Higher November 2023 Paper 3 Q23
23 Given that \(\dfrac{2x^2 + y^2}{4x^2 - y^2} = \dfrac{43}{11}\) where \(x \gt 0\) and \(y \gt 0\)
find, in its simplest form, the ratio \(x : y\) (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(3 : 5\) | P1 | for process to eliminate fractions, eg \(11(2x^2 + y^2) = 43(4x^2 - y^2)\) or \(22x^2 + 11y^2 = 172x^2 - 43y^2\) |
| P1 | for process to isolate terms in \(x^2\) and \(y^2\), eg \(54y^2 = 150x^2\) or \(y^2 = \dfrac{25x^2}{9}\) | |
| P1 | for full process to find a correct relationship between \(x\) and \(y\) eg \(y = \dfrac{5x}{3}\) oe | |
| A1 | cao |
Additional guidance
Alternative methods are acceptable
Accept square roots, eg \(\sqrt{54}\) but not decimal approximations.