Cambridge A-Level Further Pure Mathematics 1 (9231 Paper 1) Past Papers
Every year of Further Pure Mathematics 1 in one place. This page collects the 9231 Paper 1 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 1 is compulsory - it forms part of both the AS Level and the full A Level Further Mathematics.
What's on 9231 Paper 1: Further Pure Mathematics 1?
Further Pure Mathematics 1 is a 2h paper worth 75 marks, made up of the 7 syllabus areas below. Further Pure Mathematics 1 is compulsory - it forms part of both the AS Level and the full A Level Further Mathematics.
Roots of polynomial equations
Relationships between the roots and coefficients of a polynomial, and forming new equations by substitution.
Rational functions and graphs
Sketching graphs of rational functions, including asymptotes and intersections with the axes.
Summation of series
The method of differences and the standard results for the sums of powers of the natural numbers.
Matrices
Matrix operations, determinants and inverses, and matrices as linear transformations of the plane.
Polar coordinates
Curves given in polar form and the area of a region bounded by a polar curve.
Vectors
The vector (cross) product, and the equations of lines and planes in three dimensions.
Proof by induction
Proving results for series, divisibility and matrices by mathematical induction.
AS Level or A Level? AS & A Level
Further Pure Mathematics 1 is compulsory and counts toward both the AS Level and the full A Level - every Further Mathematics candidate sits it.
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 1 (9231/1) past papers by year
2025
2024
2023
2022
2021
2020
How to revise with Further Pure Mathematics 1 past papers
Work through one component at a time
Doing five years of Further Pure Mathematics 1 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 1 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 1 — Frequently asked questions
What topics are on 9231 Paper 1 (Further Pure Mathematics 1)?
What is the difference between the 9231/11, /12 and /13 variants?
Where can I get the mark schemes for Further Pure Mathematics 1?
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