OCR A Level Maths Exam Questions & Past Papers

OCR A Level Maths exam questions by topic

Every topic on the OCR A Level Maths specification, grouped by paper. Each pack has full model answers.

Paper 1: Pure Mathematics and Statistics (AS)

1.1 ProofDeduction, exhaustion, counterexample Questions Model answers

1.2 Algebra and ExpressionsIndices and surds, expanding/factorising, quadratics & completing the square, polynomial division & factor theorem Questions Model answers

1.3 Equations and InequalitiesQuadratic equations, discriminant, simultaneous equations, polynomial equations, linear & quadratic inequalities Questions Model answers

1.4 Functions and GraphsTransformations, polynomial graphs, reciprocal/rational graphs (y=a/x, y=a/x^2) Questions Model answers

1.5 Coordinate GeometryStraight lines, parallel/perpendicular, circles, tangents/normals to circles Questions Model answers

1.6 Sequences, Series and Binomial ExpansionBinomial positive integer Questions Model answers

1.7 TrigonometrySine/cosine rule, graphs (degrees), identities (tan = sin/cos, sin^2+cos^2=1), equations (degrees) Questions Model answers

1.8 Exponentials and LogarithmsExponential functions, laws of logarithms, exponential equations, log-linear graphs, growth/decay Questions Model answers

1.9 DifferentiationFirst principles, basic, tangents/normals, stationary points/optimisation Questions Model answers

1.10 Integration and Differential EquationsBasic, definite, areas Questions Model answers

1.11 Vectors2D vectors, position vectors, vector geometry (2D) Questions Model answers

1.12 Sampling and DataPopulations/samples, sampling methods, bias, location & spread, histograms & cumulative frequency, box plots/outliers, large data set Questions Model answers

1.13 Correlation and RegressionScatter diagrams, correlation (interpretation), regression lines (interpretation), interpolation Questions Model answers

1.14 ProbabilityBasic, Venn, tree, independent Questions Model answers

1.15 Probability DistributionsDiscrete RVs (simple distributions), binomial Questions Model answers

1.16 Hypothesis TestingBinomial Questions Model answers

Paper 2: Pure Mathematics and Mechanics (AS)

2.1 ProofDeduction, exhaustion, counterexample Questions Model answers

2.2 Algebra and ExpressionsIndices and surds, expanding/factorising, quadratics & completing the square, polynomial division & factor theorem Questions Model answers

2.3 Equations and InequalitiesQuadratic equations, discriminant, simultaneous equations, polynomial equations, linear & quadratic inequalities Questions Model answers

2.4 Functions and GraphsTransformations, polynomial graphs, reciprocal/rational graphs (y=a/x, y=a/x^2) Questions Model answers

2.5 Coordinate GeometryStraight lines, parallel/perpendicular, circles, tangents/normals to circles Questions Model answers

2.6 Sequences, Series and Binomial ExpansionBinomial positive integer Questions Model answers

2.7 TrigonometrySine/cosine rule, graphs (degrees), identities (tan = sin/cos, sin^2+cos^2=1), equations (degrees) Questions Model answers

2.8 Exponentials and LogarithmsExponential functions, laws of logarithms, exponential equations, log-linear graphs, growth/decay Questions Model answers

2.9 DifferentiationFirst principles, basic, tangents/normals, stationary points/optimisation Questions Model answers

2.10 Integration and Differential EquationsBasic, definite, areas Questions Model answers

2.11 Vectors2D vectors, position vectors, vector geometry (2D) Questions Model answers

2.12 Mechanics FoundationsScalars/vectors, units/modelling Questions Model answers

2.13 KinematicsSUVAT, graphs, vertical motion, variable acceleration/calculus (1D) Questions Model answers

2.14 Forces and Newton's LawsConnected particles, pulleys, equilibrium (simple, forces as vectors, no resolving or friction) Questions Model answers

Paper 1: Pure Mathematics (A Level)

3.1 ProofDeduction, exhaustion, contradiction, counterexample Questions Model answers

3.2 Algebra and ExpressionsIndices and surds, expanding/factorising, quadratics & completing the square, algebraic fractions, polynomial division & factor theorem, partial fractions Questions Model answers

3.3 Equations and InequalitiesQuadratic equations, discriminant, simultaneous equations, polynomial equations, linear & quadratic inequalities, modulus equations/inequalities Questions Model answers

