| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Read parameters from graph of transformed trig function |
| Difficulty | Moderate -0.8 Part (a) requires reading amplitude, vertical shift, and period directly from a graph using standard transformations—pure recall with no problem-solving. Part (b) involves counting intersections between the sine curve and linear functions, which is straightforward graphical reasoning once the curve is identified. This is easier than average A-level content, requiring only basic graph interpretation skills. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| 1(a) | a=4 | B1 |
| b=2 | B1 | |
| c=3 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(b)(i) | 5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(b)(ii) | 1 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(a) ---
1(a) | a=4 | B1 | Allow 4sin(2x)+3 if values of a, b and c are not stated.
b=2 | B1
c=3 | B1
3
--- 1(b)(i) ---
1(b)(i) | 5 | B1 | Ignore attempts at finding solutions.
1
--- 1(b)(ii) ---
1(b)(ii) | 1 | B1 | Ignore attempts at finding solutions.
1
Question | Answer | Marks | Guidance\includegraphics{figure_1}
The diagram shows the curve with equation $y = a\sin(bx) + c$ for $0 \leqslant x \leqslant 2\pi$, where $a$, $b$ and $c$ are positive constants.
\begin{enumerate}[label=(\alph*)]
\item State the values of $a$, $b$ and $c$. [3]
\item For these values of $a$, $b$ and $c$, determine the number of solutions in the interval $0 \leqslant x \leqslant 2\pi$ for each of the following equations:
\begin{enumerate}[label=(\roman*)]
\item $a\sin(bx) + c = 7 - x$ [1]
\item $a\sin(bx) + c = 2\pi(x - 1)$. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q1 [5]}}