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CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 6(a)

A chemical test kit is 95% accurate in detecting when a solution is acidic. However, the test kit also yields a 'false positive' result for 1% of all solutions tested. If 0.5% of the solutions tested are acidic, what is the probability that a solution is acidic given that the test result is positive?

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  1. 6(b)Determine the general solution of the differential equation dy/dx + (3/x)y = sin(2x)/x².[5 marks]
  2. 6(c)(i)Show that the general solution of the differential equation is Ae^(3x/4) sin(√19x/4) + Be^(3x/4) cos(√19x/4), where A and B are constants.[6 marks]
  3. 6(c)(ii)Hence, or otherwise, determine the particular solution of the differential equation given that at x = 0, y = 3 and y' = 0.[9 marks]

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