| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Reverse transformation (given transformed point) |
| Difficulty | Moderate -0.8 This is a straightforward function transformation question requiring recall of standard transformations (horizontal stretch factor 1/2 and vertical translation -3) and reverse application to find the original point. Part (a) tests basic knowledge, while part (b) requires simple algebraic manipulation: if (5,6) is on y=f(2x)-3, then f(2×5)-3=6, so f(10)=9, giving point (10,9). This is more routine than average A-level questions as it involves direct application of well-practiced transformation rules with no problem-solving complexity. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stretch with [scale factor] either \(\pm 2\) or \(\pm\frac{1}{2}\) | B1 | |
| Scale factor \(\frac{1}{2}\) in the \(x\)-direction | B1 | |
| Translation \(\begin{pmatrix} 0 \\ -3 \end{pmatrix}\) or translation of 3 units in negative \(y\)-direction | B1 | |
| Total | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((10, 9)\) | B1 B1 | B1 for each correct co-ordinate |
| Total | 2 |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stretch with [scale factor] either $\pm 2$ or $\pm\frac{1}{2}$ | B1 | |
| Scale factor $\frac{1}{2}$ in the $x$-direction | B1 | |
| Translation $\begin{pmatrix} 0 \\ -3 \end{pmatrix}$ or translation of 3 units in negative $y$-direction | B1 | |
| **Total** | **3** | |
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(10, 9)$ | B1 B1 | B1 for each correct co-ordinate |
| **Total** | **2** | |2 The graph of $y = \mathrm { f } ( x )$ is transformed to the graph of $y = \mathrm { f } ( 2 x ) - 3$.
\begin{enumerate}[label=(\alph*)]
\item Describe fully the two single transformations that have been combined to give the resulting transformation.\\
The point $P ( 5,6 )$ lies on the transformed curve $y = \mathrm { f } ( 2 x ) - 3$.
\item State the coordinates of the corresponding point on the original curve $y = \mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2021 Q2 [5]}}