November 2021 Paper 1 Q19
19 \(y = \mathrm{f}(x) \quad\) is the graph of a cubic function.
\(y \lt 0 \quad\) for \(\quad x \lt 5\)
\(y \geqslant 0 \quad\) for \(\quad x \geqslant 5\)
The function is
increasing for \(\quad x \lt -1\)
decreasing for \(\quad -1 \lt x \lt 2\)
increasing for \(\quad x \gt 2\)
Draw a possible sketch of \(\quad y = \mathrm{f}(x) \quad\) for values of \(x\) from \(-2\) to 6 [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Cubic curve from \(x = -2\) to \(x = 6\) and maximum point at \((-1, a)\) where \(a\) is negative and minimum point at \((2, b)\) where \(b\) is less than \(a\) and increasing through (5, 0) | B4 | B3 curve from \(x = -2\) to \(x = 6\) and maximum point at \((-1, c)\) where \(c\) is any value and minimum point at \((2, d)\) where \(d\) is less than \(c\) and \(d\) is negative and increasing through (5, 0) or a B4 response apart from cubic curve not drawn from \(x = -2\) to \(x = 6\) B2 curve with maximum point at \((-1, e)\) where \(e\) is any value and minimum point at \((2, f)\) where \(f\) is less than \(e\) B1 curve with maximum point at \((-1, g)\) where \(g\) is negative or curve with minimum point at \((2, h)\) where \(h\) is negative or curve increasing through (5, 0) SC2 max and min correct and increasing through (5, 0) but with straight lines rather than a curve. |
Additional guidance
 | B4 |