IGCSE Mathematics (9–1) 0980 · Topic 3

Coordinate geometry: past paper questions

76 real questionsasked in 10 of the last 10 exam series2019–2025usually: Find, Write, Calculate, Complete, Give

Real questions on coordinate geometry

The newest 20 of 76 written questions. Open one to see it on the real paper.

0980/11 · October/November 2025 · Q16b[4]
4-mark question — its maths and diagrams are best seen on the paper.
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0980/21 · October/November 2025 · Q16[4]
16 [Diagram: A Cartesian coordinate system with $x$ and $y$ axes. The $x$ -axis is marked from 0 to 4, and the $y$ -axis is marked from 0 to 6. A shaded region $R$ is bounded by four lines: a vertical solid line at $x = 2.5$ , a horizontal dashed line at $y = 3$ , a horizontal solid line at $y = 4$ , and a diagonal solid line pas...See it on the paper →
0980/41 · October/November 2025 · Q10[2]
10 $A$ is the point $(2, 1)$ . $A B = (24)$ Find the coordinates of $B$ . ( ................................ , ................................ ) [2]See it on the paper →
0980/41 · October/November 2025 · Q17[3]
17 Find the equation of the straight line that passes through the points $(2, 0)$ and $(0, 4)$ . Give your answer in the form $y = m x + c$ . $y =$ See it on the paper →
0980/22 · May/June 2025 · Q15c[3]
3-mark question — its maths and diagrams are best seen on the paper.
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0980/42 · May/June 2025 · Q25[5]
25 $P$ is the point $(8, 0)$ and $Q$ is the point $(20, 6)$ . Find the equation of the perpendicular bisector of $P Q$ . Give your answer in the form $y = m x + c$ .See it on the paper →
0980/42 · May/June 2025 · Q27[4]
27 [Diagram: A cube with vertices $A, B, C, D$ on the base and $P$ on the top face directly above $C$ . The text "NOT TO SCALE" is shown to the right.] The diagram shows a cube. Calculate the angle between the diagonal $A P$ and the base $A B C D$ .See it on the paper →
0980/11 · October/November 2024 · Q18a[1]
18 The diagram shows a rectangle and two points, $P$ and $C$ , on a $1 cm^{2}$ grid. [Diagram: A Cartesian grid with $x$ and $y$ axes. A shaded rectangle has vertices at $(2, 5)$ , $(7, 5)$ , $(7, 8)$ , and $(2, 8)$ . Point $P$ is at $(7, 8)$ . Point $C$ is at $(0, 5)$ .] (a) Write down the coordinates of point $C .$ See it on the paper →
0980/31 · October/November 2024 · Q9a[3]
3-mark question — its maths and diagrams are best seen on the paper.
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0980/32 · May/June 2024 · Q6b(ii)[2]
(b) A straight line has a gradient of $\frac{1}{2}$ and passes through the point $(2, 7)$ . (ii) Write down the equation of this line in the form $y = m x + c$ .See it on the paper →
0980/42 · May/June 2024 · Q10a(i)[2]
10 (a) $A$ is the point $(6, 2)$ and $B$ is the point $(3, - 4)$ . (i) Find the coordinates of the midpoint of $A B$ .See it on the paper →
0980/42 · May/June 2024 · Q10a(ii)[3]
10 (a) $A$ is the point $(6, 2)$ and $B$ is the point $(3, - 4)$ . (ii) Calculate the length $A B$ .See it on the paper →
0980/42 · May/June 2024 · Q10b(i)[2]
(b) The equation of line $l$ is $4 x + 3 y - 12 = 0$ . (i) Find the gradient of $l$ .See it on the paper →
0980/42 · May/June 2024 · Q10b(ii)[2]
(b) The equation of line $l$ is $4 x + 3 y - 12 = 0$ . (ii) Find the coordinates of the point where $l$ crosses the $y$ -axis.See it on the paper →
0980/42 · May/June 2024 · Q10b(iii)[3]
(b) The equation of line $l$ is $4 x + 3 y - 12 = 0$ . (iii) Line $p$ is perpendicular to $l$ and passes through $(6, 5)$ . Find the equation of $p$ in the form $y = m x + c$ .See it on the paper →
0980/21 · October/November 2023 · Q15[5]
5-mark question — its maths and diagrams are best seen on the paper.
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0980/31 · October/November 2023 · Q8a[2]
[Diagram: A Cartesian coordinate system with $x$ and $y$ axes. The $x$ -axis is marked from $- 3$ to $6$ . The $y$ -axis is marked from $- 10$ to $6$ . A straight line $L$ is drawn passing through the points $(0, - 5)$ and $(3, 0)$ , extending to the top right corner near $(6, 6)$ and bottom left near $(- 2, - 10)$ .] (a) Find th...See it on the paper →
0980/31 · October/November 2023 · Q8b(i)[1]
1-mark question — its maths and diagrams are best seen on the paper.
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0980/31 · October/November 2023 · Q8b(ii)[1]
[Diagram: A Cartesian coordinate system with a grid. The x-axis is marked from -3 to 6 and the y-axis from -10 to 6. A straight line $L$ is drawn passing through the points $(0, - 5)$ and $(2, 0)$ , extending to the top right corner of the grid.] (ii) Write down the coordinates of the point where the line $y = x$ interse...See it on the paper →
0980/31 · October/November 2023 · Q8c(i)[3]
(e) (i) Complete the table of values for $y = \frac{8}{x}$ | $x$ | $- 5$ | $- 4$ | $- 3$ | $- 2$ | $- 1$ | | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---|---|---|---|---|---| | $y$ | $- 1.6$ | | $- 2.7$ | | | | | | $2.7$ | | $1.6$ |See it on the paper →

