June 2017 Paper 1 Q18
18 Simplify fully \(\qquad \dfrac{24 - \sqrt{300}}{4\sqrt{3} - 5}\)
Give your answer in the form \(\ a\sqrt{b}\ \) where \(a\) and \(b\) are integers. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(10\sqrt{3}\) | B1 | |
| \(\dfrac{(24 - \text{their } 10\sqrt{3})(4\sqrt{3} + 5)}{(4\sqrt{3} - 5)(4\sqrt{3} + 5)}\) | M1 | oe |
| \(96\sqrt{3} - 120 + 120 - 50\sqrt{3}\) | M1dep | allow one sign error |
| \(48 - 25\) or 23 | M1 | |
| \(2\sqrt{3}\) | A1 | |
| Alternative method 2 | ||
| \(\dfrac{(24 - \sqrt{300})(4\sqrt{3} + 5)}{(4\sqrt{3} - 5)(4\sqrt{3} + 5)}\) | M1 | |
| \(96\sqrt{3} + 120 - 4\sqrt{900} - 5\sqrt{300}\) | M1dep | allow one sign error |
| \(96\sqrt{3} - 120 + 120 - 50\sqrt{3}\) | M1 | |
| \(48 - 25\) or 23 | M1 | |
| \(2\sqrt{3}\) | A1 | |
Additional guidance
For the 1st M1, multiplying numerator and denominator by \((4\sqrt{3} + 5)\) could legitimately be replaced by \(-4\sqrt{3} - 5\) ... almost identical working ... it just changes all the signs on the next lines of working