Quelpr
2 marksSequences

CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2 · Question 1(a)(i)

The temperature of water, x^\circ\text{ C}, in an insulated tank at time, t hours, is modelled by x = 65 + 8e^{-0.02t}.

Determine the initial temperature of the water in the tank.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 1(a)(ii)Determine the temperature at which the water in the tank will eventually stabilize.[2 marks]
  2. 1(a)(iii)Determine the time when the temperature of the water in the tank is 70^\circ\text{ C}.[4 marks]
  3. 1(b)(i)Given that y = e^{\tan^{-1}(2x)}, where -\frac{1}{2}\pi < \tan^{-1}(2x) < \frac{1}{2}\pi, show that (1 + 4x^2)\frac{\mathrm{d}y}{\mathrm{d}x} = 2y.[4 marks]
  4. 1(b)(ii)Hence, show that (1 + 4x^2)^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2} = 4y(1 - 4x).[4 marks]
  5. 1(c)(i)Determine \int \frac{4}{e^x + 1}\,\mathrm{d}x by using the substitution u = e^x.[6 marks]
  6. 1(c)(ii)Determine \int \frac{4}{e^x + 1}\,\mathrm{d}x by first multiplying both the numerator and denominator of the integrand by e^{-x} before integrating.[3 marks]

More practice: the rest of this paper · more Sequences questions · all CAPE Pure Mathematics Unit 2 past papers