A Level Maths · Pure · Year 12 and 13
Differentiation is worth more marks than almost any other topic across the three papers. Year 12 is polynomials, tangents and stationary points; Year 13 adds the chain, product and quotient rules and implicit and parametric differentiation.
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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.
Find the exact value of the gradient of the curve $y = -2x^2 + 8x$ at the point $(1, 6)$.
Then practise: skills to practise · open differentiation 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 G | Papers 1, 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 7 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.07 | 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 gradient of the chord joining the points $(2, 4)$ and $(2+h, (2+h)^2)$ on the curve $y = x^2$. Simplify your answer fully.
Mark scheme: in the 7-day free trial.
Find the x-coordinates of the stationary points on the curve with equation $y = x^3 - 3x^2 - 9x + 2$.
Every question here has a full worked solution. See them all →
Differentiate $y = \frac{e^{2x}}{x^2+1}$ with respect to $x$, giving your answer as a single algebraic fraction in its simplest form.
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: Differentiation · Further differentiation: standard functions and the chain, product and quotient rules · Implicit and parametric differentiation, convexity and rates of change
These skills sit in the Pure III · Calculus unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Differentiation 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. Differentiation is part of the A Level Maths content that every board examines: AQA section G, Edexcel Pure 7, OCR 1.07. 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.
Both. The AS content, usually taught in Year 12, is: Differentiation from first principles; Differentiating xⁿ; gradients, tangents and normals; Increasing and decreasing functions; stationary points and the second derivative; Simple optimisation problems. The full A Level adds: Differentiating eˣ, ln x, sin x and cos x; The chain, product and quotient rules; Points of inflection and convex and concave curves; Implicit and parametric differentiation; Connected rates of change and forming differential equations.
It means finding the derivative from the limit of (f(x + h) − f(x)) / h as h tends to 0, rather than using the rules. You need to show the limit step for the final marks.
Stretch yourself: original calculus and functions problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S132. All 24 →
Formulas in this topic: Chain rule · Derivative of sin x · Power rule · Product rule · Quotient rule. All formulas A–Z
Applying for maths, computer science or economics? TMUA practice on this topic: Tangents, normals and stationary points · Roots, intersections and shape. TMUA preparation: notes, questions and mock papers → Taking STEP? STEP-style problems: Functions and curve sketching.
Thinking about an EPQ? Maths EPQ ideas that use this topic: Newton or Leibniz? · How a neural network learns · The limit on wind turbine power · all 93 ideas
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