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CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2 · Question 5(a)(ii)

4-digit even numbers are formed from the digits 1, 2, 3, 4, 6, 7, 8.

Determine how many such numbers can be formed if there is no restriction on the number of times a digit may appear.

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Other parts of this question

  1. 5(a)(i)Determine how many such numbers can be formed if each digit appears at most once.[4 marks]
  2. 5(b)(i)Find the probability that the committee consists entirely of Jamaicans.[3 marks]
  3. 5(b)(ii)Find the number of ways in which the committee can be formed, given the restriction that there are as many Tobagonians on the committee as there are Guyanese.[6 marks]
  4. 5(c)(i)Find the matrix \mathbf{B}, where \mathbf{B} = \mathbf{A}^2 - 3\mathbf{A} - \mathbf{I}.[3 marks]
  5. 5(c)(ii)Show that \mathbf{AB} = -9\mathbf{I}.[1 mark]
  6. 5(c)(iii)Hence, find the inverse, \mathbf{A}^{-1}, of \mathbf{A}.[2 marks]
  7. 5(c)(iv)Solve the system of linear equations \mathbf{B} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}.[3 marks]

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