| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Two stretches from same function |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformations question requiring only recall of standard transformation rules: vertical stretch (multiply y-coordinates by 2), reflection in y-axis (negate x-coordinates), and horizontal translation (shift left by 2). No problem-solving or novel insight needed, just direct application of memorized transformation effects on key points. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| (a) Shape: Max in 1st quadrant and 2 intersections on positive \(x\)-axis | B1 |
| 1 and 4 labelled (in correct place) or clearly stated as coordinates | B1 |
| (2, 10) labelled or clearly stated | B1 |
| Answer | Marks |
|---|---|
| (b) Shape: Max in 2nd quadrant and 2 intersections on negative \(x\)-axis | B1 |
| \(-1\) and \(-4\) labelled (in correct place) or clearly stated as coordinates | B1 |
| \((-2, 5)\) labelled or clearly stated | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) \((a =) 2\) | B1 | May be implicit, i.e. \(f(x + 2)\) |
(a) Shape: Max in 1st quadrant and 2 intersections on positive $x$-axis | B1 |
1 and 4 labelled (in correct place) or clearly stated as coordinates | B1 |
(2, 10) labelled or clearly stated | B1 |
**Total for (a): 3 marks**
(b) Shape: Max in 2nd quadrant and 2 intersections on negative $x$-axis | B1 |
$-1$ and $-4$ labelled (in correct place) or clearly stated as coordinates | B1 |
$(-2, 5)$ labelled or clearly stated | B1 |
**Total for (b): 3 marks**
(c) $(a =) 2$ | B1 | May be implicit, i.e. $f(x + 2)$
Beware: The answer to part (c) may be seen on the first page.
**Total for (c): 1 mark**
**Total: 7 marks**
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ba0ee180-4c22-49f7-8a8e-a7268828b067-07_693_676_370_632}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$. The curve crosses the $x$-axis at the points $( 1,0 )$ and $( 4,0 )$. The maximum point on the curve is $( 2,5 )$.\\
In separate diagrams sketch the curves with the following equations.\\
On each diagram show clearly the coordinates of the maximum point and of each point at which the curve crosses the $x$-axis.
\begin{enumerate}[label=(\alph*)]
\item $y = 2 \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( - x )$.
The maximum point on the curve with equation $y = \mathrm { f } ( x + a )$ is on the $y$-axis.
\item Write down the value of the constant $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q6 [7]}}