| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Rational inequality algebraically |
| Difficulty | Standard +0.3 This is a straightforward FP2 inequality question requiring algebraic manipulation to a common denominator, factorization, and sign analysis around critical points. While it involves rational expressions and requires careful handling of the discontinuity at x=1, the techniques are standard for Further Maths students with no novel insight needed. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
\begin{enumerate}[label=(\alph*)]
\item Simplify the expression $\frac{(x + 3)(x + 9)}{x - 1} - (3x - 5)$, giving your answer in the form
$\frac{a(x + b)(x + c)}{x - 1}$, where $a$, $b$ and $c$ are integers. (4)
\item Hence, or otherwise, solve the inequality $\frac{(x + 3)(x + 9)}{x - 1} > 3x - 5$ (4)(Total 8 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2008 Q2}}