| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, modulus involved) |
| Difficulty | Standard +0.3 This is a standard C3 transformations question requiring application of three common transformations (horizontal translation, modulus of function, function of modulus). While it requires careful tracking of key points through each transformation, the techniques are routine and well-practiced at this level. The multi-part structure and 10 marks indicate moderate length, but no novel problem-solving is needed—just systematic application of learned transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve with equation $y = \text{f}(x)$, $-1 \leq x \leq 3$. The curve touches the $x$-axis at the origin $O$, crosses the $x$-axis at the point $A(2, 0)$ and has a maximum at the point $B(\frac{4}{3}, 1)$.
In separate diagrams, show a sketch of the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \text{f}(x + 1)$, [3]
\item $y = |\text{f}(x)|$, [3]
\item $y = \text{f}(|x|)$, [4]
\end{enumerate}
marking on each sketch the coordinates of points at which the curve
\begin{enumerate}[label=(\roman*)]
\item has a turning point,
\item meets the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q4 [10]}}