O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2019 · Q1011 Marks
The diagram shows a triangular prism. All lengths are in centimetres.
- (a)Show that the volume, Vcm³, of the prism is given by V = (40x-5x²).[3]
- (b)On the grid on the next page, draw the graph of V = 40x-5x² for 1 ≤ x ≤ 7. Three of the points have been plotted for you.[3]
- (c)Use your graph to find the possible values of x for one of these prisms with a volume of 50cm³.[2]
- (d)A cuboid has length 4 cm, width 3 cm and height x cm. By drawing a suitable line on your graph, find the value of x when the prism and the cuboid have the same volume.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [3] 1/2 (8-x) x sin 30 × 20 M2 M1 for 1/2 (8-x)x sin 30 isw (40x – 5 x²) nfww A1
- [3] Curve through (1, 35) (2, 60) (3, 75) (4, 80) (5, 75) (6, 60) (7, 35) B2 for 3 or 4 more correct points plotted or B1 for at least 2 more correct points soi
- [2] 1.5 to 1.6 and 6.4 to 6.5 B1 for either
- [3] V = 12x ruled M2 M1 for V = 4 × 3 × x soi B1 5.5 to 5.6
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