4400 Higher June 2005 Paper 3 Q22
22 Simplify fully \(\dfrac{2}{x - 1} + \dfrac{x - 11}{x^2 + 3x - 4}\)
(6)
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{x - 1} + \dfrac{x - 11}{(x - 1)(x + 4)}\) | B1 |
| \(\dfrac{2(x + 4) + (x - 11)}{(x - 1)(x + 4)}\) or \(\dfrac{2(x + 4)}{(x - 1)(x + 4)} + \dfrac{x - 11}{(x - 1)(x + 4)}\) | B1 |
| \(\dfrac{2x + 8 + x - 11}{(x - 1)(x + 4)}\) | B1 |
| \(\dfrac{3x - 3}{(x - 1)(x + 4)}\) | B1 |
| \(\dfrac{3(x - 1)}{(x - 1)(x + 4)}\) | B1 |
| \(\dfrac{3}{(x + 4)}\) | B1 |
| (6) | |
| (6 marks) |
Notes
B1: For factorising \(x^2 + 3x - 4\)
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 expanding brackets correctly in numerator
B1: For simplifying their numerator
B1: For factorising a correct numerator
B1: cao
SC If no denominator, award 3rd B1 for \(2x + 8 + x - 11\) or \(2x^2 + 6x - 8 + x^2 - 11x - x + 11\) and 4th B1 for \(3x - 3\) or \(3x^2 - 6x + 3\)