Higher November 2022 Unit 1 Q15
15.
(a) Express \(0{\cdot}6\dot{5}\dot{4}\) as a fraction. [2]
(b) Evaluate \(27^{-\frac{2}{3}}\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(x = 0{\cdot}6545454\ldots\ldots\) and \(100x = 65{\cdot}45454\ldots\) with an attempt to subtract | M1 | Complete method. Or \(10x\) and \(1000x\), or equivalent. Or a complete alternative method. x and 10 000x gives an answer of 65448 / 99990. |
| 648/990 (= 324/495 = 108/165 = 36/55 or equivalent) | A1 | An answer of 64·8/99 gains M1 only. ISW |
15.(a) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 0·6 + 0·0545454..... = 6/10 + 54/990 or equivalent | M1 | |
| 648/990 (= 36/55 or equivalent) | A1 | An answer of 64·8/99 gains M1 only. ISW |
| Scheme | Marks | Comments |
|---|---|---|
| 1/9 | B2 | B1 for \(9^{-1}\) or \(1/3^2\) or \((1/3)^2\) or \(1/\sqrt[3]{729}\) or \(1/729^{1/3}\) or \((1/729)^{1/3}\) or \(\sqrt[3]{(1/729)}\) Mark final answer. |