AS & A Level Mathematics 9709 · Pure Mathematics 1 (for Paper 1) · 1.7

Differentiation: past paper questions

300 real questionsasked in 10 of the last 10 exam series2020–2026usually: Find, Show, Determine, Use, State

Real questions on differentiation

The newest 20 of 300 written questions. Open one to see it on the real paper.

9709/12 · May/June 2026 · Q5[7]
The equation of a curve is such that $\frac{d ^{2} y}{d x ^{2}} = 6 x^{2} + p$ , where $p$ is a constant. The curve has minimum points at $(2, 3)$ and $(- 2, 3)$ . Find the coordinates of the other stationary point of the curve.See it on the paper →
9709/12 · May/June 2026 · Q9b[7]
[Diagram: A coordinate system with a curve $y = 3 2 x + 1$ , a straight line (normal) intersecting the curve at point $R (4, 9)$ , and a horizontal line $y = a$ . A shaded region is bounded by the curve, the y-axis, the x-axis, and the vertical line $x = 4$ .] The diagram shows the curve with equation $y = 3 2 x + 1$ , t...See it on the paper →
9709/32 · May/June 2026 · Q5a[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/32 · May/June 2026 · Q5b[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/32 · May/June 2026 · Q6a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/32 · May/June 2026 · Q7a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
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9709/11 · October/November 2025 · Q11a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/11 · October/November 2025 · Q11b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/12 · October/November 2025 · Q5a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/12 · October/November 2025 · Q9a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/13 · October/November 2025 · Q11a[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/13 · October/November 2025 · Q11b(i)[3]
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9709/13 · October/November 2025 · Q11b(ii)[4]
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9709/21 · October/November 2025 · Q6a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
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9709/21 · October/November 2025 · Q6b[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/21 · October/November 2025 · Q8[6]
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9709/22 · October/November 2025 · Q7a[6]
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9709/22 · October/November 2025 · Q7b[2]
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9709/23 · October/November 2025 · Q6a[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
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9709/23 · October/November 2025 · Q6b[5]
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What examiners said

Most candidates were able to correctly differentiate the given equation to find an expression for dx and understood that they needed to use x = 1 to find the gradient at the point P. After differentiating correctly, candidates usually went on to gain full marks. dy
— Examiner report, February/March 2025, 9709/12 Q2(a) (Cambridge)

Successful candidates dealt with the equation arising from = 0 and arrived at x = 3 − 5 . Some dx 4 dy candidates, however, started by differentiating their expression for and were unable to gain any dx marks. A large number of candidates did not provide answers of sufficient accuracy due to premature approximation of decimals.
— Examiner report, February/March 2025, 9709/12 Q2(b) (Cambridge)

Most candidates successfully evaluated the second derivative when x = 21 and stated that the stationary point is a minimum because the second derivative is positive. Some candidates did not justify and conclude that the second derivative is positive and consequently were unable to gain full marks. dy
— Examiner report, February/March 2025, 9709/12 Q9(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 differentiation

In the syllabus

1.7 Differentiation

understand the gradient of a curve at a point as Only an informal understanding of the idea of a limit
is expected.
e.g. includes consideration of the gradient of the
, and 2 for first and second chord joining the points with x coordinates 2 and
(2 + h) on the curve y = x3. Formal use of the general method of differentiation from first principles is not required.
use the derivative of xn (for any rational n), e.g. find , given y = 2x3 + 5 . dx
apply differentiation to gradients, tangents and Including connected rates of change, e.g. given the
rate of increase of the radius of a circle, find the rate
of increase of the area for a specific value of one of the variables.
locate stationary points and determine their Including use of the second derivative for identifying
maxima and minima; alternatives may be used in
questions where no method is specified

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