4MA0 Higher June 2012 Paper 3 Q3
3
(a) Write \(2^3 \times 2^6\) as a single power of 2 (1)
(b) Write \(\dfrac{3^9}{3^4}\) as a single power of 3 (1)
(c) \[\dfrac{5^n}{5^4 \times 5^6} = 5^3\] Find the value of \(n\). (2)
| Scheme | Marks |
|---|---|
| \(2^9\) | B1 |
| (1) |
Notes
B1: cao
Apart from Questions 9, 13, 18, 20 and 21 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| \(3^5\) | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(5^{n-4-6} = 5^3\) oe or \(5^{n-10} = 5^3\) oe or \(n - 4 - 6 = 3\) oe or \(n - 10 = 3\) oe or \(5^n = 5^3 \times 5^{10}\) oe or \(5^n = 5^{3+10}\) or \(5^n = 5^{13}\) | M1 |
| 13 | A1 |
| (2) | |
| (Total 4 marks) |
Notes
A1: cao
SC If M0, award B1 for an answer of \(5^{13}\)