O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · Oct/Nov 2019 · Q47 Marks
(i) On the axes below, sketch the graph of y = |2x²-9x-5| showing the coordinates of the points where the graph meets the axes. [Figure 4.1]
- (i)On the axes below, sketch the graph of y = |2x²-9x-5| showing the coordinates of the points where the graph meets the axes.[4]
- (ii)Find the values of k for which |2x²-9x-5|= k has exactly 2 solutions.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [4] B1 for shape, with max in first quadrant
- [4] B1 for (-0.5,0) and (5,0)
- [4] B1 for (0,5)
- [4] B1 all correct, with cusps and correct curvature for x < 0.5 and x > 5
- [1] B1 k = 0 Not from incorrect work
- [1] M1 For attempt to find y-coordinate of stationary point, must be a complete method i.e. Use of calculus Use of discriminant, Use of completing the square Use of symmetry Allow if seen in part (i), but must be used in (ii)
- [1] A1 k > 121/8 cao
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