Higher June 2022 Paper 4 Q19
19
(a) Write as a single fraction in its simplest form.\[\frac{4}{2n + 3} - \frac{2n}{n^2 + 1}\]
[4]
(b) Simplify.\[\frac{x^2 - x - 12}{2x^2 - 3x - 20}\]
[5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{4 - 6n}{(2n + 3)(n^2 + 1)}\) final answer | 4 | M1 for consistent common denominator of \((2n + 3)(n^2 + 1)\) M1 for \(4(n^2 + 1) - 2n(2n + 3)\) M1 for correct expansion of one bracket | Condone \(\frac{4 - 6n}{2n^3 + 3n^2 + 2n + 3}\) for 4 marks and allow numerator \(2(2 - 3n)\) allow e.g. \(\frac{4(n^2 + 1)}{(2n + 3)(n^2 + 1)} - \frac{2n(2n + 3)}{(2n + 3)(n^2 + 1)}\) Condone brackets crossed out |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{x + 3}{2x + 5}\) final answer | 5 | M2 for \((x + 3)(x - 4)\) or M1 for brackets which give 2 correct terms M2 for \((2x + 5)(x - 4)\) or M1 for brackets which give 2 correct terms | Condone brackets crossed out |