plumiSmall angle approximations: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on E.3 Small angle approximations, 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 7 questions on Small angle approximations, as a list
- June 2025, Paper 1, Q8 (5 marks): Show that, for small values of x, the graph with equation y = 4 + sin 5x – 3 cos 2x 1 + 2 tan x can be approximated by the straight line with equation of the fo
- June 2024, Paper 1, Q9 (5 marks): (a) Show that, for small values of θ measured in radians cos 4θ + 2 sin 3θ – tan 2θ ≈ A + Bθ + Cθ2 where A, B and C are constants to be found. [3 marks] 9 (b) U
- June 2023, Paper 1, Q4 (1 mark): Given that y is a small angle, find an approximation for cos 2y Circle your answer. [1 mark] 1 − y2 2 2 − 2y2 1 − 2y2 1 − y2 for the next question
- June 2022, Paper 1, Q6 (6 marks): (a) Find the first two terms, in ascending powers of x, of the binomial expansion of 1 × x 2 1 2 [2 marks] 6 (b) Hence, for small values of x, show that sin 4x
- November 2021, Paper 1, Q15 (10 marks): (a) Show that sin x − sinx cos 2x ≤ 2x3 for small values of x. [3 marks] 15 (b) Hence, show that the area between the graph with equation y = 8( sinx − sin x co
- November 2020, Paper 2, Q4 (4 marks): Using small angle approximations, show that for small, non-zero, values of x x tan 5x cos 4x − 1 × A where A is a constant to be determined. [4 marks]
- June 2018, Paper 3, Q5 (3 marks): Show that, for small values of x, the graph of y = 5 + 4 sin x 2 + 12 tan x 3 can be approximated by a straight line. [3 marks]
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