plumiDifferentiation: CAIE A‑Level Further Maths questions
Every CAIE A-Level Further Maths exam question on 2.3 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: + 2 Find the Maclaurin’s series for e 1 + x e 1 - up to and including the term in x2 . x [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923121-jun24-02-qp.webp)
![June 2024 Paper 2, question 3: It is given that - , for x sin - and 1 t y t cos 1 t 0 t 1 1 . = = G d y - . (a) Show that t 1 t 2 cos 1 t [3] = - + - d x 5 d 2 y (b) Find x in terms of t. [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923121-jun24-03-qp.webp)
![Specimen Paper 2, question 7: e 1 x o. [3] + 7 (a) Starting from the definition of tanh in terms of exponentials, prove that tanh−1x = 1 ln 1 2 − x e 1 − x o, show that (2x + 1)d d y + 1 = 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923102-spec-07-qp.webp)
All 3 questions on Differentiation, as a list
- June 2024, Paper 2, Q2 (4 marks): + 2 Find the Maclaurin’s series for e 1 + x e 1 - up to and including the term in x2 . x [4]
- June 2024, Paper 2, Q3 (7 marks): It is given that - , for x sin - and 1 t y t cos 1 t 0 t 1 1 . = = G d y - . (a) Show that t 1 t 2 cos 1 t [3] = - + - d x 5 d 2 y (b) Find x in terms of t. [4]
- Specimen, Paper 2, Q7 (12 marks): e 1 x o. [3] + 7 (a) Starting from the definition of tanh in terms of exponentials, prove that tanh−1x = 1 ln 1 2 − x e 1 − x o, show that (2x + 1)d d y + 1 = 0
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