| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve absolute value inequality |
| Difficulty | Standard +0.8 This FP2 question requires systematic case analysis of the absolute value equation (considering both positive and negative cases), careful algebraic manipulation to solve resulting quadratics, validation of solutions against domain restrictions, sketching with critical points, and translating graphical understanding to solve the inequality. While methodical, it demands multiple techniques and careful reasoning about when solutions are valid, placing it moderately above average difficulty. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02t Solve modulus equations: graphically with modulus function |
\begin{enumerate}[label=(\alph*)]
\item Use algebra to find the exact solutions of the equation
$$|2x^2 + 6x - 5| = 5 - 2x$$ [6]
\item On the same diagram, sketch the curve with equation $y = |2x^2 + 6x - 5|$ and the line with equation $y = 5 - 2x$, showing the $x$-coordinates of the points where the line crosses the curve. [3]
\item Find the set of values of $x$ for which
$$|2x^2 + 6x - 5| > 5 - 2x$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q6 [12]}}