A level Further Maths past papers
Every A level Further Maths exam board publishes its past papers free, with mark schemes and examiner reports. All boards set compulsory core pure papers plus optional papers in areas such as mechanics, statistics and decision maths. Pick your board below to preview, open or download its papers.
Choose your exam board
- AQA A level Further Maths past papersFurther Maths (7367): every public paper to preview or download
- Edexcel A level Further Maths past papersFurther Maths (9FM0): where to find every paper, and how they work
- OCR A level Further Maths past papersFurther Mathematics A (H245): every public paper to preview or download
How the boards compare
| Board | Papers | Marks | Time |
|---|---|---|---|
| AQA (7367) | Papers 1 and 2 pure; Paper 3 two options | 100 marks each | 2 hours each |
| Edexcel (9FM0) | Core Pure 1 and 2, then two option papers | 75 marks each | 1 hour 30 minutes each |
| OCR Further Maths A (H245) | Pure core 1 and 2, then two option papers | 75 marks each | 1 hour 30 minutes each |
How to use past papers
- Learn the content first. Use topic questions while you are still learning; save full papers for when you have covered most of the course.
- Do full papers under exam conditions: timed, no notes, with the formula sheet or booklet you will have on the day.
- Mark strictly with the mark scheme, including method marks, and add up your score.
- Read the examiner report for the questions you lost marks on: it explains the common mistakes and what full marks looked like.
- Keep an error log of every lost mark and its topic, then revise those topics before your next paper.
- Save the newest papers for your final mocks in the last few weeks.
Free A level Further Maths practice questions
Ten original questions written by our tutors in the style of the exam. Choose an answer to see if you are right and why.
Answered 0 of 10 · 0 correct
1. What is (2 + 3i)(1 − i)?
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A. 2 − 2i + 3i − 3i² = 2 + i + 3 = 5 + i.
2. What is the modulus of 3 − 4i?
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B. |3 − 4i| = √(9 + 16) = 5.
3. What is the determinant of the matrix with rows (2, 1) and (5, 3)?
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A. det = 2 × 3 − 1 × 5 = 1.
4. What is Σ r from r = 1 to 20?
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C. Σ r = n(n + 1)/2 = 20 × 21 ÷ 2 = 210.
5. What is Σ r² from r = 1 to 10?
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C. Σ r² = n(n + 1)(2n + 1)/6 = 10 × 11 × 21 ÷ 6 = 385.
6. A quadratic has roots α and β with α + β = 5 and αβ = 6. What is α² + β²?
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B. α² + β² = (α + β)² − 2αβ = 25 − 12 = 13.
7. What is the derivative of arctan x?
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A. d/dx(arctan x) = 1/(1 + x²).
8. What is cosh 0?
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B. cosh 0 = (e⁰ + e⁰)/2 = 1.
9. Write 1 + i in modulus-argument form.
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A. |1 + i| = √2 and arg(1 + i) = π/4.
10. For a proof by induction, what must you show first?
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B. Induction starts with the basis case, then shows that truth for n = k implies truth for n = k + 1.
Frequently asked questions
Which Further Maths options should I practise?
Only the options you are entered for. Your teacher chooses them, so check before you start past papers.
Is a formula booklet provided in Further Maths?
Yes. Each board provides its own formula booklet, which also includes the A level Maths formulas.
Which board am I doing?
The code on the cover is 7367 (AQA), 9FM0 (Edexcel) or H245 (OCR Further Maths A).
Is Further Maths much harder than A level Maths?
It goes further into topics such as complex numbers, matrices and proof by induction, and it moves faster. Strong A level Maths algebra is the best preparation.