| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Sequence of transformations order |
| Difficulty | Standard +0.3 Part (a) requires applying the modulus transformation (reflecting negative parts above x-axis), which is a standard C3 skill. Part (b) tests understanding of composite transformations and their order, requiring students to decompose f(2x-1) into f(2(x-1/2)), which is slightly above routine but still a textbook-style question with clear methodology. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Reflect any negative \(y\) values in the \(x\)-axis | B1 | Correct reflection of negative parts |
| All of graph at or above \(x\)-axis; positive parts unchanged | B1 | Fully correct sketch |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(f(2x-1)\): stretch scale factor \(\frac{1}{2}\) in \(x\)-direction | B1 B1 | Correct stretch |
| Followed by translation \(\left(\frac{1}{2}, 0\right)\) (or \(+\frac{1}{2}\) in \(x\)) | B1 B1 | Correct translation; correct order stated |
# Question 4:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Reflect any negative $y$ values in the $x$-axis | B1 | Correct reflection of negative parts |
| All of graph at or above $x$-axis; positive parts unchanged | B1 | Fully correct sketch |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $f(2x-1)$: stretch scale factor $\frac{1}{2}$ in $x$-direction | B1 B1 | Correct stretch |
| Followed by translation $\left(\frac{1}{2}, 0\right)$ (or $+\frac{1}{2}$ in $x$) | B1 B1 | Correct translation; correct order stated |
---4 The diagram shows a sketch of the curve with equation $y = \mathrm { f } ( x )$.\\
\includegraphics[max width=\textwidth, alt={}, center]{b8614dd6-2197-40c3-a673-5bef3e3653a5-5_629_1113_370_461}
\begin{enumerate}[label=(\alph*)]
\item On the axes below, sketch the curve with equation $y = | \mathrm { f } ( x ) |$.
\item Describe a sequence of two geometrical transformations that maps the graph of $y = \mathrm { f } ( x )$ onto the graph of $y = \mathrm { f } ( 2 x - 1 )$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2013 Q4 [6]}}