Extended: Sketching curves: past paper questions

Real questions on extended: sketching curves

The newest 17 of 17 written questions. Open one to see it on the real paper.

1. 0980/31 · October/November 2024 · Q8b(ii)[3]

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

   See it on the paper →
2. 0980/31 · October/November 2024 · Q8b(iii)[1]
   (iii) Use your graph to solve the equation $2x^2+x=30$ for $0\le x\le 5$.See it on the paper →
3. 0980/41 · October/November 2024 · Q8b(i)[2]

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

   See it on the paper →
4. 0980/41 · October/November 2024 · Q8b(ii)[1]
   (b) $\mathrm{h}(x)=3^x$ (ii) Write down the equation of the asymptote to the graph of $y=\mathrm{h}(x)$.See it on the paper →
5. 0980/41 · October/November 2024 · Q9c[4]
   [Diagram: A cuboid $ABCDEFHG$ with vertices labelled. $AB=10\text{ cm}$, $BC=8\text{ cm}$, $CG=17\text{ cm}$. The text "NOT TO SCALE" is present.] $ABCDEFHG$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. (c) Calculate the angle between $GA$ and the base $ABCD$.See it on the paper →
6. 0980/41 · October/November 2024 · Q9d[4]
   ABCDEFGH is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. (d) A straight rod $PQ$ is placed inside the cuboid. One end of the rod, $P$, is placed at the midpoint of $AB$. The other end of the rod, $Q$, rests on $GH$. $HQ:QG=4:1$. [Diagram: A cuboid ABCDEFGH with a rod PQ. P...See it on the paper →
7. 0980/32 · May/June 2024 · Q6a(ii)[4]

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

   See it on the paper →
8. 0980/32 · May/June 2024 · Q6a(iii)[1]
   (iii) Write down the equation of the line of symmetry of the graph.See it on the paper →
9. 0980/32 · May/June 2024 · Q6b(i)[2]

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

   See it on the paper →
10. 0980/32 · May/June 2024 · Q6b(iii)[2]
    (b) A straight line has a gradient of $\frac{1}{2}$ and passes through the point $(2,7)$. (iii) Write down the coordinates of the points where this line intersects the graph of $y=-x^2+8x+1$.See it on the paper →
11. 0980/21 · October/November 2022 · Q21[2]

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

    See it on the paper →
12. 0980/42 · May/June 2022 · Q12a[5]
    A curve has equation $y=x^3-k{x}^2+1$. When $x=2$, the gradient of the curve is 6. (a) Show that $k=1.5$.See it on the paper →
13. 0980/42 · May/June 2022 · Q12b[4]
    A curve has equation $y=x^3-k{x}^2+1$. When $x=2$, the gradient of the curve is 6. (b) Find the coordinates of the two stationary points of $y=x^3-1.5x^2+1$. You must show all your working.See it on the paper →
14. 0980/42 · May/June 2022 · Q12c[2]

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

    See it on the paper →
15. 0980/42 · May/June 2021 · Q2a(ii)[4]

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

    See it on the paper →
16. 0980/42 · May/June 2021 · Q2c[2]
    The table shows some values for $y=2\times 0.5^x-1$. | $x$ | $-1$ | $-0.5$ | $0$ | $0.5$ | $1$ | $1.5$ | $2$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | $3$ | $1.83$ | | $0.41$ | $0$ | $-0.29$ | | (c) There are no solutions to the equation $2\times 0.5^x-1=k$ where $k$ is an integer....See it on the paper →
17. 0980/42 · May/June 2019 · Q5b[4]

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

    See it on the paper →

What examiners said

Many curves were very well drawn with very little feathering or double lines seen. A few joined up some or all of their points with straight lines.

— Examiner report, May/June 2024, 0980/32 Q6(a)(ii) (Cambridge)

Identifying the equation of the line of symmetry was not generally well answered. Common errors included y = 4, x + y = 4, y = mx + c. 4 and (4, 17).

— Examiner report, May/June 2024, 0980/32 Q6(a)(iii) (Cambridge)

This part proved difficult and demanding for many candidates and proved to be a good discriminator, though a small number of fully correct lines were seen, and a number of lines were drawn passing through the point (2, 7) but with an incorrect gradient. This was very well answered. A few gave an incorrect statement such as 180 – 26 + 42 = 112.

— Examiner report, May/June 2024, 0980/32 Q6(b)(i) (Cambridge)