Past papers and mark schemes for A-Level Maths, Physics & Chemistry (CIE, Edexcel, OCR, AQA), IGCSE Mathematics, TMUA, MAT, and UKMT competitions — plus free online textbooks.
Free textbooks covering UK mathematics — IGCSE, A-Level, and Further Mathematics with worked examples and practice problems.
Types of numbers, HCF & LCM, standard form, surds, ratio, percentages, compound interest
Expanding, factorising, equations, simultaneous equations, quadratics, sequences, functions
Gradient, y = mx + c, parallel & perpendicular lines, distance, midpoint
Angles, polygons, circle theorems, congruence, similarity, constructions & loci
Perimeter, area, arc length, sector area, surface area, volume, similar shapes
Pythagoras, SOHCAHTOA, sine rule, cosine rule, area formula, bearings, trig graphs
Translations, reflections, rotations, enlargements, combined transformations, vectors
Basic probability, tree diagrams, Venn diagrams, set notation, conditional probability
Averages, histograms, cumulative frequency, box plots, scatter diagrams, correlation
Indices, surds, quadratics, inequalities, partial fractions, functions, transformations
Straight lines, circles, parametric equations
Arithmetic, geometric series, binomial expansion (integer and general powers)
Trig ratios, identities, radians, compound angles, harmonic form, reciprocal trig
Exponential functions, log laws, natural log, exponential models, data linearisation
First principles, standard functions, chain/product/quotient rules, implicit, parametric, optimisation
Indefinite and definite integrals, areas, substitution, by parts, partial fractions, ODEs
2D and 3D vectors, dot product, vector equations of lines
Sign change, fixed-point iteration, Newton-Raphson, trapezium rule
Proof by deduction, contradiction, modulus function, composite and inverse functions
Sampling, probability, binomial & normal distributions, hypothesis testing
Kinematics, Newton's laws, projectiles, friction, moments, energy
Cartesian and modulus-argument form, Euler's formula, de Moivre's theorem, nth roots
Geometric representation, loci (circles, half-lines, perpendicular bisectors), transformations
Matrix algebra, determinant, inverse, solving systems, invariant points and lines
2D/3D transformations, eigenvalues and eigenvectors, diagonalisation, Cayley-Hamilton
Series, divisibility, recurrences, matrix powers, inequalities
Cross product, equations of planes, angles and distances, line-plane intersections
Vieta's formulas (quadratic to quartic), transforming roots, complex roots theorem
Method of differences, standard power series, operations on series, applications
Improper integrals, inverse trig/hyperbolic integrals, arc length, reduction formulae
Homogeneous ODEs, complementary function, particular integral, initial value problems
Poisson, continuous distributions, chi-squared tests, correlation, t-tests
Collisions and restitution, circular motion, simple harmonic motion, damped oscillations
Select an exam to browse all available papers, organised by exam board and year.
CIE (9709), Edexcel, OCR & AQA — papers, mark schemes & solutions
AvailableCIE (9702), Edexcel, OCR & AQA — papers, mark schemes & solutions
AvailableCIE (9701), Edexcel, OCR & AQA — papers, mark schemes & solutions
AvailableCambridge (0580) & Edexcel (4MA1) — Core, Extended, Foundation & Higher
AvailableTest of Mathematics for University Admission — Paper 1 & 2 (2016–2023)
AvailableOxford Mathematics Admissions Test — papers & solutions (2007–2024)
AvailableJMC, IMC, SMC, Junior & Intermediate Olympiads, BMO Round 1 & 2 (2015–2025)
Available