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Edexcel A-level Further Maths questions by topic
Original topic questions for Edexcel A-level Further Maths (9FM0), set out under the sections of Pearson Edexcel's Further Mathematics specification from Proof to Decision analysis, in the order it prints them. Every question has a worked solution, and every set comes as a printable PDF.
Other specifications: Edexcel A-level Maths · AQA A-level Maths · AQA A-level Further Maths · OCR A-level Maths A · OCR A-level Further Maths A · OCR MEI A-level Maths · every topic, by unit
Core Pure: Papers 1 and 2
1 Proof30 questions2 topics
- Proof by induction: sums and series15 questions · 64 marks · 1.1 · PDF, 74 KB
- Induction: divisibility and matrices15 questions · 71 marks · 1.1 · PDF, 55 KB
1 Proof, Core Pure: Papers 1 and 2, on the specification map
2 Complex numbers76 questions5 topics
- Complex arithmetic and the Argand diagram15 questions · 56 marks · 2.1, 2.2, 2.3, 2.4 · PDF, 55 KB
- Roots of polynomials15 questions · 68 marks · 2.1, 2.3 · PDF, 77 KB
- Modulus, argument and loci16 questions · 67 marks · 2.2, 2.5, 2.6, 2.7 · PDF, 79 KB
- De Moivre's theorem and trigonometric identities15 questions · 60 marks · 2.6, 2.8, 2.9 · PDF, 77 KB
- Roots of unity and complex roots15 questions · 69 marks · 2.10, 2.11 · PDF, 77 KB
2 Complex numbers, Core Pure: Papers 1 and 2, on the specification map
3 Matrices46 questions3 topics
- Matrix algebra and transformations16 questions · 65 marks · 3.1, 3.2, 3.3 · PDF, 82 KB
- Systems of equations and invariance15 questions · 64 marks · 3.4, 3.7, 3.8 · PDF, 76 KB
- Determinants and inverses15 questions · 53 marks · 3.5, 3.6 · PDF, 74 KB
3 Matrices, Core Pure: Papers 1 and 2, on the specification map
4 Further algebra and functions45 questions3 topics
- Roots of polynomials15 questions · 68 marks · 4.1, 4.2 · PDF, 77 KB
- Summing series and the method of differences15 questions · 67 marks · 4.3, 4.4 · PDF, 77 KB
- Maclaurin series15 questions · 60 marks · 4.5, 4.6 · PDF, 73 KB
4 Further algebra and functions, Core Pure: Papers 1 and 2, on the specification map
5 Further calculus46 questions3 topics
- Volumes of revolution16 questions · 65 marks · 5.1 · PDF, 81 KB
- Mean values and improper integrals15 questions · 60 marks · 5.2, 5.3 · PDF, 75 KB
- Calculus with inverse trigonometric functions15 questions · 59 marks · 5.4, 5.5, 5.6 · PDF, 74 KB
5 Further calculus, Core Pure: Papers 1 and 2, on the specification map
6 Further vectors30 questions2 topics
- Lines and planes in three dimensions15 questions · 61 marks · 6.1, 6.2, 6.3, 6.4 · PDF, 75 KB
- Intersections, angles and distances15 questions · 58 marks · 6.3, 6.5 · PDF, 77 KB
6 Further vectors, Core Pure: Papers 1 and 2, on the specification map
7 Polar coordinates31 questions2 topics
- Polar curves16 questions · 66 marks · 7.1, 7.2 · PDF, 93 KB
- Areas with polar coordinates15 questions · 65 marks · 7.3 · PDF, 76 KB
7 Polar coordinates, Core Pure: Papers 1 and 2, on the specification map
8 Hyperbolic functions30 questions2 topics
- Hyperbolic functions and identities15 questions · 60 marks · 8.1, 8.3, 8.4 · PDF, 74 KB
- Calculus with hyperbolic functions15 questions · 62 marks · 8.2, 8.5 · PDF, 53 KB
8 Hyperbolic functions, Core Pure: Papers 1 and 2, on the specification map
9 Differential equations48 questions3 topics
- First order equations and integrating factors15 questions · 68 marks · 9.1, 9.2 · PDF, 56 KB
- Second order equations18 questions · 85 marks · 9.2, 9.4, 9.5, 9.6 · PDF, 78 KB
- Modelling with differential equations15 questions · 68 marks · 9.3, 9.7, 9.8, 9.9 · PDF, 78 KB
9 Differential equations, Core Pure: Papers 1 and 2, on the specification map
Further Pure 1: Paper 3A
1 Further Trigonometry15 questions1 topic
- The t-formulae15 questions · 61 marks · 1.1, 1.2, 1.3 · PDF, 74 KB
1 Further Trigonometry, Further Pure 1: Paper 3A, on the specification map
2 Further calculus45 questions3 topics
- Taylor series15 questions · 62 marks · 2.1 · PDF, 56 KB
