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O-LevelAdditional MathematicsFunctions4037/21 · May/June 2014 · Q35 Marks

On the axes below, sketch the graph of y = |(x - 4)(x + 2)| showing the coordinates of the points where the curve meets the x-axis.

  1. (i)On the axes below, sketch the graph of y = |(x - 4)(x + 2)| showing the coordinates of the points where the curve meets the x-axis.[2]
  2. (ii)Find the set of values of k for which |(x - 4)(x+2)|= k has four solutions.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [B1] correct shape
  2. [B1] x intercepts marked or implied by tick marks, for example or seen nearby; condone y intercept omitted
  3. [B1] x = 1 (only) soi
  4. [B1] y = ± 9 (only)
  5. [B1] 0 < k < 9 must be strict inequality in k; condone space, comma, “and”, "or"

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About this question

Topic
Functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 2 Variant 1, question 3.

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