4400 Higher June 2005 Paper 3 Q15
15
(a) Express \(\dfrac{10}{\sqrt{5}}\) in the form \(k\sqrt{5}\) where \(k\) is an integer. (2)
(b) Express \((5 + \sqrt{3})^2\) in the form \(a + b\sqrt{3}\) where \(a\) and \(b\) are integers. (2)
| Scheme | Marks |
|---|---|
| \(\dfrac{10}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) | M1 |
| \(2\sqrt{5}\) | A1 |
| (2) |
Notes
M1: Accept \(10 = k5\) or \(\sqrt{20}\)
A1: Accept \(k = 2\)
| Scheme | Marks |
|---|---|
| \(25 + 5\sqrt{3} + 5\sqrt{3} + (\sqrt{3})^2\) | M1 |
| \(28 + 10\sqrt{3}\) | A1 |
| (2) | |
| (4 marks) |
Notes
A1: Accept \(a = 28\), \(b = 10\)