| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Multiple transformation descriptions |
| Difficulty | Moderate -0.3 This is a standard C3 transformations question requiring application of vertical stretch/translation and absolute value transformation. While it requires careful tracking of turning point coordinates through multiple steps, the transformations themselves are routine textbook exercises with no novel problem-solving required. |
| Spec | 1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Shape with maximum at \((3, 6)\) | B1 | |
| Curve passes through \((3, 6)\) | B1 | |
| Curve passes through \((7, 0)\) | B1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Shape with minimum at \((3, 5)\) | B1 | |
| Curve passes through \((3, 5)\) | B1 | |
| Curve passes through \((7, 2)\) | B1 | (3) [6] |
**(a)**
Shape with maximum at $(3, 6)$ | B1
Curve passes through $(3, 6)$ | B1
Curve passes through $(7, 0)$ | B1 | (3)
**(b)**
Shape with minimum at $(3, 5)$ | B1
Curve passes through $(3, 5)$ | B1
Curve passes through $(7, 2)$ | B1 | (3) [6]
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{502d98be-7013-4ce6-816b-27c671944503-04_767_913_246_511}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the graph of $y = \mathrm { f } ( x ) , \quad 1 < x < 9$.\\
The points $T ( 3,5 )$ and $S ( 7,2 )$ are turning points on the graph.\\
Sketch, on separate diagrams, the graphs of
\begin{enumerate}[label=(\alph*)]
\item $y = 2 \mathrm { f } ( x ) - 4$,
\item $y = | \mathrm { f } ( x ) |$.
Indicate on each diagram the coordinates of any turning points on your sketch.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2009 Q3 [6]}}