| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Linear transformations |
| Type | Extract enlargement and rotation parameters |
| Difficulty | Standard +0.8 This is a Further Maths question requiring understanding that det(A) = product of individual transformation determinants, then working backwards to decompose the transformation. While the determinant calculation is trivial (1 mark), parts (b)-(d) require conceptual understanding of how transformations compose and geometric insight to identify which axis the stretch is parallel to. The multi-step reasoning and need to connect determinants to geometric transformations elevates this above a standard A-level question, though the calculations themselves remain straightforward once the approach is identified. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products4.03f Linear transformations 3D: reflections and rotations about axes4.03h Determinant 2x2: calculation |
The matrix $\mathbf{A}$ is given by $\mathbf{A} = \begin{pmatrix} 0.6 & 2.4 \\ -0.8 & 1.8 \end{pmatrix}$.
\begin{enumerate}[label=(\alph*)]
\item Find $\det \mathbf{A}$. [1]
\end{enumerate}
The matrix $\mathbf{A}$ represents a stretch parallel to one of the coordinate axes followed by a rotation about the origin.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item By considering the determinants of these transformations, determine the scale factor of the stretch. [2]
\item Explain whether the stretch is parallel to the $x$-axis or the $y$-axis, justifying your answer. [1]
\item Find the angle of rotation. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q4 [6]}}