Higher June 2018 Unit 1 Q15
15.
(a) Express \(0{\cdot}2\dot{4}\dot{5}\) as a fraction. [2]
(b) Expand and simplify \((8 - 3\sqrt{7})(5 + \sqrt{7})\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(x = 0{\cdot}2454545.....\) and \(100x = 24{\cdot}54545....\) with an attempt to subtract | M1 | Or \(10x\) and \(1000x\), or equivalent. Or a complete alternative method. |
| 243/990 or 27/110 or equivalent. | A1 | An answer of 24·3/99 gains M1 only. ISW |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 0·2 + 0·0454545..... = 1/5 + 45/990 or equivalent | M1 | |
| 243/990 or 27/110 or equivalent | A1 | ISW |
| Scheme | Marks | Comments |
|---|---|---|
| \(8 \times 5 + 8\sqrt{7} - 5 \times 3\sqrt{7} - 3(\sqrt{7})^2\) or equivalent | M1 | |
| \(= 19 - 7\sqrt{7}\) | A1 | Mark final answer. If no marks awarded, SC1 for 3 of the 4 terms correct. |