| Exam Board | Edexcel |
|---|---|
| Module | CP1 (Core Pure 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Extract enlargement and rotation parameters |
| Difficulty | Moderate -0.3 This question tests standard knowledge of transformation matrices (rotation and enlargement) with straightforward calculations. Part (a) requires recognizing that k is the scale factor (found from matrix entries) and θ from the rotation matrix form—both routine procedures. Part (b) applies the area scale factor property (k²). While it involves multiple steps and some matrix manipulation, these are well-practiced techniques without requiring problem-solving insight, making it slightly easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03i Determinant: area scale factor and orientation |
The transformation $P$ is an enlargement, centre the origin, with scale factor $k$, where $k > 0$
The transformation $Q$ is a rotation through angle $\theta$ degrees anticlockwise about the origin.
The transformation $P$ followed by the transformation $Q$ is represented by the matrix
$$\mathbf{M} = \begin{pmatrix} -4 & -4\sqrt{3} \\ 4\sqrt{3} & -4 \end{pmatrix}$$
\begin{enumerate}[label=(\alph*)]
\item Determine
\begin{enumerate}[label=(\roman*)]
\item the value of $k$,
\item the smallest value of $\theta$
\end{enumerate}
[4]
A square $S$ has vertices at the points with coordinates $(0, 0)$, $(a, -a)$, $(2a, 0)$ and $(a, a)$ where $a$ is a constant.
The square $S$ is transformed to the square $S'$ by the transformation represented by $\mathbf{M}$.
\item Determine, in terms of $a$, the area of $S'$
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel CP1 2021 Q1 [6]}}