O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · Oct/Nov 2013 · Q87 Marks
On the grid below, sketch the graph of y = |(x - 2)(x + 3)| for -5 ≤ x ≤ 4, and state the coordinates of the points where the curve meets the coordinate axes.
- (i)On the grid below, sketch the graph of y = |(x - 2)(x + 3)| for -5 ≤ x ≤ 4, and state the coordinates of the points where the curve meets the coordinate axes.[4]
- (ii)Find the coordinates of the stationary point on the curve y = |(x - 2)(x + 3)|.[2]
- (iii)Given that k is a positive constant, state the set of values of k for which |(x - 2)(x + 3)| = k has 2 solutions only.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [B1] (i) for correct shape
- [B1] for (-3, 0) or -3 seen on graph
- [B1] for (2, 0) or 2 seen on graph
- [B1] for (0, 6) or 6 seen on graph or in a table
- [B1, B1] (ii) for each
- [B1] (iii) k > 25/4 or 2 < k (≤ 14)
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