Functions: past paper questions

Real questions on functions

The newest 20 of 200 written questions. Open one to see it on the real paper.

1. 9709/12 · May/June 2026 · Q2a[5]
   In the diagram, the graph with equation $y=f(x)$ is shown with solid lines and the graph with equation $y=g(x)$ is shown with broken lines. [Diagram: A coordinate grid with $x$-axis from -1 to 8 and $y$-axis from -10 to 4. A solid line graph $y=f(x)$ consists of a line segment from $(0,-10)$ to $(2,-4)$, a line s...See it on the paper →
2. 9709/12 · May/June 2026 · Q2b[2]
   In the diagram, the graph with equation $y=f(x)$ is shown with solid lines and the graph with equation $y=g(x)$ is shown with broken lines. [Diagram: A Cartesian coordinate system with $x$-axis from -1 to 8 and $y$-axis from -10 to 4. A solid line graph $y=f(x)$ consists of a line segment from $(0,-10)$ to $(2, -4...See it on the paper →
3. 9709/11 · October/November 2025 · Q3[5]

   5-mark “Find” question — its maths and diagrams are best seen on the paper.

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4. 9709/11 · October/November 2025 · Q4a[3]

   3-mark question — its maths and diagrams are best seen on the paper.

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5. 9709/11 · October/November 2025 · Q6a[1]

   1-mark “State” question — its maths and diagrams are best seen on the paper.

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6. 9709/11 · October/November 2025 · Q6b[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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7. 9709/11 · October/November 2025 · Q6c[4]

   4-mark “Solve” question — its maths and diagrams are best seen on the paper.

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8. 9709/12 · October/November 2025 · Q8b(ii)[3]

   3-mark “Find” question — its maths and diagrams are best seen on the paper.

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9. 9709/12 · October/November 2025 · Q9b[1]

   1-mark “State” question — its maths and diagrams are best seen on the paper.

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10. 9709/12 · October/November 2025 · Q9c[1]

    1-mark “Find” question — its maths and diagrams are best seen on the paper.

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11. 9709/12 · October/November 2025 · Q9d[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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12. 9709/13 · October/November 2025 · Q3c[1]

    1-mark “State” question — its maths and diagrams are best seen on the paper.

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13. 9709/13 · October/November 2025 · Q6a[5]

    5-mark “Describe” question — its maths and diagrams are best seen on the paper.

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14. 9709/13 · October/November 2025 · Q6b[3]

    3-mark “State” question — its maths and diagrams are best seen on the paper.

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15. 9709/13 · October/November 2025 · Q7[4]

    4-mark question — its maths and diagrams are best seen on the paper.

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16. 9709/23 · October/November 2025 · Q7c[2]

    2-mark “Show” question — its maths and diagrams are best seen on the paper.

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17. 9709/33 · October/November 2025 · Q8b[2]

    2-mark question — its maths and diagrams are best seen on the paper.

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18. 9709/33 · October/November 2025 · Q8c[2]

    2-mark “Show” question — its maths and diagrams are best seen on the paper.

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19. 9709/33 · October/November 2025 · Q8d[3]

    3-mark “Give” question — its maths and diagrams are best seen on the paper.

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20. 9709/11 · May/June 2025 · Q10f[1]

    1-mark “Explain” question — its maths and diagrams are best seen on the paper.

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What examiners said

It was clear that the majority of candidates understood the concept of composite functions and were able to correctly combine the given functions. However, in many candidates’ responses, algebraic errors were present which resulted in incorrect answers or insufficient steps being shown in this ‘show that’ question.

— Examiner report, February/March 2025, 9709/12 Q11(a) (Cambridge)

In questions of this nature, where multiple transformations are to be applied, candidates are encouraged to apply them one at a time. This allows the order in which the candidate applies the transformations to be clearly expressed in their solution.

— Examiner report, February/March 2025, 9709/12 Q11(b) (Cambridge)

This part of the question proved to be very demanding for most candidates. The format of their final answer to part (b) made this part more or less straightforward when looking for the maximum value of h(x). Successful candidates’ answers to part (b) contained –8k(x – 2)2 which is non-positive, so the rest of the function determined the highest value of the range. Other starting points could event...

— Examiner report, February/March 2025, 9709/12 Q11(c) (Cambridge)