Higher January 2022 Paper 2 Q22
22 Here is a rectangle.
Diagram NOT accurately drawn
Given that the area of the rectangle is less than 75 cm2
find the range of possible values of \(x\)
(5)
| Scheme | Marks |
|---|---|
| \((2x + 3)(x - 1) \lt 75\) | B1 |
| \(2x^2 + x - 78 \lt 0\) | M1 |
\((x - 6)(2x + 13)\;(\lt 0)\) or \(x = \dfrac{-1 \pm \sqrt{(1)^2 - (4 \times 2 \times -78)}}{2 \times 2}\) or \(2\left(x + \dfrac{1}{4}\right)^2 - 2\left(\dfrac{1}{4}\right)^2 - 78 = 0\) | M1 |
| \(x = 6\) | A1 |
| \(1 \lt x \lt 6\) | A1 |
| (5) | |
| (5 marks) |
Notes
B1: For writing the correct inequality sign with a correct calculation or correct value – this could be initially or saying that \(x \lt 6\) at the end
M1: rearranged to form correct quadratic \(\lt 0\)
(allow = 0 or other incorrect inequality sign) oe
M1: first step to find critical values from the correct quadratic
A1: \(x = 6\) identified as critical value, ignore –6.5 if given
A1: correct inequality