| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2023 |
| Session | October |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find coordinates of turning points |
| Difficulty | Moderate -0.8 This question tests basic properties of trigonometric graphs (period, amplitude, transformations) and requires finding a constant using given coordinates. All parts involve standard recall and straightforward substitution with no complex problem-solving. Part (a) uses the first x-intercept to find n, part (b) reads off the minimum point, and part (c) uses two points on a sine curve to find k through simple algebra. This is easier than average A-level content. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.05f Trigonometric function graphs: symmetries and periodicities |
10.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-28_538_652_255_708}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
Figure 4 shows a sketch of part of the curve $C _ { 1 }$ with equation
$$y = 3 \cos \left( \frac { x } { n } \right) ^ { \circ } \quad x \geqslant 0$$
where $n$ is a constant.\\
The curve $C _ { 1 }$ cuts the positive $x$-axis for the first time at point $P ( 270,0 )$, as shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item State the value of $n$
\item State the period of $C _ { 1 }$
The point $Q$, shown in Figure 4, is a minimum point of $C _ { 1 }$
\end{enumerate}\item State the coordinates of $Q$.
The curve $C _ { 2 }$ has equation $y = 2 \sin x ^ { \circ } + k$, where $k$ is a constant.\\
The point $R \left( a , \frac { 12 } { 5 } \right)$ and the point $S \left( - a , - \frac { 3 } { 5 } \right)$, both lie on $C _ { 2 }$\\
Given that $a$ is a constant less than 90
\item find the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2023 Q10 [6]}}