Higher January 2022 Paper 2R Q7
7
(a) Write down an equation of the straight line with gradient \(-3\) and which passes through the point with coordinates \((0, 5)\) (2)
(b) Show, by shading on the grid, the region defined by all three of the inequalities
\(x \leqslant 6 \qquad y \geqslant 2 \qquad y \leqslant x + 1\)
Label the region R (3)
\(x \leqslant 6 \qquad y \geqslant 2 \qquad y \leqslant x + 1\)
Label the region R (3)
| Scheme | Marks |
|---|---|
| \(y = -3x + 5\) oe | B2 |
| (2) |
Notes
B2: fully correct equation eg \(y = -3x + 5\) or \(y - 5 = -3(x - 0)\)
If not B2 then B1 for
\(y = -3x + a\) with \(a \neq 5\)
or
\(y = bx + 5\) (\(b \neq 0, -3\)) or
\((L =) -3x + 5\)
| Scheme | Marks |
|---|---|
| Lines (solid or dashed) \(x = 6\) and \(y = 2\) drawn | B1 |
| Line (solid or dashed) \(y = x + 1\) drawn | B1 |
Region R shown (shaded or not shaded) Answer: Correct region identified | B1 |
| (3) | |
| (5 marks) |
Notes
B1: The lines \(x = 6\) and \(y = 2\) should extend far enough to intersect with each other.
B1: The line should extend from at least \(x = 1\) to \(x = 6\) or far enough to intersect with their horizontal and vertical lines.
B1: dep on B2