Integration: past paper questions
Real questions on integration
The newest 20 of 218 written questions. Open one to see it on the real paper.
- 9709/12 · May/June 2026 · Q9a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2026 · Q6b[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · October/November 2025 · Q8a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · October/November 2025 · Q8b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/12 · October/November 2025 · Q4b[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/12 · October/November 2025 · Q5b[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/13 · October/November 2025 · Q9[8]
8-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2025 · Q1[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2025 · Q5b[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2025 · Q6a[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2025 · Q6b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2025 · Q6c[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · October/November 2025 · Q1[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · October/November 2025 · Q5b[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2025 · Q1[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2025 · Q8[8]
8-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q4[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q8b[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q9b[4]
4-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q10a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Successful candidates began by integrating the second derivative to find , and used the fact that dx dy = 0 when x = 21 to find the constant of integration. They then integrated again to find an dx equation for y, substituted x = 21 and y = 9 to find the second constant of integration and hence found the equation of the curve. dy A significant number of candidates incorrectly used = 9 after the f...
— Examiner report, February/March 2025, 9709/12 Q9(b) (Cambridge)
Only the stronger candidates found this question straightforward. Finding the equation of the tangent at (7, 0) was required to find the area of triangle OPQ, either from integration of the tangent or from using its x and y intercepts. Some candidates omitted the step of subtracting their answer dy to part (a). A more common error was that some candidates did not realise that finding was dx initia...
— Examiner report, February/March 2025, 9709/12 Q10(b) (Cambridge)
Almost all candidates knew they needed to use integration by parts. Some candidates, having correctly integrated by parts once, did not then realise they needed to integrate by parts a second time and did not appear to recognise the structure of this second problem. Candidates who understood they needed to integrate by parts twice usually did so successfully, aside from the occasional sign or coef...
— Examiner report, February/March 2025, 9709/32 Q11 (Cambridge)
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