| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Stationary points after transformation |
| Difficulty | Standard +0.3 This is a standard C3 transformation question requiring systematic application of well-defined transformation rules (reflection, translation, stretch) to given points. While it involves multiple parts and careful coordinate manipulation, the transformations are routine textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks |
|---|---|
| [Graph showing curve with local maximum at \((-3, 6)\), local minimum at \((3, 6)\), and point \((0, 4)\) below the turning points] | B3 |
| Answer | Marks |
|---|---|
| [Graph showing curve with local minimum at \((-\frac{2}{3}, 2)\) and point \((0, 8)\) on the curve] | M2 A2 |
| Answer | Marks | Guidance |
|---|---|---|
| [Graph showing curve with point \((-3, 3)\) and point \((0, 2)\), horizontal asymptote as \(x \to \infty\), vertical asymptote at \(x = \frac{3}{2}\)] | M2 A2 | (11) |
**(a)**
[Graph showing curve with local maximum at $(-3, 6)$, local minimum at $(3, 6)$, and point $(0, 4)$ below the turning points] | B3 |
**(b)**
[Graph showing curve with local minimum at $(-\frac{2}{3}, 2)$ and point $(0, 8)$ on the curve] | M2 A2 |
**(c)**
[Graph showing curve with point $(-3, 3)$ and point $(0, 2)$, horizontal asymptote as $x \to \infty$, vertical asymptote at $x = \frac{3}{2}$] | M2 A2 | (11)6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1db60b49-1373-43d4-a74d-dfe8f9a952df-3_559_992_712_477}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the curve $y = \mathrm { f } ( x )$ which has a minimum point at $\left( - \frac { 3 } { 2 } , 0 \right)$, a maximum point at $( 3,6 )$ and crosses the $y$-axis at $( 0,4 )$.
Sketch each of the following graphs on separate diagrams. In each case, show the coordinates of any turning points and of any points where the graph meets the coordinate axes.
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( | x | )$
\item $y = 2 + \mathrm { f } ( x + 3 )$
\item $\quad y = \frac { 1 } { 2 } \mathrm { f } ( - x )$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q6 [11]}}