Integration: past paper questions
Real questions on integration
The newest 20 of 95 written questions. Open one to see it on the real paper.
- 9231/21 · October/November 2025 · Q5a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2025 · Q5b[4]
4-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2025 · Q5c[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q4b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q6a[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q6b[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q6c[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q3b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q5a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q5b[4]
4-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q5c[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/33 · October/November 2025 · Q3a[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/33 · October/November 2025 · Q3b[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2025 · Q2a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · 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 · Q4a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q4b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q3a[2]
2-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q3b[6]
6-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q8c[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Joining the line OP on the diagram from part (c) showed candidates with good sketches that the required area needed to be found in two parts. Strong candidates choose the correct limits and added the two parts. Most candidates could integrate the functions correctly, and maintained accuracy when applying the required identities for cos2 θ and sin2 2θ .
— Examiner report, October/November 2023, 9231/13 Q6(d) (Cambridge)
Almost all made a good attempt at the integration by parts with many obtaining x tanh x − lncosh x. Most converted to obtain a result in sechn and sech1. Some candidates did not make the comparison between the sum and the integral clear and there was the occasional error with inconsistent limits.
— Examiner report, October/November 2023, 9231/22 Q5(b) (Cambridge)
Most candidates successfully applied the given substitution to change the integral to Good candidates maintained accuracy when changing limits and integrating using part (a).
— Examiner report, May/June 2023, 9231/22 Q3(b) (Cambridge)
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