Extended: Sketching curves: past paper questions

Real questions on extended: sketching curves

The newest 6 of 6 written questions. Open one to see it on the real paper.

1. 0580/13 · May/June 2026 · Q20a[2]
   [Diagram: A coordinate grid with $x$ and $y$ axes ranging from $-5$ to $7$. Triangle $A$ is shaded grey with vertices at $(2,2)$, $(4,2)$, and $(3,6)$. Triangle $B$ is unshaded with vertices at $(4,-5)$, $(6,-5)$, and $(5,-1)$. Triangle $C$ is unshaded with vertices at $(1,1)$, $(2,1)$, and $(1.5,3)$.] (a) Describe ful...See it on the paper →
2. 0580/13 · May/June 2026 · Q20b[3]

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

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3. 0580/13 · May/June 2026 · Q20c[2]

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

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4. 0580/43 · May/June 2026 · Q10a[2]

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

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5. 0580/41 · May/June 2024 · Q8a[4]

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

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6. 0580/41 · May/June 2024 · Q8b(ii)[3]
   (ii) Find the coordinates of the turning point of $y=x^2-3x-28$.See it on the paper →

What examiners said

This question expected candidates to substitute x=0 into the equation to find the y intercept and factorise x2 + 7x – 18 = 0 to find the x intercepts, which some candidates did successfully. Often with these marked on the axes a smooth parabola was drawn though the symmetry was not always correct, and the minimum was frequently drawn at (0, –18), rather than to the left of the y axis. Other candid...

— Examiner report, May/June 2024, 0580/41 Q8(a) (Cambridge)

Fewer candidates knew to set their derivative to zero to find the correct turning point. Other candidates did not use their derivative but were successful in using the completing the square method, although this was less efficient in this case. Others tried to factorise the equation, and some completed a table of coordinates, neither of which was helpful.

— Examiner report, May/June 2024, 0580/41 Q8(b)(ii) (Cambridge)