Edexcel FP2 — Question 26 11 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Marks11
PaperDownload PDF ↗
TopicModulus function
TypeSolve |quadratic| compared to linear: sketch then solve equation/inequality
DifficultyStandard +0.3 This is a standard modulus function question requiring sketching a reflected quadratic, solving by cases (splitting at zeros x=2,4), and interpreting graphically. While it involves multiple steps and careful algebra, it follows a well-established template for FP2 modulus questions with no novel insights required. Slightly above average difficulty due to the multi-part nature and need for systematic case analysis.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|

  1. Sketch, on the same axes, the graph of \(y = |(x - 2)(x - 4)|\), and the line with equation \(y = 6 - 2x\). [4]
  2. Find the exact values of \(x\) for which \(|(x - 2)(x - 4)| = 6 - 2x\). [5]
  3. Hence solve the inequality \(|(x - 2)(x - 4)| < 6 - 2x\). [2]

\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same axes, the graph of $y = |(x - 2)(x - 4)|$, and the line with equation $y = 6 - 2x$. [4]

\item Find the exact values of $x$ for which $|(x - 2)(x - 4)| = 6 - 2x$. [5]

\item Hence solve the inequality $|(x - 2)(x - 4)| < 6 - 2x$. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel FP2  Q26 [11]}}