plumiIntegrating with inverse trig and hyperbolic functions: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 5.4 Integrating with inverse trig and hyperbolic functions, 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 6 questions on Integrating with inverse trig and hyperbolic functions, as a list
- June 2025, Core Pure 1, Q7 (8 marks): (a) Express 2 10 9 22 2 3 3 2 2 x x x x x in partial fractions. (4) (b) Hence, show that 2 10 9 22 2 3 2 27 4 6 3 3 2 2 0 1 x x x x x x d ln ϖ (4)
- June 2024, Core Pure 2, Q3 (5 marks): (a) Explain why 1 9 16 2 4 3 x x d is an improper integral. (1) (b) Show that 2 4 3 1 d 9 16 x kπ x where k is a constant to be determined. (4)
- 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
- June 2022, Core Pure 1, Q6 (7 marks): (a) Express as partial fractions 2 3 6 1 4 2 2 x x x x + + + ( ) + ( ) (3) (b) Hence, show that ( )( ) ( ) 2 2 2 0 2 3 6 d ln 2 1 4 x x x a bπ x x + + = + + + ∫
- November 2021, Core Pure 1, Q9 (11 marks): (a) Use a hyperbolic substitution and calculus to show that x x x x x x k 2 2 2 1 1 2 1 − = − + + ∫ d arcosh where k is an arbitrary constant. (6) y O
- 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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