| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify/describe sequence of transformations between two given equations |
| Difficulty | Moderate -0.8 Part (a) requires straightforward substitution of x→(x+1) and y→(y-3) into the equation, then rearranging—a routine application of translation formulas. Part (b) involves recognizing a horizontal stretch factor by comparing coefficients, which is standard pattern recognition. Both parts are mechanical applications of transformation rules with no problem-solving or insight required, making this easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\{(x+1)^2+2(x+1)-5\}+\{3\}\), or \(\{(x+1+1)^2\}+\{-6+3\}\) | M1 M1 | M1 for dealing with \(\begin{pmatrix}-1\\0\end{pmatrix}\) and M1 for dealing with \(\begin{pmatrix}0\\3\end{pmatrix}\) |
| \([y=]x^2+4x+1\) | A1 | Answer only given full marks. |
| Answer | Marks | Guidance |
|---|---|---|
| {Stretch}{\(x\) direction or horizontally or \(y\)-axis invariant}{factor \(\frac{1}{2}\)} | B2, 1, 0 | Additional transformation B0. |
## Question 4(a):
$\{(x+1)^2+2(x+1)-5\}+\{3\}$, or $\{(x+1+1)^2\}+\{-6+3\}$ | **M1 M1** | M1 for dealing with $\begin{pmatrix}-1\\0\end{pmatrix}$ and M1 for dealing with $\begin{pmatrix}0\\3\end{pmatrix}$
$[y=]x^2+4x+1$ | **A1** | Answer only given full marks.
**3 total**
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## Question 4(b):
{Stretch}{$x$ direction or horizontally or $y$-axis invariant}{factor $\frac{1}{2}$} | **B2, 1, 0** | Additional transformation B0.
**2 total**
---4
\begin{enumerate}[label=(\alph*)]
\item The curve with equation $y = x ^ { 2 } + 2 x - 5$ is translated by $\binom { - 1 } { 3 }$.\\
Find the equation of the translated curve, giving your answer in the form $y = a x ^ { 2 } + b x + c$.
\item The curve with equation $y = x ^ { 2 } + 2 x - 5$ is transformed to a curve with equation $y = 4 x ^ { 2 } + 4 x - 5$. Describe fully the single transformation that has been applied.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2022 Q4 [5]}}