June 2025 Paper 1 Q6
6 Simplify fully \(\qquad \dfrac{\sqrt{75} - \sqrt{27}}{\sqrt{48}}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: by simplifying | ||
| Any one of \(\left(\sqrt{75} =\right) 5\sqrt{3}\) or \(\left(\sqrt{27} =\right) 3\sqrt{3}\) or \(\left(\sqrt{48} =\right) 4\sqrt{3}\) seen | M1 | can be seen outside of the whole fraction |
| \(\dfrac{2\sqrt{3}}{4\sqrt{3}}\) or \(\dfrac{2}{4}\) or \(\dfrac{5 - 3}{4}\) or \(\sqrt{\dfrac{12}{48}}\) | M1dep | would imply first M mark |
| \(\dfrac{1}{2}\) or 0.5 | A1 | |
| Alternative method 2: by taking out a common factor of \(\sqrt{3}\) | ||
| \(\dfrac{\sqrt{25} - \sqrt{9}}{\sqrt{16}}\) or \(\dfrac{\sqrt{3}\left(\sqrt{25} - \sqrt{9}\right)}{\sqrt{3}\left(\sqrt{16}\right)}\) | M1 | |
| \(\dfrac{2}{4}\) or \(\dfrac{5 - 3}{4}\) | M1dep | would imply first M mark |
| \(\dfrac{1}{2}\) or 0.5 | A1 | |
| Alternative method 3: by rationalising | ||
| \(\dfrac{\sqrt{48}\left(\sqrt{75} - \sqrt{27}\right)}{48}\) or \(\dfrac{\left(\sqrt{3600} - \sqrt{1296}\right)}{48}\) | M1 | oe must have a denominator of 48 |
| \(\dfrac{60 - 36}{48}\) or \(\dfrac{24}{48}\) | M1dep | oe but with all surds correctly removed |
| \(\dfrac{1}{2}\) or 0.5 | A1 | |
Additional guidance
| Also possible to rationalise with \(\sqrt{3}\) or other surds. Follow Alt method 3 and mark to an equivalent level |