| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Multiple transformation descriptions |
| Difficulty | Moderate -0.3 This is a standard transformation question requiring application of well-known rules: reflection in x-axis for part (a) and horizontal stretch for part (b). Students must systematically apply transformations to key features (intercepts, stationary point, asymptote), which is routine C1/C2 content with no novel problem-solving required. Slightly easier than average due to straightforward transformations, though the horizontal stretch requires careful attention to the factor. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct shape in quadrants 2, 3 and 4 only, minimum in quadrant 2 | B1 | Must not appear in quadrant 1. Allow pen slips towards asymptote; graph should be higher than \((0,-3)\) |
| Coordinates \((-3,-9)\), \((-6,0)\) and \((0,-3)\) clearly labelled | B1 | \((-3,-9)\) is turning point in Q3, \((-6,0)\) is negative \(x\)-intercept, \((0,-3)\) is negative \(y\)-intercept. Condone coordinates reversed if point is in correct place. |
| Asymptote \(y = -1\) | B1 | May appear on diagram or in text. Must be the only horizontal asymptote offered. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct shape in quadrants 1, 2 and 3 only, maximum in quadrant 2 | B1 | Must not appear in quadrant 4. Graph should be lower than \((0,3)\). At least one coordinate or asymptote must be adapted from original \(f(x)\). |
| Coordinates \((-2,9)\), \((-4,0)\) and \((0,3)\) clearly labelled | B1 | Condone coordinates reversed if point in correct place. Allow \(-4\) or \(3\) labelled as intersection points on axes. |
| Asymptote \(y = 1\) | B1 | May appear on diagram or in text. Must be the only horizontal asymptote offered. |
# Question 3:
## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct shape in quadrants 2, 3 and 4 only, minimum in quadrant 2 | B1 | Must not appear in quadrant 1. Allow pen slips towards asymptote; graph should be higher than $(0,-3)$ |
| Coordinates $(-3,-9)$, $(-6,0)$ and $(0,-3)$ clearly labelled | B1 | $(-3,-9)$ is turning point in Q3, $(-6,0)$ is negative $x$-intercept, $(0,-3)$ is negative $y$-intercept. Condone coordinates reversed if point is in correct place. |
| Asymptote $y = -1$ | B1 | May appear on diagram or in text. Must be the only horizontal asymptote offered. |
## Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct shape in quadrants 1, 2 and 3 only, maximum in quadrant 2 | B1 | Must not appear in quadrant 4. Graph should be lower than $(0,3)$. **At least one coordinate or asymptote must be adapted from original $f(x)$.** |
| Coordinates $(-2,9)$, $(-4,0)$ and $(0,3)$ clearly labelled | B1 | Condone coordinates reversed if point in correct place. Allow $-4$ or $3$ labelled as intersection points on axes. |
| Asymptote $y = 1$ | B1 | May appear on diagram or in text. Must be the only horizontal asymptote offered. |\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{de511cb3-35c7-4225-b459-a136b6304b78-06_955_1495_217_226}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation $y = \mathrm { f } ( x )$.\\
The curve crosses the coordinate axes at the points $( - 6,0 )$ and $( 0,3 )$, has a stationary point at $( - 3,9 )$ and has an asymptote with equation $y = 1$
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = - \mathrm { f } ( x )$
\item $y = \mathrm { f } \left( \frac { 3 } { 2 } x \right)$
On each diagram, show clearly the coordinates of the points of intersection of the curve with the two coordinate axes, the coordinates of the stationary point, and the equation of the asymptote.
\includegraphics[max width=\textwidth, alt={}, center]{de511cb3-35c7-4225-b459-a136b6304b78-07_2255_45_316_36}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2019 Q3 [6]}}