| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear transformations |
| Type | Combined transformation matrix product |
| Difficulty | Moderate -0.8 This question tests standard recall of two basic transformation matrices and their multiplication. Parts (i) and (ii) are direct recall, part (iii) is straightforward matrix multiplication (2×2), and part (iv) requires recognizing the result as a reflection in y=-x. While it's a multi-part question worth several marks, each step is routine with no problem-solving or novel insight required, making it easier than average even for Further Maths. |
| 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 (i) Write down the matrix for a rotation of $90 ^ { \circ }$ anticlockwise about the origin.\\
(ii) Write down the matrix for a reflection in the line $y = x$.\\
(iii) Find the matrix for the composite transformation of rotation of $90 ^ { \circ }$ anticlockwise about the origin, followed by a reflection in the line $y = x$.\\
(iv) What single transformation is equivalent to this composite transformation?
\hfill \mbox{\textit{OCR MEI FP1 2011 Q1 [5]}}