4400 Higher November 2008 Paper 3 Q18
18 Simplify fully \(\dfrac{2}{x + 2} + \dfrac{x}{x^2 + 5x + 6}\)
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{x + 2} + \dfrac{x}{(x + 2)(x + 3)}\) | B1 |
\(\dfrac{2(x + 3) + x}{(x + 2)(x + 3)}\) or \(\dfrac{2(x + 3)}{(x + 2)(x + 3)} + \dfrac{x}{(x + 2)(x + 3)}\) or \(\dfrac{2(x^2 + 5x + 6) + x(x + 2)}{(x + 2)(x^2 + 5x + 6)}\) | B1 |
\(\dfrac{2x + 6 + x}{(x + 2)(x + 3)} = \dfrac{3x + 6}{(x + 2)(x + 3)}\) or \(\dfrac{2x + 6 + x}{x^2 + 5x + 6} = \dfrac{3x + 6}{x^2 + 5x + 6}\) | B1 |
| \(\dfrac{3(x + 2)}{(x + 2)(x + 3)}\) | B1 |
| \(\dfrac{3}{x + 3}\) | B1 |
| (5) | |
| (5 marks) |
Notes
B1: for factorising \(x^2 + 5x + 6\)
B1: for correct single fraction even if unsimplified or for correct sum of two fractions with the same denominator
ft from incorrect factorisation
B1: for \(\dfrac{2x + 6 + x}{(x + 2)(x + 3)}\) or \(\dfrac{2x + 6 + x}{x^2 + 5x + 6}\)
B1: cao
SC if no denominator, award 3rd B1 for \(2x + 6 + x\) and 4th B1 for \(3(x + 2)\)