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O-LevelAdditional MathematicsFunctions4037/22 · Oct/Nov 2011 · Q99 Marks

It is given that f(x) = 2x² – 12x + 10.

  1. (i)Find the value of a, of b and of c for which f(x) = a(x + b)² + c.[3]
  2. (ii)Sketch the graph of y = |f(x)| for −1 ≤ x ≤ 7.[4]
  3. (iii)Find the set of values of k for which the equation |f(x)| = k has 4 distinct roots.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [B1+B1+B1] (i) a = 2, b = −3, c = −8 or 2(x – 3)² - 8
  2. [B1] (ii) graph with 3 distinct parts all above and touching x axis
  3. [B1] (ii) quadratic shape for middle section reflected in x axis
  4. [B1] (ii) cusp
  5. [B1] (ii) completely correct
  6. [M1] (iii) identifies 0 and 8
  7. [A1] (iii) 0 < k < 8

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 2, question 9.

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