- Limits and L'Hôpital's rule15 questions · 59 marks · 2.2, 2.4 · PDF, 75 KB
- Leibniz's theorem and the Weierstrass substitution15 questions · 60 marks · 2.3, 2.5 · PDF, 75 KB
2 Further calculus, Further Pure 1: Paper 3A, on the specification map
3 Further differential equations15 questions1 topic
- Series solutions of differential equations15 questions · 63 marks · 3.1, 3.2 · PDF, 79 KB
3 Further differential equations, Further Pure 1: Paper 3A, on the specification map
4 Coordinate systems30 questions2 topics
- Conic sections15 questions · 60 marks · 4.1, 4.2 · PDF, 54 KB
- Tangents, normals and loci of conics15 questions · 63 marks · 4.3, 4.4 · PDF, 57 KB
4 Coordinate systems, Further Pure 1: Paper 3A, on the specification map
5 Further vectors15 questions1 topic
- The vector product and the scalar triple product15 questions · 56 marks · 5.1, 5.2, 5.3 · PDF, 78 KB
5 Further vectors, Further Pure 1: Paper 3A, on the specification map
6 Further numerical methods16 questions1 topic
- Numerical methods for differential equations16 questions · 62 marks · 6.1, 6.2 · PDF, 85 KB
6 Further numerical methods, Further Pure 1: Paper 3A, on the specification map
7 Inequalities15 questions1 topic
- Inequalities and inequations15 questions · 61 marks · 7.1 · PDF, 52 KB
7 Inequalities, Further Pure 1: Paper 3A, on the specification map
Further Pure 2: Paper 4A
1 Groups30 questions2 topics
- Groups and their axioms15 questions · 62 marks · 1.1, 1.2, 1.3 · PDF, 55 KB
- Subgroups, Lagrange's theorem and isomorphism15 questions · 60 marks · 1.3, 1.4, 1.5 · PDF, 55 KB
1 Groups, Further Pure 2: Paper 4A, on the specification map
2 Further calculus30 questions2 topics
- Reduction formulae15 questions · 69 marks · 2.1 · PDF, 55 KB
- Arc length and surface area15 questions · 64 marks · 2.2 · PDF, 75 KB
2 Further calculus, Further Pure 2: Paper 4A, on the specification map
3 Further matrix algebra30 questions2 topics
- Eigenvalues and eigenvectors15 questions · 67 marks · 3.1 · PDF, 75 KB
- Diagonalisation and the Cayley-Hamilton theorem15 questions · 63 marks · 3.2, 3.3 · PDF, 78 KB
3 Further matrix algebra, Further Pure 2: Paper 4A, on the specification map
4 Further complex numbers30 questions2 topics
- Further loci and regions in the Argand diagram15 questions · 64 marks · 4.1 · PDF, 55 KB
- Transformations of the complex plane15 questions · 66 marks · 4.2 · PDF, 56 KB
4 Further complex numbers, Further Pure 2: Paper 4A, on the specification map
5 Number theory45 questions3 topics
- The Euclidean algorithm and Bézout's identity15 questions · 62 marks · 5.1, 5.2 · PDF, 55 KB
- Modular arithmetic and Fermat's little theorem15 questions · 60 marks · 5.3, 5.4, 5.5, 5.6 · PDF, 74 KB
- Combinatorics15 questions · 56 marks · 5.7 · PDF, 54 KB
5 Number theory, Further Pure 2: Paper 4A, on the specification map
6 Further sequences and series15 questions1 topic
- Recurrence relations15 questions · 77 marks · 6.1, 6.2, 6.3 · PDF, 77 KB
6 Further sequences and series, Further Pure 2: Paper 4A, on the specification map
Further Statistics 1: Paper 3B
1 Discrete probability distributions15 questions1 topic
2 Poisson and binomial distributions15 questions1 topic
- The Poisson distribution15 questions · 65 marks · 2.1, 2.2, 2.3 · PDF, 77 KB
2 Poisson and binomial distributions, Further Statistics 1: Paper 3B, on the specification map
3 Geometric and negative binomial distributions15 questions1 topic
- Geometric and negative binomial distributions15 questions · 57 marks · 3.1, 3.2, 3.3 · PDF, 58 KB
4 Hypothesis Testing15 questions1 topic
- Hypothesis tests for Poisson and geometric models15 questions · 58 marks · 4.1, 4.2 · PDF, 81 KB
4 Hypothesis Testing, Further Statistics 1: Paper 3B, on the specification map
5 Central Limit Theorem15 questions1 topic
- The Central Limit Theorem15 questions · 60 marks · 5.1 · PDF, 77 KB
5 Central Limit Theorem, Further Statistics 1: Paper 3B, on the specification map
6 Chi Squared Tests32 questions2 topics
- Goodness-of-fit tests16 questions · 67 marks · 6.1 · PDF, 85 KB
