Higher November 2018 Paper 1 Q20
20 Show that \(\dfrac{(\sqrt{18} + \sqrt{2})^2}{\sqrt{8} - 2}\) can be written in the form \(a(b + \sqrt{2})\) where \(a\) and \(b\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| fully correct working leading to \(16(1 + \sqrt{2})\) | C1 | for expanding the numerator, eg \(18 + 2\sqrt{2}\sqrt{18} + 2\) or \(\sqrt{324} + \sqrt{36} + \sqrt{36} + \sqrt{4}\ (= 32)\) or for simplifying \(\sqrt{18}\), eg. \(\sqrt{18} = 3\sqrt{2}\) or \(\sqrt{18} + \sqrt{2} = 4\sqrt{2}\) |
| C1 | (indep) for method to rationalise the denominator, eg. \(\dfrac{\text{\text{``}numerator\text{''}}}{\sqrt{8} - 2} \times \dfrac{\sqrt{8} + 2}{\sqrt{8} + 2}\) | |
| C1 | for fully correct working leading to \(16(1 + \sqrt{2})\) |
Additional guidance
Expanded terms need not be simplified
Accept \(a = 16\), \(b = 1\)