Logarithmic and exponential functions: past paper questions
Real questions on logarithmic and exponential functions
The newest 8 of 8 written questions. Open one to see it on the real paper.
- 9709/11 · May/June 2025 · Q10a[5]
5-mark “Describe” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · May/June 2025 · Q10b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · May/June 2025 · Q10c[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · May/June 2025 · Q10d[1]
1-mark “State” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/11 · May/June 2025 · Q10e[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2023 · Q4a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2023 · Q4b[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/22 · May/June 2021 · Q5c[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
The candidates needed to consider the left-hand side of the modulus graph which was equivalent to the equation y = 4 − 5 x . The best way to show by calculation that α lies between 0.36 and 1 1 − x − x 0.37, is to make use of the expression 3 − e 2 + 5 x − 4 or 3 + e 2 − 5 x + 4 and substitute in the values of 0.36 and 0.37. Many candidates did just this. It is essential that the resulting decimal...
— Examiner report, May/June 2023, 9709/22 Q4(b) (Cambridge)
Most candidates realised that the x term from part (b) needed to be replaced by e −3 y . Fewer deduced that there was only one possible solution of e −3 y = 2 , with some candidates considering either solutions from incorrect responses to part (b) as well. For this question it was necessary to give an exact answer, with some candidates giving their answers in decimal form.
— Examiner report, May/June 2021, 9709/22 Q5(c) (Cambridge)
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