| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find coordinates of turning points |
| Difficulty | Easy -1.3 This question requires only basic understanding of cosine graph transformations. Part (a) is direct reading from the minimum value, and part (b) uses the standard period of cosine (360°) to find the maximum point location. No complex calculations or problem-solving insight needed—purely routine application of cosine graph properties. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(A = -3\) | B1 | |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(y = 3\) | B1 | Correct \(y\) coordinate only; others must be discarded |
| e.g. \(x = 30 + 5 \times 180\) or \(x = 210 + 720\) or \(x = 180 + 2 \times 360 + 30\) | M1 | Correct strategy for the \(x\) coordinate; values embedded is sufficient |
| \(x = 930\) | A1 | Correct \(x\) coordinate only; others must be discarded. Isw. Note \((930, 3)\) with no incorrect working scores full marks |
| Special Case: If they give \((3, 930)\) or \(\left(\frac{31}{6}\pi, 3\right)\) rather than \((930, 3)\) score B1M1A0 | ||
| Total: 3 |
## Question 9:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $A = -3$ | B1 | |
| | | **Total: 1** |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $y = 3$ | B1 | Correct $y$ coordinate only; others must be discarded |
| e.g. $x = 30 + 5 \times 180$ or $x = 210 + 720$ or $x = 180 + 2 \times 360 + 30$ | M1 | Correct strategy for the $x$ coordinate; values embedded is sufficient |
| $x = 930$ | A1 | Correct $x$ coordinate only; others must be discarded. Isw. Note $(930, 3)$ with no incorrect working scores full marks |
| | | **Special Case:** If they give $(3, 930)$ or $\left(\frac{31}{6}\pi, 3\right)$ rather than $(930, 3)$ score B1M1A0 |
| | | **Total: 3** |
---9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6c320b71-8793-461a-a078-e4f64c144a3a-28_784_1324_260_312}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
Figure 4 shows part of the curve with equation
$$y = A \cos ( x - 30 ) ^ { \circ }$$
where $A$ is a constant.
The point $P$ is a minimum point on the curve and has coordinates $( 30 , - 3 )$ as shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $A$.
The point $Q$ is shown in Figure 4 and is a maximum point.
\item Find the coordinates of $Q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2022 Q9 [4]}}