A Level Maths · Pure · Year 12 and 13
Vectors in A Level Maths are about geometry and forces rather than equations of lines (that is Further Maths). Year 12 works in two dimensions; Year 13 extends to three.
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AS content is usually taught in Year 12. The full A Level adds the Year 13 content. Sitting AS exams or mocks? See the AS Level Maths checklist.
Given that the magnitude of the vector $4\mathbf{i} + k\mathbf{j} - 2\mathbf{k}$ is $6$, find the possible values of the constant $k$.
Then practise: skills to practise · open vectors practice questions.
Try it: vector calculator (free, shows the working)
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 J | Paper 2 |
| Edexcel 9MA0 | Edexcel topic Pure 10 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.10 | Paper 1, and the pure sections of Papers 2 and 3 |
Three examples from the question bank, one with its full mark scheme open. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
Find the exact magnitude of the vector $\mathbf{a} = 3\mathbf{i} - 4\mathbf{j} + 12\mathbf{k}$.
Mark scheme: in the 7-day free trial.
Find a unit vector in the direction of $2\mathbf{i} - 2\mathbf{j} + \mathbf{k}$.
Every question here has a full worked solution. See them all →
The vertices of a triangle are $A(1, 0, 0)$, $B(0, 1, 0)$, and $C(0, 0, 1)$. Find the exact area of the triangle.
Mark scheme: in the 7-day 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.
Revision notes: Vectors in two dimensions · Vectors in three dimensions
These skills sit in the Pure II unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Vectors 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 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 |
| AQA 7357 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
| OCR H240 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Vectors is part of the A Level Maths content that every board examines: AQA section J, Edexcel Pure 10, OCR 1.10. It is assessed in AQA Paper 2; 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: Vectors in two dimensions: column vectors and i, j notation; Magnitude and direction; unit vectors; Adding vectors and multiplying by a scalar; position vectors and distances; Using vectors to solve geometric problems. The full A Level adds: Vectors in three dimensions, using i, j and k; Position vectors and geometric problems in 3D.
No. The scalar (dot) product and vector equations of lines are in A Level Further Maths, not A Level Maths. A Level Maths needs magnitude, direction, position vectors and geometric problems in 2D and 3D.
Stretch yourself: original geometry problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S78 · Problem S21 · Problem S77 · Problem S20. All 22 →
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