Logarithmic and exponential functions: past paper questions
Real questions on logarithmic and exponential functions
The newest 20 of 53 written questions. Open one to see it on the real paper.
- 9709/32 · May/June 2026 · Q2[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · October/November 2025 · Q5a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2025 · Q1[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2025 · Q3b[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · October/November 2025 · Q2[3]
3-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · October/November 2025 · Q5a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2025 · Q2[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2025 · Q2a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2025 · Q2b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q2[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q1[5]
5-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · May/June 2025 · Q2[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · February/March 2025 · Q1[3]
3-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · October/November 2024 · Q1[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q6[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2024 · Q3a[3]
3-mark “State” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2024 · Q3b[2]
2-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/21 · May/June 2024 · Q3c[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/23 · May/June 2024 · Q2[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · May/June 2024 · Q2[4]
4-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Many candidates were able to gain full marks by re-arranging to obtain 1 – e–2x = e–3 before solving an equation of the form e–2x = a to find the solution. Some candidates did not obtain the last accuracy mark due to quoting the answer to three decimal places instead of the required four. A significant number of candidates struggled with this question, demonstrating a lack of knowledge of the rule...
— Examiner report, February/March 2025, 9709/32 Q1 (Cambridge)
For the candidates who rearranged this as a quadratic equation in ex , this was a very straight-forward question. There were many candidates who attempted to rewrite the laws of logarithms and worked through to obtain incorrect equations such as 3ln2x − 4ln ( −2x ) = ln5. In solutions with a correct initial method, the most common error was to try to process a negative value for ex .
— Examiner report, May/June 2023, 9709/31 Q1 (Cambridge)
Those candidates who applied the laws of logarithms correctly usually obtained x 2 = 2 . Many did not reject the negative root as being impossible. The question asks for an exact answer, so those candidates who only stated the decimal equivalent were not awarded the final mark.
— Examiner report, May/June 2023, 9709/32 Q2 (Cambridge)
Past papers, syllabus and examiner reports © UCLES (Cambridge University Press & Assessment). Questions are matched to topics from the official syllabus. AssessPro is independent and not endorsed by Cambridge.