| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve inequality with reciprocal in modulus |
| Difficulty | Standard +0.3 This is a straightforward modulus equation question requiring standard techniques: solving by cases (positive/negative), sketching familiar functions (linear and reciprocal with modulus), and reading inequalities from the graph. While it's Further Maths content, the methods are routine and well-practiced, making it slightly easier than average overall but still requiring careful algebraic manipulation. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities1.02t Solve modulus equations: graphically with modulus function |
\begin{enumerate}[label=(\alph*)]
\item Find, in the simplest surd form where appropriate, the exact values of $x$ for which
$$\frac{x}{2} + 3 = \left|\frac{4}{x}\right|.$$ (5)
\item Sketch, on the same axes, the line with equation $y = \frac{x}{2} + 3$ and the graph of
$$y = \left|\frac{4}{x}\right|, x \neq 0.$$ (3)
\item Find the set of values of $x$ for which $\frac{x}{2} + 3 > \left|\frac{4}{x}\right|$. (2)(Total 10 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2008 Q6}}