4MA0 Higher January 2018 Paper 4R Q11
11
(a) Simplify \(2a^3b^4 \times 4a^2b^5\) (2)
\(c^k = \dfrac{1}{\sqrt[4]{c^2}}\)
(b) Work out the value of \(k\) (2)
(c) Simplify fully \(\dfrac{4(x + 2)^2}{6(x + 2)}\) (2)
(d) Factorise completely \(3x^2 - 75y^2\) (2)
| Scheme | Marks |
|---|---|
| M1 | |
| \(8a^5b^9\) | A1 |
| (2) |
Notes
M1: For two correct from 8, \(a^5\) or \(b^9\) written as a product.
| Scheme | Marks |
|---|---|
Eg \(\dfrac{1}{c^{2/4}}\) or \(c^{2/4}\) or \(\left(c^k\right)^4 = \dfrac{1}{c^2}\) or \(c^{4k} = \dfrac{1}{c^2}\) or \(4k = -2\) | M1 |
| \(-\dfrac{1}{2}\) oe | A1 |
| (2) |
Notes
M1: For a correct first step
A1: Eg \(-\dfrac{2}{4}\)
| Scheme | Marks |
|---|---|
| M1 | |
| \(\dfrac{2(x + 2)}{3}\) | A1 |
| (2) |
Notes
M1: For \(\dfrac{4(x + 2)}{6}\) or \(\dfrac{4x + 8}{6}\) or \(\dfrac{2(x + 2)^2}{3(x + 2)}\)
A1: Accept \(\dfrac{2x + 4}{3}\) or \(\dfrac{2}{3}(x + 2)\) or \(\dfrac{2}{3}x + \dfrac{4}{3}\)
| Scheme | Marks |
|---|---|
| \(3(x^2 - 25y^2)\) | M1 |
| \(3(x + 5y)(x - 5y)\) | A1 |
| (2) | |
| (8 marks) |
Notes
M1: For \(3(x^2 - 25y^2)\) or
\((3x - 15y)(x + 5y)\) or
\((x - 5y)(3x + 15y)\) or
\((\sqrt{3}x + \sqrt{75}y)(\sqrt{3}x - \sqrt{75}y)\) oe