| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Solve transformed function equations |
| Difficulty | Moderate -0.8 This C1 question tests basic understanding of function transformations (horizontal/vertical shifts and stretches) with straightforward coordinate substitution. While multi-part, each transformation is standard textbook material requiring only direct application of rules rather than problem-solving or insight. The calculations are routine for A-level students who have learned transformations. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
10.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{089c3b5b-22ab-4fa2-8383-4f30cefa792a-14_515_833_251_552}
\captionsetup{labelformat=empty}
\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 C1 2012 Q10 [8]}}