4MA0 Higher June 2014 Paper 3 Q23
23 Solve the equation \(\dfrac{3}{(x + 2)} + \dfrac{4}{(x - 3)} = 2\)
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{3(x - 3) + 4(x + 2)}{(x + 2)(x - 3)}\) or \(\dfrac{3(x - 3)}{(x + 2)(x - 3)} + \dfrac{4(x + 2)}{(x + 2)(x - 3)}\ (=2)\) | M1 |
| \(3(x - 3) + 4(x + 2) = 2(x + 2)(x - 3)\) \(7x - 1 = 2(x^2 - x - 6)\) oe | M1 |
| \(2x^2 - 9x - 11\ (= 0)\) | A1 |
| \((2x - 11)(x + 1)\ (=0)\) | M1 |
| \(x = -1\) \(x = 5.5\) oe | A1 |
| (5 marks) |
Notes
M1: correct single fraction
M1: correct removal of denominator to give a correct equation
A1: correct 3 part quadratic (eg \(2x^2 - 9x - 11\ (= 0)\) or \(2x^2 - 9x = 11\) or \(2x^2 = 9x + 11\) oe)
M1: for \((2x - 11)(x + 1)\ (=0)\) or
a fully correct substitution into the quadratic formula
eg \(\dfrac{--9 \pm \sqrt{(-9)^2 - 4 \times 2 \times -11}}{2 \times 2}\) condone no brackets around – 9
or \(\dfrac{9 \pm \sqrt{169}}{4}\)
A1: dep on last M1