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7 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2004 · Paper 2 · Question 2(a)(i)

Express f(x) = 12x-2x² in the form A + B(x+p)² where A, B and p are real numbers, and find the maximum value of 12x - 2x².

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Other parts of this question

  1. 2(a)(ii)Hence, sketch the graph of f(x) = 12x - 2x², showing clearly its main features.[5 marks]
  2. 2(a)(iii)Show that f(x) = 12x - 2x² is NOT one-to-one.[2 marks]
  3. 2(b)(i)a)Copy and complete the following table for the function f(x) = sin x, 0≤x≤ 2π.[4 marks]
  4. 2(b)(i)b)Sketch the graph of f.[4 marks]
  5. 2(b)(ii)On a separate diagram, sketch the graph of f(x) = | sin x |, 0 ≤ x ≤ 2π.[4 marks]
  6. 2(b)(iii)By comparing the diagrams in (b)(i) and (ii) above, determine the solution set of the equation sin x = | sin x |, 0≤ x ≤ 2π.[3 marks]

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