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O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · May/June 2014 · Q35 Marks

Sketch the graph of y = |(2x+1)(x-2)| for -2 ≤ x ≤ 3, showing the coordinates of the points where the curve meets the x- and y-axes.

  1. (i)Sketch the graph of y = |(2x+1)(x-2)| for -2 ≤ x ≤ 3, showing the coordinates of the points where the curve meets the x- and y-axes.[3]
  2. (ii)Find the non-zero values of k for which the equation |(2x + 1)(x - 2)|= k has two solutions only.[2]

Mark scheme

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

  1. [B1] (i) B1 for shape
  2. [B1] (i) B1 for y = 2 (must have a graph)
  3. [B1] (i) B1 for x = -0.5 and 2 (must have a graph)
  4. [M1] (ii) M1 for obtaining the value of y at the maximum point, by either completing the square, differentiation, use of discriminant or symmetry.
  5. [A1] (ii) Must have the correct sign for A1 Ignore any upper limits

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About this question

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

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