What examiners said

This part also had a high omission rate, although not quite as high as part (b). Many candidates were unsure which line needed to be drawn on the graph, resulting in either incorrect line placements or no line drawn at all. Common incorrect lines were y = –x or a line between (–2, 0) and (0, 2) or (–2, –2) and (2, 0) or other combinations of these coordinates. Others tried drawing tangents on both...
— Examiner report, May/June 2025, 0980/22 Q15(c) (Cambridge)

This question differentiated well between candidates. The most successful responses showed a correct calculation for the gradient of the line joining the two points P and Q, used this to find the gradient of the perpendicular, identified the midpoint of the line segment joining the two given points and made the appropriate substitutions in order to determine the required equation of the perpendicu...
— Examiner report, May/June 2025, 0980/42 Q25 (Cambridge)

Writing down the equation of the line of this line was not generally well answered. Stating the correct gradient was more successful than stating the correct intercept. The majority of candidates answered this very well. Almost all recognised it as a sine rule problem and were able to show the substitution and rearrangement of the sine rule leading to the answer. There were a number of candidates...
— Examiner report, May/June 2024, 0980/32 Q6(b)(ii) (Cambridge)

Practise this topic

Answer these questions online and get each one marked against the official mark scheme, with what you missed and how to fix it.

Practise these questions

In the syllabus

1 0580.C3.5.01 — use and request lines in the forms.

use and request lines in the forms.
involve finding the equation when the graph is.
ask for the gradient or y-intercept of a graph.

2 0580.C3.5.02 — involve finding the equation when the graph is.

involve finding the equation when the graph is.

3 0580.C3.5.03 — ask for the gradient or y-intercept of a graph.

ask for the gradient or y-intercept of a graph.

4 0580.E3.2.01 — y = –2x + 5.

y = –2x + 5.
y = 7 – 4x.
3x + 2y = 5.

5 0580.E3.2.02 — y = 7 – 4x.

y = 7 – 4x.

6 0580.E3.2.03 — 3x + 2y = 5.

3x + 2y = 5.

7 0580.E3.5.01 — use and request lines in different forms, e.g.

use and request lines in different forms, e.g.
involve finding the equation when the graph is.
ask for the gradient or y-intercept of a graph.

8 0580.E3.5.02 — involve finding the equation when the graph is.

involve finding the equation when the graph is.

9 0580.E3.5.03 — ask for the gradient or y-intercept of a graph.

ask for the gradient or y-intercept of a graph.

10 Extended: Perpendicular lines

find the equation of the perpendicular bisector.

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