4400 Higher November 2010 Paper 4 Q20
20 Solve the simultaneous equations
\[\begin{aligned} y &= x^2 \\ y &= 7x - 10 \end{aligned}\](5)
| Scheme | Marks |
|---|---|
| \(x^2 = 7x - 10\) (may be implied by 2nd M1) | M1 |
| \(x^2 - 7x + 10\ (= 0)\) oe | M1 |
\((x - 5)(x - 2)\ (= 0)\) oe or \(\dfrac{7 \pm \sqrt{9}}{2}\) or \(\dfrac{7 \pm \sqrt{49 - 40}}{2}\) or \(\dfrac{7 \pm 3}{2}\) | M1 |
| \(x = 2\), \(x = 5\) | A1 |
| \(x = 2\), \(y = 4\) \(x = 5\), \(y = 25\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: \(y = \left(\dfrac{y + 10}{7}\right)^2\)
M1: \(y^2 - 29y + 100\ (= 0)\) oe
M1: \((y - 4)(y - 25)\ (= 0)\)
or \(\dfrac{29 \pm \sqrt{441}}{2}\)
or \(\dfrac{29 \pm \sqrt{841 - 400}}{2}\)
or \(\dfrac{29 \pm 21}{2}\)
A1: \(y = 4\), \(y = 25\)
dep on all method marks
A1: dep on all method marks (may be implied by 2nd M1)