| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic matrix transformations and inverse properties. Parts (a)-(d) require simple recall and standard matrix multiplication, while part (e) is a routine verification of a standard result. The question involves multiple parts but each is mechanically straightforward with no problem-solving or novel insight required. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03n Inverse 2x2 matrix4.03p Inverse properties: (AB)^(-1) = B^(-1)*A^(-1)4.03q Inverse transformations |
In this question you must show detailed reasoning.
S is the 2-D transformation which is a stretch of scale factor 3 parallel to the x-axis. A is the matrix which represents S.
\begin{enumerate}[label=(\alph*)]
\item Write down A. [1]
\item By considering the transformation represented by $\mathbf{A}^{-1}$, determine the matrix $\mathbf{A}^{-1}$. [2]
\end{enumerate}
Matrix B is given by $\mathbf{B} = \begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}$. T is the transformation represented by B.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Describe T. [1]
\item Determine the matrix which represents the transformation S followed by T. [2]
\item Demonstrate, by direct calculation, that $(\mathbf{BA})^{-1} = \mathbf{A}^{-1}\mathbf{B}^{-1}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q1 [8]}}