June 2024 Paper 1 Q18
18 Rationalise the denominator and simplify fully
\[\frac{3\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}\][4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\times \dfrac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}\) | M1 | oe eg \(\dfrac{3\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} \times \dfrac{-\sqrt{5} - \sqrt{3}}{-\sqrt{5} - \sqrt{3}}\) |
| Denominator \(5 - 3\) or 2 | M1dep | |
| Numerator \(15 + 3 + 3\sqrt{15} + \sqrt{15}\) | M1dep | oe three terms correct could be simplified without writing 4 terms which would imply original terms if done correctly eg \(18 + 2\sqrt{15} + \sqrt{15}\) or \(18 + 3\sqrt{15}\) whereas \(17 + 3\sqrt{15} + \sqrt{15}\) could be two errors so wouldn’t get M1 accept \(\sqrt{3}\sqrt{5}\) for \(\sqrt{15}\) for this mark do not accept \(\sqrt{3}\sqrt{3}\) or \(\sqrt{9}\) for 3 or \(\sqrt{5}\sqrt{5}\) or \(\sqrt{25}\) for 5 this would count as one error dep on first M mark only |
| \(9 + 2\sqrt{15}\) | A1 |
Additional guidance
| For M dep marks numerator and denominator can be seen separately | |
| Follow an equivalent MS for any student using \(\dfrac{3\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} \times \dfrac{-\sqrt{5} - \sqrt{3}}{-\sqrt{5} - \sqrt{3}}\) | |
| M marks may be seen in a grid method | |
| Untidy mathematical notation can be condoned as long as it’s recovered | |
| Missing brackets can be recovered |