Quelpr
3 marksCounting

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 6(a)(i)

Two fair coins and one fair die are tossed at the same time.

Calculate the number of outcomes in the sample space.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 6(a)(ii)Find the probability of obtaining exactly one head.[2 marks]
  2. 6(a)(iii)Calculate the probability of obtaining at least one head on the coins and an even number on the die on a particular attempt.[4 marks]
  3. 6(b)Determine whether y = C_1 x + C_2 x^2 is a solution to the differential equation (x^2 / 2) y'' - x y' + y = 0, where C_1 and C_2 are constants.[6 marks]
  4. 6(c)(i)Show that the general solution to the differential equation 3(x^2 + x) dy/dx = 2y(1 + 2x) is y = C * ((x^2 + x)^2)^(1/3), where C in R.[7 marks]
  5. 6(c)(ii)Hence, given that y(1) = 1, solve 3(x^2 + x) dy/dx = 2y(1 + 2x).[3 marks]

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