plumiDifferentiation: CAIE A‑Level Maths questions
Every CAIE A-Level Maths exam question on 2.4 Differentiation, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 2, question 2: A curve has equation x 2 ln y y 2 4 x 9 . + + = Find the gradient of the curve at the point (2, 1). [5]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970921-jun24-02-qp.webp)
![Specimen Paper 2, question 6: The parametric equations of a curve are x = e2t, y = 4tet. d y 2 ( t 1 ) + (a) Show that = . [4] d x e t 11 (b) Find the equation of the normal to the curve at](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970902-spec-06-qp.webp)
All 5 questions on Differentiation, as a list
- June 2024, Paper 2, Q1 (3 marks): A curve has equation y 2 tan x 5 sin x for 0 x 1 1 r. = - G 2 Find the x-coordinate of the stationary point of the curve. Give your answer correct to 3 signific
- June 2024, Paper 2, Q2 (5 marks): A curve has equation x 2 ln y y 2 4 x 9 . + + = Find the gradient of the curve at the point (2, 1). [5]
- June 2024, Paper 2, Q5 (9 marks): e x 2 + 5 A curve has equation y . The curve has exactly one stationary point P. = 1 3 x + d and hence show that the x-coordinate of P satisfies the equation x
- Specimen, Paper 2, Q5 (9 marks): y M x O α 1 2ϖ for 0 ⩽ x ⩽ 2 sin 2 x 1 π. The x-coordinate of the maximum point M is The diagram shows the curve y = x 2 + denoted by α. d y and show that α sat
- Specimen, Paper 2, Q6 (8 marks): The parametric equations of a curve are x = e2t, y = 4tet. d y 2 ( t 1 ) + (a) Show that = . [4] d x e t 11 (b) Find the equation of the normal to the curve at
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