| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation sketch |
| Difficulty | Moderate -0.3 This question tests standard knowledge of the inverse cosine function and a simple vertical transformation. Part (a) requires recall of the arccos graph shape and domain/range, while part (b) applies a straightforward reflection in y=π/2. The transformation is direct substitution with no problem-solving required, making it slightly easier than average but not trivial since inverse trig functions are less routine than basic functions. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
6
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = \cos ^ { - 1 } x$, where $y$ is in radians. State the coordinates of the end points of the graph.
\item Sketch the graph of $y = \pi - \cos ^ { - 1 } x$, where $y$ is in radians. State the coordinates of the end points of the graph.\\
(2 marks)\\
\includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_759_1258_678_431}\\
\includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_751_1241_1564_443}
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2013 Q6 [4]}}