4MA0 Higher June 2014 Paper 4R Q17
17
(a) Simplify \(\;(16x^4y^2)^{\frac{1}{2}}\) (2)
(b) Simplify fully \(\;\dfrac{2x^2 - 8}{4x^2 - 8x}\) (3)
| Scheme | Marks |
|---|---|
| \(4x^2y\) | B2 |
| (2) |
Notes
B2: (B1 for \(ax^ny^m\) with two of \(a = 4\); \(n = 2\); \(m = 1\))
| Scheme | Marks |
|---|---|
| \(2(x - 2)(x + 2)\) or \((2x - 4)(x + 2)\) or \((x - 2)(2x + 4)\) | M1 |
| \(4x(x - 2)\) or \(2x(2x - 4)\) | M1 |
| \(\dfrac{x + 2}{2x}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for numerator factorised
M1: for denominator factorised
A1: accept \(\dfrac{1}{2} + \dfrac{1}{x}\)
Alternative to (b)
| Scheme | Marks |
|---|---|
\(\dfrac{2x^2 - 8}{4x^2 - 8x} = \dfrac{x^2 - 4}{2x^2 - 4x} = \dfrac{(x - 2)(x + 2)}{2x(x - 2)}\) Answer: \(\dfrac{x + 2}{2x}\) | M1 M1 A1 |
Notes
M1 M1 A1: In order to use this mark scheme, correct simplification of the original fraction must be seen
M1 \((x - 2)(x + 2)\)
M1 \(2x(x - 2)\)
A1 accept \(\dfrac{1}{2} + \dfrac{1}{x}\)