4400 Higher June 2007 Paper 3 Q19
19 Solve the simultaneous equations
\[y = 3x - 1\]\[x^2 + y^2 = 5\](6)
| Scheme | Marks |
|---|---|
| \(x^2 + (3x - 1)^2 = 5\) | M1 |
| \(x^2 + 9x^2 - 3x - 3x + 1 = 5\) or \(x^2 + 9x^2 - 6x + 1 = 5\) | B1 |
| \(10x^2 - 6x - 4 = 0\) | B1 |
\((5x + 2)(2x - 2) = 0\) or \((5x + 2)(x - 1) = 0\) or \((10x + 4)(x - 1) = 0\) or \(\dfrac{6 \pm \sqrt{196}}{20}\) or \(\dfrac{3 \pm \sqrt{49}}{10}\) or \(\dfrac{3}{10} \pm \dfrac{\sqrt{49}}{10}\) | B1 |
| \(x = -\frac{2}{5}\) or \(x = 1\) | A1 |
| \(x = -\frac{2}{5}\), \(y = -2\frac{1}{5}\) \(x = 1\), \(y = 2\) | A1 |
| (6) | |
| (6 marks) |
Notes
M1: for correct substitution
B1: (indep) for correct expansion of \((3x - 1)^2\) even if unsimplified
B1: for correct simplification
B1: for correct factorisation
or for correct substitution into the quadratic formula and correct evaluation of ‘\(b^2 - 4ac\)’
or for using square completion correctly as far as indicated
A1: for both values of \(x\)
A1: for complete, correct solutions