4MA0 Higher June 2012 Paper 3 Q21
21 Solve the simultaneous equations \[\begin{aligned} y &= 2x^2 \\ y &= 20 - 3x \end{aligned}\] Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| \(2x^2 = 20 - 3x\) May be implied by second M1 | M1 |
| \(2x^2 + 3x - 20 (= 0)\) | M1 |
\((2x - 5)(x + 4) (= 0)\) or \(2x(x + 4) - 5(x + 4) (= 0)\) or \(x(2x - 5) + 4(2x - 5) (= 0)\) or \(\dfrac{-3 \pm \sqrt{3^2 - 4 \times 2 \times (-20)}}{2 \times 2}\) or \(\dfrac{-3 \pm \sqrt{9 + 160}}{4}\) or \(\dfrac{-3 \pm \sqrt{169}}{4}\) or \(\dfrac{-3 \pm 13}{4}\) | M1 |
| \(x = \frac{5}{2}\), \(x = -4\) | A1 |
| \(x = \frac{5}{2}\), \(y = \frac{25}{2}\) \(x = -4\), \(y = 32\) | A1 |
| (Total 5 marks) |
Notes
M1: or \(y = 2\left(\dfrac{20 - y}{3}\right)^2\)
May be implied by second M1
M1: or \(2y^2 - 89y + 800 (= 0)\)
M1: or \((2y - 25)(y - 32) (= 0)\)
or \(2y(y - 32) - 25(y - 32) (= 0)\)
or \(y(2y - 25) - 32(2y - 25) (= 0)\)
or \(\dfrac{89 \pm \sqrt{(-89)^2 - 4 \times 2 \times 800}}{2 \times 2}\)
or \(\dfrac{89 \pm \sqrt{7921 - 6400}}{4}\)
or \(\dfrac{89 \pm \sqrt{1521}}{4}\) or \(\dfrac{89 \pm 39}{4}\)
A1: or \(y = \frac{25}{2}\), \(y = 32\)
dep on all method marks
A1: dep on all preceding marks
Accept answers given as coordinates