| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Describe transformation from graph |
| Difficulty | Standard +0.3 This is a standard function transformation question requiring students to identify and describe transformations from a graph, then express them algebraically. While it involves multiple transformations (3 steps), these are routine AS-level skills with clear visual cues. The algebraic form in part (b) follows directly from part (a), making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| 5(a) | Reflection [in] y-axis | B1 B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 0 | B1* | B1 for ‘translation’ and a correct vector/description. |
| Answer | Marks | Guidance |
|---|---|---|
| Stretch, factor 2, parallel to y-axis | B2,1,0 | B2 all correct OE. |
| Answer | Marks | Guidance |
|---|---|---|
| Correct order and three correctly named transformations only | DB1 | If a fourth transformation is given this mark is not awarded and |
| Answer | Marks | Guidance |
|---|---|---|
| 0 | B1* | B1 for ‘translation’ and correct vector/description. |
| Reflection [in] y-axis | B1 B1 | B1 for ‘reflection’, B1 for ‘in y-axis’. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 5(b) | g(x)=2f(−x−1) or a=2, b=−1, c=−1 | B1 |
| Answer | Marks |
|---|---|
| B1 | Second B1 forb=−1 andc=−1. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 5:
--- 5(a) ---
5(a) | Reflection [in] y-axis | B1 B1 | B1 for reflection B1 mention of y-axis, OE.
SC B2 for stretch, SF –1, parallel to x-axis.
−1
Translation or shift
0 | B1* | B1 for ‘translation’ and a correct vector/description.
Do not accept ‘left’/’right’.
If two translations then B0 and B0 for the order.
Stretch, factor 2, parallel to y-axis | B2,1,0 | B2 all correct OE.
B1 any 2 parts correct.
This can be at any point in the sequence.
Correct order and three correctly named transformations only | DB1 | If a fourth transformation is given this mark is not awarded and
no marks are given for the two transformations of the same
type, except where the reflection is described as a stretch.
If any transformation is incorrectly named this cannot be given.
−1 1
If translation is not or then DB0 is given.
0 0
Alternative Solution for first 3 marks
1
Translation or shift
0 | B1* | B1 for ‘translation’ and correct vector/description.
Reflection [in] y-axis | B1 B1 | B1 for ‘reflection’, B1 for ‘in y-axis’.
Alternative solutions
There are alternative solutions which can be marked in the same way
−4
e.g. the given stretch, translation , reflect in x=−2.5
0
6
Question | Answer | Marks | Guidance
--- 5(b) ---
5(b) | g(x)=2f(−x−1) or a=2, b=−1, c=−1 | B1 | First B1 for a=2 and no additional terms added to the
function.
a=−2 is B0.
B1 | Second B1 forb=−1 andc=−1.
2
Question | Answer | Marks | Guidance\includegraphics{figure_5}
In the diagram, the graph with equation $y = \text{f}(x)$ is shown with solid lines and the graph with equation $y = \text{g}(x)$ is shown with broken lines.
\begin{enumerate}[label=(\alph*)]
\item Describe fully a sequence of three transformations which transforms the graph of $y = \text{f}(x)$ to the graph of $y = \text{g}(x)$. [6]
\item Find an expression for g(x) in the form $af(bx + c)$, where $a$, $b$ and $c$ are integers. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q5 [8]}}