plumiIntegrating with inverse trig and hyperbolic functions: OCR A‑Level Further Maths questions
OCR 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 11 questions on Integrating with inverse trig and hyperbolic functions, as a list
- June 2025, Pure Core 1, Q3 (6 marks): 3 The region R1 is bounded by the curve y , the line x k and the coordinate axes, as = = 2 25 x - shown in Fig. 1. Fig. 1 80 y = y 2 x 25 - R1 x O x=k (a) In th
- June 2025, Pure Core 2, Q7 (10 marks): In this question you must show detailed reasoning. 2 4 x 5 x 17 - + - (a) Express x in partial fractions. [6] 3 2 x 3 x 3 - + - y 3 2 4 x 5 x 17 - + - (b) Hence
- June 2024, Pure Core 1, Q5 (5 marks): 12 x 5 Express ( using partial fractions. [5] 2 2 x 1 2 )( x 1 ) + +
- June 2024, Pure Core 1, Q6 (4 marks): In this question you must show detailed reasoning. 3 y 18 Determine the exact value of d x . [4] 2 x x 9
- June 2024, Pure Core 2, Q7 (10 marks): bx + x 7 (a) Express 17 coshx - 15 sinhx in the form e - ( a e c ) where a, b and c are integers to be determined. [3] 1 A function is defined by ( ) f x . The
- June 2023, Pure Core 2, Q4 (4 marks): In this question you must show detailed reasoning. 1 The region R is bounded by the curve with equation y , the x-axis and the lines = 2 x x 3 3 1 - + 1 with eq
- June 2022, Pure Core 1, Q7 (10 marks): x 18 A B Cx D + + 7 (a) Determine the values of A, B, C and D such that . [4] / + + 2 2 2 2 x ( x 9 ) x x x 9 + + (b) In this question you must show detailed re
- November 2021, Pure Core 2, Q7 (10 marks): In this question you must show detailed reasoning. 3 2 x x x Bx C 9 1 + + - + (a) Find the values of A, B and C for which x A . [1] / + 3 2 3 2 x 4 x 4 x x 4 x
- November 2020, Pure Core 1, Q8 (10 marks): 8 (a) Using exponentials, show that cosh 2 u 2 sinh u 1 . [2] / + (b) By differentiating both sides of the identity in part (a) with respect to u, show that sin
- November 2020, Pure Core 1, Q12 (6 marks): ^ h < 4 3 r 12 Show that d x ln a b where a, b and c are integers to be determined. [6] = + + c 4 1 x - 0
- June 2019, Pure Core 1, Q6 (6 marks): tan 1 6 You are given that y - 2 x . = d . y (a) Find d [2] x x 1 y (b) Show that d x k where k is a number to be determined in exact form. [4] 2 ^ h = r 2 2 x
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