| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Describe enlargement or stretch from matrix |
| Difficulty | Moderate -0.8 This is a straightforward recall question testing recognition of standard transformation matrices (enlargement, reflection, stretch, rotation). Each part requires identifying a basic transformation type with minimal calculation, making it easier than average even for Further Maths students who should know these standard forms. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Enlargement (centre \(O\)) scale factor 6 | B1 | Enlargement (centre O) scale factor 6 |
| 1 mark | ||
| (ii) Reflection; Mirror line is \(y = x\) | B1 | Reflection |
| B1 | Mirror line is \(y = x\) | |
| 2 marks | ||
| (iii) Stretch in \(y\) direction; Scale factor 6, must be a stretch | B1 | Stretch in \(y\) direction |
| B1 | Scale factor 6, must be a stretch | |
| 2 marks | ||
| (iv) Rotation; \(36.9°\) clockwise or equivalent | B1 | Rotation |
| B1 | \(36.9°\) clockwise or equivalent | |
| 2 marks |
**(i)** Enlargement (centre $O$) scale factor 6 | B1 | Enlargement (centre O) scale factor 6
| **1 mark**
**(ii)** Reflection; Mirror line is $y = x$ | B1 | Reflection
| B1 | Mirror line is $y = x$
| **2 marks**
**(iii)** Stretch in $y$ direction; Scale factor 6, must be a stretch | B1 | Stretch in $y$ direction
| B1 | Scale factor 6, must be a stretch
| **2 marks**
**(iv)** Rotation; $36.9°$ clockwise or equivalent | B1 | Rotation
| B1 | $36.9°$ clockwise or equivalent
| **2 marks**7 Describe fully the geometrical transformation represented by each of the following matrices:\\
(i) $\left( \begin{array} { l l } 6 & 0 \\ 0 & 6 \end{array} \right)$,\\
(ii) $\left( \begin{array} { l l } 0 & 1 \\ 1 & 0 \end{array} \right)$,\\
(iii) $\left( \begin{array} { l l } 1 & 0 \\ 0 & 6 \end{array} \right)$,\\
(iv) $\left( \begin{array} { r r } 0.8 & 0.6 \\ - 0.6 & 0.8 \end{array} \right)$.
\hfill \mbox{\textit{OCR FP1 2008 Q7 [7]}}