- Contingency tables16 questions · 62 marks · 6.1 · PDF, 83 KB
6 Chi Squared Tests, Further Statistics 1: Paper 3B, on the specification map
7 Probability generating functions15 questions1 topic
- Probability generating functions15 questions · 66 marks · 7.1, 7.2, 7.3 · PDF, 76 KB
7 Probability generating functions, Further Statistics 1: Paper 3B, on the specification map
8 Quality of tests15 questions1 topic
Further Statistics 2: Paper 4B
1 Linear Regression15 questions1 topic
- Least squares regression and residuals15 questions · 60 marks · 1.1, 1.2 · PDF, 79 KB
1 Linear Regression, Further Statistics 2: Paper 4B, on the specification map
2 Continuous probability distributions45 questions3 topics
- Continuous random variables: density and distribution functions15 questions · 61 marks · 2.1, 2.2 · PDF, 78 KB
- Mean, variance and skewness of continuous variables15 questions · 63 marks · 2.3 · PDF, 78 KB
- The continuous uniform distribution15 questions · 67 marks · 2.4 · PDF, 56 KB
2 Continuous probability distributions, Further Statistics 2: Paper 4B, on the specification map
3 Correlation31 questions2 topics
- Correlation coefficients: product moment and Spearman16 questions · 64 marks · 3.1, 3.2 · PDF, 84 KB
- Testing a correlation coefficient15 questions · 63 marks · 3.3 · PDF, 79 KB
3 Correlation, Further Statistics 2: Paper 4B, on the specification map
4 Combinations of random variables15 questions1 topic
5 Estimation, confidence intervals and tests using a normal distribution30 questions2 topics
- Estimators, standard error and confidence intervals15 questions · 57 marks · 5.1, 5.2, 5.3 · PDF, 79 KB
- Comparing two normal means15 questions · 59 marks · 5.4, 5.5 · PDF, 79 KB
6 Other hypothesis tests and confidence intervals15 questions1 topic
7 Confidence intervals and tests using the t-distribution15 questions1 topic
Further Mechanics 1: Paper 3C
1 Momentum and impulse31 questions2 topics
- Momentum and impulse16 questions · 72 marks · 1.1 · PDF, 107 KB
- Impulse and momentum as vectors15 questions · 60 marks · 1.2 · PDF, 79 KB
1 Momentum and impulse, Further Mechanics 1: Paper 3C, on the specification map
2 Work, energy and power15 questions1 topic
- Work, energy and power15 questions · 65 marks · 2.1 · PDF, 79 KB
2 Work, energy and power, Further Mechanics 1: Paper 3C, on the specification map
3 Elastic strings and springs and elastic energy30 questions2 topics
- Hooke's law and elastic strings15 questions · 60 marks · 3.1 · PDF, 80 KB
- Elastic potential energy15 questions · 64 marks · 3.2 · PDF, 80 KB
4 Elastic collisions in one dimension30 questions2 topics
- Direct impact and Newton's law of restitution15 questions · 65 marks · 4.1 · PDF, 80 KB
- Successive impacts and impacts with a wall15 questions · 64 marks · 4.2 · PDF, 79 KB
4 Elastic collisions in one dimension, Further Mechanics 1: Paper 3C, on the specification map
5 Elastic collisions in two dimensions15 questions1 topic
Further Mechanics 2: Paper 4C
1 Motion in a circle30 questions2 topics
- Angular speed and horizontal circular motion15 questions · 69 marks · 1.1 · PDF, 81 KB
- Motion in a vertical circle15 questions · 66 marks · 1.2 · PDF, 80 KB
1 Motion in a circle, Further Mechanics 2: Paper 4C, on the specification map
2 Centres of mass of plane figures45 questions3 topics
- Centre of mass of a discrete distribution15 questions · 59 marks · 2.1 · PDF, 56 KB
- Centres of mass of plane figures and frameworks15 questions · 58 marks · 2.2 · PDF, 59 KB
- Equilibrium, suspension, toppling and sliding15 questions · 57 marks · 2.2 · PDF, 59 KB
2 Centres of mass of plane figures, Further Mechanics 2: Paper 4C, on the specification map
3 Further centres of mass30 questions2 topics
- Centres of mass by integration15 questions · 72 marks · 3.1 · PDF, 57 KB
- Equilibrium, suspension, toppling and sliding15 questions · 57 marks · 3.2, 3.3 · PDF, 59 KB
3 Further centres of mass, Further Mechanics 2: Paper 4C, on the specification map
4 Further dynamics46 questions3 topics
- Newton's laws with a variable force15 questions · 65 marks · 4.1 · PDF, 80 KB
