AS & A Level Further Mathematics (9231) — real past-paper questions, marked by AI
Further Mathematics (9231) assumes you already know A Level Mathematics (9709) and builds straight on top of it, across Further Pure 1, Further Pure 2, Further Mechanics and Further Probability & Statistics. The command words — determine, show that, sketch — carry more weight here, because the working expected is longer and the algebra less forgiving than the core syllabus.
This hub holds 993 real 9231 questions from 63 papers set between 2023 and 2025. Rational functions and their asymptotes lead the topic table with 9 questions, ahead of vectors and the equation of a plane, summation of series by the method of differences, and proof by induction. Write out your full method and the AI examiner marks it instantly against the real Cambridge mark scheme, crediting each step the way a human examiner would rather than judging only the final line.
Sweep one component at a time — Further Pure, Further Mechanics, Further Probability & Statistics — before combining them into a timed paper. It is free, with no signup needed.
New: How AS & A Level Further Mathematics is marked — command words, examiner-report findings and revision strategy.
Past papers by year
2025
| Paper | Session | Questions |
|---|---|---|
| Paper 11 | May–June 2025 | 7 |
| Paper 12 | May–June 2025 | 7 |
| Paper 13 | May–June 2025 | 7 |
| Paper 21 | May–June 2025 | 8 |
| Paper 22 | May–June 2025 | 8 |
| Paper 23 | May–June 2025 | 8 |
| Paper 24 | May–June 2025 | 8 |
| Paper 31 | May–June 2025 | 7 |
| Paper 32 | May–June 2025 | 7 |
| Paper 33 | May–June 2025 | 7 |
| Paper 34 | May–June 2025 | 7 |
| Paper 41 | May–June 2025 | 6 |
| Paper 42 | May–June 2025 | 6 |
| Paper 43 | May–June 2025 | 6 |
| Paper 44 | May–June 2025 | 6 |
2024
| Paper | Session | Questions |
|---|---|---|
| Paper 11 | May–June 2024 | 1 |
| Paper 12 | May–June 2024 | 7 |
| Paper 13 | May–June 2024 | 7 |
| Paper 21 | May–June 2024 | 8 |
| Paper 22 | May–June 2024 | 8 |
| Paper 23 | May–June 2024 | 8 |
| Paper 31 | May–June 2024 | 7 |
| Paper 32 | May–June 2024 | 7 |
| Paper 33 | May–June 2024 | 7 |
| Paper 41 | May–June 2024 | 7 |
| Paper 42 | May–June 2024 | 7 |
| Paper 43 | May–June 2024 | 6 |
| Paper 11 | October–November 2024 | 7 |
| Paper 12 | October–November 2024 | 7 |
| Paper 13 | October–November 2024 | 7 |
| Paper 21 | October–November 2024 | 8 |
| Paper 22 | October–November 2024 | 8 |
| Paper 23 | October–November 2024 | 8 |
| Paper 31 | October–November 2024 | 7 |
| Paper 32 | October–November 2024 | 7 |
| Paper 33 | October–November 2024 | 7 |
| Paper 41 | October–November 2024 | 6 |
| Paper 42 | October–November 2024 | 6 |
| Paper 43 | October–November 2024 | 6 |
2023
| Paper | Session | Questions |
|---|---|---|
| Paper 11 | May–June 2023 | 7 |
| Paper 12 | May–June 2023 | 7 |
| Paper 13 | May–June 2023 | 7 |
| Paper 21 | May–June 2023 | 8 |
| Paper 22 | May–June 2023 | 8 |
| Paper 23 | May–June 2023 | 8 |
| Paper 31 | May–June 2023 | 7 |
| Paper 32 | May–June 2023 | 7 |
| Paper 33 | May–June 2023 | 7 |
| Paper 41 | May–June 2023 | 6 |
| Paper 42 | May–June 2023 | 6 |
| Paper 43 | May–June 2023 | 6 |
| Paper 11 | October–November 2023 | 7 |
| Paper 12 | October–November 2023 | 7 |
| Paper 13 | October–November 2023 | 7 |
| Paper 21 | October–November 2023 | 8 |
| Paper 22 | October–November 2023 | 8 |
| Paper 23 | October–November 2023 | 8 |
| Paper 31 | October–November 2023 | 6 |
| Paper 32 | October–November 2023 | 7 |
| Paper 33 | October–November 2023 | 6 |
| Paper 41 | October–November 2023 | 6 |
| Paper 42 | October–November 2023 | 5 |
| Paper 43 | October–November 2023 | 6 |
Practise AS & A Level Further Mathematics by topic
- Matrices (38 questions)
- Inference and hypothesis testing (31 questions)
- Summation of series (28 questions)
- Differential equations (24 questions)
- Hooke's law and elasticity (21 questions)
- Hyperbolic functions (18 questions)
- Projectiles (18 questions)
- Non-parametric tests (18 questions)
- Complex numbers (17 questions)
- Vectors (16 questions)
- Equilibrium of a rigid body (16 questions)
- Continuous random variables (16 questions)
- Chi-squared tests (16 questions)
- Probability generating functions (16 questions)
- Roots of polynomial equations (15 questions)
- Rational functions and graphs (14 questions)
- Polar coordinates (14 questions)
- Momentum and impulse (14 questions)
- Circular motion (14 questions)
- Linear motion under a variable force (11 questions)
- Proof by induction (9 questions)
- Differentiation (8 questions)
- Reduction formulae (7 questions)
- Maclaurin series (7 questions)
- Integration (6 questions)
- Arc length and surface area (6 questions)
Frequently asked questions
Which 9231 papers and years are covered?
Every May–June and October–November session from 2023 to 2025 — 63 papers across Papers 1 to 4 and their variants.
Do I need A Level Maths before starting Further Maths?
Yes — Further Mathematics assumes knowledge of A Level Mathematics (9709), and the 9231 papers build directly on that content with harder, longer problems.
How does the AI marking work for 9231 answers?
You type out your full method, and an AI examiner checks each line against the official Cambridge mark scheme for that question, awarding marks step by step as a human marker would.
What do Papers 1 to 4 cover in 9231?
The four papers cover Further Pure 1, Further Pure 2, Further Mechanics and Further Probability & Statistics. Practise the component numbers your course actually studies.
Is it really free?
Yes — every question, mark scheme and AI marking run is free, with no signup and no card required.
Are these official Cambridge papers?
Questions are transcribed from real Cambridge papers and marked against the real mark schemes, which remain © Cambridge International. Cambridge Papers is an independent study tool, not affiliated with or endorsed by Cambridge.