A Level Maths · Pure · Year 12 and 13
Coordinate geometry joins algebra to pictures: straight lines, circles and, in Year 13, curves given by parametric equations. Sketch first; most lost marks come from a wrong gradient or a sign slip in the circle equation.
AS content is usually taught in Year 12. The full A Level adds the Year 13 content.
The line passing through the points $(k, 3)$ and $(4, 11)$ has a gradient of $2$. Find the value of $k$.
Then practise: skills to practise · open coordinate geometry practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section C | Paper 1, and Section A of Papers 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 3 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.03 | Paper 1, and the pure sections of Papers 2 and 3 |
Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
Find the gradient of the line passing through the points $(2, 8)$ and $(6, -2)$.
Mark scheme: in the 48-hour free trial.
Find the gradient of the perpendicular bisector of the line segment joining the points $(1, 1)$ and $(5, 9)$.
Mark scheme: in the 48-hour free trial.
Find the Cartesian equation of the curve with parametric equations $x = \cos 2\theta$ and $y = \sin \theta$.
Mark scheme: in the 48-hour free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
These skills sit in the Pure I unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Coordinate geometry can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 |
| AQA 7357 | Paper 1: June 2023, June 2022, November 2021 Paper 2: June 2023, June 2022, November 2021 Paper 3: June 2023, June 2022, November 2021 |
| OCR H240 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 Paper 3: June 2024, June 2023, June 2022 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Coordinate Geometry is part of the A Level Maths content that every board examines: AQA section C, Edexcel Pure 3, OCR 1.03. It is assessed in AQA Paper 1, and Section A of Papers 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.
Both. The AS content, usually taught in Year 12, is: Equations of straight lines, gradients, parallel and perpendicular lines; The equation of a circle, completing the square to find centre and radius; Tangents, chords and perpendicular bisectors; where a line meets a circle. The full A Level adds: Parametric equations of curves and converting between parametric and Cartesian form; Using parametric equations in modelling.
Complete the square in x and in y so the equation reads (x − a)² + (y − b)² = r². The centre is (a, b) and the radius is r. Check that r² is positive.
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