Higher June 2018 Paper 3 Q20
20 All dimensions are in centimetres.
Not drawn accurately
Use Pythagoras’ theorem to work out the exact value of \(\;\dfrac{x}{y}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x^2 + (7x)^2 = (10y)^2\) or \(x^2 + 49x^2 = 100y^2\) | M1 | oe |
| \(50x^2 = 100y^2\) or 1.41(…) | A1 | oe equation with terms collected eg \(\dfrac{x^2}{y^2} = \dfrac{100}{50}\) or \(x^2 = 2y^2\) or \(x = 1.41y\) |
| \(\sqrt{2}\) or \(\dfrac{2}{\sqrt{2}}\) | A1 | Do not accept further working |
Additional guidance
| \(x^2 + 7x^2 = 10y^2\) | M0 |
| \(\sqrt{2} = 1.41\) | M1A1A0 |
| \(x^2 + (7x)^2 = (10y)^2\) \(x^2 + 14x^2 = 20y^2\) | M1 A0 |