4MA0 Higher June 2011 Paper 3 Q22
22 Solve the simultaneous equations \[\begin{aligned} y &= 2x - 3 \\ x^2 + y^2 &= 2 \end{aligned}\]
(6)
| Scheme | Marks |
|---|---|
| \(x^2 + (2x - 3)^2 = 2\) | M1 |
| \(x^2 + 4x^2 - 6x - 6x + 9 = 2\) or \(x^2 + 4x^2 - 12x + 9 = 2\) | B1 |
| \(5x^2 - 12x + 7 (= 0)\) | B1 |
\((5x - 7)(x - 1) (= 0)\) or \(\dfrac{12 \pm \sqrt{4}}{10}\) or \(\dfrac{12}{10} \pm \dfrac{\sqrt{4}}{10}\) or \(\dfrac{6}{5} \pm \dfrac{1}{5}\) | B1 |
| \(x = 1\) or \(x = 1\frac{2}{5}\) | A1 |
| \(x = 1\), \(y = -1\) \(x = 1\frac{2}{5}\), \(y = -\frac{1}{5}\) | A1 |
| (Total 6 marks) |
Notes
M1: for correct substitution
B1: (indep) for correct expansion of \((2x - 3)^2\) even if unsimplified
B1: for correct simplification
Condone omission of ‘= 0’
B1: for correct factorisation
or for correct substitution into quadratic formula and correct evaluation of ‘\(b^2 - 4ac\)’
or for using square completion correctly as far as indicated
A1: for both values of \(x\)
dep on all preceding marks
A1: for complete, correct solutions (need not be paired)
dep on all preceding marks
No marks for \(x = 1\), \(y = -1\) with no working