Higher June 2022 Paper 4 Q20
20 Solve this inequality.
\[x^2 + 4x - 12 \leqslant 0\]Give your answer using set notation.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\{x : -6 \leqslant x \leqslant 2\}\) final answer and with correct working | 5 | “correct working” requires at least M2 e.g. \((x + 6)(x - 2)\) | |
| B4 for \(-6 \leqslant x \leqslant 2\) with correct working and not written separately | |||
| OR | |||
| M2 for \((x + 6)(x - 2)\) or \(\frac{-4 \pm \sqrt{4^2 - 4 \times 1 \times -12}}{2}\) or M1 for brackets which give two correct terms or the formula with at most two errors B1 −6 and 2 | condone \(x(x - 2) + 6(x - 2)\) for M2 could be seen as roots on a sketch of graph or with incorrect inequality symbols completing the square : allow \((x + 2)^2 - 16\) for M2 or \((x + 2)^2 + k\) for M1 | ||
| If 0 or 1 scored award instead SC2 for \(\{x : -6 \leqslant x \leqslant 2\}\) If 0 scored SC1 for \(-6 \leqslant x \leqslant 2\) | |||