FP2 June 2011 Q1
1. Find the set of values of \(x\) for which \[\frac{3}{x + 3} > \frac{x - 4}{x}\] (7)
| Scheme | Marks |
|---|---|
| \(3x = (x - 4)(x + 3) \qquad x^2 - 4x - 12 = 0\) | M1 |
| \(x = -2,\ x = 6\) both | A1 |
| Other critical values are \(x = -3,\ x = 0\) | B1, B1 |
| \(-3 < x < -2, \qquad 0 < x < 6\) | M1 A1 A1 |
| (7 marks) |
Notes
1st M1 for \(\pm(x^2 - 4x - 12)\) – ‘=0’ not required.
B marks can be awarded for values appearing in solution e.g. on sketch of graph or in final answer.
2nd M1 for attempt at method using graph sketch or +/-
If cvs correct but correct inequalities are not strict award A1A0.