4MA0 Higher January 2014 Paper 4R Q22
22 Solve the simultaneous equations \[\begin{aligned} x^2 + y^2 &= 26 \\ y &= 3 - 2x \end{aligned}\]
Show clear algebraic working.
(6)
| Scheme | Marks |
|---|---|
| \(x^2 + (3 - 2x)^2 = 26\) \(x^2 + 9 - 6x - 6x + 4x^2 = 26\) | M2 |
| \(5x^2 - 12x - 17\;(= 0)\) | A1 |
\((5x - 17)(x + 1)\;(= 0)\) or \(\dfrac{--12 \pm \sqrt{(-12)^2 - 4 \times 5 \times -17}}{2 \times 5}\) condone no brackets around − 12 | M1 |
| \(x = 3.4,\; y = -3.8\) \(x = -1\;\; y = 5\) | A1 A1 |
| (6) | |
| (6 marks) |
Notes
M2: M1 for \(9 - 6x - 6x + 4x^2\)
A1: Correct 3 part quadratic
M1: Factorising correctly or correct use of quadratic formula
A1 A1: A1 Both correct \(x\) values or 1 correct pairing, dependent on previous M1
A1 4 fully correct values (pairing need not be explicit), dependent on previous M1
The mark scheme states that for this question the correct answer alone does not imply a correct method.