| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| 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 is a straightforward question testing basic understanding of sine graph transformations. Part (a) requires knowing sin x has maximum value 1 at x=π/2. Part (b) involves a simple vertical translation. Part (c) requires understanding horizontal translations and that minimum occurs when sin=-1. All parts are routine applications of standard transformations with no problem-solving or novel insight required. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = \frac{5\pi}{2}\) or \(y = 12\) | B1 | One coordinate correct; may be in coordinate pair or vector |
| \(x = \frac{5\pi}{2}\) and \(y = 12\) | B1 | Both coordinates correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = \frac{3\pi}{2}\) or \(y = -21\) | B1 | One coordinate correct |
| \(x = \frac{3\pi}{2}\) and \(y = -21\) | B1 | Both coordinates correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(A = -12\) | B1 | "\(A=\)" not required but must be clear it is the answer to (i) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(B = \frac{5\pi}{4}\) | B1 | "\(B=\)" not required but must be clear it is the answer to (ii); if written as coordinate pair \(\left(\frac{5\pi}{4}, -12\right)\) score B0B0 |
## Question 11:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = \frac{5\pi}{2}$ or $y = 12$ | B1 | One coordinate correct; may be in coordinate pair or vector |
| $x = \frac{5\pi}{2}$ and $y = 12$ | B1 | Both coordinates correct |
**(2 marks)**
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = \frac{3\pi}{2}$ or $y = -21$ | B1 | One coordinate correct |
| $x = \frac{3\pi}{2}$ and $y = -21$ | B1 | Both coordinates correct |
**(2 marks)**
### Part (c)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $A = -12$ | B1 | "$A=$" not required but must be clear it is the answer to (i) |
### Part (c)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $B = \frac{5\pi}{4}$ | B1 | "$B=$" not required but must be clear it is the answer to (ii); if written as coordinate pair $\left(\frac{5\pi}{4}, -12\right)$ score B0B0 |
**(2 marks) — Total 6**11.
\begin{tikzpicture}[scale=0.55]
% Axes
\draw[->] (-3.5,0) -- (10.5,0) node[right] {$x$};
\draw[->] (0,-14) -- (0,15) node[above] {$y$};
\node[below left] at (0,0) {$O$};
% Curve y = 12 sin x
\draw[thick, domain=-3.14:9.9, samples=200] plot (\x, {12*sin(\x r)});
% Point P at (pi/2, 12)
\fill (1.5708,12) circle (3pt);
\node[above right] at (1.5708,12) {$P$};
\end{tikzpicture}
Figure 4 shows a sketch of part of the curve $C _ { 1 }$ with equation
$$y = 12 \sin x$$
where $x$ is measured in radians.\\
The point $P$ shown in Figure 4 is a maximum point on $C _ { 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of $P$.
The curve $C _ { 2 }$ has equation
$$y = 12 \sin x + k$$
where $k$ is a constant.\\
Given that the maximum value of $y$ on $C _ { 2 }$ is 3
\item find the coordinates of the minimum point on $C _ { 2 }$ which has the smallest positive $x$ coordinate.
The curve $C _ { 3 }$ has equation
$$y = 12 \sin ( x + B )$$
where $B$ is a positive constant.\\
Given that $\left( \frac { \pi } { 4 } , A \right)$, where $A$ is a constant, is the minimum point on $C _ { 3 }$ which has the smallest positive $x$ coordinate,
\item find
\begin{enumerate}[label=(\roman*)]
\item the value of $A$,
\item the smallest possible value of $B$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2024 Q11 [6]}}