| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | March |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Find equation after sequence of transformations |
| Difficulty | Moderate -0.5 This question tests standard function transformations applied sequentially to a trigonometric function. Part (a) requires identifying the minimum of a sine curve (routine). Part (b) involves applying two basic transformations in order—translation then reflection—which is straightforward bookwork requiring careful tracking of the transformations but no novel insight. The question is slightly easier than average as it's a direct application of transformation rules with clear step-by-step structure. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| State \((3\pi, -k)\) | B1 | |
| 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Obtain equation of form \(y = c \pm k\sin\frac{1}{2}x\) | M1 | Any non-zero \(c\) |
| Obtain correct equation \(y = 2 - k\sin\frac{1}{2}x\) | A1 | OE |
| State \((3\pi,\ 2+k)\) | B1 FT | Following part (a), i.e. (*their x*, \(2-\) *their y*) |
| 3 |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| State $(3\pi, -k)$ | B1 | |
| | **1** | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Obtain equation of form $y = c \pm k\sin\frac{1}{2}x$ | M1 | Any non-zero $c$ |
| Obtain correct equation $y = 2 - k\sin\frac{1}{2}x$ | A1 | OE |
| State $(3\pi,\ 2+k)$ | B1 FT | Following part **(a)**, i.e. (*their x*, $2-$ *their y*) |
| | **3** | |2\\
\includegraphics[max width=\textwidth, alt={}, center]{b5eb378d-a9cb-40e0-9203-374b58f1dcf9-03_451_597_255_735}
The diagram shows part of the curve with equation $\mathrm { y } = \mathrm { ksin } \frac { 1 } { 2 } \mathrm { x }$, where $k$ is a positive constant and $x$ is measured in radians. The curve has a minimum point $A$.
\begin{enumerate}[label=(\alph*)]
\item State the coordinates of $A$.
\item A sequence of transformations is applied to the curve in the following order.
Translation of 2 units in the negative $y$-direction\\
Reflection in the $x$-axis\\
Find the equation of the new curve and determine the coordinates of the point on the new curve corresponding to $A$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q2 [4]}}