plumiArc length and surface area: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on E.8 Arc length and surface area, 2019–2025, 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 5 questions on Arc length and surface area, as a list
- June 2025, Paper 1, Q16 (7 marks): The picture shows a solar cooker. Part of the solar cooker is a parabolic dish. The shape of the internal surface of the dish is formed by rotating the part of
- June 2024, Paper 1, Q15 (5 marks): A curve is defined parametrically by the equations x = 3 2t3 + 5 y = t 9 2 (t ≥ 0) Show that the arc length of the curve from t = 0 to t = 2 is equal to 26 unit
- June 2023, Paper 1, Q16 (11 marks): (a) Show that ( 4 0:5 1 t ln t dt = a(ln 2)2 where a is a rational number to be found. [4 marks] 16 (b) A curve C is defined parametrically for t > 0 by x = 2t
- November 2021, Paper 2, Q7 (7 marks): y t = 0 x t = 2 The diagram shows a curve known as an astroid. The curve has parametric equations x = 4 cos3 t y = 4 sin3 t (0 × t < 2p) The section of the curv
- June 2019, Paper 2, Q5 (4 marks): A curve has equation y = coshx Show that the arc length of the curve from x = a to x = b , where 0 < a < b , is equal to sinh b − sinha [4 marks]
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