Higher November 2016 Unit 1 Q17
17. Simplify
\[\frac{\left(5\sqrt{3}\right)^2 - \dfrac{2\sqrt{18}}{\sqrt{2}}}{\sqrt{32} \times \sqrt{2}}\]and state whether your answer is rational or irrational. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \((5\sqrt{3})^2 = 25 \times 3\) (= 75) | B1 | For first three marks, accept a correct product of integers in each case, e.g. 2 × 2 × 2 (=8). |
| \(\dfrac{2\sqrt{18}}{\sqrt{2}} = 2 \times \sqrt{9}\) (= 2 × 3 = 6) | B1 | |
| \(\sqrt{32} \times \sqrt{2} = \sqrt{64}\) (= 8) | B1 | |
| (Answer =) 69/8 or equivalent. | B1 | C.A.O. Equivalent answer must be simplified. So B0 for (75 – 6) / 8. ISW. |
| Rational | B1 | F.T. ‘their final answer’ provided at least 2 out of first 3 B1s are awarded. |