Higher November 2020 Paper 2R Q18
18
(a) Complete the table of values for \(y = \dfrac{1}{2}x^3 - 2x + 3\) (2)
| \(x\) | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
| \(y\) | –4.5 | 3 | 3 |
(b) On the grid, draw the graph of \(y = \dfrac{1}{2}x^3 - 2x + 3\) for \(-3 \leqslant x \leqslant 3\) (2)
(c) By drawing a suitable straight line on the grid, find an estimate for the solution of the equation \(\dfrac{1}{2}x^3 - x + 4 = 0\) (2)
| Scheme | Marks |
|---|---|
| (−4.5) 3 4.5 (3) 1.5 (3) 10.5 | B2 |
| (2) |
Notes
B2: for all correct
(B1 for any two correct)
No points in table but correctly plotted on grid, award mark
| Scheme | Marks |
|---|---|
| (−3, −4.5) (−2, 3) (−1, 4.5) (0, 3) (1, 1.5) (2, 3) (3, 10.5) Answer: Smooth curve | B2 |
| (2) |
Notes
B2: for a correct smooth curve. Points or curve passing through correct values within half a small square.
(B1 for at least 5 points plotted correctly; ft from table for plotting only provided B1 awarded in part (a))
| Scheme | Marks |
|---|---|
| M1 | |
| Working required Answer: −2.3 to −2.4 | A1 |
| (2) | |
| (6 marks) |
Notes
M1: for drawing \(y = -x - 1\) with two correct points plotted and intersection with curve.
or for stating \(y = -x - 1\)
or for \(\dfrac{1}{2}x^3 - 2x + 3 = -x - 1\) seen
A1: ft their curve dep on M1 and line \(y = -x - 1\) drawn