Higher November 2022 Paper 6 Q15
15 The region R is shown on this grid.
A is the point (0, 3) and B is the point (3, 4.5).
(a) Show that an equation of the straight line through A and B is \(2y = x + 6\). [3]
(b) Write down the three inequalities that define region R. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [gradient =] (4.5 – 3) ÷ (3 – 0) oe | 1 | Must show a correct calculation of the gradient | Working backwards scores 0 |
| \(y\) = (their 0.5)\(x\) + \(c\) or \(y = mx + 3\) or \(y - y_1\) = their 0.5(\(x - x_1\)) or \(y - 4.5 = m(x - 3)\) or \(y - 3 = m(x\) [– 0]) | 1 | This can be \(y = 0.5x + 3\) or \(\frac{y - 3}{x\,[-0]}\) = their 0.5 oe or \(y - 4.5 = 0.5(x - 3)\) oe | |
| \(y = 0.5x + 3\) or \(y - 4.5 = 0.5(x - 3)\) oe or \(y - 3 = 0.5(x\) [– 0]) oe AND \(2y = x + 6\) | 1 | If 0 scored SC1 for verification of A and B | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x \leqslant 3\) oe \(x + y \gt 3\) oe \(2y \leqslant x + 6\) oe | 5 | B2 for \(x \leqslant 3\) oe or B1 for \(x = 3\) oe or \(x \lt 3\) oe or SC1 for \(x \geqslant 3\) oe or for \(0 \leqslant x \leqslant 3\) AND B2 for \(x + y \gt 3\) oe or B1 for \(x + y = 3\) oe or SC1 for \(x + y \geqslant 3\) oe AND B1 for \(2y \leqslant x + 6\) | |