Higher June 2022 Paper 3 Q22
22 L is the straight line with equation \(y = 2x - 5\)
C is a graph with equation \(y^2 = 6x^2 - 25x - 8\)
Using algebra, find the coordinates of the points of intersection of L and C.
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| (−3, −11) and (5.5, 6) | M1 | for method to eliminate one variable, eg \((2x - 5)^2 = 6x^2 - 25x - 8\) or \(y^2 = 6\left(\dfrac{y + 5}{2}\right)^2 - 25\left(\dfrac{y + 5}{2}\right) - 8\) |
| M1 | for expanding the square to give, eg \(4x^2 - 20x + 25 = 6x^2 - 25x - 8\) or \(y^2 = 6\left(\dfrac{y^2 + 10y + 25}{4}\right) - 25\left(\dfrac{y + 5}{2}\right) - 8\) | |
| M1 | for method to solve equation \(2x^2 - 5x - 33\ (= 0)\), eg \((2x - 11)(x + 3)\ (= 0)\) or \(x = \dfrac{--5 \pm \sqrt{(-5)^2 - 4 \times 2 \times -33}}{2 \times 2}\) or \(-3\), 5.5 oe or for method to solve equation \(2y^2 + 10y - 132\ (= 0)\), eg \((2y + 22)(y - 6)\ (= 0)\) or \(y = \dfrac{-10 \pm \sqrt{10^2 - 4 \times 2 \times -132}}{2 \times 2}\) or \(-11\), 6 | |
| A1 | for \((-3, -11)\) | |
| A1 | for \((5.5, 6)\) oe |