June 2018 Paper 1 Q14
14 Work out the value of \(\quad \left(3^{\frac{1}{2}} + 3^{\frac{3}{2}}\right)^2\)
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(3^{\frac{1}{2}} \times 3^{\frac{1}{2}} + 3^{\frac{1}{2}} \times 3^{\frac{3}{2}} + 3^{\frac{1}{2}} \times 3^{\frac{3}{2}} + 3^{\frac{3}{2}} \times 3^{\frac{3}{2}}\) or \(\sqrt{3}\sqrt{3} + \sqrt{3}\sqrt{27} + \sqrt{3}\sqrt{27} + \sqrt{27}\sqrt{27}\) | M1 | oe allow an error in one term |
| 3 or 9 or 27 | M1dep | |
| 48 | A1 | |
| Alternative method 2 | ||
| \(\sqrt{3}\) and \(3\sqrt{3}\) | M1 | \(3\sqrt{3}\) must come from correct working |
| \((4\sqrt{3})^2\) | M1dep | |
| 48 | A1 | |
| Alternative method 3 | ||
| \(\left(3^{\frac{1}{2}}\right)^2(1 + 3)^2\) | M1 | oe |
| \(3 \times 4^2\) | M1dep | oe |
| 48 | A1 | |
Additional guidance
| Alt 1 mark scheme … likely to see a 3 (or 9 or 27) somewhere, so need to be careful that the M1 mark has been earned before awarding A1 | |
| In alt 1, for the first M1, we want to see an attempt at the full expansion of the correct terms. Probably 4 terms, but there could be 3 if they combine the middle two terms. eg \((\sqrt{3} + 27)(\sqrt{3} + 27)\) scores M0 because it ought to be \(\sqrt{27}\) not 27 |