Higher November 2020 Unit 1 Q14
14.
(a) Express \(0{\cdot}8\dot{1}\dot{2}\) as a fraction. [2]
(b) Simplify \(\sqrt{72}\).
Circle your answer. [1]
Circle your answer. [1]
\(2\sqrt{6}\) \(6\sqrt{2}\) \(6\sqrt{12}\) \(36\) \(36\sqrt{2}\)
(c) Expand and simplify \(\left(7 - 2\sqrt{5}\right)\left(3 + \sqrt{5}\right)\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(10x = 8{\cdot}121212\ldots\) and \(1000x = 812{\cdot}1212\ldots\) with an attempt to subtract on both sides | M1 | Or \(x\) and \(100x\), or equivalent. Or a complete alternative method. |
| 804/990 (= 402/495 = 134/165) | A1 | An answer of 80·4/99 gains M1 only. ISW |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 0·8 + 0·0121212….. = 8/10 + 12/990 or equivalent | M1 | |
| 804/990 (= 402/495 = 134/165) | A1 | ISW |
| Scheme | Marks | Comments |
|---|---|---|
| \(6\sqrt{2}\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(7 \times 3 + 7\sqrt{5} - 3 \times 2\sqrt{5} - 2(\sqrt{5})^2\) or equivalent | M1 | |
| \(= 11 + \sqrt{5}\) | A1 | Mark final answer. Accept \(11 + 1\sqrt{5}\). If no marks awarded, SC1 for 3 correctly simplified terms i.e. 21, \(7\sqrt{5}\), \(-6\sqrt{5}\), \(-10\). |