Foundation November 2024 Paper 2 Q23
23
(a) On the grid, draw the straight line with equation
(i) \(x = 3\) (ii) \(y = 1\) (iii) \(x + y = 7\)
Label each line with its equation. (3)
(i) \(x = 3\) (ii) \(y = 1\) (iii) \(x + y = 7\)
Label each line with its equation. (3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
\(x \geqslant 3 \qquad y \geqslant 1 \qquad x + y \leqslant 7\)
Label the region R (1)
\(x \geqslant 3 \qquad y \geqslant 1 \qquad x + y \leqslant 7\)
Label the region R (1)
| Scheme | Marks |
|---|---|
| (i) | B1 |
| (ii) | B1 |
(iii) If unlabelled, award: \(x = 3\) and \(y = 3\) B1 B0 \(y = 1\) and \(x = 1\) B0 B1 \(x = 3\) and \(x = 1\) and \(y = 1\) B0 B1 \(x = 3\) and \(y = 1\) and \(y = 3\) B1 B0 \(x = 3\) and \(x = 1\), \(y = 1\) and \(y = 3\) B0 B0 | B1 |
| (3) |
Notes
B1: \(x = 3\) drawn
B1: \(y = 1\) drawn
B1: \(x + y = 7\) drawn
Allow dashed lines or solid lines for graphs of minimum length 2 squares condone lack of labels if unambiguous
| Scheme | Marks |
|---|---|
| B1 | |
| (1) | |
| (4 marks) |
Notes
B1: correct region shaded – shaded in or out – labelled R or clear intention to be the required region (ft only for one vertical line (not \(x = 0\)), one horizontal line (not \(y = 0\)) and one line with a negative gradient eg \(x = 1\), \(y = 3\) and \(x + y = 7\))