| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Reflections |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring only standard recall of reflection and horizontal stretch rules. Students apply y → -y (reflecting in x-axis) and x → 2x (horizontal scale factor 1/2) to given coordinates using memorized transformations, with no problem-solving or conceptual insight needed beyond basic pattern application. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Reflection in \(x\)-axis | B1 | |
| 2 and 4 labelled (or \((2, 0)\) and \((4, 0)\) seen) | B1 | |
| Image of \(P\) \((3, 2)\) | B1 | (3 marks) |
| (b) Stretch parallel to \(x\)-axis | M1 | |
| 1 and 2 labelled (or \((1, 0)\) and \((2, 0)\) seen) | A1 | |
| Image of \(P\) \((1\frac{1}{2}, -2)\) | A1 | (3 marks) |
**(a)** Reflection in $x$-axis | B1 |
2 and 4 labelled (or $(2, 0)$ and $(4, 0)$ seen) | B1 |
Image of $P$ $(3, 2)$ | B1 | (3 marks)
**(b)** Stretch parallel to $x$-axis | M1 |
1 and 2 labelled (or $(1, 0)$ and $(2, 0)$ seen) | A1 |
Image of $P$ $(1\frac{1}{2}, -2)$ | A1 | (3 marks)
**Total: 6 marks**
---6.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{bace07ee-1eb8-43d6-8229-152d1f74ab59-10_515_714_292_609}
\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 $( 2,0 )$ and $( 4,0 )$. The minimum point on the curve is $P ( 3 , - 2 )$.
In separate diagrams sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = - \mathrm { f } ( x )$,
\item $y = \mathrm { f } ( 2 x )$.
On each diagram, give the coordinates of the points at which the curve crosses the $x$-axis, and the coordinates of the image of $P$ under the given transformation.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2005 Q6 [6]}}