| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Solve trigonometric equation with approximate values |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question on transformed trigonometric functions. Part (i) requires basic equation solving with inverse cosine, (ii) is a standard graph sketch with vertical shift and horizontal stretch, (iii) tests understanding of one-to-one functions (the restricted domain ensures this), and (iv) involves routine inverse function manipulation. All parts are textbook-standard with no novel insight required, making it slightly easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
The function $\text{f} : x \mapsto 5 + 3\cos(\frac{1}{3}x)$ is defined for $0 \leqslant x \leqslant 2\pi$.
\begin{enumerate}[label=(\roman*)]
\item Solve the equation $\text{f}(x) = 7$, giving your answer correct to 2 decimal places. [3]
\item Sketch the graph of $y = \text{f}(x)$. [2]
\item Explain why $\text{f}$ has an inverse. [1]
\item Obtain an expression for $\text{f}^{-1}(x)$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2015 Q8 [9]}}