Higher June 2022 Paper 2R Q19
19 \(\mathrm{f}(x) = x^2 - 4\)
\(\mathrm{g}(x) = 2x + 1\)
Solve \(\mathrm{fg}(x) \gt 0\)
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
| eg \((\mathrm{fg}(x) =)\;(2x + 1)^2 - 4\) | M1 |
| eg \(4x^2 + 4x - 3\;(\gt 0)\) or \(4x^2 + 4x - 3\;(= 0)\) or \((2x + 1)^2 \gt 4\) or \((2x + 1)^2 = 4\) | M1 |
| \(-\dfrac{3}{2}\) oe (and) \(\dfrac{1}{2}\) oe | A1 |
Working required Answer: \(x \lt -\dfrac{3}{2}\), \(x \gt \dfrac{1}{2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for finding \(\mathrm{fg}(x)\)
M1: For a correct expansion and \(\mathrm{fg}(x)\) written as a 3 term quadratic
or
a start to write quadratic in correct form for completing square
A1: for finding the two correct critical values (dep on previous M1) (values seen with any signs between)
A1: two fully correct inequalities, oe (dep on 2nd M1)