plumiDifferentiation: CAIE A‑Level Maths questions
Every CAIE A-Level Maths exam question on 3.4 Differentiation, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 3, question 5: esinx 5 The equation of a curve is y for 0 x 2 r. = G G cos 2 x d and hence find the x-coordinates of the stationary points of the curve. y Find x [7] d](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-05-qp.webp)
![June 2024 Paper 3, question 10: , show that y d 2 10 (a) Given that 2 = x tan y . [3] = d x 1 4 x 2 + 3 y (b) Hence find the exact value of 2 x tan - 1 ( 2 x ) d x . [7] 1 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-10-qp.webp)
![Specimen Paper 3, question 5: d x 2 5 (a) Show that dx x ( − tan − 1 x ) = . [2] 1 + x 2 3 (b) Show that y x tan − 1 x x d = 2 − 1 3 . [5] r 3 2 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970903-spec-05-qp.webp)
![Specimen Paper 3, question 9: y M x O 1 2π The diagram shows the curve y = sin2 2x cos x for 0 ⩽ x ⩽ 2 1 π, and its maximum point M. (a) Find the x-coordinate of M. [6] 17 (b) Using the subs](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970903-spec-09-qp.webp)
All 5 questions on Differentiation, as a list
- June 2024, Paper 3, Q5 (7 marks): esinx 5 The equation of a curve is y for 0 x 2 r. = G G cos 2 x d and hence find the x-coordinates of the stationary points of the curve. y Find x [7] d
- June 2024, Paper 3, Q10 (10 marks): , show that y d 2 10 (a) Given that 2 = x tan y . [3] = d x 1 4 x 2 + 3 y (b) Hence find the exact value of 2 x tan - 1 ( 2 x ) d x . [7] 1 2
- Specimen, Paper 3, Q4 (9 marks): The parametric equations of a curve are x = e2t–3, y = 4 ln t, where t > 0. When t = a the gradient of the curve is 2. 1 (3 – ln a). (a) Show that a satisfies t
- Specimen, Paper 3, Q5 (7 marks): d x 2 5 (a) Show that dx x ( − tan − 1 x ) = . [2] 1 + x 2 3 (b) Show that y x tan − 1 x x d = 2 − 1 3 . [5] r 3 2 0
- Specimen, Paper 3, Q9 (10 marks): y M x O 1 2π The diagram shows the curve y = sin2 2x cos x for 0 ⩽ x ⩽ 2 1 π, and its maximum point M. (a) Find the x-coordinate of M. [6] 17 (b) Using the subs
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