4400 Higher November 2006 Paper 3 Q18
18 Solve the simultaneous equations
\[y = x^2\]\[y = 2x + 15\](5)
| Scheme | Marks |
|---|---|
| \(x^2 = 2x + 15\) | M1 |
| \(x^2 - 2x - 15 = 0\) | M1 |
| \((x + 3)(x - 5) = 0\) \(x = \dfrac{2 \pm 8}{2}\) | M1 |
| \(x = -3\) or \(x = 5\) | A1 |
| −3, 9 and 5, 25 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: \(\left(\dfrac{y - 15}{2}\right)^2 = y\)
M1: \(y^2 - 34y + 225 = 0\)
M1: \((y - 25)(y - 9) = 0\)
A1: \(y = 9\) or \(y = 25\)