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8 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 1(b)

Use mathematical induction to prove that 10ⁿ⁺¹ + 3(10ⁿ) + 5 is divisible by 9 for all natural numbers.

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Other parts of this question

  1. 1(a)(i)Copy and complete the truth table below for the propositions (p ^ q) → r and (p → r) ^ (q → r).[5 marks]
  2. 1(a)(ii)Hence, determine whether or not (p ^ q) → r and (p → r) ^ (q → r) are logically equivalent. Justify your response.[2 marks]
  3. 1(c)Solve the equation x³ – 6x² – 69x + 154 = 0.[10 marks]

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