Higher November 2023 Paper 1 Q23
23 Work out \(\quad \dfrac{7}{\sqrt{2}} \times \dfrac{\sqrt{3}}{\sqrt{10}}\)
Give your answer in the form \(\quad \dfrac{x\sqrt{15}}{y} \quad\) where \(x\) and \(y\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{7\sqrt{3}}{\sqrt{20}} \times \dfrac{\sqrt{20}}{\sqrt{20}}\) | M1 | oe eg \(\dfrac{7\sqrt{3}}{\sqrt{2}\sqrt{10}} \times \dfrac{\sqrt{2}\sqrt{10}}{\sqrt{2}\sqrt{10}}\) |
| \(\dfrac{7\sqrt{60}}{20}\) | M1dep | oe single rationalised fraction |
| \(\dfrac{7\sqrt{15}}{10}\) or \(\dfrac{14\sqrt{15}}{20}\) | A1 | oe in the form \(\dfrac{x\sqrt{15}}{y}\) where \(x\) and \(y\) are integers |
| Alternative method 2 | ||
| \(\dfrac{7\sqrt{3}}{2\sqrt{5}}\) | M1 | |
| \(\dfrac{7\sqrt{3}}{2\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) | M1dep | oe rationalisation eg \(\dfrac{7\sqrt{3}}{2\sqrt{5}} \times \dfrac{2\sqrt{5}}{2\sqrt{5}}\) |
| \(\dfrac{7\sqrt{15}}{10}\) or \(\dfrac{14\sqrt{15}}{20}\) | A1 | oe in the form \(\dfrac{x\sqrt{15}}{y}\) where \(x\) and \(y\) are integers |
| Alternative method 3 | ||
| \(\dfrac{7}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\) or \(\dfrac{7\sqrt{2}}{2}\) or \(\dfrac{\sqrt{3}}{\sqrt{10}} \times \dfrac{\sqrt{10}}{\sqrt{10}}\) or \(\dfrac{\sqrt{30}}{10}\) | M1 | oe |
| \(\dfrac{7\sqrt{2}}{2} \times \dfrac{\sqrt{30}}{10}\) or \(\dfrac{7\sqrt{60}}{20}\) | M1dep | oe rationalised |
| \(\dfrac{7\sqrt{15}}{10}\) or \(\dfrac{14\sqrt{15}}{20}\) | A1 | oe in the form \(\dfrac{x\sqrt{15}}{y}\) where \(x\) and \(y\) are integers |
| Alternative method 4 | ||
| \(\dfrac{7}{\sqrt{2}} \times \dfrac{\sqrt{3}}{\sqrt{10}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) | M1 | oe |
| \(\dfrac{7\sqrt{5}}{\sqrt{10}} \times \dfrac{\sqrt{3}}{\sqrt{10}}\) or \(\dfrac{7}{\sqrt{2}} \times \dfrac{\sqrt{15}}{\sqrt{50}}\) or \(\dfrac{7\sqrt{15}}{\sqrt{100}}\) | M1dep | oe one term or product of two terms with numerator \(7\sqrt{15}\) |
| \(\dfrac{7\sqrt{15}}{10}\) or \(\dfrac{14\sqrt{15}}{20}\) | A1 | oe in the form \(\dfrac{x\sqrt{15}}{y}\) where \(x\) and \(y\) are integers |