Higher November 2021 Paper 4 Q12
12
(a) 
The region R is shown on this grid.
Region R is defined by four inequalities.
One of the inequalities is \(x \geqslant 0\).
Use the symbols \(\leqslant\) and \(\geqslant\) to complete the other three inequalities.
\[\begin{aligned} x &\geqslant 0 \\ y &\ \ldots\ \tfrac{1}{2}x \\ x + 2y &\ \ldots\ 24 \\ y &\ \ldots\ x + 6 \end{aligned}\][2]
(b) The inequality \(x \geqslant 0\) is replaced by a new inequality.
Region R is then a kite.
Region R is then a kite.
Write down the new inequality. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\geqslant\) \(\leqslant\) \(\leqslant\) | 2 | B1 for two correct or “\(>\ <\ <\)” | i.e correct but no equals |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x + y \geqslant 6\) or \(y \geqslant 6 - x\) oe | 3 | B1 for the correct straight line drawn | implied by e.g. \(x + y = 6\) oe and accept a ruled or good freehand line bold line shows minimum length |
| B1 for correct equation for their line e.g. \(x + y = 6\) oe | implied by e.g. answer of \(x + y \leqslant 6\) oe | ||