Edexcel P1 2021 January — Question 3 5 marks

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeFind coordinates of turning points
DifficultyEasy -1.8 This question requires only direct recall of basic cosine graph properties (amplitude, period, max/min values) and simple vertical translation. No calculation, problem-solving, or novel insight needed—purely testing knowledge of standard trig graph features.
Spec1.05f Trigonometric function graphs: symmetries and periodicities1.05g Exact trigonometric values: for standard angles
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6a5d0ffc-a725-404b-842a-f3b6000e6fed-08_625_835_264_557} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve \(C _ { 1 }\) with equation \(y = 4 \cos x ^ { \circ }\) The point \(P\) and the point \(Q\) lie on \(C _ { 1 }\) and are shown in Figure 1.
  1. State
    1. the coordinates of \(P\),
    2. the coordinates of \(Q\). The curve \(C _ { 2 }\) has equation \(y = 4 \cos x ^ { \circ } + k\), where \(k\) is a constant.
      Curve \(C _ { 2 }\) has a minimum \(y\) value of - 1
      The point \(R\) is the maximum point on \(C _ { 2 }\) with the smallest positive \(x\) coordinate.
  2. State the coordinates of \(R\).
Question 3:
Part (a)(i)
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(P(-180, -4)\)B1 \((-180, \ldots)\) or \((\ldots, -4)\) — condone \(x\) in radians
\(P(-180, -4)\) (both values)B1 Must be in degrees; SC1 for \((-4, -180)\)
Part (a)(ii)
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(Q(450, 0)\)B1 \(x = 450,\ y = 0\); condone \(\left(\frac{5}{2}\pi, 0\right)\)
Part (b)
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(R(360, 7)\)B1 \((360, \ldots)\) or \((\ldots, 7)\) — condone \(x\) in radians
\(R(360, 7)\) (both values)B1 Must be in degrees; ignore any reference to \((0,7)\); SC1 for \((7, 360)\)
*Note: If radians used throughout max score: (a)(i) \((-\pi, -4)\) B1B0; (a)(ii) \(\left(\frac{5}{2}\pi, 0\right)\) B1; (b) \((2\pi, 7)\) B1B0*
# Question 3:

## Part (a)(i)

| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(-180, -4)$ | B1 | $(-180, \ldots)$ or $(\ldots, -4)$ — condone $x$ in radians |
| $P(-180, -4)$ (both values) | B1 | Must be in degrees; SC1 for $(-4, -180)$ |

## Part (a)(ii)

| Answer/Working | Mark | Guidance |
|---|---|---|
| $Q(450, 0)$ | B1 | $x = 450,\ y = 0$; condone $\left(\frac{5}{2}\pi, 0\right)$ |

## Part (b)

| Answer/Working | Mark | Guidance |
|---|---|---|
| $R(360, 7)$ | B1 | $(360, \ldots)$ or $(\ldots, 7)$ — condone $x$ in radians |
| $R(360, 7)$ (both values) | B1 | Must be in degrees; ignore any reference to $(0,7)$; SC1 for $(7, 360)$ |

*Note: If radians used throughout max score: (a)(i) $(-\pi, -4)$ B1B0; (a)(ii) $\left(\frac{5}{2}\pi, 0\right)$ B1; (b) $(2\pi, 7)$ B1B0*

---
3.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{6a5d0ffc-a725-404b-842a-f3b6000e6fed-08_625_835_264_557}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

Figure 1 shows a sketch of part of the curve $C _ { 1 }$ with equation $y = 4 \cos x ^ { \circ }$ The point $P$ and the point $Q$ lie on $C _ { 1 }$ and are shown in Figure 1.
\begin{enumerate}[label=(\alph*)]
\item State
\begin{enumerate}[label=(\roman*)]
\item the coordinates of $P$,
\item the coordinates of $Q$.

The curve $C _ { 2 }$ has equation $y = 4 \cos x ^ { \circ } + k$, where $k$ is a constant.\\
Curve $C _ { 2 }$ has a minimum $y$ value of - 1\\
The point $R$ is the maximum point on $C _ { 2 }$ with the smallest positive $x$ coordinate.
\end{enumerate}\item State the coordinates of $R$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel P1 2021 Q3 [5]}}
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