GCSE Maths Topics (Full List for AQA, Edexcel and OCR)
The complete list of GCSE maths topics for AQA, Edexcel and OCR, organised by the six main areas and by tier.
GCSE maths is split into six main areas: number, algebra, ratio and proportion, geometry and measures, probability, and statistics. Every exam board, including AQA, Edexcel and OCR, covers the same core content set by the national curriculum. Foundation tier covers grades 1 to 5 and Higher tier covers grades 4 to 9, with Higher adding extra topics. The full topic list is below.
What topics are in GCSE maths?
GCSE maths content is the same across exam boards and is organised into six areas. Foundation and Higher share most topics, with Higher including additional, more advanced ones.
The six areas of GCSE maths
Number (N)
- ordering integers, decimals and fractions
- the four operations
- order of operations and inverse operations
- prime numbers, factors, multiples, HCF and LCM
- systematic listing and counting
- powers and roots
- index laws (integer and fractional)
- surds and rationalising denominators
- standard form
- terminating and recurring decimals and converting to fractions
- fractions, decimals and percentages as operators
- standard and compound units
- estimation and approximation
- rounding, significant figures and error intervals
- upper and lower bounds
Algebra (A)
- algebraic notation and vocabulary
- substituting into formulae
- expressions, equations, formulae, identities and inequalities
- simplifying, expanding and factorising
- factorising quadratics
- algebraic fractions
- changing the subject of a formula
- functions, including inverse and composite functions
- coordinates and plotting graphs
- straight-line graphs, gradients, parallel and perpendicular lines
- quadratic graphs and completing the square
- recognising and sketching graphs (linear, quadratic, cubic, reciprocal, exponential and trigonometric)
- transformations of graphs
- real-life graphs and gradients and areas under graphs
- equation of a circle and its tangent
- solving linear equations
- solving quadratic equations
- simultaneous equations
- iterative methods
- setting up and solving equations from context
- linear and quadratic inequalities
- sequences
- special sequences (arithmetic, geometric, triangular, square, cube, Fibonacci and quadratic)
- the nth term of linear and quadratic sequences
Ratio, proportion and rates of change (R)
- converting between units and compound units
- scale factors, scale diagrams and maps
- expressing one quantity as a fraction or ratio of another
- ratio notation, simplifying and dividing in a given ratio
- percentages, percentage change and reverse percentages
- simple and compound interest, growth and decay
- direct and inverse proportion
- compound measures (speed, density, pressure and rates)
- gradient of a graph as a rate of change
- rates of change from chords and tangents
- comparing lengths, areas and volumes using ratio and similarity
Geometry and measures (G)
- geometric terms, notation and labelling
- ruler and compass constructions and loci
- angle facts, parallel lines and angles in polygons
- properties of triangles, quadrilaterals and plane figures
- congruence criteria for triangles
- similar shapes and similarity
- transformations (rotation, reflection, translation and enlargement, including negative and fractional scale factors)
- combinations of transformations and invariance
- circle definitions, properties and theorems
- coordinate geometry
- properties of 3D shapes, plans and elevations
- units of measure, perimeter, area and volume
- scale drawings and bearings
- area and volume formulae (including circles, sectors, prisms, cylinders, spheres, pyramids and cones)
- arc lengths and areas of sectors
- lengths, areas and volumes of similar shapes
- Pythagoras' theorem and trigonometry in right-angled triangles
- exact values of trigonometric ratios
- the sine rule, cosine rule and area of a triangle
- vectors and vector proofs
Probability (P)
- recording and analysing outcomes (frequency tables and frequency trees)
- randomness, fairness and equally likely outcomes
- relative frequency and expected frequency
- the probability scale and theoretical probability
- mutually exclusive and exhaustive events
- sample spaces for single and combined experiments
- Venn diagrams, tree diagrams and set notation
- independent and dependent (conditional) events
Statistics (S)
- sampling and drawing inferences about populations
- interpreting and constructing tables, charts and diagrams (bar charts, pie charts, pictograms, line graphs and time series)
- histograms and cumulative frequency graphs
- averages and measures of spread (mean, median, mode, range, quartiles and interquartile range)
- box plots and comparing distributions
- scatter graphs, correlation and lines of best fit
Foundation tier vs Higher tier topics
GCSE maths has two tiers. Foundation tier covers grades 1 to 5 and Higher tier covers grades 4 to 9. Higher tier includes all of the Foundation content plus additional, more advanced topics. The balance of the six areas also shifts between tiers: for example, algebra makes up a larger share at Higher (30 percent) than at Foundation (20 percent), while number carries more weight at Foundation. The official weightings are below.
| Area | Foundation % | Higher % |
|---|---|---|
| Number | 25 | 15 |
| Algebra | 20 | 30 |
| Ratio, proportion and rates of change | 25 | 20 |
| Geometry and measures | 15 | 20 |
| Probability and Statistics | 15 | 15 |
These weightings are set by Ofqual and are common to all exam boards.
Are GCSE maths topics the same for AQA, Edexcel and OCR?
Yes. AQA, Edexcel and OCR all follow the same national curriculum content for GCSE maths, so the topics are the same. The differences are in how each board structures its papers, the style of questions, and the exact wording, not the topics themselves.
Which GCSE maths topics are the hardest?
Some topics, such as algebra, trigonometry and ratio problems, are commonly found harder than others. For a fuller breakdown, see our guide to the hardest GCSE maths topics.
How to revise GCSE maths topics
Work through each of the six areas in turn, practise with past-paper questions, and check the marks you need for your target grade using our GCSE maths grade boundaries tool. Understanding the GCSE maths exam structure also helps. If you are sitting IGCSE rather than GCSE, see our IGCSE maths topics list and check the IGCSE maths grade boundaries instead.
You can also work from a printable GCSE maths topics checklist to track what you have covered.
Topics are based on the Department for Education GCSE mathematics subject content, which is common to all exam boards.
Frequently Asked Questions
What topics are covered in GCSE maths?
GCSE maths covers six main areas: number, algebra, ratio proportion and rates of change, geometry and measures, probability, and statistics. The full list of topics in each area is above.
How many topics are there in GCSE maths?
GCSE maths is organised into six main areas, each containing a set of topics. Exam boards group and count them slightly differently, so there is no single fixed number, but the full content is listed above.
What is the difference between Foundation and Higher GCSE maths topics?
Foundation tier covers grades 1 to 5 and Higher tier covers grades 4 to 9. Higher includes all Foundation topics plus additional, more advanced ones, and the balance of the areas shifts, with more algebra at Higher.
Are AQA and Edexcel GCSE maths topics the same?
Yes. AQA, Edexcel and OCR all follow the same Department for Education subject content, so the topics are the same. The boards differ in how they structure papers and word questions, not in the topics.
What are the hardest GCSE maths topics?
Students often find topics such as algebra, trigonometry and ratio problems the most challenging. See our guide to the hardest GCSE maths topics for more detail.
Want help mastering these topics?
Explore 1-to-1 GCSE Maths tutoring built around your exam board and target grade, with past-paper practice and clear explanations for every topic area.