Higher June 2024 Paper 6 Q8
8
(a) Complete this table for \(y = x^3 - 3x^2\).
[2]
| \(x\) | \(-2\) | \(-1\) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| \(y\) | \(-20\) | 0 | \(-2\) | \(-4\) | 16 |
(b) Draw the graph of \(y = x^3 - 3x^2\) for values of \(x\) from \(-2\) to 4. [3]
(c) Use the graph to solve the equation \(x^3 - 3x^2 = 5\).
Give your answer to 1 decimal place. [1]
Give your answer to 1 decimal place. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| -4 and 0 | 2 | B1 for one correct value | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
Correct curve | 3 | B2FT for 6 or 7 points accurately plotted or B1FT for 4 or 5 accurately plotted | Mark curve first. Curve must pass within ½ small square of the correct seven points FT their values from the table in (a) but accept only the correct curve Accuracy ± ½ small square radially If no points plotted mark the curve at the \(x\)-values Condone curve not having max at (0, 0) and min at (2, -4) as long as it passes through correct points Condone wobbly curve and slight feathering Do not condone straight line segments |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3.4 | 1FT | Strict FT from graph to 1 d.p. | Do not accept answers to more than 1 d.p. or answers without a graph If curve is between two grid lines accept either value eg if crossing between 3.4 and 3.5 accept 3.4 or 3.5 If curve has more than one \(x\) value where \(y = 5\) then they must give all |