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3 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 2 · Question 1(b)(i)

A binary operator ⊕ is defined on a set of positive real numbers by y ⊕ x = y³ + x² + ay² + ax² - 5y – 5x + 16 where a is a real number.

State, giving a reason for your answer, if ⊕ is commutative in R.

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Other parts of this question

  1. 1(a)Construct a truth table for the statement (p → q) ∧ (r → q).[5 marks]
  2. 1(b)(ii)a)find the value of a[4 marks]
  3. 1(b)(ii)b)factorize f(x) completely.[3 marks]
  4. 1(c)Use mathematical induction to prove that 1² + 3² + 5² + ..... + (2n - 1)² = n/3 (4n² - 1) for n ∈ N.[10 marks]

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