Higher November 2017 Paper 4 Q15
15 Show that \(\dfrac{4 + 2\sqrt{5}}{\sqrt{5} - 1}\) can be simplified to \(\dfrac{3\sqrt{5} + 7}{2}\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{(4 + 2\sqrt{5})(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)}\) | M1 | ||
| \((4\sqrt{5} + 4 + 10 + 2\sqrt{5})\) oe or better | M1 | condone one error | bracket expansion could be in a table |
| \((5 - \sqrt{5} + \sqrt{5} - 1)\) oe or better | M1 | soi by 5 −1 or 4 condone one error | |
| \(\dfrac{6\sqrt{5} + 14}{4} = \dfrac{3\sqrt{5} + 7}{2}\) | A1 | i.e. dividing by 2 | |