November 2021 Paper 2 Q8
8 A function f is given by
\[\begin{aligned} \mathrm{f}(x) &= 4x && x \lt 0 \\ &= x^2 - 8x && 0 \leqslant x \leqslant 8 \\ &= 16 - 2x && x \gt 8 \end{aligned}\]A sketch of \(\quad y = \mathrm{f}(x) \quad\) is shown.
Not drawn accurately
Work out all the values of \(x\) for which \(\quad \mathrm{f}(x) = -12\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(-3 \quad 2 \quad 6 \quad 14\) with no other solutions | B4 | B3 three correct with at most one incorrect B2 two correct with at most two incorrect B1 one correct with at most three incorrect SC2 \(-3 \quad 2 \quad 6 \quad 14\) with no other values seen SC1 Two or three of \(-3 \quad 2 \quad 6 \quad 14\) with no other values seen |
Additional guidance
| Solutions may be in any order eg1 \(-3 \quad 14 \quad 6 \quad 2\) eg2 \(14 \quad -3\) | B4 B2 |
| \(x \lt -3 \quad 2 \lt x \lt 6 \quad x \gt 14\) | SC2 |
| \(2 \leqslant x \leqslant 6\) | SC1 |
| \(-3 \quad 2 \quad 6 \quad 14\) seen in working with no other values and answer line \(-3 \leqslant x \leqslant 14\) | SC2 |