Higher November 2018 Paper 1 Q24
24 Show that \(\quad \dfrac{2\sqrt{6}}{\sqrt{5}} - \dfrac{\sqrt{3}}{\sqrt{10}} \quad\) can be written in the form \(\quad \dfrac{c\sqrt{d}}{10}\)
where \(c\) and \(d\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{2\sqrt{6}}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) or \(\dfrac{\sqrt{3}}{\sqrt{10}} \times \dfrac{\sqrt{10}}{\sqrt{10}}\) | M1 | |
| \(\dfrac{2\sqrt{30}}{5}\) or \(\dfrac{4\sqrt{30}}{10}\) or \(\dfrac{\sqrt{30}}{10}\) | M1dep | |
| \(\dfrac{3\sqrt{30}}{10}\) | A1 | |
| Alternative method 2 | ||
| \(\dfrac{2\sqrt{6}\sqrt{2}}{\sqrt{10}} - \dfrac{\sqrt{3}}{\sqrt{10}}\) or \(\dfrac{2\sqrt{12}}{\sqrt{10}} - \dfrac{\sqrt{3}}{\sqrt{10}}\) | M1 | oe common denominator eg \(\dfrac{2\sqrt{60}}{\sqrt{50}} - \dfrac{\sqrt{15}}{\sqrt{50}}\) |
| \(\dfrac{4\sqrt{3}}{\sqrt{10}} - \dfrac{\sqrt{3}}{\sqrt{10}}\) or \(\dfrac{3\sqrt{3}}{\sqrt{10}}\) | M1dep | oe common denominator and common surd in numerator \(\dfrac{4\sqrt{15}}{\sqrt{50}} - \dfrac{\sqrt{15}}{\sqrt{50}}\) or \(\dfrac{3\sqrt{15}}{\sqrt{50}}\) |
| \(\dfrac{3\sqrt{30}}{10}\) | A1 | |
Additional guidance
| Ignore an attempt at further simplification after \(\dfrac{3\sqrt{30}}{10}\) | M1M1A1 |