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5 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 2 · Question 1(b)

A binary operator ⊕ is defined on a set of positive real numbers by y ⊕ x = y² + x² + 2y + x – 5xy.

Solve the equation 2 ⊕ x = 0.

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Other parts of this question

  1. 1(a)Construct a truth table for the statements[1 mark]
  2. 1(a)(i)p → q[1 mark]
  3. 1(a)(ii)~(p ∧ q).[2 marks]
  4. 1(c)Use mathematical induction to prove that 5ⁿ + 3 is divisible by 2 for all values of n ∈ N.[8 marks]
  5. 1(d)(i)Given that (x + 1) is a factor of f(x), show that p = 6.[2 marks]
  6. 1(d)(ii)Factorise f(x) completely.[4 marks]
  7. 1(d)(iii)Hence, or otherwise, solve f(x) = 0.[3 marks]

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