4400 Higher June 2006 Paper 4 Q13
13
(a) Express \(8^{\frac{1}{2}}\) as a power of 2 (2)
(b) Express \(\sqrt{3}\) as a power of 9 (2)
(c) Express \(\dfrac{1}{4\sqrt{2}}\) as a power of 2 (3)
| Scheme | Marks |
|---|---|
| \(2^3\) seen | M1 |
| \(2^{3/2}\) or \(2^{1.5}\) or \(2^{1\frac{1}{2}}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(9^{1/2}\) seen | M1 |
| \(9^{1/4}\) or \(9^{0.25}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{2^2 \times 2^{\frac{1}{2}}}\) or \(\dfrac{1}{\sqrt{32}}\) or \(\dfrac{\sqrt{2}}{8}\) | M1 |
| \(\dfrac{1}{2^{\frac{5}{2}}}\) or \(\dfrac{1}{\sqrt{2^5}}\) or \(\dfrac{2^{0.5}}{2^3}\) | M1 |
| \(2^{-5/2}\) or etc | A1 |
| (3) | |
| (7 marks) |
Notes
M1: or \(2^{-2} \times 2^{-1/2}\) : M2