignment only. For the official specification and assessment rules, use the OCR website directly.
How should a student use these?
Work one chapter at a time, all four pages in order, and do the retest a few days later before calling a topic secure. 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 notebooks in order, two or three chapters a week. The retest step is the point: a topic only counts as learned when the method can be reproduced from a blank page a few days later, without looking at the examples.
If the exam is weeks away
Go straight to the chapters for your weakest topics and read only the first two pages, the idea and the method, then attempt the independent practice. Anything under about six out of eight goes on a retest list for the following week.
If you are aiming for grade 8 or 9
Treat the reasoning prompt on every apply and reason page as compulsory, and write the explanation out in full. OCR Higher rewards a justified conclusion, not just a correct number, and that habit is built here rather than in the exam.
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 guideLesson notebook questions
The short version: the notebooks are free for personal use, they teach each topic from scratch with answers included, and they are written for the OCR Higher tier, grades 4 to 9.
Are these OCR textbook pages or past paper questions?
No. Every explanation, example, question, diagram and solution is original and independently written. The notebooks are organised around the OCR J560 content references and do not reproduce OCR question papers, mark schemes, examiner reports, textbook pages or specification text, so they can be used alongside official past papers without overlap.
How is a lesson notebook different from an exam questions book?
They do different jobs. A lesson notebook teaches the topic: what the idea means, why the method works, how it appears in real life and where students go wrong, with a short practice set. The OCR Higher exam questions assume the method has been taught and exist to practise it under exam-style demand. Use a notebook first when a topic is new or has never made sense.
Do the notebooks include answers?
Yes. Every notebook collects the practice answers at the end with a method cue for each question, so a student can see which step went wrong and repair it rather than copy the final value. The check questions, guided tries and reasoning prompts inside each chapter are answered by the worked examples on the same page or the one before it.
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. The notebooks are written for the OCR J560 Higher tier, grades 4 to 9, and every Higher-only topic is included: surds, fractional and negative indices, quadratics by completing the square, functions and iteration, circle theorems, the sine and cosine rules, vectors, histograms and conditional probability among them. Each chapter ends with a reasoning prompt that asks for the justification the top grades require.
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, keeping fractions, powers and π exact rather than reaching for a decimal. 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.