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5 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 6(c)(i)

A piece of thin cardboard, 16 cm by 10 cm, has shaded squares of side x cm removed from each corner. The remainder is folded to form a tray, as shown in a diagram not drawn to scale.

Show that the volume, V cm³, of the tray is given by V = 4(x³ - 13x² + 40x).

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Other parts of this question

  1. 6(a)Show that d²y/dx² + 4y = 0.[6 marks]
  2. 6(b)Given that ∫₀ᵃ (x + 1) dx = 3 ∫₀ᵃ (x - 1) dx, a > 0, find the value of the constant a.[6 marks]
  3. 6(c)(ii)Hence, find a possible value of x such that V is a maximum.[8 marks]

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