| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |f(x)| compared to |g(x)| with parameters: sketch then solve |
| Difficulty | Standard +0.3 This is a straightforward modulus function question requiring standard techniques: sketching V-shaped graphs, solving linear equations with modulus (splitting into cases), function composition, and solving the resulting equation. All parts follow predictable patterns with no novel insight required, making it slightly easier than average for C3. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
The functions $f$ and $g$ are defined by
$$f: x \mapsto |x - a| + a, \quad x \in \mathbb{R},$$
$$g: x \mapsto 4x + a, \quad x \in \mathbb{R},$$
where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item On the same diagram, sketch the graphs of $f$ and $g$, showing clearly the coordinates of any points at which your graphs meet the axes. [5]
\item Use algebra to find, in terms of $a$, the coordinates of the point at which the graphs of $f$ and $g$ intersect. [3]
\item Find an expression for $fg(x)$. [2]
\item Solve, for $x$ in terms of $a$, the equation
$$fg(x) = 3a.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q31 [13]}}