Quelpr
2 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 5(c)(iii)

A farmer plans to construct an enclosure for his sheep, using one side of a barn 150 m long. With 500 m of fencing, a fence QRSTP will be built to form a rectangular enclosure PRST with the barn wall PQ. The length of QR is x metres.

Simplifying your answers where possible, find expressions in terms of x for the area, A, of PRST.

This question uses a figure or table from the paper — you'll see it when you practise.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 5(a)Using differentiation, determine the range of real values of x for which the function f: x → 12 + 6x² - x³ is decreasing.[5 marks]
  2. 5(b)Differentiate x³ with respect to x from first principles.[6 marks]
  3. 5(c)(i)Simplifying your answers where possible, find expressions in terms of x for the length of TS.[1 mark]
  4. 5(c)(ii)Simplifying your answers where possible, find expressions in terms of x for the length of RS.[4 marks]
  5. 5(c)(iv)Simplifying your answers where possible, find expressions in terms of x for the stationary value of x and show that it is a maximum.[5 marks]
  6. 5(c)(v)Simplifying your answers where possible, find expressions in terms of x for the maximum area of the sheep enclosure.[2 marks]

More practice: the rest of this paper · more Differentiation I questions · all CAPE Pure Mathematics Unit 1 past papers