June 2019 Paper 1 Q16
16 Rationalise the denominator and simplify fully \(\qquad \dfrac{21 - 11\sqrt{5}}{3 - \sqrt{5}}\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{(21 - 11\sqrt{5})(3 + \sqrt{5})}{(3 - \sqrt{5})(3 + \sqrt{5})}\) | M1 | could be \(-3 - \sqrt{5}\) condone missing final bracket of \(3 + \sqrt{5}\) if written in this form. Brackets not needed if written as two separate fractions |
| Denominator of 4 | A1 | would be \(-4\) if \(-3 - \sqrt{5}\) used |
| Numerator \(63 - 33\sqrt{5} + 21\sqrt{5} - 55\) or \(8 - 12\sqrt{5}\) | M1dep | allow three terms correct in a 4 term expansion. If error appears in 2 or 3 term simplification and 4 term expansion not seen award M0 expansion could be seen in a grid |
| \(2 - 3\sqrt{5}\) or \(-3\sqrt{5} + 2\) | A1 | penalise further working |
Additional guidance
| Correct first A mark and M1dep mark would assume first M mark correct if not seen. |