Higher November 2024 Paper 1 Q20
20
(a) Show that \(\quad \dfrac{\sqrt{363}}{\sqrt{3}} \quad\) simplifies to an integer. [2 marks]
(b) Rationalise the denominator and simplify \(\quad \dfrac{20}{\sqrt{5}}\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{\sqrt{121}\sqrt{3}}{\sqrt{3}}\) or \(\dfrac{11\sqrt{3}}{\sqrt{3}}\) or \(\sqrt{121}\) or \(\dfrac{\sqrt{363}}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}}\) or \(\dfrac{\sqrt{363}\sqrt{3}}{3}\) or \(\dfrac{11\sqrt{3}\sqrt{3}}{3}\) or \(\dfrac{\sqrt{1089}}{3}\) | M1 | oe with at least partial simplification of the numerator oe with correct method to rationalise the denominator rationalised |
| 11 and \(\dfrac{\sqrt{121}\sqrt{3}}{\sqrt{3}}\) or \(\dfrac{11\sqrt{3}}{\sqrt{3}}\) or \(\sqrt{121}\) or 11 and \(\dfrac{11\sqrt{3}\sqrt{3}}{3}\) or \(\dfrac{\sqrt{1089}}{3}\) | A1 |
Additional guidance
For M1, allow multiplication or division by \(\sqrt{1}\) throughout
| Answer | Mark | Comments |
|---|---|---|
| Correct expression with rationalisation of denominator seen or used | M1 | eg \(\dfrac{20}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\) or \(\dfrac{20\sqrt{5}}{5}\) or \(\dfrac{4 \times \sqrt{5} \times \sqrt{5}}{\sqrt{5}}\) or \(\dfrac{4\sqrt{5}}{1}\) |
| \(4\sqrt{5}\) | A1 |