- Simple harmonic motion16 questions · 78 marks · 4.2 · PDF, 84 KB
- Oscillations on strings and springs15 questions · 65 marks · 4.2 · PDF, 80 KB
4 Further dynamics, Further Mechanics 2: Paper 4C, on the specification map
5 Further kinematics15 questions1 topic
Decision Mathematics 1: Paper 3D
1 Algorithms and graph theory30 questions2 topics
- Algorithms, sorting and bin packing15 questions · 67 marks · 1.1, 1.2 · PDF, 58 KB
- Graphs: order, Eulerian paths and planarity15 questions · 57 marks · 1.3, 1.4 · PDF, 57 KB
1 Algorithms and graph theory, Decision Mathematics 1: Paper 3D, on the specification map
2 Algorithms on graphs32 questions2 topics
- Minimum spanning trees: Prim and Kruskal16 questions · 60 marks · 2.1 · PDF, 67 KB
- Shortest paths: Dijkstra and Floyd16 questions · 76 marks · 2.2 · PDF, 62 KB
2 Algorithms on graphs, Decision Mathematics 1: Paper 3D, on the specification map
3 Algorithms on graphs II30 questions2 topics
- Route inspection15 questions · 66 marks · 3.1 · PDF, 57 KB
- The travelling salesman problem15 questions · 71 marks · 3.2 · PDF, 57 KB
3 Algorithms on graphs II, Decision Mathematics 1: Paper 3D, on the specification map
4 Critical path analysis31 questions2 topics
- Critical path analysis16 questions · 66 marks · 4.1, 4.2, 4.3 · PDF, 59 KB
- Float, Gantt charts and scheduling15 questions · 58 marks · 4.4, 4.5, 4.6 · PDF, 57 KB
4 Critical path analysis, Decision Mathematics 1: Paper 3D, on the specification map
5 Linear programming31 questions2 topics
- Linear programming: formulation and graphical solution16 questions · 65 marks · 5.1, 5.2 · PDF, 63 KB
- The Simplex algorithm15 questions · 68 marks · 5.3, 5.4 · PDF, 58 KB
5 Linear programming, Decision Mathematics 1: Paper 3D, on the specification map
Decision Mathematics 2: Paper 4D
1 Transportation problems31 questions2 topics
- Transportation problems and the north-west corner method16 questions · 70 marks · 1.1 · PDF, 63 KB
- The stepping-stone method15 questions · 70 marks · 1.2, 1.3 · PDF, 79 KB
1 Transportation problems, Decision Mathematics 2: Paper 4D, on the specification map
2 Allocation (assignment) problems15 questions1 topic
- Allocation and the Hungarian algorithm15 questions · 65 marks · 2.1, 2.2 · PDF, 59 KB
2 Allocation (assignment) problems, Decision Mathematics 2: Paper 4D, on the specification map
3 Flows in networks31 questions2 topics
- Flows in networks: cuts and capacity16 questions · 66 marks · 3.1, 3.4 · PDF, 64 KB
- Maximum flow and the labelling procedure15 questions · 59 marks · 3.2, 3.3, 3.5 · PDF, 59 KB
3 Flows in networks, Decision Mathematics 2: Paper 4D, on the specification map
4 Dynamic programming15 questions1 topic
5 Game theory30 questions2 topics
- Game theory: play safe and stable solutions15 questions · 65 marks · 5.1, 5.2, 5.3 · PDF, 58 KB
- Mixed strategies in game theory15 questions · 70 marks · 5.4, 5.5 · PDF, 57 KB
5 Game theory, Decision Mathematics 2: Paper 4D, on the specification map
6 Recurrence relations15 questions1 topic
- Recurrence relations15 questions · 77 marks · 6.1, 6.2 · PDF, 77 KB
6 Recurrence relations, Decision Mathematics 2: Paper 4D, on the specification map
7 Decision analysis15 questions1 topic
- Decision trees, expected monetary value and utility15 questions · 66 marks · 7.1, 7.2 · PDF, 59 KB
7 Decision analysis, Decision Mathematics 2: Paper 4D, on the specification map
A topic is listed under every section its lesson teaches, so some appear more than once. The codes beside each one are the specification references it covers in that section.
All questions, worked solutions and marking guidance are original InkMaths material. They are not copied from awarding-body papers or mark schemes. The codes show how InkMaths allocates the stated total; an awarding body may credit a valid alternative method differently.
The sections and codes are Pearson Edexcel's. Check the current specification when a mark depends on it. The 9FM0 specification map lists every statement, with the lesson that teaches it.