| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, modulus involved) |
| Difficulty | Moderate -0.3 This is a standard C3 transformations question requiring application of well-defined transformation rules (modulus, inverse, composite stretch/scale) to a given curve. While it tests understanding of three different transformations, each follows routine procedures taught explicitly in the syllabus. The transformations are applied separately rather than combined, and the key points can be found by direct application of transformation formulas without requiring problem-solving insight. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02v Inverse and composite functions: graphs and conditions for existence1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks |
|---|---|
| Mod graph, reflect for \(y < 0\) | M1 |
| \((0,2)\), \((3,0)\) marked on axes | A1 |
| Correct shape, including cusp | A1 (3) |
| Answer | Marks |
|---|---|
| Attempt at reflection in \(y = x\) | M1 |
| Curvature correct | A1 |
| \((-2,0)\), \((0,3)\) or equiv. | B1 (3) |
| Answer | Marks |
|---|---|
| Attempt at 'stretches' | M1 |
| \((0,-1)\) or equiv. | B1 |
| \((1,0)\) | B1 (3) |
# Question 3:
## Part (a)
Mod graph, reflect for $y < 0$ | M1 |
$(0,2)$, $(3,0)$ marked on axes | A1 |
Correct shape, including cusp | A1 (3) |
## Part (b)
Attempt at reflection in $y = x$ | M1 |
Curvature correct | A1 |
$(-2,0)$, $(0,3)$ or equiv. | B1 (3) |
## Part (c)
Attempt at 'stretches' | M1 |
$(0,-1)$ or equiv. | B1 |
$(1,0)$ | B1 (3) |
---\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{f0f328ed-3550-4b8d-8b80-016df8773b21-04_568_881_312_504}
\end{center}
\end{figure}
Figure 1 shows part of the curve with equation $y = \mathrm { f } ( x ) , x \in \mathbb { R }$, where f is an increasing function of $x$. The curve passes through the points $P ( 0 , - 2 )$ and $Q ( 3,0 )$ as shown.
In separate diagrams, sketch the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = | f ( x ) |$,
\item $y = \mathrm { f } ^ { - 1 } ( x )$,
\item $y = \frac { 1 } { 2 } \mathrm { f } ( 3 x )$.
Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2006 Q3 [9]}}