| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Standard +0.3 This question involves finding constants from given stationary points (straightforward substitution and using cos properties), then finding an inverse function of a transformed cosine. Part (i) is routine; part (ii) requires rearranging and applying arccos, which is standard C3 material but slightly more involved than basic inverse function questions. Overall slightly easier than average due to the structured guidance. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.05f Trigonometric function graphs: symmetries and periodicities |
Fig. 4 shows the curve $y = f(x)$, where
$$f(x) = a + \cos bx, \quad 0 \leq x \leq 2\pi,$$
and $a$ and $b$ are positive constants. The curve has stationary points at $(0, 3)$ and $(2\pi, 1)$.
\includegraphics{figure_4}
\begin{enumerate}[label=(\roman*)]
\item Find $a$ and $b$. [2]
\item Find $f^{-1}(x)$, and state its domain and range. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2014 Q4 [7]}}