plumiDifferentiation: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP3.3 Differentiation, 2019–2025, with its mark scheme and examiner’s report.
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All 9 questions on Differentiation, as a list
- June 2025, Further Pure 3 (FP3), Q4 (5 marks): y x x x arsinh arsinh 1 0 > (a) Show that d d y x x x x 1 1 2 (b) Hence determine the exact value of y for which d d y x = 0, giving your answer as a sim
- January 2025, Further Pure 3 (FP3), Q8 (6 marks): Given that y = e 3x cosh 2x prove by induction that for n ∈ 3 d 1 1 e cosh 2 2 5 s 5 inh 2 2 d n n n x n y x x x
- June 2024, Further Pure 3 (FP3), Q3 (7 marks): y = arsinh x 2 1 x > 1 (a) Prove that d d y x x 1 1 2 f (x) = 1 3 arsinh x 2 1 – arctan x x > 1 (b) Determine the exact values of x for which f′ (x) = 0
- January 2024, Further Pure 3 (FP3), Q7 (9 marks): y = arccos(sech x) x > 0 (a) Show that d d y x x = sech O P C x y Figure 1 Figure 1 shows a sketch of part of the curve C with equation y = f(x) where f(x) = ar
- January 2023, Further Pure 3 (FP3), Q1 (3 marks): Given that (a) determine an expression for d d y x (b) Hence determine the exact value of d d y x when x = 1 4 , giving your answer in the form a b ϖ where a an
- June 2022, Further Pure 3 (FP3), Q4 (4 marks): y = artanh cos cos x a x a + − where a is a non‑zero constant. Show that d d y x = k tan x where k is a constant to be determined.
- January 2022, Further Pure 3 (FP3), Q3 (9 marks): (a) Given that y = arsech x 2 , where 0 < x 2, show that d d y x p x q x = − 2 where p and q are constants to be determined. In part (b) solutions b
- June 2021, Further Pure 3 (FP3), Q4 (8 marks): (i) f(x) = x arccos x −1 x 1 Find the exact value of f ′(0.5). (ii) g(x) = arctan(e 2x) Show that g′′(x) = k sech(2x) tanh(2x) where k is a constant to be f
- January 2021, Further Pure 3 (FP3), Q2 (6 marks): y = ln (tanh 2x) x > 0 (a) Show that d d y x = p cosech 4x where p is a constant to be determined. (b) Hence determine, in simplest form, the exact value of x f
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