OCR MEI FP1 2011 June — Question 1 5 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeCombined transformation matrix product
DifficultyModerate -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.
Spec4.03a 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
  1. Write down the matrix for a rotation of \(90 ^ { \circ }\) anticlockwise about the origin.
  2. Write down the matrix for a reflection in the line \(y = x\).
  3. Find the matrix for the composite transformation of rotation of \(90 ^ { \circ }\) anticlockwise about the origin, followed by a reflection in the line \(y = x\).
  4. What single transformation is equivalent to this composite transformation?

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?

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