June 2024 Paper 1 Q11
11 It is given that
\[\mathrm{f}(x) = x(x - a)(x - 6)\]where \(0 \lt a \lt 6\)
(a) Sketch the graph of \(y = \mathrm{f}(x)\) on the axes below. [3 marks]
(b) Sketch the graph of \(y = \mathrm{f}(-2x)\) on the axes below. [2 marks]
| Scheme | Marks | AO |
|---|---|---|
| Draws cubic graph with exactly two turning points | M1 | 1.1a |
| Draws cubic graph of correct orientation passing through the origin and positive \(x\)-axis at two points. | A1 | 1.1b |
| Draws fully correct sketch with \(x\)-axis intercepts correctly labelled \(a\) and 6. Ignore labelling on the \(y\)-axis. | R1 | 1.1b |
| (3) |
Typical solution
| Scheme | Marks | AO |
|---|---|---|
| Draws cubic graph of correct orientation passing through the origin and negative \(x\)-axis at two points. Or Substitutes \(-2x\) into \(\mathrm{f}(x)\) Or Describes the reflection in the \(y\)-axis and a stretch of scale factor \(\dfrac{1}{2}\) in the \(x\)-direction or a stretch scale factor \(-\dfrac{1}{2}\) in the \(x\)-direction. | M1 | 3.1a |
| Draws fully correct sketch with \(x\)-axis intercepts correctly labelled \(-\dfrac{a}{2}\) and \(-3\). | R1 | 2.2a |
| (2) | ||
| (5 marks) |
Typical solution
