Higher November 2016 Unit 2 Q12
12.
(a) Factorise \((x - 7)^2 + 2(x - 7)\). [2]
(b) Factorise \(12x^2 - 27y^2\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| \((x - 7)(x - 5)\) | B2 | B1 for \((x - 7)(x - 7 + 2)\) or \((x - 7)(x + k)\) with \(k \neq 0\) OR \((x \ldots 7)(x \ldots 5)\) |
| Scheme | Marks | Comments |
|---|---|---|
| \(3(4x^2 - 9y^2)\) | B1 | |
| \(3(2x + 3y)(2x - 3y)\) | B2 | B1 for \(3(2x \ldots\ 3y)(2x \ldots\ 3y)\) OR \((2x + 3y)(2x - 3y)\) |
Alternative method
Award B2 for:
\((6x + 9y)(2x - 3y)\) or \((2x + 3y)(6x - 9y)\)
SC2
\(12(x + 1.5y)(x - 1.5y)\)
OR \(27\left(\tfrac{2}{3}x + y\right)\left(\tfrac{2}{3}x - y\right)\) or equivalent.
SC1
\((\sqrt{12}x + \sqrt{27}y)(\sqrt{12}x - \sqrt{27}y)\)
OR \((2\sqrt{3}x + 3\sqrt{3}y)(2\sqrt{3}x - 3\sqrt{3}y)\) o.e.