| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2023 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch trig curve and straight line, count intersections |
| Difficulty | Moderate -0.3 This question tests basic understanding of tan x periodicity and counting intersections graphically. Part (a) is direct recall, parts (b)(i)-(ii) require simple visual reasoning from the given graph, and part (b)(iii) extends the pattern arithmetically (200 periods × 2 intersections per period + 1 at origin = 401). While multi-part, each step is straightforward with no complex problem-solving required, making it slightly easier than average. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.05a Sine, cosine, tangent: definitions for all arguments1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\pi\) | B1 | Period is \(\pi\) radians but condone \(180°\) or just \(180\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(3\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(5\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(201\) | B1 |
# Question 9(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\pi$ | B1 | Period is $\pi$ radians but condone $180°$ or just $180$ |
# Question 9(b)(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $3$ | B1 | |
# Question 9(b)(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $5$ | B1 | |
# Question 9(b)(iii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $201$ | B1 | |
---9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-24_675_835_251_616}
\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 $\tan x$
\item Write down the number of roots of the equation
\begin{enumerate}[label=(\roman*)]
\item $\tan x = ( \pi + 2 ) x$ in the interval $- \pi < x < \pi$
\item $\tan x = \pi x$ in the interval $- 2 \pi < x < 2 \pi$
\item $\tan x = \pi x$ in the interval $- 100 \pi < x < 100 \pi$
\end{itemize}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2023 Q9 [4]}}