4MA0 Higher January 2016 Paper 4 Q22
22 Solve the equation \(\dfrac{6}{x - 2} - \dfrac{6}{x + 1} = 1\)
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
\(\dfrac{6(x + 1) - 6(x - 2)}{(x - 2)(x + 1)}\) or \(\dfrac{6(x + 1)}{(x - 2)(x + 1)} - \dfrac{6(x - 2)}{(x - 2)(x + 1)}\) (=1) oe | M1 |
| \(6(x + 1) - 6(x - 2) = (x + 1)(x - 2)\) oe (\(18 = x^2 - x - 2\)) | M1 |
| \(x^2 - x - 20\) (=0) | A1 |
| \((x + 4)(x - 5)\) (= 0) | M1 |
| \(x = 5\), \(x = -4\) | A1 |
| (5) |
Notes
M1: Correct single fraction or 2 fractions with the same correct common denominator
If expanded, condone 1 error in numerator
M1: Correct removal of denominator (M2 if a candidate goes straight to this stage) if expanded, condone 1 error
A1: Correct 3 part quadratic
(eg \(x^2 - x - 20\) (=0) or \(x^2 - x = 20\) or \(x^2 = x + 20\))
M1: \((x + 4)(x - 5)\) (= 0) or a fully correct substitution into the quadratic formula
eg \(\dfrac{--1 \pm \sqrt{(-1)^2 - 4 \times 1 \times -20}}{2 \times 1}\)
Condone no brackets around −1
or \(\dfrac{1 \pm \sqrt{81}}{2}\)
A1: dep on last M1