Year 10 Math Practice Questions and Topics

Year 10 (ages 14–15) is the first of the two GCSE Maths years, and the syllabus broadens considerably compared to Key Stage 3: number, algebra, ratio and proportion, geometry and measures, probability and statistics are all covered at GCSE depth, spanning foundation to higher difficulty. Simultaneous equations and quadratics are introduced or formalised, alongside inequalities, coordinate geometry, trigonometry, circle theorems, surface area and volume of 3D shapes, compound measures (speed, density, pressure), and financial maths (compound interest, and similar real-world percentage problems). Functions and transformations of graphs also typically appear this year.

By the end of Year 10, a student should solve a pair of simultaneous equations, factorise and solve a quadratic equation, use basic trigonometry (sine, cosine, tangent) to find a missing side or angle in a right-angled triangle, calculate the volume and surface area of common 3D shapes, and apply compound interest to a financial problem.

The most common difficulty is quadratics — factorising a quadratic expression is a distinct skill from factorising a simple linear one, and many students initially try to apply linear-equation instincts (isolate x, do the same to both sides) to an equation that has two solutions, not one, which requires a genuinely different method. The second frequent struggle is trigonometry: remembering which ratio (sine, cosine or tangent) applies to which pair of sides is a common sticking point, and it's often taught as a memory trick (SOHCAHTOA) without enough practice actually labelling triangles correctly first, which is where most real errors happen.

This year covers the bulk of new GCSE content, with Year 11 largely consolidating, practising past-paper technique, and filling gaps — so what's learned solidly in Year 10 has a direct, outsized effect on how manageable Year 11 feels.

The most useful thing a parent can do is encourage regular, varied practice across topics rather than mastering one and moving on, since GCSE questions frequently combine several topics in one problem (a trigonometry question embedded in a real-world context, for instance). For quadratics and trigonometry specifically, practising the method on several different examples, out loud, tends to fix errors faster than reviewing a single worked example repeatedly.