4400 Higher November 2010 Paper 3 Q20
20
(a) Write \(\dfrac{1}{16}\) as a power of 2 (2)
(b) Write 2 as a power of 8 (2)
(c) Rationalise the denominator of \(\dfrac{a + \sqrt{a}}{\sqrt{a}}\) where \(a\) is a prime number.
Simplify your answer as much as possible. (2)
Simplify your answer as much as possible. (2)
| Scheme | Marks |
|---|---|
| \(2^4\) or −4 seen | M1 |
| \(2^{-4}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(2^3\) or \(\frac{1}{3}\) seen | M1 |
| \(8^{1/3}\) | A1 |
| (2) |
Notes
A1: accept \(8^{0.\dot{3}}\)
| Scheme | Marks |
|---|---|
| \(\dfrac{(a + \sqrt{a})}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}\) | M1 |
| \(\sqrt{a} + 1\) | A1 |
| (2) | |
| (6 marks) |
Notes
M1: multiply numerator & denominator by \(\sqrt{a}\) or \((a\sqrt{a} + a)/a\)