OCR MEI FP1 2006 June — Question 1 4 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeCombined transformation matrix product
DifficultyEasy -1.3 This question tests basic recall of standard transformation matrices and simple matrix multiplication. Parts (i) and (ii) require only memorization of standard results, while part (iii) involves straightforward 2×2 matrix multiplication with no conceptual difficulty. Despite being Further Maths content, these are foundational transformations that require minimal problem-solving.
Spec4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear

  1. State the transformation represented by the matrix \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\). [1]
  2. Write down the \(2 \times 2\) matrix for rotation through \(90°\) anticlockwise about the origin. [1]
  3. Find the \(2 \times 2\) matrix for rotation through \(90°\) anticlockwise about the origin, followed by reflection in the \(x\)-axis. [2]

\begin{enumerate}[label=(\roman*)]
\item State the transformation represented by the matrix $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$. [1]

\item Write down the $2 \times 2$ matrix for rotation through $90°$ anticlockwise about the origin. [1]

\item Find the $2 \times 2$ matrix for rotation through $90°$ anticlockwise about the origin, followed by reflection in the $x$-axis. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI FP1 2006 Q1 [4]}}