| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| 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 rules: horizontal translation moves x-coordinates, vertical stretch multiplies y-coordinates, and vertical translation adds to y-coordinates. The calculations are simple arithmetic with clearly defined transformations and no problem-solving or insight required beyond direct application of memorized transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Horizontal translation of \(\pm 3\) | M1 | Accept coordinates of \((1,3)\) or \((6,-5)\) seen; i.e. max in 1st quad and min on the \(y\)-axis |
| \((-5, 3)\) marked on sketch or in text | B1 | |
| \((0, -5)\) and min intentionally on \(y\)-axis; condone \((-5, 0)\) if correctly placed on negative \(y\)-axis | A1 | For minimum clearly on negative \(y\)-axis and at least \(-5\) marked |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Correct shape through \((0,0)\) between max and min | B1 | Ignore coordinates for this mark |
| \((-2, 6)\) marked on graph or in text | B1 | Coordinates/points on sketch override coordinates given in text |
| \((3, -10)\) marked on graph or in text | B1 | \((3, 10)\) is B0 even if in 4th quadrant |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((a=)\ 5\) | B1 | May be at bottom of page or in the question |
## Question 6:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Horizontal translation of $\pm 3$ | M1 | Accept coordinates of $(1,3)$ or $(6,-5)$ seen; i.e. max in 1st quad and min on the $y$-axis |
| $(-5, 3)$ marked on sketch or in text | B1 | |
| $(0, -5)$ and min intentionally on $y$-axis; condone $(-5, 0)$ if correctly placed on negative $y$-axis | A1 | For minimum clearly on negative $y$-axis and at least $-5$ marked |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct shape through $(0,0)$ between max and min | B1 | Ignore coordinates for this mark |
| $(-2, 6)$ marked on graph or in text | B1 | Coordinates/points on sketch override coordinates given in text |
| $(3, -10)$ marked on graph or in text | B1 | $(3, 10)$ is B0 even if in 4th quadrant |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(a=)\ 5$ | B1 | May be at bottom of page or in the question |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{65d61b2c-2e47-402e-b08f-2d46bb00c188-08_568_942_269_498}
\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 has a maximum point $A$ at $( - 2,3 )$ and a minimum point $B$ at $( 3 , - 5 )$.
On separate diagrams sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x + 3 )$
\item $y = 2 \mathrm { f } ( x )$
On each diagram show clearly the coordinates of the maximum and minimum points.\\
The graph of $y = \mathrm { f } ( x ) + a$ has a minimum at (3, 0), where $a$ is a constant.
\item Write down the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2010 Q6 [7]}}