Higher November 2022 Paper 1 Q27
27 Work out \(\quad \sqrt{2\dfrac{13}{16}} - \dfrac{2}{\sqrt{5}}\)
Give your answer in the form \(\quad \dfrac{a\sqrt{5}}{b} \quad\) where \(a\) and \(b\) are integers. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\left(\sqrt{2\dfrac{13}{16}} =\right) \sqrt{\dfrac{45}{16}}\) or \(\dfrac{\sqrt{45}}{4}\) or \(\dfrac{3\sqrt{5}}{4}\) | M1 | oe conversion from a mixed number |
| \(\dfrac{2}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) or \(\dfrac{2\sqrt{5}}{5}\) | M1 | oe rationalisation |
| \(\dfrac{15\sqrt{5}}{20} - \dfrac{8\sqrt{5}}{20}\) or \((0.75\sqrt{5} - 0.4\sqrt{5} =)\ 0.35\sqrt{5}\) | M1dep | oe with common surd in numerator and common non-surd denominator do not allow fraction(s) in numerator(s) or denominator dep on M1M1 |
| \(\dfrac{7\sqrt{5}}{20}\) | A1 | oe in the form \(\dfrac{a\sqrt{5}}{b}\) eg \(\dfrac{28\sqrt{5}}{80}\) |
| Alternative method 2 | ||
| \(\left(\sqrt{2\dfrac{13}{16}} =\right) \sqrt{\dfrac{45}{16}}\) or \(\dfrac{\sqrt{45}}{4}\) or \(\dfrac{3\sqrt{5}}{4}\) | M1 | oe conversion from a mixed number |
| \(\dfrac{\sqrt{45}\sqrt{5}}{4\sqrt{5}} - \dfrac{8}{4\sqrt{5}}\) or \(\dfrac{15}{4\sqrt{5}} - \dfrac{8}{4\sqrt{5}}\) or \(\dfrac{7}{4\sqrt{5}}\) | M1dep | oe with common denominator do not allow fraction(s) in numerator(s) or denominator |
| \(\dfrac{15}{4\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}} - \dfrac{8}{4\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) or \(\dfrac{7}{4\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) | M1dep | oe with all denominators rationalised |
| \(\dfrac{7\sqrt{5}}{20}\) | A1 | oe in the form \(\dfrac{a\sqrt{5}}{b}\) eg \(\dfrac{28\sqrt{5}}{80}\) |