| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Topic | Reciprocal Trig & Identities |
| Type | Inverse function graphs and properties |
| Difficulty | Standard +0.3 This question tests recognition of transformed trig graphs and inverse trig properties. Part (a) requires identifying amplitude and period from a sec graph (routine for Further Maths students). Part (b) involves reading a horizontal translation and finding coordinates from an arccos graph. All parts are direct graph reading with minimal calculation—standard bookwork with no problem-solving required. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
5. (a) The diagram shows the graph of $y = a \sec ( b x ) + 1$ for $x \in [ 0 , \pi )$. Find the values of $a$ and $b$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ace492d8-1dd0-401e-af74-505ca19d5e9c-12_818_556_201_897}\\
(b) The diagram shows the graph of $y = \arccos ( x + c )$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ace492d8-1dd0-401e-af74-505ca19d5e9c-12_511_766_1667_790}
\begin{enumerate}[label=(\roman*)]
\item State the value of c .
\item State the coordinates of the point $P$.\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q5 [5]}}