| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2015 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch transformed curve from description |
| Difficulty | Standard +0.3 This is a straightforward curve transformation question requiring application of standard rules (vertical stretch and reflection in y-axis). Students need to systematically apply transformations to key features, but this is routine Core 1/2 material with no problem-solving or novel insight required—slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| Shape similar to before with stretch in \(y\) direction by at least one correct trait: \(y\) intercept \((0,27)\), maximum point \((1,33)\) or asymptote indicated at 9 | B1 |
| Intercept \((0,27)\), max \((1,33)\) and \(x\) intercept \((2.5,0)\) all three seen | B1 |
| Equation of asymptote \(y=9\) correct | B1 [3] |
| Answer | Marks |
|---|---|
| Shape (reflection in \(y\) axis) | B1 |
| \((-1,11)\), \((0,9)\) and \((-2.5,0)\) seen | B1 |
| \(y=3\) (must be equation) | B1 [3] |
# Question 3:
## Part (a)
Shape similar to before with stretch in $y$ direction by at least one correct trait: $y$ intercept $(0,27)$, maximum point $(1,33)$ or asymptote indicated at 9 | B1 |
Intercept $(0,27)$, max $(1,33)$ and $x$ intercept $(2.5,0)$ all three seen | B1 |
Equation of asymptote $y=9$ correct | B1 [3] |
## Part (b)
Shape (reflection in $y$ axis) | B1 |
$(-1,11)$, $(0,9)$ and $(-2.5,0)$ seen | B1 |
$y=3$ (must be equation) | B1 [3] |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3b99072a-cd16-4c1d-9e44-085926a3ba24-05_645_933_258_463}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation $y = \mathrm { f } ( x )$.\\
The curve crosses the coordinate axes at the points ( $2.5,0$ ) and ( 0,9 ), has a stationary point at ( 1,11 ), and has an asymptote $y = 3$
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = 3 \mathrm { f } ( x )$
\item $y = \mathrm { f } ( - x )$
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.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2015 Q3 [6]}}