| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Sequence of transformations order |
| Difficulty | Standard +0.3 This is a standard C3 transformations question requiring identification of stretch and translation (routine), sketching a modulus function (standard technique), and solving modulus equations/inequalities (straightforward application). All parts follow predictable patterns with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function1.02w Graph transformations: simple transformations of f(x) |
5
\begin{enumerate}[label=(\alph*)]
\item Describe a sequence of two geometrical transformations that maps the graph of $y = \ln x$ onto the graph of $y = 4 \ln ( x - \mathrm { e } )$.
\item Sketch, on the axes given below, the graph of $y = | 4 \ln ( x - \mathrm { e } ) |$, indicating the exact value of the $x$-coordinate where the curve meets the $x$-axis.
\item \begin{enumerate}[label=(\roman*)]
\item Solve the equation $| 4 \ln ( x - e ) | = 4$.
\item Hence, or otherwise, solve the inequality $| 4 \ln ( x - e ) | \geqslant 4$.\\
\includegraphics[max width=\textwidth, alt={}, center]{7aa76d26-e3c4-4374-ae4f-8bb61e61b135-3_655_1428_2023_315}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C3 2012 Q5 [13]}}