| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Transformations of modulus graphs from given f(x) sketch |
| Difficulty | Moderate -0.3 This is a standard C3 modulus transformation question requiring sketching of |f(x)| (reflect negative parts) and 2f(-x)+3 (reflect in y-axis, stretch, translate), plus identifying parameters from a V-shaped graph. Routine application of transformation rules with straightforward coordinate calculations, slightly easier than average due to clear visual guidance and standard techniques. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| 'W' shape | B1 | Arms need not be symmetrical but two bottom points must appear at same height. Do not accept rounded W's. |
| \((0,11)\) and \((6,1)\) | B1 | W shape in quadrants 1 and 2 sitting on \(x\)-axis. Accept 11 marked on \(y\)-axis for \(P'\). Condone \(P'=(11,0)\) on correct axis. \(Q'=(1,6)\) is B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| 'V' shape | B1 | Arms need not be symmetrical. Do not accept rounded or upside-down V's |
| \((-6,1)\) | B1 | Minimum point, must be in correct quadrant |
| \((0,25)\) | B1 | \(y\)-intercept; line must cross axis. Accept 25 on correct axis. Condone \(P'=(25,0)\) on positive \(y\)-axis |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| One of \(a=2\) or \(b=6\) | B1 | Can be implied by writing \(y=2\ |
| \(a=2\) and \(b=6\) | B1 | Can be implied by \(y=2\ |
## Question 4:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| 'W' shape | B1 | Arms need not be symmetrical but two bottom points must appear at same height. Do not accept rounded W's. |
| $(0,11)$ and $(6,1)$ | B1 | W shape in quadrants 1 and 2 sitting on $x$-axis. Accept 11 marked on $y$-axis for $P'$. Condone $P'=(11,0)$ on correct axis. $Q'=(1,6)$ is B0 |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| 'V' shape | B1 | Arms need not be symmetrical. Do not accept rounded or upside-down V's |
| $(-6,1)$ | B1 | Minimum point, must be in correct quadrant |
| $(0,25)$ | B1 | $y$-intercept; line must cross axis. Accept 25 on correct axis. Condone $P'=(25,0)$ on positive $y$-axis |
### Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| One of $a=2$ or $b=6$ | B1 | Can be implied by writing $y=2\|x-6\|-1$ or $y=2\|x-.\|-1$ |
| $a=2$ and $b=6$ | B1 | Can be implied by $y=2\|x-6\|-1$. Stated answer takes precedence over written expression |
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{16c69ee4-255e-4d77-955a-92e1eb2f7d3e-05_665_776_233_584}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows part of the graph with equation $y = \mathrm { f } ( x ) , x \in \mathbb { R }$.
The graph consists of two line segments that meet at the point $Q ( 6 , - 1 )$.
The graph crosses the $y$-axis at the point $P ( 0,11 )$.
Sketch, on separate diagrams, the graphs of
\begin{enumerate}[label=(\alph*)]
\item $y = | f ( x ) |$
\item $y = 2 f ( - x ) + 3$
On each diagram, show the coordinates of the points corresponding to $P$ and $Q$.\\
Given that $\mathrm { f } ( x ) = a | x - b | - 1$, where $a$ and $b$ are constants,
\item state the value of $a$ and the value of $b$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2014 Q4 [7]}}