| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch trig curve and straight line, count intersections |
| Difficulty | Moderate -0.8 This question tests basic properties of tan x and counting intersections from a given graph. Part (a) is direct recall of period. Parts (b)(i)-(iii) require understanding that steeper/shallower lines intersect tan x differently and that the pattern repeats, but the reasoning is straightforward visual analysis with minimal calculation. The most challenging aspect is recognizing the pattern for part (iii), but this is still routine problem-solving for A-level standard. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b063f4ea-372b-4193-b8fe-a9f8017d7349-18_718_882_219_596}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows a sketch of
\begin{itemize}
\item the curve with equation $y = \tan x$
\item the straight line $l$ with equation $y = \pi x$\\
in the interval $- \pi < x < \pi$
\begin{enumerate}[label=(\alph*)]
\item State the period of $\tan x$\\
(1)
\item Write down the number of roots of the equation
\begin{enumerate}[label=(\roman*)]
\item $\tan x = ( \pi + 2 ) x$ in the interval $- \pi < x < \pi$\\
(1)
\item $\tan x = \pi x$ in the interval $- 2 \pi < x < 2 \pi$\\
(1)
\item $\tan x = \pi x$ in the interval $- 100 \pi < x < 100 \pi$\\
(1)
\end{itemize}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q9 [4]}}