Higher June 2022 Paper 1 Q18
18.
(a) Write \(5^3 \div 5^{-4}\) as a single power of 5. [1]
(b) Calculate the value of \(10\,000^{\frac{3}{4}}\). [2]
(c) Simplify \(\sqrt{49\times10^{2n}}\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(5^7\) | B1 | mark final answer |
| Scheme | Marks | Comments |
|---|---|---|
| \(\left(\sqrt[4]{10\,000}\right)^3\) or \(\sqrt[4]{10\,000^3}\) si | B1 | First correct step implied by sight of \(10^3\) or \(\sqrt[4]{1\,000\,000\,000\,000}\) |
| 1000 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(7\times10^n\) | B2 | B1 for \(49^{\frac{1}{2}}\times\left(10^{2n}\right)^{\frac{1}{2}}\) or \(\sqrt{49}\times\left(10^{2n}\right)^{\frac{1}{2}}\) oe |
| (5) |