O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2021 · Q311 Marks
Complete the table for y = x³/2 - 3x - 1. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 y | | 1 | 1.5 | | -3.5 | -3 | 3.5 Line L passes through the points (1, 1) and (-2, -1).
- (a)Complete the table for y = x³/2 - 3x - 1.[1]
- (b)On the grid, draw the graph of y = x³/2 - 3x - 1 for -3 ≤ x ≤ 3. [Figure X.X][3]
- (c)Use your graph to explain why x³ - 6x - 2 = 6 has only one solution.[2]
- (d)(i)On the grid, draw line L. [Figure X.X][1]
- (d)(ii)Work out the gradient of line L.[2]
- (d)(iii)Find the x-coordinates of the points where line L intersects the curve y = x³/2 - 3x - 1.[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 (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [1]
- [3] B2FT for 6 or 7 points correctly plotted or B1FT for 4 or 5 points correctly plotted
- [2] M1 for x³/2 - 3x - 1 = 3 soi or y = 3 soi
- [1]
- [2] M1 for gradient = (1+1)/(1+2) oe
- [2] B1FT for two correct
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