Higher June 2019 Paper 1R Q22
22 Solve the simultaneous equations
\[\begin{aligned} 2x^2 + 3y^2 &= 5 \\ y &= 2x + 1 \end{aligned}\]Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
\(2x^2 + 3(2x + 1)^2 = 5\) or \(2\left(\dfrac{y - 1}{2}\right)^2 + 3y^2 = 5\) | M1 |
| eg \(14x^2 + 12x - 2 = 0\) or if completing the square, allow \(14x^2 + 12x = 2\) oe or \(7y^2 - 2y - 9 = 0\) or if completing the square, allow \(7y^2 - 2y = 9\) oe | A1 |
eg \((7x - 1)(x + 1)\) or \((7x - 1)(2x + 2)\) eg \(\dfrac{-12 \pm \sqrt{12^2 - 4 \times 14 \times -2}}{2 \times 14}\) oe eg \(14\left(\left(x + \dfrac{3}{7}\right)^2 - \dfrac{9}{49}\right) = 2\) oe (corrected from the printed mark scheme: \(7\left(\left(x + \dfrac{3}{7}\right)^2 - \dfrac{9}{49}\right) = 2\)) or eg \((7y - 9)(y + 1)\) eg \(\dfrac{2 \pm \sqrt{(-2)^2 - 4 \times 7 \times -9}}{2 \times 7}\) oe eg \(7\left(\left(y - \dfrac{1}{7}\right)^2 - \dfrac{1}{49}\right) = 9\) oe | M1 |
\(x = \dfrac{1}{7}\), \(x = -1\) (need both) or \(y = \dfrac{9}{7}\), \(y = -1\) (need both) | A1 |
Working required Answer: \(x = \dfrac{1}{7}\), \(y = \dfrac{9}{7}\) \(x = -1\), \(y = -1\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: ft as long as M1 awarded and 3 term quadratic
A1: Dep on M1
Must be paired correctly
Must be 3 sf or better (0.142857…) (1.28571…)