| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | January |
| Marks | 10 |
| Topic | Linear transformations |
| Type | Decompose matrix into transformation sequence |
| Difficulty | Standard +0.3 This is a straightforward Further Maths linear transformations question requiring students to: (i) read coordinates from a diagram to write a 2×2 matrix, (ii) recognize a standard 90° rotation matrix, and (iii) find Q by computing T×P^(-1) and describe it geometrically. All steps are routine applications of matrix multiplication and recognition of standard transformations, making it slightly easier than average even for Further Maths. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03e Successive transformations: matrix products |
9.\\
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The diagram shows the unit square $O A B C$ and its image $O A ^ { \prime } B ^ { \prime } C ^ { \prime }$ under a transformation T .\\
(i) Write down the matrix that represents T .
The transformation T is equivalent to a transformation P followed by a transformation Q . The matrix that represents $P$ is $\left( \begin{array} { r r } 0 & - 1 \\ 1 & 0 \end{array} \right)$.\\
(ii) Give a geometrical description of transformation P .\\
(iii) Find the matrix that represents transformation Q and give a geometrical description of transformation Q .\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q9 [10]}}