Differentiation: past paper questions
Real questions on differentiation
The newest 20 of 95 written questions. Open one to see it on the real paper.
- 9231/11 · October/November 2025 · Q3[7]
7-mark “Prove” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2025 · Q7a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2025 · Q8c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2025 · Q8d[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q3a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q3b[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q7a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q2a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q2b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q3a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q7a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q2a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q2b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q6b[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q6c[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q6d[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q7[10]
10-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2024 · Q6b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q2a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q2b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Most candidates understand the structure of a proof by induction but need to be sure that their statements are accurate. For the base case, a full solution needed the result of differentiating once to be shown to be the same as substituting n = 1 into the given formula. The inductive step was a straightforward application of the chain rule and the best solutions showed, and stated, that this was t...
— Examiner report, October/November 2023, 9231/12 Q2 (Cambridge)
Most used the substitution method and showed the expansion of ( y − 1) fully to justify their arrival at the given answer. Some found the coefficients of the new equation using the sums and products from the original equation and this also worked effectively in this case.
— Examiner report, October/November 2023, 9231/12 Q4(a) (Cambridge)
The stationary points were usually correct, with only a few errors in arithmetic.
— Examiner report, October/November 2023, 9231/13 Q7(b) (Cambridge)
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