Free A-Level Maths Solver

A-Level Maths (GCE Advanced Level Mathematics) is the UK post-16 maths qualification, taken across Year 12 (AS content, often not examined separately since 2017 reforms) and Year 13 (full A-Level). It's split into three strands: Pure Mathematics (roughly two-thirds of the course), Statistics (one-sixth), and Mechanics (one-sixth). All three awarding bodies — AQA, Edexcel (Pearson), and OCR — cover broadly the same content under the DfE core specification, with minor notation differences.

Pure Mathematics: proof, algebra and functions, coordinate geometry in the (x, y) plane, sequences and series (arithmetic, geometric, binomial), trigonometry (identities, compound and double-angle formulas, R-form), exponentials and logarithms, differentiation (including product, quotient, chain, implicit, parametric), integration (including by parts, by substitution, partial fractions), numerical methods (iteration, Newton-Raphson), and vectors. This is the backbone — 60%+ of your exam marks come from Pure.

Statistics: probability (set notation, independence, conditional, tree diagrams), discrete and continuous distributions (binomial, normal), sampling, hypothesis testing (one-tailed and two-tailed, for proportions, means, and correlation). Mechanics: kinematics (suvat, variable acceleration), Newton's laws, connected particles, friction, moments, projectile motion.

The exam structure: typically three 2-hour papers. Paper 1 and Paper 2 are Pure (some boards combine Pure/Stats/Mechanics; check your board). Paper 3 is usually Statistics & Mechanics combined. Calculators are allowed throughout — for A-Level you should have a graphical calculator (Casio fx-CG50 is the standard choice), though scientific calculators work for most questions.

Mark schemes reward method over answer. A 4-mark differentiation question splits: 1 mark for stating the relevant rule (product, quotient, chain), 2 marks for correct application with sufficient working shown, 1 mark for the fully simplified final answer. The solver above follows this exact mark-scheme discipline — every step labelled, rules named explicitly, final form factorised or simplified as examiners expect.

A* vs A separator: the hardest questions on Paper 1/2 involve novel combinations (proof with calculus, integration with logarithms, parametric differentiation leading to stationary-point analysis). These reward students who know the standard methods inside-out AND can combine them under time pressure. Practise both past papers AND the solver's 'what if' extensions to build this combinatorial fluency.