AS & A Level Mathematics 9709 · Pure Mathematics 1 (for Paper 1) · 1.3

Coordinate geometry: past paper questions

179 real questionsasked in 10 of the last 10 exam series2020–2026usually: Find, Show, Sketch, State, Write

Real questions on coordinate geometry

The newest 20 of 179 written questions. Open one to see it on the real paper.

9709/12 · May/June 2026 · Q3[6]
The perpendicular bisector of the line joining $(4, 3)$ and $(- 2, 6)$ meets the line $x - 4 y - 4 = 0$ at the point $P$ . Find the coordinates of $P$ .See it on the paper →
9709/12 · May/June 2026 · Q8a[4]
A diameter of a circle has end-points at $(- 2, 4)$ and $(8, 8)$ . (a) Find an equation of the circle.See it on the paper →
9709/12 · May/June 2026 · Q8b[7]
A diameter of a circle has end-points at $(- 2, 4)$ and $(8, 8)$ . (b) The line with equation $y = x + 6$ intersects the circle at the points $P$ and $Q$ . Find the exact distance $P Q$ . Give your answer in the form $a b$ , where $a$ and $b$ are both integers greater than 1.See it on the paper →
9709/11 · October/November 2025 · Q4b[3]
3-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/11 · October/November 2025 · Q7a[2]
2-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/11 · October/November 2025 · Q10a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/11 · October/November 2025 · Q10b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/11 · October/November 2025 · Q11c[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/12 · October/November 2025 · Q3a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/12 · October/November 2025 · Q3b[2]
2-mark “Write” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/13 · October/November 2025 · Q3a[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/13 · October/November 2025 · Q3b[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/13 · October/November 2025 · Q5b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/13 · October/November 2025 · Q8a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/13 · October/November 2025 · Q8b[17]
17-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/32 · October/November 2025 · Q1a[1]
1-mark “Sketch” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/32 · October/November 2025 · Q1b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/43 · October/November 2025 · Q1b[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/43 · October/November 2025 · Q4a[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
9709/43 · October/November 2025 · Q4b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →

What examiners said

The majority of candidates scored full marks on this question. Candidates usually found AB by the cosine rule, or 21 AB using the trigonometric formulae for right-angled triangles. Correct answers were obtained by finding the arc CD using rθ and adding this and 8 to AB. Candidates who changed from radians to degrees and worked out a fraction of the circumference often lost accuracy in their final...
— Examiner report, February/March 2025, 9709/12 Q4(a) (Cambridge)

Many candidates scored full marks on this question. As in part (a), candidates who worked in degrees often lost accuracy in their final answer. The most straightforward method was to subtract the area of sector OCD from the area of the triangle OAB, using 21 r2 and 21 ab sinC respectively.
— Examiner report, February/March 2025, 9709/12 Q4(b) (Cambridge)

Many candidates obtained the correct coordinates in terms of r, but a large number had the coordinates in the wrong order.
— Examiner report, February/March 2025, 9709/12 Q6(a) (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 coordinate geometry

In the syllabus

1.3 Coordinate geometry

find the equation of a straight line given e.g. given two points, or one point and the gradient.
interpret and use any of the forms y = mx + c, Including calculations of distances, gradients,
midpoints, points of intersection and use of the
relationship between the gradients of parallel and perpendicular lines.
understand that the equation Including use of the expanded form
x 2 + y 2 + 2gx + 2fy + c = 0.
use algebraic methods to solve problems Including use of elementary geometrical properties
of circles, e.g. tangent perpendicular to radius, angle in a semicircle, symmetry
Implicit differentiation is not included.
understand the relationship between a graph e.g. to determine the set of values of k for which the
line y = x + k intersects, touches or does not meet
a quadratic curve.

Past papers, syllabus and examiner reports © UCLES (Cambridge University Press & Assessment). Questions are matched to topics from the official syllabus. AssessPro is independent and not endorsed by Cambridge.