Cambridge A-Level Further Pure Mathematics 2 (9231 Paper 2) Past Papers
Every year of Further Pure Mathematics 2 in one place. This page collects the 9231 Paper 2 question papers and mark schemes for all variants, from 2020 to 2025 — so you can work through one component start to finish instead of hunting session by session.
Further Pure Mathematics 2 is examined only in the full A Level Further Mathematics.
What's on 9231 Paper 2: Further Pure Mathematics 2?
Further Pure Mathematics 2 is a 2h paper worth 75 marks, made up of the 6 syllabus areas below. Further Pure Mathematics 2 is examined only in the full A Level Further Mathematics.
Hyperbolic functions
Definitions and identities, and the inverse hyperbolic functions.
Matrices
Eigenvalues and eigenvectors, and the diagonalisation of a matrix.
Differentiation
Further techniques, including the derivatives of inverse and hyperbolic functions.
Integration
Reduction formulae, arc length, and the area of a surface of revolution.
Complex numbers
De Moivre's theorem, the nth roots of a complex number, and the exponential form.
Differential equations
First- and second-order linear differential equations.
AS Level or A Level? A Level only
Further Pure Mathematics 2 is taken only for the full A Level Further Mathematics; it is not part of any AS Level route.
Centres choose the component combination - if you are unsure which papers your route needs, check with your school's exams officer.
When is this paper next sat?
Cambridge examines A-Level Mathematics in the June and October/November series each year (with a February/March series in some countries). The next sitting is the October/November 2026 series.
Further Pure Mathematics 2 (9231/2) past papers by year
2025
2024
2023
2022
2021
2020
How to revise with Further Pure Mathematics 2 past papers
Work through one component at a time
Doing five years of Further Pure Mathematics 2 back-to-back trains the specific question styles and topic weighting of this one paper far better than jumping between components. Patterns repeat - you will start to recognise them.
Time yourself at 2h
Sit each paper at the real duration. Pacing is a skill in itself, and Further Pure Mathematics 2 rewards finishing every question with time to check.
Mark with the matching scheme
Self-mark with the mark scheme for the same session and variant. Note where you lost method marks versus accuracy marks - they need different fixes.
Practise across variants
Variants 1, 2 and 3 test the same syllabus at equivalent difficulty. Working all three for a year gives you three fresh sittings of the same paper.
Tip: open a question paper and its mark scheme side-by-side in our free Exam Hub.
Other Further Mathematics 9231 papers
9231 Paper 2 — Frequently asked questions
What topics are on 9231 Paper 2 (Further Pure Mathematics 2)?
What is the difference between the 9231/21, /22 and /23 variants?
Where can I get the mark schemes for Further Pure Mathematics 2?
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