Higher June 2023 Paper 5 Q14
14 The graphs of \(x = -3\) and \(y = -x\) are drawn on the grid.
The region R satisfies the following inequalities.
\[x \leqslant -3 \qquad y \leqslant -x \qquad y - 1 \gt \frac{1}{2}x\]By drawing one more line, find and label the region R. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
Correct region indicated | 5 | B2 for \(y - 1 = \frac{1}{2}x\) broken line or B1 for \(y - 1 = \frac{1}{2}x\) solid line AND B1FT for \(R\) correct side of \(y - 1 = \frac{1}{2}x\) B1 for \(R\) correct side of \(x = -3\) B1 for \(R\) correct side of \(y = -x\) | Use overlay as a guide for accuracy must pass through or touch small circles (when extended if necessary) position is 2 small dots each way from correct position of ends of line Allow shorter accurate line provided it defines their region See marks on diagram for next 3 marks Grid assumes \(y - 1 = \frac{1}{2}x\) is correct Mark position of R first. If R not labelled then accept other clear indication. If \(y - 1 = \frac{1}{2}x\) not attempted then allow B1B1 max for region FT dep on sloping line drawn that is long enough to define the region chosen on grid |