| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Write down transformation matrix |
| Difficulty | Easy -1.2 This is a straightforward recall question requiring knowledge of shear transformation matrices. Given that the y-axis is invariant and one image point, students simply need to write down the standard 2×2 shear matrix form and substitute the given information. No problem-solving or derivation is required beyond basic matrix knowledge. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
1 The transformation S is a shear with the $y$-axis invariant (i.e. a shear parallel to the $y$-axis). It is given that the image of the point $( 1,1 )$ is the point $( 1,0 )$.\\
(i) Draw a diagram showing the image of the unit square under the transformation S .\\
(ii) Write down the matrix that represents S .
\hfill \mbox{\textit{OCR FP1 2008 Q1 [4]}}