Edexcel FP2 2008 June — Question 2

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeRational inequality algebraically
DifficultyStandard +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.
Spec1.02g Inequalities: linear and quadratic in single variable1.02k Simplify rational expressions: factorising, cancelling, algebraic division

  1. 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)
  2. Hence, or otherwise, solve the inequality \(\frac{(x + 3)(x + 9)}{x - 1} > 3x - 5\) (4)(Total 8 marks)

\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}}