| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Solve transformed function equations |
| Difficulty | Moderate -0.3 This question tests standard transformations of curves (horizontal translation, horizontal stretch, vertical translation) with straightforward coordinate changes. While it requires understanding of transformations and careful tracking of key points, the transformations are basic C1/C2 content with no complex problem-solving—students apply learned rules to find new coordinates of given points. Slightly easier than average due to its routine nature. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
10.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1528bec3-7a7a-42c5-bac2-756ff3493818-18_508_812_306_644}
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\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve $C$ with equation $y = \mathrm { f } ( x )$, where
$$f ( x ) = x ^ { 2 } ( 9 - 2 x ) .$$
There is a minimum at the origin, a maximum at the point $( 3,27 )$ and $C$ cuts the $x$-axis at the point $A$.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of the point $A$.
\item On separate diagrams sketch the curve with equation
\begin{enumerate}[label=(\roman*)]
\item $y = \mathrm { f } ( x + 3 )$,
\item $y = \mathrm { f } ( 3 x )$.
On each sketch you should indicate clearly the coordinates of the maximum point and any points where the curves cross or meet the coordinate axes.
The curve with equation $y = \mathrm { f } ( x ) + k$, where $k$ is a constant, has a maximum point at $( 3,10 )$.
\end{enumerate}\item Write down the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q10 [8]}}