OCR A Level Further Maths B (MEI) exam questions and past papers

Free OCR A Level Further Maths B (MEI) exam questions by topic, with mark schemes, past papers and model answers.

How to use the exam questions

Pick a topic and work through as many questions as you need until it really clicks. Spend extra time on the topics you find hardest, as that is where the biggest improvements come from. Each file includes the mark scheme, so check every answer as you go, see where you lost marks and learn exactly what a full-mark answer looks like.

OCR A Level Further Maths B (MEI) exam questions by topic

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

Y410: Core Pure (AS)
1.1 Proof and Mathematical InductionSeries, matrices QuestionsModel answers
1.2 Complex NumbersArithmetic & Argand, modulus-argument, loci QuestionsModel answers
1.3 MatricesMatrix arithmetic, 2D/3D transformations, determinants & inverses, simultaneous equations (intersection of three planes) QuestionsModel answers
1.4 Further Vectors and 3D GeometryScalar product, planes, intersections, angles QuestionsModel answers
1.5 Further Algebra and FunctionsRoots & coefficients, transformed roots, summation of series, method of differences QuestionsModel answers

Y411: Mechanics a (AS)
2.1 Further Kinematics and DynamicsDimensional analysis QuestionsModel answers
2.2 Moments and Rigid BodiesMoments, equilibrium, rods/ladders (incl. couples, rigid-body equilibrium) QuestionsModel answers
2.3 Work, Energy and PowerWork, energy, power QuestionsModel answers
2.4 Momentum and CollisionsMomentum & impulse, restitution (direct impact) QuestionsModel answers
2.5 Centres of Mass and Rigid BodiesComposite, toppling QuestionsModel answers

Y412: Statistics a (AS)
3.1 Discrete Probability DistributionsPoisson, geometric, discrete uniform QuestionsModel answers
3.2 Further ProbabilityLinear combinations of RVs (discrete) QuestionsModel answers
3.3 Correlation and RegressionPMCC, rank correlation, least squares QuestionsModel answers
3.4 Further Hypothesis TestingChi-squared goodness of fit, chi-squared contingency QuestionsModel answers
3.5 Sampling and DataPopulations/samples, sampling methods, bias QuestionsModel answers

Y413: Modelling with Algorithms (AS)
4.1 AlgorithmsComplexity, sorting, bin packing QuestionsModel answers
4.2 Graphs and NetworksMST Kruskal/Prim, shortest path (Dijkstra, Floyd) QuestionsModel answers
4.3 Network Flows and MatchingNetwork flows QuestionsModel answers
4.4 Critical Path AnalysisCPA, float, resource scheduling QuestionsModel answers
4.5 Linear ProgrammingGraphical, simplex, two-stage QuestionsModel answers

Y414: Numerical Methods (AS)
5.1 Numerical MethodsSign change, iteration, Newton-Raphson, trapezium rule, convergence/error QuestionsModel answers
5.2 Numerical MethodsNumerical integration (midpoint, trapezium, Simpson), numerical differentiation, error QuestionsModel answers

Y420: Core Pure (A Level)
6.1 Proof and Mathematical InductionSeries, matrices (sequences, series and matrix powers) QuestionsModel answers
6.2 Complex NumbersArithmetic & Argand, modulus-argument, loci, exponential form, de Moivre, roots of unity QuestionsModel answers
6.3 MatricesMatrix arithmetic, 2D/3D transformations (incl. invariance), determinants & inverses (3x3), simultaneous equations (intersections of planes) QuestionsModel answers
6.4 Further Vectors and 3D GeometryScalar product, vector product, lines, planes, intersections, angles, shortest distances QuestionsModel answers
6.5 Further Algebra and FunctionsRoots & coefficients, transformed roots, summation of series, method of differences, Maclaurin/Taylor (Maclaurin, convergence) QuestionsModel answers
6.6 Further CalculusImproper integrals, volumes, further trig integration (inverse trig, trig substitution, partial fractions, mean value) QuestionsModel answers
6.7 Polar CoordinatesConversion, sketching, area QuestionsModel answers
6.8 Hyperbolic FunctionsDefinitions & graphs, identities & equations, inverse hyperbolic functions, differentiation & integration QuestionsModel answers
6.9 Differential EquationsFirst order linear, second order homogeneous, second order non-homogeneous, coupled, modelling QuestionsModel answers
6.10 Differential Equations in MechanicsSHM, damped/forced QuestionsModel answers

Y421: Mechanics Major (A Level)
7.1 Further Kinematics and DynamicsDimensional analysis, variable forces, vector kinematics, resistance QuestionsModel answers
7.2 Moments and Rigid BodiesMoments, equilibrium, rods/ladders (incl. couples) QuestionsModel answers
7.3 Work, Energy and PowerWork, energy, power, variable forces QuestionsModel answers
7.4 Momentum and CollisionsMomentum & impulse, restitution, oblique collisions QuestionsModel answers
7.5 Circular MotionHorizontal, vertical QuestionsModel answers
7.6 Elastic Strings and SpringsHooke's law, EPE QuestionsModel answers
7.7 Centres of Mass and Rigid BodiesLaminae, composite, toppling (incl. solids of revolution) QuestionsModel answers
7.8 KinematicsProjectiles (incl. vector form) QuestionsModel answers

