Cambridge International AS & A Level · 9231
Cambridge A Level Further Mathematics 9231 topical past papers
Cambridge International AS & A Level Further Mathematics (9231) is a second mathematics qualification for students who are taking, or have completed, Cambridge International AS & A Level Mathematics (9709), often with mathematics, physics, engineering or computer science in view. Further Pure Mathematics extends algebra and calculus to matrices, complex numbers, polar coordinates, series, hyperbolic functions, proof by induction and differential equations. Further Mechanics and Further Probability & Statistics build on the 9709 applied papers, and each 9231 paper assumes particular 9709 papers as prior knowledge.
- Questions
- 2,422
- Past papers
- 282
- Years
- 2010–2026
- With mark scheme
- 99%
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
Further Mathematics 9231 chapters
The chapters the bank files this subject’s questions under, in syllabus order. Each has a page of its own.
Revising Further Mathematics 9231 by topic
There are four papers: Paper 1, Further Pure Mathematics 1; Paper 2, Further Pure Mathematics 2, which assumes the Paper 1 content; Paper 3, Further Mechanics; and Paper 4, Further Probability & Statistics. Each consists of structured questions, all compulsory. AS Level candidates take Paper 1 with either Paper 3 or Paper 4, and the full A Level requires all four papers. A booklet of formulae and statistical tables is provided in the examination. The current syllabus applies to examinations in 2026 and 2027.
- Before the current four-paper structure, Paper 1 covered all the pure content and Paper 2 was a mixed paper of mechanics and statistics. When you filter older years by paper, expect mechanics and statistics under Paper 2 and complex numbers or differential equations under Paper 1; filtering by chapter avoids the confusion.
- Rotation of a rigid body and bivariate data are no longer in the syllabus, and simple harmonic motion is not a named topic of Further Mechanics. Questions on these come from the older papers, so leave them aside unless you need them for another course.
- Matrices are split across both pure papers: Paper 1 asks about transformations and invariant points and lines, while Paper 2 asks for eigenvalues, eigenvectors, diagonalisation and the Cayley–Hamilton theorem. Use the paper filter on the Matrices chapter to practise each part at the right stage.
- Proof by induction and summation of series are marked on presentation as much as on the result: the base case, the inductive hypothesis, the step and the conclusion, or the method of differences set out line by line. Compare your layout with the mark scheme, not only your final answer.
- In Paper 4, tests using the t-distribution, chi-squared tests and non-parametric tests are marked for the hypotheses, the test statistic, the critical value and a conclusion in context. Practise them as complete tests, then use the mock exam builder to set a paper that matches the AS or A Level route you are taking.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.
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