June 2023 Paper 1 Q10
10 Rationalise the denominator and simplify fully
\[\frac{1 + \sqrt{5}}{3 - \sqrt{5}}\][4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{\left(1 + \sqrt{5}\right)\left(3 + \sqrt{5}\right)}{\left(3 - \sqrt{5}\right)\left(3 + \sqrt{5}\right)}\) | M1 | oe \(\dfrac{\left(1 + \sqrt{5}\right)\left(-3 - \sqrt{5}\right)}{\left(3 - \sqrt{5}\right)\left(-3 - \sqrt{5}\right)}\) (if this method is used then follow equivalent MS for \(-4\) and \(-3 - 5 - \sqrt{5} - 3\sqrt{5}\)) could be seen separately or in a grid |
| Denominator = 4 or \(9 - 5\) | M1dep | |
| Numerator \(3 + 5 + \sqrt{5} + 3\sqrt{5}\) | M1dep | oe any 3 terms out of 4 correct (terms may have already been simplified eg \(3 + 4\sqrt{5}\) just one error so M1dep) do not accept \(\sqrt{5}\,\sqrt{5}\) or \(\sqrt{25}\) for 5 this would be one error could be implied from \(\dfrac{8 + 4\sqrt{5}}{4}\) only dependent on first M mark |
| \(2 + \sqrt{5}\) | A1 | condone \(2 + 1\sqrt{5}\) don’t condone \(\dfrac{2 + \sqrt{5}}{1}\) |
Additional guidance
| Untidy mathematical notation can be condoned as long as it’s recovered |