Y422: Statistics Major (A Level)
8.1 Discrete Probability DistributionsPoisson, geometric, discrete uniform QuestionsModel answers
8.2 Further ProbabilityLinear combinations of RVs QuestionsModel answers
8.3 Correlation and RegressionPMCC, rank correlation, least squares QuestionsModel answers
8.4 Further Hypothesis TestingChi-squared goodness of fit, chi-squared contingency, t-tests/means, non-parametric (Wilcoxon signed-rank) QuestionsModel answers
8.5 Continuous Probability DistributionsPdf, cdf, continuous uniform, exponential QuestionsModel answers
8.6 Statistical EstimationCLT, unbiased estimators, confidence intervals QuestionsModel answers
8.7 Statistical Modelling and SimulationStatistical modelling, simulation QuestionsModel answers

Y431: Mechanics Minor (A Level)
9.1 Further Kinematics and DynamicsDimensional analysis QuestionsModel answers
9.2 Moments and Rigid BodiesMoments, equilibrium, rods/ladders (incl. couples, rigid-body equilibrium) QuestionsModel answers
9.3 Work, Energy and PowerWork, energy, power QuestionsModel answers
9.4 Momentum and CollisionsMomentum & impulse, restitution (direct impact) QuestionsModel answers
9.5 Centres of Mass and Rigid BodiesComposite, toppling QuestionsModel answers

Y432: Statistics Minor (A Level)
10.1 Discrete Probability DistributionsPoisson, geometric, discrete uniform QuestionsModel answers
10.2 Further ProbabilityLinear combinations of RVs (discrete) QuestionsModel answers
10.3 Correlation and RegressionPMCC, rank correlation, least squares QuestionsModel answers
10.4 Further Hypothesis TestingChi-squared goodness of fit, chi-squared contingency QuestionsModel answers
10.5 Sampling and DataPopulations/samples, sampling methods, bias QuestionsModel answers

Y433: Modelling with Algorithms (A Level)
11.1 AlgorithmsComplexity, sorting, bin packing QuestionsModel answers
11.2 Graphs and NetworksMST Kruskal/Prim, shortest path (Dijkstra, Floyd) QuestionsModel answers
11.3 Network Flows and MatchingNetwork flows QuestionsModel answers
11.4 Critical Path AnalysisCPA, float, resource scheduling QuestionsModel answers
11.5 Linear ProgrammingGraphical, simplex, two-stage QuestionsModel answers

Y434: Numerical Methods (A Level)
12.1 Numerical MethodsSign change, iteration, Newton-Raphson, trapezium rule, convergence/error QuestionsModel answers
12.2 Numerical MethodsNumerical integration (midpoint, trapezium, Simpson), numerical differentiation, error QuestionsModel answers
12.3 Interpolation and Approximating FunctionsLinear and quadratic interpolation, Lagrange and difference methods, approximating functions QuestionsModel answers

Y435: Extra Pure (A Level)
13.1 Further Algebra and FunctionsRecurrence QuestionsModel answers
13.2 Number Theory and Abstract AlgebraGroups, subgroups, cyclic groups, isomorphisms, modular arithmetic (as group examples) QuestionsModel answers
13.3 MatricesEigenvalues/eigenvectors, diagonalisation, Cayley-Hamilton QuestionsModel answers
13.4 Multivariable CalculusFunctions of two variables, partial differentiation, stationary points (surfaces, tangent planes) QuestionsModel answers

Y436: Further Pure with Technology (A Level)
14.1 Further Coordinate GeometryParametric, loci (families of curves, conics, investigation with graphing software) QuestionsModel answers
14.2 Number Theory and Abstract AlgebraDivisibility, Euclidean algorithm, modular arithmetic, Diophantine (incl. Pell) QuestionsModel answers
14.3 Differential EquationsFirst order linear, modelling (tangent fields) QuestionsModel answers
14.4 Numerical MethodsEuler, improved Euler (numerical solution of DEs) QuestionsModel answers

StemUp Extreme Papers

Our hardest Further Maths B (MEI) questions, for students aiming for an A*. Every paper comes with full model answers.

Extreme Further Pure Mathematics120 marks · StemUp Further Maths B (MEI) Question paper Model answers
Extreme Further Mechanics90 marks · StemUp Further Maths B (MEI) Question paper Model answers
Extreme Further Statistics90 marks · StemUp Further Maths B (MEI) Question paper Model answers
Extreme Further Decision Mathematics80 marks · StemUp Further Maths B (MEI) Question paper Model answers

Past papers

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

2025 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2025 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2024 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2023 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2022 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2021 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
October 2020 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2019 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2018 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y420 (Core Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y421 (Mechanics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y422 (Statistics Major)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y431 (Mechanics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y432 (Statistics Minor)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y433 (Modelling with Algorithms)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y434 (Numerical Methods)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y435 (Extra Pure)A Level Further Maths B (MEI) Question paperMark schemeModel answers
2017 Y436 (Further Pure with Technology)A Level Further Maths B (MEI) Question paperMark schemeModel answers

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