Rational functions and graphs: past paper questions
Real questions on rational functions and graphs
The newest 20 of 105 written questions. Open one to see it on the real paper.
- 9231/11 · October/November 2025 · Q7d[2]
2-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2025 · Q7e[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · October/November 2025 · Q7a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/13 · October/November 2025 · Q7c[3]
3-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/13 · October/November 2025 · Q7d[2]
2-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · May/June 2025 · Q7d[1]
1-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · May/June 2025 · Q7e[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · May/June 2025 · Q7a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · May/June 2025 · Q7b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · May/June 2025 · Q7c[3]
3-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · May/June 2025 · Q7d[1]
1-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · May/June 2025 · Q7e[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2024 · Q3a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2024 · Q4b[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2024 · Q6c[5]
5-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/11 · October/November 2024 · Q6d[2]
2-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · October/November 2024 · Q6a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · October/November 2024 · Q6c[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · October/November 2024 · Q6d[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/12 · October/November 2024 · Q6e[4]
4-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
The stationary points were usually correct, with only a few errors in arithmetic.
— Examiner report, October/November 2023, 9231/11 Q7(b) (Cambridge)
The strongest candidates could sketch y = by reference to the graph of y = f ( x ) . Good f (x) sketches used y = 1 as the only asymptote. They also made clear the intersection at (–1, 0), the maximum point and that the graph then approached the asymptote from above.
— Examiner report, October/November 2023, 9231/11 Q7(d) (Cambridge)
Most diagrams were of acceptable shape and labelled correctly. Good sketches clearly showed C1 as a semi-circle with P on the right-hand side of C1 .
— Examiner report, October/November 2023, 9231/13 Q6(c) (Cambridge)
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