: Edexcel past-paper questions pack
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Small-angle approximations

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 23

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 · 9 parts, 23 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · Paper 2 · Q6(a) · 2 marks
6. In this question you must show detailed reasoning. (a) Given that x is small and in radians, use the small angle approximation for cos theta to show that 2 (2x) ≈ 4x 2 – 4x 1 – cos (2)
2. June 2025 · Paper 2 · Q6(b) · 2 marks
(b) Given that x is small and in radians, use • the answer to part (a) • the small angle approximations for sin theta and tan theta to show that / x cos a bx x x sin tan where a and b are constants to be found. (2)
3. June 2025 · Paper 2 · Q6(c) · 2 marks
(c) Hence, given that x is very small, deduce an approximate value for / x cos x x sin tan giving a reason for your answer. (2)
4. June 2024 · Paper 2 · Q5 · 3 marks
5. Given that theta is small and in radians, use the small angle approximations to find an approximate numerical value of theta tan 2 theta cos3 theta (3)
5. June 2023 · Paper 1 · Q4(a) · 3 marks
4. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve C has equation y = f(x) where x ∈ ℝ Given that f′(x) = 2x + 1 • 2 cos x • the curve has a stationary point with x coordinate alpha • alpha is small (a) use the small angle approximation for cos x to estimate the value of alpha to 3 decimal places. (3)
6. Oct 2021 · Paper 2 · Q4 · 3 marks
4. Given that theta is small and measured in radians, use the small angle approximations to show that 4 sin theta 2 + 3 cos2 theta » a + b theta + c theta 2 where a, b and c are integers to be found. (3)
7. June 2019 · Paper 1 · Q2(b) · 3 marks
Given that the root of the equation is Į, and that Į is small, (b) use the small angle approximation for cos x to estimate the value of Į to 3 decimal places. (3)
8. June 2019 · Paper 1 · Q14(b) · 2 marks
(b) (i) Use the small angle approximation for sin 2y to find an equation linking x and y for points close to the origin. (ii) Explain the relationship between the answers to (a) and (b)(i). (2)
9. June 2018 · Paper 1 · Q1 · 3 marks
1. Given that theta is small and is measured in radians, use the small angle approximations to find an approximate value of theta - cos4 theta theta 2 sin3 (3)

Mark schemes

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

June 2025 · Paper 2 · Q6
Mark scheme June 2025 Paper 2 Q6(c)
June 2024 · Paper 2 · Q5
Mark scheme June 2024 Paper 2 Q5
June 2023 · Paper 1 · Q4
Mark scheme June 2023 Paper 1 Q4(a)
Oct 2021 · Paper 2 · Q4
Mark scheme Oct 2021 Paper 2 Q4
June 2019 · Paper 1 · Q2
Mark scheme June 2019 Paper 1 Q2(b)
June 2019 · Paper 1 · Q14
Mark scheme June 2019 Paper 1 Q14(b)
June 2018 · Paper 1 · Q1
Mark scheme June 2018 Paper 1 Q1