4MA0 Higher January 2017 Paper 4R Q15
15
(a) Factorise \(\;y^2 - 2y - 48\) (2)
(b) Solve \(\;\dfrac{4}{e - 3} = 5\) (2)
(c) Simplify fully \(\;\dfrac{3}{x + 1} - \dfrac{2}{x - 1}\) (3)
| Scheme | Marks |
|---|---|
| M1 | |
| \((y - 8)(y + 6)\) | A1 |
| (2) |
Notes
M1: For \((y \pm 8)(y \pm 6)\)
A1: cao
| Scheme | Marks |
|---|---|
| \(4 = 5(e - 3)\) or \(4 = 5e - 15\) or \(\dfrac{4}{5} = e - 3\) | M1 |
| \(\dfrac{19}{5}\) | A1 |
| (2) |
Notes
A1: \(3\frac{4}{5}\) or 3.8
| Scheme | Marks |
|---|---|
| \(\dfrac{3(x - 1) - 2(x + 1)}{(x + 1)(x - 1)}\) or \(\dfrac{3(x - 1)}{(x + 1)(x - 1)} - \dfrac{2(x + 1)}{(x + 1)(x - 1)}\) | M1 |
| \(\dfrac{3x - 3 - 2x - 2}{(x + 1)(x - 1)}\) oe | M1 |
| \(\dfrac{x - 5}{(x + 1)(x - 1)}\) | A1 |
| (3) | |
| (7 marks) |
Notes
M1: oe e.g. \(\dfrac{3(x - 1) - 2(x + 1)}{x^2 - 1}\)
A1: oe e.g. \(\dfrac{x - 5}{x^2 - 1}\)