GCSE Maths topics list: what's on the exam

Place value, the four operations with integers, decimals and fractions, factors, multiples and primes (HCF and LCM), powers and roots, standard form, rounding and estimation, and fractions, decimals and percentages. Higher: surds, recurring decimals to fractions, upper and lower bounds.

Notation and expanding and factorising, substitution, rearranging formulae, linear equations and inequalities, simultaneous equations, quadratics (factorising), sequences and nth terms, and straight-line graphs ($y = mx + c$). Higher: the quadratic formula and completing the square, quadratic inequalities, functions, algebraic proof, iteration, graph transformations, circle equations, gradients and areas under curves.

Ratio and sharing, direct and inverse proportion, percentage change and compound interest, speed, density and pressure, and best-buy problems. Higher: proportion equations ($y \propto x^2$), growth and decay, and rates of change on graphs.

Angles and polygons, perimeter, area and volume, circles, Pythagoras, right-angled trigonometry, transformations, constructions and loci, bearings, similarity and congruence. Higher: circle theorems, the sine and cosine rules, $\tfrac{1}{2}ab\sin C$, 3D Pythagoras and trigonometry, and vectors.

Probability: basic probability, relative frequency, Venn diagrams, tree diagrams. Statistics: averages and range, charts and graphs, scatter graphs and correlation, sampling. Higher: conditional probability, histograms, cumulative frequency and box plots.

Rate each topic red (can't do it), amber (sometimes) or green (confident), then plan revision around red and amber topics with spaced, mixed practice. See how to revise for GCSE Maths and the free mock papers to find gaps.

Whichever tier you sit, a large share of marks comes from skills that run through every area:

• Fractions, decimals and percentages, including percentage change and reverse percentages.
• Ratio and proportion, such as sharing in a ratio and best-buy problems.
• Solving linear equations and rearranging formulae.
• Area, perimeter and volume, and angle facts.
• Averages and charts, and basic probability.

These skills also appear inside harder questions, so securing them first makes everything else easier. Use the GCSE Maths mock papers to check how secure they are.

Questions also test three kinds of skill:

• AO1, use and apply standard techniques: 50% of Foundation and 40% of Higher.
• AO2, reason, interpret and communicate mathematically: 25% of Foundation and 30% of Higher.
• AO3, solve problems: 25% of Foundation and 30% of Higher.

That's why knowing the methods isn't enough, especially on Higher: you also need to practise explaining, proving and solving multi-step problems.

1. Rate each topic red, amber or green, using a past paper rather than guesswork.
2. Start with red topics in the shared core, because they also appear inside harder questions.
3. Mix topics in each session so you practise choosing the right method. See interleaved practice.
4. Revisit amber topics every week or two, and green ones occasionally.
5. Test the whole list with a full paper every few weeks.

The revision timetable generator can spread topics across the weeks before your exams.