| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Easy -1.2 This question tests standard recall of transformation matrices from FP1. Part (a) requires memorizing the reflection matrix, part (b)(i) is straightforward identification of a stretch, and part (b)(ii) involves recognizing a rotation matrix from its cos/sin structure. All parts are direct applications of learned material with no problem-solving or novel insight required, making this easier than average even for Further Maths. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| Answer | Marks | Guidance |
|---|---|---|
| \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) | B1B1 2 | Each column correct; SC B2 use correct matrix from MF1; Can be trig form |
| Answer | Marks |
|---|---|
| B1B1 2 | Stretch, in \(x\)-direction sf \(5\) |
| Answer | Marks |
|---|---|
| B1B1 2 | Rotation, \(60°\) clockwise |
## (a)
$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ | B1B1 2 | Each column correct; SC B2 use correct matrix from MF1; Can be trig form
## (b)
### (i)
| B1B1 2 | Stretch, in $x$-direction sf $5$
### (ii)
| B1B1 2 | Rotation, $60°$ clockwise
---\begin{enumerate}[label=(\alph*)]
\item Write down the matrix that represents a reflection in the line $y = x$. [2]
\item Describe fully the geometrical transformation represented by each of the following matrices:
\begin{enumerate}[label=(\roman*)]
\item $\begin{pmatrix} 5 & 0 \\ 0 & 1 \end{pmatrix}$, [2]
\item $\begin{pmatrix} \frac{1}{2} & \frac{1}{2}\sqrt{3} \\ -\frac{1}{2}\sqrt{3} & \frac{1}{2} \end{pmatrix}$. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2010 Q5 [6]}}