Higher June 2023 Paper 1 Q16
16.
(a) Write \(13^{-2} \times 13^{7}\) as a single power of 13. [1]
(b) Calculate the value of \(\left(8^{-1}\right)^{\frac{1}{3}}\). [2]
(c) \(3^{\frac{5}{a}} = b\sqrt{3}\) where \(a\) and \(b\) are integers.
Find the value of \(a\) and the value of \(b\). [2]
Find the value of \(a\) and the value of \(b\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(13^{5}\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1}{2}\) | B2 | B1 for sight of either:
|
| Scheme | Marks | Comments |
|---|---|---|
| \(a = 2,\ b = 9\) OR \(a = 10,\ b = 1\) | B2 | Allow embedded answers, provided not contradicted. B1 for one of the following:
|
| (5) |