| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |f(x)| compared to |g(x)| with parameters: sketch then solve |
| Difficulty | Moderate -0.3 This is a straightforward modulus function question requiring standard techniques: sketching V-shaped graphs with axis intercepts, applying a horizontal stretch transformation, and solving a modulus equation using cases. All parts follow predictable patterns with no novel problem-solving required, making it slightly easier than average for C3. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x) |
The function f is defined by
$$f: x \mapsto |2x - a|, \quad x \in \mathbb{R}$$
where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = f(x)$, showing the coordinates of the points where the graph cuts the axes. [2]
\item On a separate diagram, sketch the graph of $y = f(2x)$, showing the coordinates of the points where the graph cuts the axes. [2]
\item Given that a solution of the equation f(x) = $\frac{1}{2}x$ is $x = 4$, find the two possible values of $a$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q3 [8]}}