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6 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 2(a)

The roots of the quadratic equation 2x² + 4x + 5 = 0 are α and β.

Without solving the equation, find a quadratic equation with roots 2/α and 2/β.

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Other parts of this question

  1. 2(b)Express f as a set of ordered pairs.[4 marks]
  2. 2(b)(ii)a)State TWO reasons why f is NOT a function.[2 marks]
  3. 2(b)(ii)b)Hence, with MINIMUM changes to f, construct a function g : A → B as a set of ordered pairs.[4 marks]
  4. 2(b)(ii)c)Determine how many different functions are possible for g in (ii) b) above.[2 marks]
  5. 2(c)Find the value of f[f(20)].[3 marks]
  6. 2(c)(ii)Find the value of f[f(8)].[2 marks]
  7. 2(c)(iii)Find the value of f[f(3)].[2 marks]

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