FP2 June 2012 Q1
1. Find the set of values of \(x\) for which \[\left|x^2 - 4\right| > 3x\] (5)
| Scheme | Marks |
|---|---|
| \(x^2 - 4 = 3x\) and \(x^2 - 4 = -3x\), or graphical method, or squaring both sides, leading to \(x = \ldots\) | M1 |
| \((x = -4,\ x = -1)\) \(x = 1,\ x = 4\) seen anywhere | B1 B1 |
| Using only 2 critical values to find an inequality | dM1 |
| \(x < 1\) \(x > 4\) both strict, ignore ‘and’ | A1 |
| (5) | |
| (5 marks) |
Notes
1st M1 accept \(\pm(x^2 - 4) > 3x\) or \(\pm(x^2 - 4) = 3x\). Require modulus of parabola and straight line with positive gradient through origin for graphical method.
1st B1 for \(x = 1\), 2nd B1 for \(x = 4\)
2nd M1 dependent upon first M1
A0 for error in solution of quadratic leading to correct answer.