| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2023 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Sequence of transformations order |
| Difficulty | Moderate -0.3 This question tests understanding of transformation order and composition, which is conceptually important but mechanically straightforward. Part (a) and (b) require systematic application of standard transformations (reflection and translation), while part (c) requires recognizing the relationship between the results. The calculations are routine for A-level, involving basic substitutions and algebraic manipulation, though students must be careful about order. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\{-(x-3)^2\}\ \{-1\}\) | B1 B1 | OE. Must be a quadratic e.g. \(3x-1\) B0 B0. SC B1 for correct use of generalised function notation |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\{-(x-3)^2\}\ \{+1\}\) | B1 B1 | OE. Must be a quadratic. SC B1 for correct use of generalised function notation |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\{\text{Translation}\}\ \begin{pmatrix}\{0\}\\\{2\}\end{pmatrix}\) | B2, 1, 0 | FT from (a) and (b) if a translation parallel to the \(y\)-axis. B2 for fully correct, B1 with two elements correct. \(\{\}\) indicates different elements |
| Total: 2 |
## Question 4:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\{-(x-3)^2\}\ \{-1\}$ | B1 B1 | OE. Must be a quadratic e.g. $3x-1$ B0 B0. SC B1 for correct use of generalised function notation |
| **Total: 2** | | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\{-(x-3)^2\}\ \{+1\}$ | B1 B1 | OE. Must be a quadratic. SC B1 for correct use of generalised function notation |
| **Total: 2** | | |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\{\text{Translation}\}\ \begin{pmatrix}\{0\}\\\{2\}\end{pmatrix}$ | B2, 1, 0 | FT from (a) and (b) if a translation parallel to the $y$-axis. B2 for fully correct, B1 with two elements correct. $\{\}$ indicates different elements |
| **Total: 2** | | |
---4 The transformation R denotes a reflection in the $x$-axis and the transformation T denotes a translation of $\binom { 3 } { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the equation, $y = \mathrm { g } ( x )$, of the curve with equation $y = x ^ { 2 }$ after it has been transformed by the sequence of transformations R followed by T .
\item Find the equation, $y = \mathrm { h } ( x )$, of the curve with equation $y = x ^ { 2 }$ after it has been transformed by the sequence of transformations T followed by R .
\item State fully the transformation that maps the curve $y = \mathrm { g } ( x )$ onto the curve $y = \mathrm { h } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2023 Q4 [6]}}