4400 Higher June 2008 Paper 4 Q23
23
(a) Simplify \(\dfrac{x^2 - 9}{x^2 + 3x}\) (3)
\(\mathrm{f}(x) = \dfrac{x^2 - 9}{x^2 + 3x} \qquad \mathrm{g}(x) = \dfrac{1}{x^2}\)
(b) Use your answer to part (a) to find and simplify \(\mathrm{fg}(x)\). (2)
| Scheme | Marks |
|---|---|
| \((x - 3)(x + 3)\) | M1 |
| \(x(x + 3)\) | M1 |
| \(\dfrac{x - 3}{x}\) | A1 |
| (3) |
Notes
A1: \(1 - \dfrac{3}{x}\)
| Scheme | Marks |
|---|---|
| \(\dfrac{\frac{1}{x^2} - 3}{\frac{1}{x^2}}\) or \(1 - \dfrac{3}{\frac{1}{x^2}}\) | M1 |
| \(1 - 3x^2\) | A1 |
| (2) | |
| (5 marks) |
Notes
M1: ft \(\dfrac{x + 3}{x}\) only
A1: cao