| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, standard transformations) |
| Difficulty | Moderate -0.3 This is a standard C3 transformation question requiring application of well-defined rules (reflection, translation, stretch) to given points. While it tests multiple transformations across three parts, each follows routine procedures taught explicitly in the syllabus with no problem-solving or novel insight required—making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Shape with maximum in quadrant 2 and minimum in quadrant 1 or on positive \(y\)-axis | B1 | |
| Either \((0, 2)\) or \(A'(-2, 4)\) | B1 | |
| Both \((0, 2)\) and \(A'(-2, 4)\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Any translation of the original curve | B1 | |
| Translated maximum has either \(x\)-coordinate of 0 (implied) or \(y\)-coordinate of 6 | B1 | |
| Maximum at \((0, 6)\) in correct position on Cartesian axes | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Shape with minimum in quadrant 2 and maximum in quadrant 1 | B1 | |
| Either \((0, 2)\) or \(A'(1, 6)\) | B1 | |
| Both \((0, 2)\) and \(A'(1, 6)\) | B1 |
## Question 6:
### Part (i): $y = f(-x) + 1$
| Answer/Working | Mark | Guidance |
|---|---|---|
| Shape with maximum in quadrant 2 and minimum in quadrant 1 or on positive $y$-axis | B1 | |
| Either $(0, 2)$ or $A'(-2, 4)$ | B1 | |
| Both $(0, 2)$ and $A'(-2, 4)$ | B1 | |
### Part (ii): $y = f(x+2) + 3$
| Answer/Working | Mark | Guidance |
|---|---|---|
| Any translation of the original curve | B1 | |
| Translated maximum has either $x$-coordinate of 0 (implied) or $y$-coordinate of 6 | B1 | |
| Maximum at $(0, 6)$ in correct position on Cartesian axes | B1 | |
### Part (iii): $y = 2f(2x)$
| Answer/Working | Mark | Guidance |
|---|---|---|
| Shape with minimum in quadrant 2 and maximum in quadrant 1 | B1 | |
| Either $(0, 2)$ or $A'(1, 6)$ | B1 | |
| Both $(0, 2)$ and $A'(1, 6)$ | B1 | |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b2f133cc-1723-4512-a351-c319daf80fca-07_380_574_269_722}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of the graph of $y = \mathrm { f } ( x )$.\\
The graph intersects the $y$-axis at the point $( 0,1 )$ and the point $A ( 2,3 )$ is the maximum turning point.
Sketch, on separate axes, the graphs of\\
(i) $y = \mathrm { f } ( - x ) + 1$,\\
(ii) $y = \mathrm { f } ( x + 2 ) + 3$,\\
(iii) $y = 2 \mathrm { f } ( 2 x )$.
On each sketch, show the coordinates of the point at which your graph intersects the $y$-axis and the coordinates of the point to which $A$ is transformed.
\hfill \mbox{\textit{Edexcel C3 2010 Q6 [9]}}