| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 9 |
| Topic | Linear transformations |
| Type | Find image coordinates under transformation |
| Difficulty | Standard +0.3 This is a standard FP1 matrix transformation question requiring routine application of learned techniques: applying a 2×2 matrix to vertices, finding invariant points by solving (M-I)x=0, and interpreting the determinant. While it involves multiple parts, each step follows textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03g Invariant points and lines4.03h Determinant 2x2: calculation |
The matrix **M** is given by $\mathbf{M} = \begin{pmatrix} -\frac{3}{5} & \frac{4}{5} \\ \frac{4}{5} & \frac{3}{5} \end{pmatrix}$.
\begin{enumerate}[label=(\roman*)]
\item The diagram in the Printed Answer Booklet shows the unit square $OABC$. The image of the unit square under the transformation represented by **M** is $OA'B'C'$. Draw and clearly label $OA'B'C'$. [3]
\item Find the equation of the line of invariant points of this transformation. [3]
\item \begin{enumerate}[label=(\alph*)]
\item Find the determinant of **M**. [1]
\item Describe briefly how this value relates to the transformation represented by **M**. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2017 Q5 [9]}}