| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve inequality with reciprocal in modulus |
| Difficulty | Moderate -0.3 This is a straightforward modulus function question requiring standard sketching techniques and routine algebraic manipulation. Parts (a)-(c) involve basic graph sketching and visual interpretation (4 marks), while part (d) requires solving a modulus equation by considering cases—a standard C3 technique. The algebra is mechanical once the cases are identified, and no novel insight is required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02s 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 $y = |2x + a|, a > 0$, showing the coordinates of the points where the graph meets the coordinate axes. [2]
\item On the same axes, sketch the graph of $y = \frac{1}{x}$. [1]
\item Explain how your graphs show that there is only one solution of the equation
$$x|2x + a| - 1 = 0.$$ [1]
\item Find, using algebra, the value of $x$ for which $x|2x + 1| - 1 = 0$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q21 [7]}}