| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Rational inequality algebraically |
| Difficulty | Standard +0.3 This is a standard FP2 rational inequality requiring students to bring terms to one side, find a common denominator, identify critical points, and test intervals. While it's Further Maths content, the technique is routine and mechanical with no conceptual surprises, making it slightly easier than average overall. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks |
|---|---|
| \(3x = (x-4)(x+3)\) | M1 |
| \(x^2 - 4x - 12 = 0\) | |
| \(x = -2, x = 6\) | A1 |
| both | |
| Other critical values are \(x = -3, x = 0\) | B1 |
| \(-3 < x < -2, \quad 0 < x < 6\) | M1 A1 A1 |
| (7) | 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. |
| $3x = (x-4)(x+3)$ | M1 | |
| $x^2 - 4x - 12 = 0$ | | |
| $x = -2, x = 6$ | A1 | |
| both | | |
| Other critical values are $x = -3, x = 0$ | B1 | |
| $-3 < x < -2, \quad 0 < x < 6$ | M1 A1 A1 | |
| | (7) | 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. |\begin{enumerate}
\item Find the set of values of $x$ for which
\end{enumerate}
$$\frac { 3 } { x + 3 } > \frac { x - 4 } { x }$$
\hfill \mbox{\textit{Edexcel FP2 2011 Q1 [7]}}