Edexcel P1 2020 January — Question 7 5 marks

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2020
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeFind coordinates of turning points
DifficultyEasy -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.
Spec1.05f Trigonometric function graphs: symmetries and periodicities1.05g Exact trigonometric values: for standard angles1.05o Trigonometric equations: solve in given intervals

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{28839dd5-b9c1-4cbd-981e-8f79c43ba086-18_599_723_274_614} \captionsetup{labelformat=empty} \caption{Figure 3}
\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.
  1. State
    1. the coordinates of \(P\),
    2. 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.
  2. State the coordinates of \(R\). Figure 3

Question 7:
Part (a)(i):
AnswerMarks Guidance
AnswerMarks 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):
AnswerMarks Guidance
AnswerMarks Guidance
\(Q = (540°, 0)\)B1 Allow \(x = 540\), \(y = 0\)
Part (b):
AnswerMarks Guidance
AnswerMarks 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
## 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]}}