Higher June 2022 Paper 6 Q18
18 The graph of \(y = 2x + 1\) is drawn on this one centimetre grid.
The region \(R\) satisfies these inequalities.
\[y \leqslant 2x + 1 \qquad y \geqslant 5 \qquad x + y \leqslant 13\]Show that the area of region \(R\) is 12 cm². [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
E.g. Correct inequalities shown on diagram, correct region \(R\) identified and correct area calculation \(\frac{1}{2} \times 6 \times 4\) [= 12] | 6 | B1 for line \(y = 5\) B1 for line \(x + y = 13\) | Condone good freehand lines, which can be dashed or solid. Lines need only be one square long for line mark but they must be fit for purpose to define their region. |
| AND B1 for correct side of \(y = 2x + 1\) B1 for correct side of \(y = 5\) B1 for correct side of \(x + y = 13\) | Mark the region which is labelled, but if no labelling mark the single region which is shaded (or unshaded) or implied by area calculation of correct region \(R\) Use diagram for these three marks If extra lines, mark those bounding \(R\). If no \(R\), mark poorest two | ||
| AND M1dep for \(\frac{1}{2} \times 6 \times 4\) [= 12] oe | Dep on region \(R\) being correct Accept counting squares but check areas bounding \(y = 2x + 1\) Accept split into two triangles 4 and 8 oe | ||