OCR FP1 2008 January — Question 1 4 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeWrite down transformation matrix
DifficultyEasy -1.2 This is a straightforward recall question requiring knowledge of shear transformation matrices. Given that the y-axis is invariant and one image point, students simply need to write down the standard 2×2 shear matrix form and substitute the given information. No problem-solving or derivation is required beyond basic matrix knowledge.
Spec4.03d Linear transformations 2D: reflection, rotation, enlargement, shear

1 The transformation S is a shear with the \(y\)-axis invariant (i.e. a shear parallel to the \(y\)-axis). It is given that the image of the point \(( 1,1 )\) is the point \(( 1,0 )\).
  1. Draw a diagram showing the image of the unit square under the transformation S .
  2. Write down the matrix that represents S .

1 The transformation S is a shear with the $y$-axis invariant (i.e. a shear parallel to the $y$-axis). It is given that the image of the point $( 1,1 )$ is the point $( 1,0 )$.\\
(i) Draw a diagram showing the image of the unit square under the transformation S .\\
(ii) Write down the matrix that represents S .

\hfill \mbox{\textit{OCR FP1 2008 Q1 [4]}}