| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Stationary points after transformation |
| Difficulty | Moderate -0.5 This is a straightforward application of function transformations working backwards through given transformations. Students need to understand how translations and stretches affect key points (max/min), but the question explicitly tells them which transformations were applied and in what order. The calculations are routine: finding the stretch factor from the vertical distance between max/min, determining the radius, and reversing the transformations step-by-step. No problem-solving insight or novel approach is required—just systematic application of standard transformation rules. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| \(3\) | B1 | Ignore any description. |
| Answer | Marks | Guidance |
|---|---|---|
| \(2\) | B1 | Ignore any description. |
| Answer | Marks | Guidance |
|---|---|---|
| \((8, 2)\) | B1 B1 | Ignore any description. Allow vector notation and absence of brackets. |
| Answer | Marks | Guidance |
|---|---|---|
| \((1, 5)\) | B1 FT | FT each coordinate, (\(their\ 8 - 7\), \(their\ 2 + 3\)). Allow vector notation and absence of brackets. |
| B1 FT |
## Question 5:
### Part 5(a):
$3$ | **B1** | Ignore any description.
### Part 5(b):
$2$ | **B1** | Ignore any description.
### Part 5(c):
$(8, 2)$ | **B1 B1** | Ignore any description. Allow vector notation and absence of brackets.
### Part 5(d):
$(1, 5)$ | **B1 FT** | FT each coordinate, ($their\ 8 - 7$, $their\ 2 + 3$). Allow vector notation and absence of brackets.
| **B1 FT** |
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{8eb3d21b-dc45-493c-9e5c-3c0535c505e8-06_743_750_269_687}
The diagram shows a curve which has a maximum point at $( 8,12 )$ and a minimum point at $( 8,0 )$. The curve is the result of applying a combination of two transformations to a circle. The first transformation applied is a translation of $\binom { 7 } { - 3 }$. The second transformation applied is a stretch in the $y$-direction.
\begin{enumerate}[label=(\alph*)]
\item State the scale factor of the stretch.
\item State the radius of the original circle.
\item State the coordinates of the centre of the circle after the translation has been completed but before the stretch is applied.
\item State the coordinates of the centre of the original circle.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2022 Q5 [6]}}