| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Multiple transformation descriptions |
| Difficulty | Standard +0.3 This is a standard C3 transformations question requiring students to apply three separate transformations (modulus, horizontal translation, and modulus of x) to a given curve. While it requires careful attention to asymptotes and turning points, these are routine textbook transformations with predictable effects. The question is slightly easier than average because the transformations are independent (not combined) and follow standard patterns taught in C3. |
| Spec | 1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| Correct shape for \(x < 0\) | B1 | shape |
| Correct shape for \(0 < x < 1\) | B1 | shape |
| Correct shape for \(x > 1\) | B1 | shape |
| Key points correct: \((-0.5, 2)\), \((0.4, 4)\) | B1 | points (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| Any translation shown | M1 | |
| Translation in correct direction | M1 | |
| Points correct: \((2.5, -2)\), \((3.4, -4)\) | B1 | points |
| Asymptotes at \(x=3\), \(x=4\) shown | B1 | asymptotes (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| Correct shape for region \(> 0\) | B1 | |
| Correct shape for region \(< 0\) | B1 | |
| Points correct: \((-0.4, -4)\), \((0.4, -4)\) | B1 | points |
| Asymptotes at \(x=-1\), \(x=0\), \(x=1\) | B1 | asymptotes (4 marks) |
# Question 6:
## Part (a)
| Answer/Working | Marks | Notes |
|---|---|---|
| Correct shape for $x < 0$ | B1 | shape |
| Correct shape for $0 < x < 1$ | B1 | shape |
| Correct shape for $x > 1$ | B1 | shape |
| Key points correct: $(-0.5, 2)$, $(0.4, 4)$ | B1 | points (4 marks) |
## Part (b)
| Answer/Working | Marks | Notes |
|---|---|---|
| Any translation shown | M1 | |
| Translation in correct direction | M1 | |
| Points correct: $(2.5, -2)$, $(3.4, -4)$ | B1 | points |
| Asymptotes at $x=3$, $x=4$ shown | B1 | asymptotes (4 marks) |
## Part (c)
| Answer/Working | Marks | Notes |
|---|---|---|
| Correct shape for region $> 0$ | B1 | |
| Correct shape for region $< 0$ | B1 | |
| Points correct: $(-0.4, -4)$, $(0.4, -4)$ | B1 | points |
| Asymptotes at $x=-1$, $x=0$, $x=1$ | B1 | asymptotes (4 marks) |
**Total: 12 marks**
---6.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{ddc10fc0-f3f2-4c5f-b152-eba68a21990f-08_871_1495_286_273}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation $y = \mathrm { f } ( x ) , x \in \mathbb { R }$.
The curve has a minimum point at $( - 0.5 , - 2 )$ and a maximum point at $( 0.4 , - 4 )$. The lines $x = 1$, the $x$-axis and the $y$-axis are asymptotes of the curve, as shown in Fig. 1.
On a separate diagram sketch the graphs of
\begin{enumerate}[label=(\alph*)]
\item $y = | \mathrm { f } ( x ) |$,
\item $y = \mathrm { f } ( x - 3 )$,
\item $y = \mathrm { f } ( | x | )$.
In each case show clearly
\begin{enumerate}[label=(\roman*)]
\item the coordinates of any points at which the curve has a maximum or minimum point,
\item how the curve approaches the asymptotes of the curve.\\
6. continued
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q6 [12]}}