| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | December |
| Marks | 6 |
| Topic | Trig Graphs & Exact Values |
| Type | Read parameters from graph of transformed trig function |
| Difficulty | Moderate -0.8 This is a straightforward parameter identification question for a transformed sine curve. Students can read amplitude and vertical shift directly from the given max/min points, calculate period from the distance between them, and find phase shift using standard substitution. All steps are routine applications of sine transformation formulas with no problem-solving insight required. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities |
The following diagram shows the curve $y = a \sin(b(x + c)) + d$, where $a, b, c$ and $d$ are all positive constants and $x$ is measured in radians. The curve has a maximum point at $(1, 3.5)$ and a minimum point at $(2, 0.5)$.
\includegraphics{figure_4}
\begin{enumerate}[label=(\roman*)]
\item Write down the value of $a$ and the value of $d$. [2]
\item Find the value of $b$. [2]
\item Find the smallest possible value of $c$, given that $c > 0$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q4 [6]}}