| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical stretch y = af(x) |
| Difficulty | Easy -1.2 This is a straightforward C1 transformation question requiring only direct application of standard rules: vertical stretch multiplies y-coordinates by 3, horizontal translation shifts x-coordinates by -2. No problem-solving or conceptual insight needed—purely mechanical application of memorized transformation rules to given coordinates. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct \(\cap\) shape through \((0,0)\) and \((k, 0)\) where \(k > 0\) | B1 | Shape |
| Maximum at \((3, 15)\) and \(6\) labelled at \((6, 0)\) | B1 (2) | Points; condone \((15,3)\) if 3 and 15 correct on axes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct \(\cap\) shape NOT through \((0,0)\), cutting \(x\)-axis twice | M1 | |
| \(x\)-intercepts at \(-2\) and \(4\) (or \((-2,0)\) and \((4,0)\)) | A1 | |
| Maximum at \((1, 5)\), clearly in 1st quadrant | A1 (3) | Condone \((5,1)\) |
## Question 4:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct $\cap$ shape through $(0,0)$ and $(k, 0)$ where $k > 0$ | B1 | Shape |
| Maximum at $(3, 15)$ and $6$ labelled at $(6, 0)$ | B1 (2) | Points; condone $(15,3)$ if 3 and 15 correct on axes |
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct $\cap$ shape NOT through $(0,0)$, cutting $x$-axis twice | M1 | |
| $x$-intercepts at $-2$ and $4$ (or $(-2,0)$ and $(4,0)$) | A1 | |
| Maximum at $(1, 5)$, clearly in 1st quadrant | A1 (3) | Condone $(5,1)$ |
---4.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{5a195cf1-37d9-43e9-ab47-c6892a18ba80-05_689_920_292_511}
\end{center}
\end{figure}
Figure 1 shows a sketch of the curve with equation $y = \mathrm { f } ( x )$. The curve passes through the origin $O$ and through the point $( 6,0 )$. The maximum point on the curve is $( 3,5 )$.
On separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = 3 \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( x + 2 )$.
On each diagram, show clearly the coordinates of the maximum point and of each point at which the curve crosses the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2005 Q4 [5]}}