4400 Higher November 2005 Paper 4 Q18
18
(a) Express \(\sqrt{2} + \sqrt{8}\) in the form \(a\sqrt{2}\), where \(a\) is an integer. (1)
(b) Express \(\left(\dfrac{1}{\sqrt{2}}\right)^9\) in the form \(\dfrac{\sqrt{b}}{c}\), where \(b\) and \(c\) are integers. (3)
| Scheme | Marks |
|---|---|
| \(3\sqrt{2}\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{16\sqrt{2}}\) or \(\dfrac{\sqrt{2}}{\sqrt{2}} \times \dfrac{1}{(\sqrt{2})^9}\) | M1 |
| \(\dfrac{\sqrt{2}}{\sqrt{2}} \times \dfrac{1}{16\sqrt{2}}\) or \(\dfrac{\sqrt{2}}{(\sqrt{2})^{10}}\) | M1 |
| \(\dfrac{\sqrt{2}}{32}\) or \(\dfrac{\sqrt{512}}{512}\) | A1 |
| (3) | |
| (4 marks) |
Notes
M1: or \(\left(\dfrac{\sqrt{2}}{2}\right)^9\) or \(\dfrac{1}{\sqrt{512}}\)
M1: or \(\dfrac{16\sqrt{2}}{512}\) or \(\dfrac{1}{\sqrt{512}} \times \dfrac{\sqrt{512}}{\sqrt{512}}\)