Higher November 2018 Unit 1 Q15
15.
(a) Express \(0{\cdot}3\dot{7}\) as a fraction. [2]
(b)
(i) Calculate \(\left(\sqrt{8} - \sqrt{2}\right)^2\). [2]
(ii) Calculate \(\dfrac{\sqrt{6} \times \sqrt{20}}{\sqrt{3}}\).
Give your answer in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers, and \(b\) is as small as possible. [2]
Give your answer in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers, and \(b\) is as small as possible. [2]
(c) Evaluate \(16^{-\frac{3}{2}}\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(x = 0{\cdot}37777\)….. \(10x = 3{\cdot}7777\)….. with an attempt to subtract | M1 | Or \(10x\) and \(100x\), or equivalent. Or an alternative method. |
| 34/90 or 17/45 or equivalent e.g. 374/990 | A1 | An answer of 3·4/9 gains M1 only. Mark final answer. Do not ignore incorrect cancelling. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 0·3 + 0·07777….. = 3/10 + 7/90 or equivalent | M1 | |
| 34/90 or 17/45 or equivalent | A1 | Mark final answer. Do not ignore incorrect cancelling. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(\sqrt{8}\sqrt{8} - \sqrt{8}\sqrt{2} - \sqrt{8}\sqrt{2} + \sqrt{2}\sqrt{2}\) or \(\sqrt{64} - \sqrt{8}\sqrt{2} - \sqrt{8}\sqrt{2} + \sqrt{4}\) or equivalent (= 8 − 4 − 4 + 2) | M1 | |
| = 2 | A1 | Mark final answer. If no marks, award SC1 for 3 correctly evaluated terms. |
| (ii) \(2\sqrt{10}\) | B2 | B1 for \(\sqrt{40}\) or \(\sqrt{2}\) x \(2\sqrt{5}\) or 2 x \(\sqrt{30}/\sqrt{3}\) |
Alternative method: (b)(i)
| Scheme | Marks | Comments |
|---|---|---|
| \((2\sqrt{2} - \sqrt{2})^2\) | M1 | |
| = 2 | A1 | An answer of \((\sqrt{2})^2\) gains M1A0 only Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| 1/64 | B2 | B1 for \(64^{-1}\) or \(1/4^3\) or \((1/4)^3\) or \(1/\sqrt{4096}\) or \(1/4096^{1/2}\) or \((1/4096)^{1/2}\) or \(\sqrt{(1/4096)}\) or SC1 for – 1/64 Allow ±1/64 for B2 |