4MA0 Higher January 2015 Paper 4R Q20
20
(a) Factorise \(4x^2 - 1\) (2)
(b) Solve \(\dfrac{4}{2x + 1} + \dfrac{1}{4x^2 - 1} = 3\)
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| M1 | |
| \((2x - 1)(2x + 1)\) | A1 |
| (2) |
Notes
M1: \((2x \pm 1)(2x \pm 1)\)
A1: cao
| Scheme | Marks |
|---|---|
\(\dfrac{4(2x - 1)}{(2x - 1)(2x + 1)} + \dfrac{1}{4x^2 - 1}\,[= 3]\) or \(\dfrac{4(4x^2 - 1)}{(2x + 1)(4x^2 - 1)} + \dfrac{(2x + 1)}{(2x + 1)(4x^2 - 1)}\,[= 3]\) or \(\dfrac{4(4x^2 - 1)}{2x + 1} + \dfrac{1(4x^2 - 1)}{4x^2 - 1} = 3(4x^2 - 1)\) or \(4(4x^2 - 1) + (2x + 1) = 3(2x + 1)(4x^2 - 1)\) | M1 |
| \(4(2x - 1) + 1 = 3(4x^2 - 1)\) oe or \(4(4x^2 - 1) + 2x + 1 = 3(2x + 1)(4x^2 - 1)\) oe | M1 |
| \(12x^2 - 8x = 0\) or \(8x - 12x^2 = 0\) or \(24x^3 - 4x^2 - 8x = 0\) or \(8x + 4x^2 - 24x^3 = 0\) | M1 |
| 0, \(\dfrac{2}{3}\) | A1 |
| (4) | |
| (6 marks) |
Notes
M1: multiply all terms by \((4x^2 - 1)\) or
correct equation with fractions with a common denominator
NB \((4x^2 - 1)\) may be factorised throughout
M1: correct equation with no fractions
M1: correct simplified equation with all terms on one side
A1: dep on M2