Higher November 2019 Paper 1 Q24
24 Work out \(\quad \sqrt{18} - \dfrac{28}{\sqrt{50}}\)
Give your answer in the form \(\quad \dfrac{\sqrt{a}}{b} \quad\) where \(a\) and \(b\) are integers. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((\sqrt{18} =)\ \sqrt{9}\sqrt{2}\) or \(3\sqrt{2}\) or \((\sqrt{50} =)\ \sqrt{25}\sqrt{2}\) or \(5\sqrt{2}\) | M1 | oe simplifies one surd implied by \(\dfrac{28}{5\sqrt{2}}\) |
| \(\dfrac{28}{\sqrt{50}} \times \dfrac{\sqrt{50}}{\sqrt{50}}\) or \(\dfrac{28\sqrt{50}}{50}\) | M1 | oe rationalises second term \(\dfrac{28}{5\sqrt{2}} \times \dfrac{5\sqrt{2}}{5\sqrt{2}}\) or \(\dfrac{140\sqrt{2}}{50}\) or \(\dfrac{14\sqrt{2}}{5}\) implies M1M1 |
| \(3\sqrt{2} - \dfrac{140\sqrt{2}}{50}\) or \(\dfrac{150\sqrt{2} - 140\sqrt{2}}{50}\) or \(\dfrac{10\sqrt{2}}{50}\) | M1dep | dep on M2 oe both terms rational with a common surd |
| \(\dfrac{\sqrt{2}}{5}\) or \(a = 2\), \(b = 5\) | A1 | oe in the form \(\dfrac{\sqrt{a}}{b}\) eg \(\dfrac{\sqrt{50}}{25}\) or \(\dfrac{\sqrt{200}}{50}\) |
| Alternative method 2 | ||
| \((\sqrt{18} =)\ \sqrt{9}\sqrt{2}\) or \(3\sqrt{2}\) or \((\sqrt{50} =)\ \sqrt{25}\sqrt{2}\) or \(5\sqrt{2}\) or \(\dfrac{\sqrt{18}\sqrt{50}}{\sqrt{50}}\) or \(\dfrac{\sqrt{900}}{\sqrt{50}}\) | M1 | oe simplifies one surd implied by \(\dfrac{28}{5\sqrt{2}}\) or changes first term to match second |
| \(\dfrac{\sqrt{900}}{\sqrt{50}} - \dfrac{28}{\sqrt{50}}\) or \(\dfrac{3\sqrt{2} \times 5\sqrt{2}}{\sqrt{50}} - \dfrac{28}{\sqrt{50}}\) or \(\dfrac{30 - 28}{\sqrt{50}}\) or \(\dfrac{2}{\sqrt{50}}\) | M1dep | oe common denominator |
| \(\dfrac{30 - 28}{\sqrt{50}} \times \dfrac{\sqrt{50}}{\sqrt{50}}\) or \(\dfrac{2\sqrt{50}}{50}\) | M1dep | oe rationalisation of a single term |
| \(\dfrac{\sqrt{2}}{5}\) or \(a = 2\), \(b = 5\) | A1 | oe in the form \(\dfrac{\sqrt{a}}{b}\) eg \(\dfrac{\sqrt{50}}{25}\) or \(\dfrac{\sqrt{200}}{50}\) |
Additional guidance
| Ignore further work after a correct value, eg \(\dfrac{\sqrt{50}}{25} = \sqrt{2}\) | M1M1M1A1 |