OCR MEI FP1 2009 January — Question 3 5 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeFind image coordinates under transformation
DifficultyModerate -0.3 This is a straightforward matrix transformation question requiring reading coordinates from a diagram, writing down a 2×2 matrix, performing matrix multiplication, and describing a composite transformation. All steps are routine FP1 techniques with no novel problem-solving required, making it slightly easier than average but not trivial since it involves multiple parts and matrix operations.
Spec4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar4.03e Successive transformations: matrix products
3 Fig. 3 shows the unit square, OABC , and its image, \(\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }\), after undergoing a transformation. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{35094899-149c-438e-b6c8-b333d2fefc0c-2_465_531_806_806} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. Write down the matrix \(\mathbf { P }\) representing this transformation.
  2. The parallelogram \(\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }\) is transformed by the matrix \(\mathbf { Q } = \left( \begin{array} { r r } 2 & - 1 \\ 0 & 3 \end{array} \right)\). Find the coordinates of the vertices of its image, \(\mathrm { OA } ^ { \prime \prime } \mathrm { B } ^ { \prime \prime } \mathrm { C } ^ { \prime \prime }\), following this transformation.
  3. Describe fully the transformation represented by \(\mathbf { Q P }\).
3 Fig. 3 shows the unit square, OABC , and its image, $\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$, after undergoing a transformation.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{35094899-149c-438e-b6c8-b333d2fefc0c-2_465_531_806_806}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}

(i) Write down the matrix $\mathbf { P }$ representing this transformation.\\
(ii) The parallelogram $\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$ is transformed by the matrix $\mathbf { Q } = \left( \begin{array} { r r } 2 & - 1 \\ 0 & 3 \end{array} \right)$. Find the coordinates of the vertices of its image, $\mathrm { OA } ^ { \prime \prime } \mathrm { B } ^ { \prime \prime } \mathrm { C } ^ { \prime \prime }$, following this transformation.\\
(iii) Describe fully the transformation represented by $\mathbf { Q P }$.

\hfill \mbox{\textit{OCR MEI FP1 2009 Q3 [5]}}
This paper (10 questions)
View full paper
Q1 5 Q2 4 Q3 5 Q4 3 Q5 6 Q6 6 Q7 7 Q8 12 Q9 12 Q10 12