| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| 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 on shear transformations. Students need to recognize that a shear parallel to the x-axis has form [[1,k],[0,1]], then use the given point mapping to find k=-1. The diagram in part (i) is routine visualization. While this is Further Maths content, it requires only direct application of a standard formula with minimal problem-solving. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i) Diagram: Blue parallelogram/elliptical shape | M1 | For 2 other correct vertices |
| A1, 2 | For completely correct diagram | |
| Part (ii) Matrix: \(\begin{pmatrix} 1 & -1 \\ 0 & 1 \end{pmatrix}\) | B1, B1, 2 | Each column correct |
**Part (i)** Diagram: Blue parallelogram/elliptical shape | M1 | For 2 other correct vertices
| A1, 2 | For completely correct diagram
**Part (ii)** Matrix: $\begin{pmatrix} 1 & -1 \\ 0 & 1 \end{pmatrix}$ | B1, B1, 2 | Each column correct2 The transformation S is a shear parallel to the $x$-axis in which the image of the point ( 1,1 ) is the point $( 0,1 )$.\\
(i) Draw a diagram showing the image of the unit square under S .\\
(ii) Write down the matrix that represents S .
\hfill \mbox{\textit{OCR FP1 2006 Q2 [4]}}