Higher January 2019 Paper 1R Q18
18 Show that \(\dfrac{\sqrt{8}}{\sqrt{8} - 2}\) can be written in the form \(n + \sqrt{n}\), where \(n\) is an integer.
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| \(\dfrac{\sqrt{8}}{\sqrt{8} - 2} \times \dfrac{\sqrt{8} + 2}{\sqrt{8} + 2}\) | M1 |
| \(\dfrac{\sqrt{8}\left(\sqrt{8} + 2\right)}{8 - 4} = \dfrac{8 + 2\sqrt{8}}{4} = \dfrac{8 + 4\sqrt{2}}{4}\) | M1 |
\(= 2 + \sqrt{2}\) Answer: Shown | A1 |
| (3) | |
| (3 marks) |
Notes
M1: or \(\dfrac{2\sqrt{2}}{2\sqrt{2} - 2}\) or \(\dfrac{\sqrt{2}}{\sqrt{2} - 1}\)
M1: or \(\dfrac{\sqrt{2}}{\sqrt{2} - 1} \times \dfrac{\sqrt{2} + 1}{\sqrt{2} + 1}\)
A1: (dep on M2) Conclusion - need not state the value of \(n\)