Coordinate geometry: past paper questions

Real questions on coordinate geometry

The newest 20 of 121 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q18b[4]

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

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2. 0580/11 · May/June 2026 · Q18c[1]

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

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3. 0580/11 · May/June 2026 · Q18d[2]

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

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4. 0580/11 · May/June 2026 · Q20[3]
   20 The diagram shows line $L$ on a grid. [Diagram: A Cartesian grid with $x$-axis from 0 to 10 and $y$-axis from 0 to 5. A straight line $L$ is drawn passing through the points $(0,4)$ and $(10,1)$.] Find the equation of line $L$ in the form $y=mx+c$.See it on the paper →
5. 0580/21 · May/June 2026 · Q12[2]
   12 The coordinates of $A$ are $(3,20)$. The coordinates of $B$ are $(5,10)$. Work out the gradient of $AB$.See it on the paper →
6. 0580/21 · May/June 2026 · Q17a[2]

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

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7. 0580/21 · May/June 2026 · Q17b[3]

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

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8. 0580/22 · May/June 2026 · Q12a[5]

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

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9. 0580/22 · May/June 2026 · Q12b[2]

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

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10. 0580/22 · May/June 2026 · Q23a[3]
    The equation of a curve is $y=2x^2-11x+12$. (a) Find the gradient of the tangent to the curve at $x=2$.See it on the paper →
11. 0580/22 · May/June 2026 · Q23b[4]
    The equation of a curve is $y=2x^2-11x+12$. (b) Line $L$ intersects the curve at $x=2$. Line $L$ is perpendicular to the tangent to the curve at $x=2$. Find the equation of line $L$.See it on the paper →
12. 0580/23 · May/June 2026 · Q8b[2]

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

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13. 0580/31 · May/June 2026 · Q7c[1]

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

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14. 0580/32 · May/June 2026 · Q8[2]

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

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15. 0580/33 · May/June 2026 · Q11b(i)[1]

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

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16. 0580/42 · May/June 2026 · Q5[2]
    5 $P$ is the point $(-3,5)$ and $\overrightarrow{PQ}$ is $\left(\begin{array}{c}8\\ -3\end{array}\right)$. Find the coordinates of the point $Q$.See it on the paper →
17. 0580/42 · May/June 2026 · Q16c[4]
    16 [Diagram: A square-based pyramid ABCDE with apex A and base BCDE. The base is a square with side length 16.5 cm. The diagonals EC and BD intersect at F. The line AF is perpendicular to the base at F, with length 28 cm. The diagram is marked NOT TO SCALE.] $ABCDE$ is a square-based pyramid. $EC$ and $BD$ intersect at...See it on the paper →
18. 0580/43 · May/June 2026 · Q6a[2]

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

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19. 0580/43 · May/June 2026 · Q11d[1]
    11 The table shows some values for $y=3\times 2^x-5$ correct to 1 decimal place. | $x$ | $-2$ | $-1.5$ | $-1$ | $-0.5$ | $0$ | $0.5$ | $1$ | $1.5$ | $2$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | | $-3.9$ | | $-2.9$ | | $-0.8$ | $1$ | $3.5$ | $7$ | (d) Find the equation of...See it on the paper →
20. 0580/43 · May/June 2026 · Q14a[3]
    14 $A$ is the point $(5,2)$ and $B$ is the point $(-3,6)$. (a) Calculate the length of $AB$.See it on the paper →

What examiners said

This part of the question required candidates to use their graph to solve a pair of simultaneous equations. Many candidates recognised that the intersection of the given line and the line that they had drawn in (a) would give the answer required and read off the appropriate x and y values (allowing for follow through from their line in (a)). Some candidates did not show evidence of using the graph...

— Examiner report, May/June 2025, 0580/21 Q6(b) (Cambridge)

In the first part of this question, candidates were asked to draw a tangent touching the given curve and passing through the point P. They were asked to identify the coordinates of the point where this tangent touched the curve. Candidates who understood what was required for a tangent generally drew this accurately using a ruler, and correctly identified the required coordinates. The most common...

— Examiner report, May/June 2025, 0580/21 Q11(a) (Cambridge)

For this part of the question, candidates were asked to find the equation of the tangent. Not many candidates answered this part of the question successfully. Whilst some candidates accurately managed to find the equation of the line that they had drawn, it was common to see incorrect answers or blank responses where candidates had not attempted the question part. Candidates often struggled to wor...

— Examiner report, May/June 2025, 0580/21 Q11(b) (Cambridge)