4MA0 Higher January 2013 Paper 4 Q14
14 Solve \(\dfrac{2}{5x - 2} = \dfrac{3}{6x + 1}\)
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
\(2(6x + 1) = 3(5x - 2)\) or \(\dfrac{2(6x + 1)}{(5x - 2)(6x + 1)} = \dfrac{3(5x - 2)}{(5x - 2)(6x + 1)}\) | M1 |
\(12x + 2 = 15x - 6\) or \(\dfrac{12x + 2}{(5x - 2)(6x + 1)} = \dfrac{15x - 6}{(5x - 2)(6x + 1)}\) | M1 |
| \(3x = 8\) or \(-3x = -8\) or \(3x = 2 + 6\) or \(-3x = -6 - 2\) or \(15x - 12x = 8\) or \(12x - 15x = -8\) or \(3x - 8 = 0\) | M1 |
| \(2\tfrac{2}{3}\) oe | A1 |
| (4) |
Notes
M1: Need to see both expressions in an equation
May be implied by second M1;
NB: Denominators must be correct
M1: Need to see both expressions in an equation
NB: Denominators must be correct
M1: dep on awarding first two method marks
for correct rearrangement with \(x\) terms on one side and numbers on the other AND correct collection of terms on at least one side
or for \(3x - 8 = 0\)
A1: for \(2\tfrac{2}{3}\) oe including decimal equivalent rounded or truncated to at least 2 decimal places
Award 4 marks if first two method marks scored and answer correct.