GCSE foundation maths topics: what's on the paper

GCSE maths (all boards) is built on six content areas: number, algebra, ratio, proportion and rates of change, geometry and measures, probability, and statistics. The foundation tier covers grades 1–5 and is examined in three papers of 1 hour 30 minutes and 80 marks each — Paper 1 without a calculator, Papers 2 and 3 with one. Number and ratio between them carry roughly half the foundation marks.

Place value and ordering, the four operations with whole numbers, decimals and negatives, factors, multiples and primes, powers and roots, fractions (all four operations, and fractions of amounts), converting between fractions, decimals and percentages, rounding and estimation, standard form, and using a calculator efficiently.

Simplifying and expanding expressions, factorising into a single bracket (and simple quadratics at the top of foundation), substituting into formulae, solving linear equations and simple inequalities, sequences (including the nth term), straight-line graphs and plotting simple quadratic graphs, and using coordinates.

Simplifying and sharing in a ratio, direct and inverse proportion, percentages of amounts, percentage increase and decrease, reverse percentages, simple and compound interest, unit conversions, speed, density and best-buy problems. This area is worth far more marks than its length suggests, and it's where most resit candidates have their biggest gaps.

Angle facts (on a line, around a point, in triangles and quadrilaterals, parallel lines), properties of 2-D and 3-D shapes, perimeter and area (rectangles, triangles, parallelograms, trapeziums, circles and compound shapes), volume and surface area of prisms and cylinders, transformations, constructions and loci, Pythagoras' theorem, and basic trigonometry in right-angled triangles.

The probability scale, listing outcomes, probability of an event and of it not happening, sample spaces, tree diagrams and Venn diagrams, relative frequency; then averages and range (from lists and from tables), bar charts, pie charts, pictograms, scatter graphs and correlation, and comparing distributions.

You don't need everything above. Grade boundaries are set after each series, and a grade 4 on foundation has consistently been reachable with reliable performance on the accessible topics: number, percentages, ratio, simple algebra, area and perimeter, angles, averages and reading charts. Get those solid and pick up method marks on the rest.

Use a diagnostic to find out which of them you actually have, then practise the missing ones. That's what ResitReady's free diagnostic does — it maps your answers to this list, skill by skill.