3.4 Functions and GraphsNotation/domain/range, composite & inverse functions, transformations, polynomial graphs, reciprocal/rational graphs, modulus graphs Questions Model answers

3.5 Coordinate GeometryStraight lines, parallel/perpendicular, circles, tangents/normals to circles, parametric equations Questions Model answers

3.6 Sequences, Series and Binomial ExpansionArithmetic, geometric, sum to infinity, sigma notation, recurrence relations, binomial positive integer, binomial fractional/negative Questions Model answers

3.7 TrigonometrySine/cosine rule, graphs, radians/arc/sector, identities, equations, reciprocal & inverse trig, compound/double angle, R formula, small angle approximations Questions Model answers

3.8 Exponentials and LogarithmsExponential functions, laws of logarithms, exponential equations, log-linear graphs, growth/decay Questions Model answers

3.9 DifferentiationFirst principles, basic, tangents/normals, stationary points/optimisation, product, quotient, chain, implicit, parametric, trig/exp/log, connected rates Questions Model answers

3.10 Integration and Differential EquationsBasic, definite, areas, trig, exp/log, substitution, parts, partial fractions, parametric, differential equations (first order separable) Questions Model answers

3.11 Numerical MethodsSign change, iteration, Newton-Raphson, trapezium rule, convergence/error Questions Model answers

3.12 Vectors2D vectors, 3D vectors, position vectors, vector geometry Questions Model answers

Paper 2: Pure Mathematics and Statistics (A Level)

4.1 ProofDeduction, exhaustion, contradiction, counterexample Questions Model answers

4.2 Algebra and ExpressionsIndices and surds, expanding/factorising, quadratics & completing the square, algebraic fractions, polynomial division & factor theorem, partial fractions Questions Model answers

4.3 Equations and InequalitiesQuadratic equations, discriminant, simultaneous equations, polynomial equations, linear & quadratic inequalities, modulus equations/inequalities Questions Model answers

4.4 Functions and GraphsNotation/domain/range, composite & inverse functions, transformations, polynomial graphs, reciprocal/rational graphs, modulus graphs Questions Model answers

4.5 Coordinate GeometryStraight lines, parallel/perpendicular, circles, tangents/normals to circles, parametric equations Questions Model answers

4.6 Sequences, Series and Binomial ExpansionArithmetic, geometric, sum to infinity, sigma notation, recurrence relations, binomial positive integer, binomial fractional/negative Questions Model answers

4.7 TrigonometrySine/cosine rule, graphs, radians/arc/sector, identities, equations, reciprocal & inverse trig, compound/double angle, R formula, small angle approximations Questions Model answers

4.8 Exponentials and LogarithmsExponential functions, laws of logarithms, exponential equations, log-linear graphs, growth/decay Questions Model answers

4.9 DifferentiationFirst principles, basic, tangents/normals, stationary points/optimisation, product, quotient, chain, implicit, parametric, trig/exp/log, connected rates Questions Model answers

4.10 Integration and Differential EquationsBasic, definite, areas, trig, exp/log, substitution, parts, partial fractions, parametric, differential equations (first order separable) Questions Model answers

4.11 Numerical MethodsSign change, iteration, Newton-Raphson, trapezium rule, convergence/error Questions Model answers

4.12 Vectors2D vectors, 3D vectors, position vectors, vector geometry Questions Model answers

4.13 Sampling and DataPopulations/samples, sampling methods, bias, location & spread, histograms & cumulative frequency, box plots/outliers, large data set Questions Model answers

4.14 Correlation and RegressionScatter diagrams, correlation (interpretation), regression lines (interpretation), interpolation Questions Model answers

4.15 ProbabilityBasic, Venn, tree, independent, conditional Questions Model answers

4.16 Probability DistributionsDiscrete RVs (simple distributions), binomial, normal (incl. normal approximation to binomial) Questions Model answers

4.17 Hypothesis TestingBinomial, normal (mean of a normal, known variance), correlation tests (PMCC) Questions Model answers

Paper 3: Pure Mathematics and Mechanics (A Level)

5.1 ProofDeduction, exhaustion, contradiction, counterexample Questions Model answers

5.2 Algebra and ExpressionsIndices and surds, expanding/factorising, quadratics & completing the square, algebraic fractions, polynomial division & factor theorem, partial fractions Questions Model answers

5.3 Equations and InequalitiesQuadratic equations, discriminant, simultaneous equations, polynomial equations, linear & quadratic inequalities, modulus equations/inequalities Questions Model answers

