Edexcel IALMathematicsGeneral Applications6 Marks
Sketch the curve with equation y = x(x-3)², showing the coordinates of the points where the curve crosses or touches the coordinate axes.
- (a)Sketch the curve with equation y = x(x-3)², showing the coordinates of the points where the curve crosses or touches the coordinate axes.[4]
- (b)Hence, find the range of values of x for which x(x-3)² < 0.[2]
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. The mark or mark type is shown in brackets.
- Part (a) M1: For a correct shape of a cubic curve (y=ax³ with a>0, so starts negative ends positive or from bottom left to top right) with one minimum and one maximum. (Allow max to be higher than origin but min must be at $(3,0)$).
- Part (a) B1: For touching the x-axis at $(3,0)$. Can be implied by diagram.
- Part (a) B1: For crossing the x-axis at $(0,0)$. Can be implied by diagram.
- Part (a) A1: For $(0,0)$ and $(3,0)$ marked on the sketch and minimum point at $(3,0)$. Max must be to the left of 3. (If no labels on axes, but the coordinates are written near the intersection points, award B1 B1).
- Part (b) M1: For identifying x<0 from their graph. Allow x ≤ 0 if consistent with their graph. (Must refer to their sketch in part (a)).
- Part (b) A1: x<0. Do not allow x ≤ 0.
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