Graphs of functions Notes and examples: past paper questions

Real questions on graphs of functions notes and examples

The newest 20 of 29 written questions. Open one to see it on the real paper.

1. 4024/22 · October/November 2025 · Q17a[2]

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

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2. 4024/11 · October/November 2024 · Q21[2]
   21 The diagram shows the speed–time graph for a journey. [Diagram: A speed-time graph. The vertical axis is labelled "Speed (m/s)" and the horizontal axis is labelled "Time (seconds)". The graph starts at the origin $(0,0)$, rises linearly to the point $(10,10)$, continues horizontally to the point $(30,10)$, and the...See it on the paper →
3. 4024/11 · October/November 2024 · Q22a[1]
   22 $f(x)=3x^2+5$ (a) Work out $f(-1)$.See it on the paper →
4. 4024/21 · October/November 2024 · Q3b[3]

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

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5. 4024/21 · October/November 2024 · Q3c[1]

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

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6. 4024/22 · October/November 2024 · Q6b[3]

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

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7. 4024/22 · October/November 2024 · Q6c[2]
   (c) The equation $\frac{x}{4}(2x^2-x-10)=k$ has exactly two solutions. Use your graph to find the possible values of $k$. $k=\dots$ or $k=\dots$See it on the paper →
8. 4024/22 · October/November 2024 · Q6d[4]

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

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9. 4024/12 · May/June 2024 · Q22a[2]

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

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10. 4024/21 · May/June 2024 · Q8b[3]

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

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11. 4024/21 · May/June 2023 · Q1c[3]

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

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12. 4024/22 · October/November 2022 · Q3c[3]

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

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13. 4024/22 · October/November 2022 · Q3d[1]
    [Diagram: A cuboid with height $h$ and square base of edge $x$] A cuboid has height $h$ cm and a square base of edge $x$ cm. The volume of the cuboid is $60{\text{ cm}}^3$. (d) Find the minimum possible surface area of the cuboid.See it on the paper →
14. 4024/22 · October/November 2022 · Q3e[3]
    [Diagram: A cuboid with height $h$ and a square base of edge $x$] A cuboid has height $h$ cm and a square base of edge $x$ cm. The volume of the cuboid is $60{\text{ cm}}^3$. (e) The cuboid has a surface area of $120{\text{ cm}}^2$. The height of the cuboid is greater than the length of the edge of its base. Find the dim...See it on the paper →
15. 4024/12 · May/June 2022 · Q16b[3]

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

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16. 4024/12 · October/November 2021 · Q14c[3]
    14 The diagram shows the speed-time graph for the start of a cyclist's journey. [Diagram: A speed-time graph. The vertical axis is labelled "Speed (m/s)" with tick marks at 0, 5, 10, 15, 20. The horizontal axis is labelled "Time ($t$ seconds)" with tick marks at 0, 10, 20, 30, 40, 50. The graph is a line starting at th...See it on the paper →
17. 4024/21 · October/November 2021 · Q7b(i)[2]

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

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18. 4024/21 · October/November 2021 · Q7b(iii)[4]

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

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19. 4024/21 · May/June 2021 · Q7c(ii)[4]

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

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20. 4024/21 · October/November 2020 · Q4c[2]

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

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What examiners said

Many good responses were seen to this question. Most candidates plotted the points correctly. The most common error was seen when plotting the y values of 78.75 and 93.75. The points were then usually joined with a smooth curve.

— Examiner report, May/June 2023, 4024/21 Q1(c) (Cambridge)

A significant number of candidates correctly plotted the required graph. However, a number of candidates did not manage to use the vertical scale of 4 units to 1 small square correctly leading to inaccurate plotting of some of the points. The most common incorrect plots were (6, 112) plotted at (6, 104) and (1, 242) plotted at (0.5, 242). Unusually, there were several candidates who plotted bar ch...

— Examiner report, October/November 2022, 4024/22 Q3(c) (Cambridge)

Some candidates understood the need to read the graph at A = 120, but not all gave the minimum value with some choosing to give both values in their dimensions. Having obtained a value for x, many candidates did not know how to use this value correctly in relation to the question to obtain the other two dimensions. It was common to see a dimension of 2, possibly from assuming the values had to be...

— Examiner report, October/November 2022, 4024/22 Q3(e) (Cambridge)