| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Combined transformation matrix product |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring recognition of standard transformations (reflection in y-axis, rotation 90° clockwise) and basic matrix multiplication. While it's Further Maths content, the operations are routine and the transformations are standard examples from the syllabus, making it easier than average overall. |
| Spec | 4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar4.03c Matrix multiplication: properties (associative, not commutative)4.03d Linear transformations 2D: reflection, rotation, enlargement, shear |
1 You are given that the matrix $\left( \begin{array} { r r } - 1 & 0 \\ 0 & 1 \end{array} \right)$ represents a transformation $A$, and that the matrix $\left( \begin{array} { r r } 0 & 1 \\ - 1 & 0 \end{array} \right)$ represents a transformation B .\\
(i) Describe the transformations A and B .\\
(ii) Find the matrix representing the composite transformation consisting of A followed by B .\\
(iii) What single transformation is represented by this matrix?
\hfill \mbox{\textit{OCR MEI FP1 2012 Q1 [5]}}