Hyperbolic functions: past paper questions
Real questions on hyperbolic functions
The newest 20 of 56 written questions. Open one to see it on the real paper.
- 9231/21 · May/June 2025 · Q6a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2025 · Q6b[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2025 · Q6c[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · 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 · Q6a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · May/June 2025 · Q2a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/42 · October/November 2024 · Q3a[1]
1-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2024 · Q4a[5]
5-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2024 · Q6a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2024 · Q6a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2023 · Q6a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2023 · Q6b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2023 · Q7a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2023 · Q6a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2023 · Q6b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2023 · Q8a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2023 · Q8c[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2023 · Q8a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2023 · Q8b[5]
5-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2023 · Q8c[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Almost all worked from one side of the equation to the other, after writing cosh and sinh in terms of exponentials, to fully justify the given identity.
— Examiner report, October/November 2023, 9231/21 Q6(a) (Cambridge)
Almost all used the given substitution with the identity from part (a) and integrated to get 4 4 sinh3 x + sinh5 x + C , although it was common to see the arbitrary constant omitted. 3 5
— Examiner report, October/November 2023, 9231/21 Q6(b) (Cambridge)
The majority of candidates presented the proof of the identity clearly, working from one side to the other and labelling the variable consistently.
— Examiner report, October/November 2023, 9231/22 Q7(a) (Cambridge)
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