| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|linear| and y=linear with unknown constants, then solve |
| Difficulty | Standard +0.8 This FP2 question requires understanding modulus function graphs and solving modulus inequalities with parameters. Part (a) is straightforward (V-shaped graph), but part (b) requires systematic case analysis (considering x < 2a and x ≥ 2a), algebraic manipulation, and careful interpretation of which solution regions are valid. The presence of parameter 'a' throughout adds complexity beyond standard numerical modulus inequalities, though the technique is well-established for FP2 students. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = | x - 2 a |$, given that $a > 0$.
\item Solve $| x - 2 a | > 2 x + a$, where $a > 0$.\\
(3)(Total 5 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2005 Q1 [5]}}