A Level Maths · Pure · Year 13
Numerical methods is Year 13 only. It is about approximating what you cannot solve exactly: locating roots, iteration, Newton-Raphson and the trapezium rule, and explaining when each method fails.
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This topic is A Level only: it is not on the AS exam.
None: numerical methods starts in Year 13.
The equation $e^{2x} - 5x = 0$ has a root $\alpha$. Show that this equation can be rearranged into the iterative formula $x_{n+1} = \frac{1}{2}\ln(5x_n)$.
Then practise: skills to practise · open numerical methods 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 I | Papers 1, 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 9 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.09 | 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.
Show that the equation $x^3 - 3x + 1 = 0$ has a root $\alpha$ in the interval $[1, 2]$.
Every question here has a full worked solution. See them all →
Explain why the function $f(x) = \frac{1}{x-2}$ has a change of sign between $x=1$ and $x=3$, but does not have a root in this interval.
Mark scheme: in the 7-day free trial.
Explain the significance of the gradient of the curve $y = g(x)$ near a root $\alpha$ when using the iterative formula $x_{n+1} = g(x_n)$.
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: Roots: change of sign, iteration and Newton–Raphson · Numerical integration and numerical methods in context
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.
Numerical methods 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. Numerical Methods is part of the A Level Maths content that every board examines: AQA section I, Edexcel Pure 9, OCR 1.09. It is assessed in AQA Papers 1, 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.
Numerical Methods is A Level only, so it is usually taught in Year 13 and is not on the AS exam.
It divides by f′(x), so it breaks down when the starting value is at or near a stationary point, and it can jump to a different root if the starting value is poor.
Stretch yourself: original algebra problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S25 · Problem S89 · Problem S24 · Problem S88. All 22 →
Thinking about an EPQ? Maths EPQ ideas that use this topic: When does iteration converge? · How a neural network learns · Quick routes for the travelling salesman · all 93 ideas
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