OCR GCSE Mathematics (J560): complete guide to Number, Algebra, Ratio, Geometry, Probability and Statistics and the exams

OCR GCSE Mathematics (specification J560) is a single linear course assessed by three written papers sat at the end of the course. There is no coursework. This page is the index: below is a map of the six content areas, the tier structure, the exam papers, the formulae sheet, the assessment objectives, and how to study each area, with a direct link to every dot point.

The six content areas

The specification is organised into six areas, each with its own reference letter. Number and Algebra are the foundation that everything else builds on.

Number (N)

The structure of the number system and calculation, fractions, decimals and percentages, standard form and indices, surds, rounding, estimation and bounds, and factors, multiples and primes.

Algebra (A)

Algebraic manipulation, solving linear and simultaneous equations, quadratic equations, sequences, straight line graphs, inequalities and other graphs and functions.

Ratio, proportion and rates of change (R)

Ratio and scale, direct and inverse proportion, percentage change and interest, compound measures, and growth, decay and rates of change.

Geometry and measures (G)

Angles and polygons, Pythagoras and trigonometry, area and volume, circles and circle theorems, transformations, vectors, and constructions and loci.

Probability (P)

The probability scale and combined events, tree diagrams, Venn diagrams and set notation, and relative frequency and expected outcomes.

Statistics (S)

Sampling and types of data, averages and spread, statistical charts and graphs, and scatter graphs and correlation.

Foundation and Higher tiers

The qualification is tiered. You sit all three papers at one tier.

• Foundation tier targets grades 1 to 5 and covers core number, algebra, ratio, geometry, probability and statistics.
• Higher tier targets grades 4 to 9 and adds harder material such as surds, algebraic fractions, the quadratic formula, completing the square, the sine and cosine rules, vectors and vector proof, circle theorems, histograms and more demanding reasoning.

In the OCR specification grid each content statement sits in up to three columns (initial learning, Foundation additional, Higher additional), and the columns are cumulative: Higher candidates are responsible for everything in all three.

Exam structure

OCR GCSE Mathematics is assessed by three written papers, all sat at the end of the course. Each paper is 100 marks and 1 hour 30 minutes, and each is worth one third of the grade.

• Paper 1 (Foundation J560/01, Higher J560/04) - calculator allowed. 1 hour 30 minutes, 100 marks, one third.
• Paper 2 (Foundation J560/02, Higher J560/05) - non-calculator. 1 hour 30 minutes, 100 marks, one third.
• Paper 3 (Foundation J560/03, Higher J560/06) - calculator allowed. 1 hour 30 minutes, 100 marks, one third.

Note that the non-calculator paper sits in the middle of the three. Any paper may assess content from across the whole specification, so you cannot revise paper by paper.

Assessment objectives

The same three assessment objectives apply across the full qualification, but their weightings depend on the tier you enter.

So at Foundation half the marks reward reasoning and problem solving (AO2 plus AO3), rising to 60 percent at Higher. Either way OCR rewards clear method, worded justification and multi-step problem solving heavily, and Higher candidates in particular cannot rely on routine calculation alone.

The formulae sheet

For the 2025 to 2027 exams OCR provides a formulae sheet with every paper, with separate Foundation and Higher sheets (the Higher sheet lists additional formulae such as the sine rule, the cosine rule and the area of a triangle as $\frac{1}{2}ab\sin C$). Some formulae are still expected to be recalled, including the area of a circle $A = \pi r^2$, Pythagoras' theorem $a^2 + b^2 = c^2$ and the trigonometric ratios. You still need to know when to use each formula, so practise selecting the right tool rather than relying on the sheet alone.

How to study OCR Mathematics

Mathematics rewards fluent technique, clear working and accurate arithmetic.

1. Work from the specification statements. Each reference (for example N10 on standard form, A15 on the quadratic formula) is a checklist; questions are written from them.
2. Master Number and Algebra first. They underpin every area, so weak algebra leaks marks everywhere.
3. Show full working. Method marks are secure even when a final answer slips, so set out every step, and remember AO2 and AO3 reward reasoning.
4. Practise non-calculator skills. Paper 2 (or Paper 5 at Higher) has no calculator, so drill mental and written methods separately.
5. Finish with timed past papers. Sit full papers across all three to build speed and exam stamina.

Syllabus, dot point by dot point

Each area has specification-statement-level answer pages with worked exam questions and cross-links, plus an overview guide and quiz. Browse the full set at /gcse-ocr/mathematics/syllabus.

Number

• The structure of the number system and calculation
• Fractions, decimals and percentages
• Standard form and indices
• Surds
• Rounding, estimation and bounds
• Factors, multiples and primes

Algebra

• Algebraic manipulation
• Solving linear equations
• Quadratic equations
• Simultaneous equations
• Sequences
• Straight line graphs
• Inequalities and other graphs

Ratio, proportion and rates of change

• Ratio and scale
• Direct and inverse proportion
• Percentage change and interest
• Compound measures
• Growth, decay and rates of change

Geometry and measures

• Angles and polygons
• Pythagoras and trigonometry
• Area and volume
• Circles and circle theorems
• Transformations
• Vectors
• Constructions and loci

Probability

• Probability basics
• Tree diagrams
• Venn diagrams and set notation
• Relative frequency and expected outcomes

Statistics

• Sampling and data
• Averages and spread
• Statistical charts and graphs
• Scatter graphs and correlation

For the official specification

OCR publishes the full specification (J560), past papers and mark schemes at ocr.org.uk. Always revise from the current specification and OCR's own past papers, because question style is board-specific.