| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Year | 2018 |
| Session | January |
| Marks | 6 |
| 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 transformations question requiring students to apply modulus and composite transformations to a given V-shaped graph. While it involves multiple steps (identifying key points, applying transformations, finding new coordinates), these are routine A-level techniques with no novel problem-solving required. The transformations f(|x|) and 2f(x+5) are textbook examples, making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| W shape anywhere on page | M1 | Allow for \(y = \ |
| Intercepts at \((5,0)\), \((-5,0)\) and \((0,-1)\) | A1 | Allow 5, -5 and -1 written on correct axes; do NOT allow \((0,5)\) for \((5,0)\) etc. |
| Vertices at both \((2,-3)\) and \((-2,-3)\) | A1 | Both vertices required |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| V shape (correct way up) anywhere on page | M1 | Do not award for original V; condone lack of symmetry or appearing as a tick |
| Intercepts through \(O\) and \((-6,0)\) | A1 | Allow -6 written on correct axis; do NOT allow \((0,-6)\) for \((-6,0)\) |
| Single vertex at \((-3,-6)\) | A1 | — |
## Question 4:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| W shape anywhere on page | M1 | Allow for $y = \|f(x)\|$; condone lack of symmetry |
| Intercepts at $(5,0)$, $(-5,0)$ and $(0,-1)$ | A1 | Allow 5, -5 and -1 written on correct axes; do NOT allow $(0,5)$ for $(5,0)$ etc. |
| Vertices at both $(2,-3)$ and $(-2,-3)$ | A1 | Both vertices required |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| V shape (correct way up) anywhere on page | M1 | Do not award for original V; condone lack of symmetry or appearing as a tick |
| Intercepts through $O$ and $(-6,0)$ | A1 | Allow -6 written on correct axis; do NOT allow $(0,-6)$ for $(-6,0)$ |
| Single vertex at $(-3,-6)$ | A1 | — |
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{7d07e1ad-d87a-4eb5-a15e-05b927892915-08_771_1189_212_379}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the graph with equation $y = \mathrm { f } ( x ) , \quad x \in \mathbb { R }$\\
The graph consists of two half lines that meet at the point $P ( 2 , - 3 )$, the vertex of the graph.\\
The graph cuts the $y$-axis at the point $( 0 , - 1 )$ and the $x$-axis at the points $( - 1,0 )$ and $( 5,0 )$.\\
Sketch, on separate diagrams, the graph of
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( | x | )$,
\item $y = 2 \mathrm { f } ( x + 5 )$.
In each case, give the coordinates of the points where the graph crosses or meets the coordinate axes.
Also give the coordinates of any vertices corresponding to the point $P$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C34 2018 Q4 [6]}}