4MA0 Higher June 2015 Paper 3 Q17
17 \(\mathrm{f}(x) = \dfrac{3}{x + 1} + \dfrac{1}{x - 2}\)
(a) State one value of \(x\) which cannot be included in any domain of f. (1)
(b) Find the value of f(0) (1)
(c) Find the value of \(x\) for which f(\(x\)) = 0
Show clear algebraic working. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| −1 or 2 | B1 |
| (1) |
Notes
B1: for −1 or for 2 or both
| Scheme | Marks |
|---|---|
| \(\dfrac{5}{2}\) oe | B1 |
| (1) |
| Scheme | Marks |
|---|---|
\(\dfrac{3(x - 2)}{(x + 1)(x - 2)} + \dfrac{x + 1}{(x + 1)(x - 2)}\) or \(\dfrac{3(x - 2)(x + 1)}{(x + 1)} + \dfrac{(x - 2)(x + 1)}{(x - 2)}\) or \(3(x - 2) + x + 1\) | M1 |
| \(3(x - 2) + x + 1 = 0\) oe or \(4x - 5 = 0\) | M1 |
| \(\dfrac{5}{4}\) oe | A1 |
| (3) |
Notes
M1: for correct method to clear fractions
M1: for clearing fractions and obtaining a correct equation
A1: (depending on at least M1)