| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2020 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find coordinates of turning points |
| Difficulty | Easy -1.3 This question tests basic knowledge of sine graph properties (amplitude, period, turning points) with minimal calculation. Part (a) requires reading standard turning point coordinates from y=3sin(x), and part (b) involves a simple vertical translation. All values are straightforward with no problem-solving or novel insight required. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05g Exact trigonometric values: for standard angles1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P = (90°, 3)\) | M1 | For one value in the coordinate pair of \((90°, 3)\). Condone lack of brackets and do not be concerned with \(x\) or \(y\) correctly paired. Allow in radians. |
| \(P = (90°, 3)\) | A1 | For both values. Allow \(x = 90\), \(y = 3\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(Q = (540°, 0)\) | B1 | Allow \(x = 540\), \(y = 0\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((270°, 4)\) | M1 | For one value in the coordinate pair of \((270°, 4)\). Condone lack of brackets. Allow in radians. |
| \((270°, 4)\) | A1 | For both values. Allow \(x = 270\), \(y = 4\) |
## Question 7:
### Part (a)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P = (90°, 3)$ | M1 | For one value in the coordinate pair of $(90°, 3)$. Condone lack of brackets and do not be concerned with $x$ or $y$ correctly paired. Allow in radians. |
| $P = (90°, 3)$ | A1 | For both values. Allow $x = 90$, $y = 3$ |
### Part (a)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $Q = (540°, 0)$ | B1 | Allow $x = 540$, $y = 0$ |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(270°, 4)$ | M1 | For one value in the coordinate pair of $(270°, 4)$. Condone lack of brackets. Allow in radians. |
| $(270°, 4)$ | A1 | For both values. Allow $x = 270$, $y = 4$ |
**Note:** For answers missing brackets or radians in all parts, penalise the first time the A or B mark is due. For all correct values the wrong way round $(3, 90°), (0, 540°), (4, 270°)$ **SC M1A0B0M1A1**
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7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{28839dd5-b9c1-4cbd-981e-8f79c43ba086-18_599_723_274_614}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows part of the curve $C _ { 1 }$ with equation $y = 3 \sin x$, where $x$ is measured in degrees.
The point $P$ and the point $Q$ lie on $C _ { 1 }$ and are shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item State
\begin{enumerate}[label=(\roman*)]
\item the coordinates of $P$,
\item the coordinates of $Q$.
A different curve $C _ { 2 }$ has equation $y = 3 \sin x + k$, where $k$ is a constant.\\
The curve $C _ { 2 }$ has a maximum $y$ value of 10\\
The point $R$ is the minimum point on $C _ { 2 }$ with the smallest positive $x$ coordinate.
\end{enumerate}\item State the coordinates of $R$.
Figure 3
\begin{itemize}
\item \end{itemize}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2020 Q7 [5]}}