Cambridge A-Level Pure Mathematics 3 (9709 Paper 3) Past Papers
Every year of Pure Mathematics 3 in one place. This page collects the 9709 Paper 3 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.
Pure Mathematics 3 is the pure paper for the full A Level. It includes all of the Pure 2 content and extends it.
What's on 9709 Paper 3: Pure Mathematics 3?
Pure Mathematics 3 is a 1h 50min paper worth 75 marks, made up of the 9 syllabus areas below. Pure Mathematics 3 includes everything in Pure Mathematics 2 and extends it further. Pure Mathematics 3 is the pure paper for the full A Level. It includes all of the Pure 2 content and extends it.
Algebra
Partial fractions, and the binomial expansion for any rational power.
Logarithms and exponentials
Modelling exponential growth and decay, and solving log and exponential equations.
Trigonometry
Addition and double-angle formulae, and the R sin(x + a) form for solving equations.
Differentiation
Implicit and parametric differentiation, building on the Pure 2 rules.
Integration
Integration by parts and by substitution, and integrating partial fractions.
Numerical solution of equations
Iterative methods for roots that cannot be found exactly.
Vectors
Vectors in three dimensions, the scalar product, and the equation of a line.
Differential equations
Forming and solving first-order equations by separating the variables.
Complex numbers
Arithmetic, the Argand diagram, modulus-argument form, and loci.
AS Level or A Level? A Level only
Pure Mathematics 3 is the pure paper for the full A Level, taken instead of Paper 2. It includes all of the Pure 2 content and extends it, and is combined with Paper 1 and two applied papers for the complete A Level.
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.
Pure Mathematics 3 (9709/3) past papers by year
2025
2024
2023
2022
2021
2020
How to revise with Pure Mathematics 3 past papers
Work through one component at a time
Doing five years of Pure Mathematics 3 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 1h 50min
Sit each paper at the real duration. Pacing is a skill in itself, and Pure Mathematics 3 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 Mathematics 9709 papers
9709 Paper 3 — Frequently asked questions
What topics are on 9709 Paper 3 (Pure Mathematics 3)?
What is the difference between the 9709/31, /32 and /33 variants?
Where can I get the mark schemes for Pure Mathematics 3?
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