4MA0 Higher June 2013 Paper 4 Q23
23 Solve \(\dfrac{3}{(x + 1)} + \dfrac{2}{(2x - 3)} = 1\)
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{3(2x-3) + 2(x+1)}{(x+1)(2x-3)}\;(=1)\) | M1 |
| \(8x - 7 = (x + 1)(2x - 3)\) oe | M1 |
| \(2x^2 - 9x + 4\;(= 0)\) | A1 |
| \((2x - 1)(x - 4)\;(=0)\) | M1 |
| \(x = \tfrac{1}{2}\) or 4 | A1 |
| (5) |
Notes
M1: or \(3(2x - 3) + 2(x + 1) = (x + 1)(2x - 3)\)
M1: \(8x - 7 = \text{“}(x + 1)(2x - 3)\text{”}\)
A1: oe correct 3-part quadratic in the form \(ax^2 + bx + c\) (=0)
M1: or \(\dfrac{--9 \pm \sqrt{(-9)^2 - 4 \times 2 \times 4}}{2 \times 2}\)
A1: dep on previous M1