Edexcel A Level Further Maths exam questions and past papers
Free Edexcel A Level Further Maths 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.
Edexcel A Level Further Maths exam questions by topic
Every topic on the Edexcel A Level Further Maths specification, grouped by paper. Each pack has full model answers.
Paper 1: Core Pure Mathematics (AS)
1.3
MatricesMatrix arithmetic, 2D/3D transformations (incl. invariant points and lines), determinants & inverses, simultaneous equations (three equations, geometric interpretation)
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1.4
Further Algebra and FunctionsRoots & coefficients, transformed roots, summation of series (sums of r, r^2, r^3)
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1.6
Further Vectors and 3D GeometryScalar product, lines, planes, intersections, angles, shortest distances
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Paper 2: Further Pure Mathematics 1 (option) (AS)
2.1
Further Coordinate GeometryParabola, hyperbola (rectangular only), parametric, loci (focus-directrix, tangents and normals)
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2.2
Further Vectors and 3D GeometryVector product (incl. scalar triple product)
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2.3
Numerical MethodsEuler, improved Euler (numerical solution of first and second order DEs)
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2.5
t-Formulaet = tan(x/2) substitution: identities, trig equations and integration
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Paper 2: Further Pure Mathematics 2 (option) (AS)
3.1
Number Theory and Abstract AlgebraDivisibility (incl. tests), Euclidean algorithm (incl. Bezout), modular arithmetic, groups, subgroups (incl. Lagrange), cyclic groups
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Paper 2: Further Statistics 1 (option) (AS)
4.1
Discrete Probability DistributionsPoisson (incl. additive property and hypothesis tests for a Poisson mean), approximations (Poisson approximation to binomial)
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4.2
Further Hypothesis TestingChi-squared goodness of fit, chi-squared contingency
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4.3
Probability DistributionsDiscrete RVs, expectation & variance (incl. E(g(X)))
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Paper 2: Further Statistics 2 (option) (AS)
5.1
Correlation and RegressionPMCC, rank correlation, least squares (incl. residuals, hypothesis tests for zero correlation)
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Paper 2: Further Mechanics 1 (option) (AS)
6.1
Momentum and CollisionsMomentum & impulse, restitution (direct, successive impacts)
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Paper 2: Further Mechanics 2 (option) (AS)
7.2
Centres of Mass and Rigid BodiesLaminae, composite (incl. frameworks, equilibrium of laminas)
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7.3
Further Kinematics and DynamicsVariable forces (acceleration as a function of t, v or x)
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Paper 2: Decision Mathematics 1 (option) (AS)
8.2
Graphs and NetworksEulerian/Hamiltonian (Eulerian, semi-Eulerian), MST Kruskal/Prim, shortest path (Dijkstra), route inspection
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8.3
Critical Path AnalysisCPA, float, resource scheduling (incl. Gantt charts)
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Paper 2: Decision Mathematics 2 (option) (AS)
9.1
Network Flows and MatchingNetwork flows (cuts, labelling, max-flow min-cut)
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9.4
Allocation, Transportation and Dynamic ProgrammingAllocation (Hungarian algorithm), transportation problems and dynamic programming
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Paper 1: Core Pure Mathematics 1 (A Level)
10.2
Complex NumbersArithmetic & Argand, modulus-argument, loci, exponential form, de Moivre, roots of unity
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10.3
MatricesMatrix arithmetic, 2D/3D transformations (incl. invariant points and lines), determinants & inverses, simultaneous equations (incl. geometric interpretation with planes)
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10.4
Further Algebra and FunctionsRoots & coefficients, transformed roots, summation of series, method of differences, Maclaurin/Taylor (Maclaurin)
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10.5
Further CalculusImproper integrals, volumes, further trig integration (inverse trig, partial fractions, mean value)
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10.6
Further Vectors and 3D GeometryScalar product, lines, planes, intersections, angles, shortest distances
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10.8
Hyperbolic FunctionsDefinitions & graphs, identities & equations, inverse hyperbolic functions, differentiation & integration
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10.9
Differential EquationsFirst order linear, second order homogeneous, second order non-homogeneous, coupled, modelling
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Paper 2: Core Pure Mathematics 2 (A Level)
11.2
Complex NumbersArithmetic & Argand, modulus-argument, loci, exponential form, de Moivre, roots of unity
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11.3
MatricesMatrix arithmetic, 2D/3D transformations (incl. invariant points and lines), determinants & inverses, simultaneous equations (incl. geometric interpretation with planes)
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11.4
Further Algebra and FunctionsRoots & coefficients, transformed roots, summation of series, method of differences, Maclaurin/Taylor (Maclaurin)
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11.5
Further CalculusImproper integrals, volumes, further trig integration (inverse trig, partial fractions, mean value)
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11.6
Further Vectors and 3D GeometryScalar product, lines, planes, intersections, angles, shortest distances
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11.8
Hyperbolic FunctionsDefinitions & graphs, identities & equations, inverse hyperbolic functions, differentiation & integration
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11.9
Differential EquationsFirst order linear, second order homogeneous, second order non-homogeneous, coupled, modelling
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Paper 3A: Further Pure Mathematics 1 (A Level)
12.2
Further Algebra and FunctionsMaclaurin/Taylor (Taylor series, limits, series solutions of DEs), inequalities/modulus
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12.3
Further Coordinate GeometryEllipse, hyperbola, parabola, parametric, loci
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12.4
Further Vectors and 3D GeometryVector product (incl. scalar triple product)
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12.5
Numerical MethodsEuler, improved Euler (midpoint), numerical integration (Simpson's rule)
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12.6
t-Formulaet = tan(x/2) substitution: identities, trig equations and integration
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Paper 4A: Further Pure Mathematics 2 (A Level)
13.1
Number Theory and Abstract AlgebraDivisibility, Euclidean algorithm, modular arithmetic, Diophantine, groups, subgroups, cyclic groups, isomorphisms (incl. Bezout, Fermat's little theorem)
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Paper 3B: Further Statistics 1 (A Level)
14.1
Discrete Probability DistributionsPoisson, geometric, negative binomial, approximations
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14.2
Further Hypothesis TestingType I/II, power (quality of tests), chi-squared goodness of fit, chi-squared contingency
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14.5
Probability DistributionsDiscrete RVs, expectation & variance (incl. E(g(X)))
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Paper 4B: Further Statistics 2 (A Level)
15.5
Further Hypothesis TestingT-tests/means, variances (chi-squared and F tests)
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Paper 3C: Further Mechanics 1 (A Level)
16.1
Momentum and CollisionsMomentum & impulse, restitution, oblique collisions
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Paper 4C: Further Mechanics 2 (A Level)
17.2
Centres of Mass and Rigid BodiesLaminae, composite, toppling (incl. solids and calculus)
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17.3
Further Kinematics and DynamicsVariable forces, resistance (further dynamics and kinematics)
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Paper 3D: Decision Mathematics 1 (A Level)
18.2
Graphs and NetworksEulerian/Hamiltonian, planar, MST Kruskal/Prim, shortest path, route inspection, TSP
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Paper 4D: Decision Mathematics 2 (A Level)
19.4
Allocation, Transportation and Dynamic ProgrammingAllocation (Hungarian algorithm), transportation problems and dynamic programming
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StemUp Extreme Papers
Our hardest Further Maths questions, for students aiming for an A*. Every paper comes with full model answers.
AS Level papers
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Past papers
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