4400 Higher June 2006 Paper 3 Q23
23 \(\mathrm{f}(x) = x^2\)
\(\mathrm{g}(x) = 2x + 3\)
Solve \(\mathrm{fg}(x) = \mathrm{f}(x)\).
(5)
| Scheme | Marks |
|---|---|
| \((2x + 3)^2 = x^2\) | M1 |
| \(4x^2 + 12x + 9 = x^2\) or \(4x^2 + 6x + 6x + 9 = x^2\) | M1 |
| \(3x^2 + 12x + 9 = 0\) | M1 |
| \((x + 1)(x + 3)\) | M1 |
| −1 \(\quad\) −3 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for \((2x + 3)^2\) seen
M1: Accept \((3x + 3)(x + 3)\) & \((3x + 9)(x + 1)\) or \(\dfrac{-12 \pm 6}{6}\) or \(\dfrac{-4 \pm 2}{2}\)
A1: for both solutions isw
Condone coordinates
Alternative
| \((2x + 3)^2 = x^2\) | M1 |
| \(2x + 3 = \pm x\) | M2 |
| \(x + 3 = 0\) or \(3x + 3 = 0\) | M1 |
| −1 \(\quad\) −3 | A1 |
M2: (M1 for \(2x + 3 = x\))
M1: for both
A1: for both solutions isw. Condone coordinates