: Edexcel past-paper questions pack
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Reciprocal and inverse trigonometric functions

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 42

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 12 parts, 42 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 1 · Q16(a) · 4 marks
16. y C R x Figure 5 Figure 5 shows a sketch of the curve C with equation y = 0 < x < 2 x - x The region R, shown shaded in Figure 5, is bounded by C, the line with equation x = 1, the x‑axis and the line with equation x = (a) Use the substitution x = 2 sin u to show that the area of R is given by b∫k cosec 2 u du a where a, b and k are constants to be found. (4)
2. June 2025 · Paper 1 · Q16(b) · 3 marks
(b) Hence, using algebraic integration, find the exact area of R. Give your answer in simplest form. (3)
3. June 2024 · Paper 2 · Q8(a) · 3 marks
8. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Prove that / o 2tan sec theta theta theta n , n < cosec theta cosec theta (3)
4. June 2024 · Paper 2 · Q8(b) · 4 marks
(b) Hence solve, for 0 < x < 90°, the equation O cot x x sec x x cosec cosec Give each answer, in degrees, to one decimal place. (4)
5. June 2023 · Paper 3 (Mechanics) · Q6(b) · 3 marks
The magnitude of the normal reaction of the wall on the rod at B is S. In an initial model, the rod is modelled as being uniform. Use this initial model to answer parts (b), (c) and (d). (b) By taking moments about A, show that S = 1 2 Mg cot theta (3)
6. Oct 2021 · Paper 2 · Q13(a) · 3 marks
13. The curve C has parametric equations x = sin 2 theta y = cosec3 theta 0 < theta < pi (a) Find an expression for d y x in terms of theta d (3)
7. Oct 2021 · Paper 2 · Q13(b) · 3 marks
(b) Hence find the exact value of the gradient of the tangent to C at the point where y = 8 (3)
8. Oct 2020 · Paper 1 · Q12(a) · 3 marks
12. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Show that cosec theta - sin theta ≡ cos theta cot theta theta ≠ (180n)° n (3)
9. Oct 2020 · Paper 1 · Q12(b) · 5 marks
(b) Hence, or otherwise, solve for 0 < x < 180° cosec x - sin x = cos x cot (3x - 50°) (5)
10. Oct 2020 · Paper 1 · Q15(a) · 4 marks
15. The curve C has equation pi x2 tan y = 9 0 < y < 2 (a) Show that d y x = - x d x + (4)
11. June 2019 · Paper 2 · Q12(b) · 3 marks
(b) Hence solve, for 90° : ș : 180°, the equation cos3 theta + sin3 theta theta theta = 4 sin cos giving any solutions to one decimal place. (3)
12. June 2018 · Paper 2 · Q7(i) · 4 marks
pi , the equation 7. (i) Solve, for 0 x < 2 4 sin x = sec x (4)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · Paper 1 · Q16
Mark scheme June 2025 Paper 1 Q16(b)
June 2024 · Paper 2 · Q8
Mark scheme June 2024 Paper 2 Q8(b)
June 2023 · Paper 3 (Mechanics) · Q6
Mark scheme June 2023 Paper 3 (Mechanics) Q6(b)
Oct 2021 · Paper 2 · Q13
Mark scheme Oct 2021 Paper 2 Q13(b)
Oct 2020 · Paper 1 · Q12
Mark scheme Oct 2020 Paper 1 Q12(b)
Oct 2020 · Paper 1 · Q15
Mark scheme Oct 2020 Paper 1 Q15(a)
June 2019 · Paper 2 · Q12
Mark scheme June 2019 Paper 2 Q12(b)
June 2018 · Paper 2 · Q7
Mark scheme June 2018 Paper 2 Q7(i)