| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |quadratic| compared to linear: sketch then solve equation/inequality |
| Difficulty | Standard +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. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b| |
\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]}}