OCR MEI FP1 2012 June — Question 1 5 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeCombined transformation matrix product
DifficultyModerate -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.
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 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 .
  1. Describe the transformations A and B .
  2. Find the matrix representing the composite transformation consisting of A followed by B .
  3. What single transformation is represented by this matrix?

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]}}