| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch transformed curve from description |
| Difficulty | Moderate -0.8 This is a straightforward transformations question testing standard Core 1/2 knowledge. Parts (a)-(c) require direct application of transformation rules (horizontal stretch, vertical translation, reading from graph), while part (d) is a routine reflection in the x-axis. All transformations are basic with no problem-solving or novel insight required. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((8, 5)\) | B1 | Accept \(x=8\), \(y=5\) or sketch of \(y=f\!\left(\frac{1}{4}x\right)\) with minimum marked at \((8,5)\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(y = 7\) | B1 | Must be an equation, not just '\(7\)' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(5 < k < 10\) | M1, A1 | M1: accept one "side" of inequality, condoning misunderstanding of whether boundary included; allow \(k>5\), \(k\geq5\), \(k<10\), \(k\leq10\); condone different variable; A1: cao \(5 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Shape (reflection in \(x\)-axis) | B1 | Look for shape shown in scheme; tolerant of slips at either end |
| \((0,-8)\) and \((2,-5)\) marked | B1 | Graph has intercept \((0,-8)\) and single maximum at \((2,-5)\); accept \(-8\) marked on \(y\)-axis; condone \((-8,0)\) if marked on correct axis |
| Asymptote \(y=-10\) | B1 | Graph must clearly be asymptotic; tolerant of slips |
# Question 7 (Graph Transformations):
## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(8, 5)$ | B1 | Accept $x=8$, $y=5$ or sketch of $y=f\!\left(\frac{1}{4}x\right)$ with minimum marked at $(8,5)$ | **(1)** |
## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $y = 7$ | B1 | Must be an equation, not just '$7$' | **(1)** |
## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $5 < k < 10$ | M1, A1 | M1: accept one "side" of inequality, condoning misunderstanding of whether boundary included; allow $k>5$, $k\geq5$, $k<10$, $k\leq10$; condone different variable; A1: cao $5<k<10$; allow $k>5\ \textbf{and}\ k<10$; $(5,10)$; $\{k\in\mathbb{R}: 5<k<10\}$; do not allow $k>5\ \textbf{or}\ k<10$ | **(2)** |
## Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Shape (reflection in $x$-axis) | B1 | Look for shape shown in scheme; tolerant of slips at either end |
| $(0,-8)$ and $(2,-5)$ marked | B1 | Graph has intercept $(0,-8)$ and single **maximum** at $(2,-5)$; accept $-8$ marked on $y$-axis; condone $(-8,0)$ if marked on correct axis |
| Asymptote $y=-10$ | B1 | Graph must clearly be asymptotic; tolerant of slips | **(3)(7 marks)** |
---7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{08b1be3e-2d9a-4832-b230-d5519540f494-20_588_839_219_550}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows a sketch of part of the curve with equation $y = \mathrm { f } ( x )$.
The curve crosses the $y$-axis at the point $( 0,8 )$.
The line with equation $y = 10$ is the only asymptote to the curve.\\
The curve has a single turning point, a minimum point at $( 2,5 )$, as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item State the coordinates of the minimum point of the curve with equation $y = \mathrm { f } \left( \frac { 1 } { 4 } x \right)$
\item State the equation of the asymptote to the curve with equation $y = \mathrm { f } ( x ) - 3$
The curve with equation $y = \mathrm { f } ( x )$ meets the line with equation $y = k$, where $k$ is a constant, at two distinct points.
\item State the set of possible values for $k$.
\item Sketch the curve with equation $y = - \mathrm { f } ( x )$. On your sketch, show clearly the coordinates of the turning point, the coordinates of the intersection with the $y$-axis and the equation of the asymptote.
\section*{\textbackslash section*\{D\}}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2017 Q7 [7]}}