4400 Higher June 2005 Paper 3 Q14
14 Solve \(\dfrac{x - 1}{2} + \dfrac{2x + 3}{4} = 1\)
(4)
| Scheme | Marks |
|---|---|
| \(2(x - 1) + 2x + 3 = 4\) or \(\dfrac{2(x - 1) + 2x + 3}{4} = 1\) or \(\dfrac{2(x - 1)}{4} + \dfrac{2x + 3}{4} = 1\) | M1 |
| \(2x - 2 + 2x + 3 = 4\) or \(\dfrac{2x - 2 + 2x + 3}{4} = 1\) or \(\dfrac{2x - 2}{4} + \dfrac{2x + 3}{4} = 1\) | M1 |
| \(4x = 3\) | M1 |
| \(\frac{3}{4}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Clear attempt to multiply both sides by 4 (or multiple) or expressing LHS with a denominator of 4 or a multiple of 4
M1: (dep) expanding brackets or M2 for \(\dfrac{x}{2} - \dfrac{1}{2} + \dfrac{2x}{4} + \dfrac{3}{4} = 1\) (M1 if one error)
M1: (dep on first M1) reducing to form \(ax = b\) using a correct method or \(\dfrac{x}{2} + \dfrac{2x}{4} = 1 + \dfrac{1}{2} - \dfrac{3}{4}\)
A1: oe