5.4 Functions and GraphsNotation/domain/range, composite & inverse functions, transformations, polynomial graphs, reciprocal/rational graphs, modulus graphs Questions Model answers

5.5 Coordinate GeometryStraight lines, parallel/perpendicular, circles, tangents/normals to circles, parametric equations Questions Model answers

5.6 Sequences, Series and Binomial ExpansionArithmetic, geometric, sum to infinity, sigma notation, recurrence relations, binomial positive integer, binomial fractional/negative Questions Model answers

5.7 TrigonometrySine/cosine rule, graphs, radians/arc/sector, identities, equations, reciprocal & inverse trig, compound/double angle, R formula, small angle approximations Questions Model answers

5.8 Exponentials and LogarithmsExponential functions, laws of logarithms, exponential equations, log-linear graphs, growth/decay Questions Model answers

5.9 DifferentiationFirst principles, basic, tangents/normals, stationary points/optimisation, product, quotient, chain, implicit, parametric, trig/exp/log, connected rates Questions Model answers

5.10 Integration and Differential EquationsBasic, definite, areas, trig, exp/log, substitution, parts, partial fractions, parametric, differential equations (first order separable) Questions Model answers

5.11 Numerical MethodsSign change, iteration, Newton-Raphson, trapezium rule, convergence/error Questions Model answers

5.12 Vectors2D vectors, 3D vectors, position vectors, vector geometry Questions Model answers

5.13 Mechanics FoundationsScalars/vectors, units/modelling, resolving Questions Model answers

5.14 KinematicsSUVAT, graphs, vertical motion, variable acceleration/calculus, projectiles Questions Model answers

5.15 Forces and Newton's LawsConnected particles, pulleys, inclined planes, friction, equilibrium Questions Model answers

5.16 Moments and Rigid BodiesMoments, equilibrium, rods/ladders Questions Model answers

StemUp Extreme Papers

Our hardest Maths questions, for students aiming for an A*. Every paper comes with full model answers.

Extreme Pure Mathematics120 marks · StemUp Maths Question paper Model answers

Extreme Mechanics90 marks · StemUp Maths Question paper Model answers

Extreme Statistics90 marks · StemUp Maths Question paper Model answers

AS Level papers

Sit them timed, mark with the mark scheme, then compare with our model answers.

2025 Paper 1 (Pure and Statistics)AS Level Maths Question paper Mark scheme

2025 Paper 2 (Pure and Mechanics)AS Level Maths Question paper Mark scheme

2024 Paper 1 (Pure and Statistics)AS Level Maths Question paper Mark scheme

2024 Paper 2 (Pure and Mechanics)AS Level Maths Question paper Mark scheme

2023 Paper 1 (Pure and Statistics)AS Level Maths Question paper Mark scheme

2023 Paper 2 (Pure and Mechanics)AS Level Maths Question paper Mark scheme

October 2020 Paper 1 (Pure and Statistics)AS Level Maths Question paper Mark scheme

October 2020 Paper 2 (Pure and Mechanics)AS Level Maths Question paper Mark scheme

2019 Paper 1 (Pure and Statistics)AS Level Maths Question paper Mark scheme

2019 Paper 2 (Pure and Mechanics)AS Level Maths Question paper Mark scheme

Past papers

Sit them timed, mark with the mark scheme, then compare with our model answers.

2025 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2025 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2025 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

2024 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2024 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2024 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

2023 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2023 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2023 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

2022 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2022 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2022 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

October 2021 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

October 2021 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

October 2021 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

October 2020 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

October 2020 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

October 2020 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

2019 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2019 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2019 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

2018 Paper 1 (Pure Mathematics)A Level Maths Question paper Mark scheme

2018 Paper 2 (Pure and Statistics)A Level Maths Question paper Mark scheme

2018 Paper 3 (Pure and Mechanics)A Level Maths Question paper Mark scheme

About OCR A Level Maths

The OCR A Level Maths exam (specification H240) is made up of three two-hour written papers, each worth 100 marks. OCR A Level Maths Paper 1, Pure Mathematics, covers pure content only, from proof, algebra and functions to differentiation, integration and vectors. Paper 2, Pure Mathematics and Statistics, combines pure maths with statistical sampling, probability, distributions and hypothesis testing, including questions on the large data set. Paper 3, Pure Mathematics and Mechanics, combines pure maths with kinematics, forces and Newton’s laws and moments.