| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Read parameters from graph of transformed trig function |
| Difficulty | Easy -1.2 This question requires reading amplitude, frequency, and vertical shift directly from a clearly labeled sine graph. It's pure pattern recognition with no calculation or problem-solving—students simply identify p from the amplitude (distance from center to peak), q from the period, and r from the vertical shift. This is easier than average A-level work as it tests only basic graph interpretation skills. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([p =]\ 3\) | B1 | |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([q =]\ \frac{1}{2}\) | B1 | |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([r =]\ -2\) | B1 | |
| 1 |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[p =]\ 3$ | **B1** | |
| | **1** | |
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[q =]\ \frac{1}{2}$ | **B1** | |
| | **1** | |
## Question 2(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[r =]\ -2$ | **B1** | |
| | **1** | |2\\
\includegraphics[max width=\textwidth, alt={}, center]{89a18f20-a4d6-4a42-8b00-849f4fb89692-04_657_1253_269_431}
The diagram shows part of the curve with equation $y = p \sin ( q \theta ) + r$, where $p , q$ and $r$ are constants.
\begin{enumerate}[label=(\alph*)]
\item State the value of $p$.
\item State the value of $q$.
\item State the value of $r$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2022 Q2 [3]}}