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Examiner-informed A-Level diagnostic
The 15-mark A* decider
One optimisation question, worth a whole grade boundary. The calculus is not hard — but capable students throw marks away all the way through it. Here's exactly where.
The question15 marks
A solid triangular prism has an equilateral triangular cross-section of side 2x cm and length l cm. Its total surface area is S cm² and its volume is V cm³.
(a) Show that S = 2x²√3 + 6xl (3)
(b) Given S = 960, show that V = 160x√3 − x³ (5)
(c) Use calculus to find the maximum value of V (nearest integer) (5)
(d) Justify that your value of V is a maximum (2)
Guffick Tuition · Premium online A-Level & GCSE mathematics · Examiner-informed. Questions are original, written in the style of recurring exam types.
