plumiMean value of a function: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 5.3 Mean value of a function, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 4 questions on Mean value of a function, as a list
- June 2023, Core Pure 1, Q2 (6 marks): (a) Write x 2 + 4x – 5 in the form (x + p) 2 + q where p and q are integers. (1) (b) Hence use a standard integral from the formula book to find 1 4 5 2x x x d
- November 2021, Core Pure 1, Q5 (7 marks): (i) Evaluate the improper integral 2 1 1 2 e d ∞ − ∫ x x (3) (ii) The air temperature, θ °C, on a particular day in London is modelled by the equation θ = 8 – 5
- November 2020, Core Pure 2, Q5 (10 marks): (a) y = tan−1 x Assuming the derivative of tan x , prove that d d y x x = + 1 1 2 (3) f ( x ) = x tan−1 4x (b) Show that f d ( ) tan tan x x Ax x Bx C x k ∫ = +
- June 2019, Core Pure 2, Q3 (6 marks): f ( ) x x = + 1 4 9 2 (a) Using a substitution, that should be stated clearly, show that f (x)dx = A sinh–1 (Bx) + c where c is an arbitrary constant and A an
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