Edexcel A-Level Mathematics AS Fp1 6 3 Combinations of Transformations Questions

Practise Edexcel IAL FP1.6.3 by multiplying transformation matrices in the correct order, combining rotations with stretches or enlargements, and evaluating matrix powers.

Exam points

multiply transformation matrices in the correct order to obtain the matrix mapping one shape onto its image
represent a combined rotation and stretch or enlargement with one exact 2×2 matrix
use powers of a transformation matrix, including finding n with Aⁿ = I

[Maximum number: 3]

\mathbf{A}=\left(\begin{array}{cc} -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & -\frac{\sqrt{3}}{2} \end{array}\right)

(a)

Hence determine the smallest positive integer value of n for which $\mathbf{A}^{n}=\mathbf{I}$

The matrix B represents a stretch scale factor 4 parallel to the x-axis.

[ 1 ]

n=12

Cao but can be embedded
ie $A^{12}=I$
(1)

(b)

Determine the matrix C

The parallelogram P is transformed onto the parallelogram $P^{\prime}$ by the matrix C

[ 2 ]

$C=BA= \left(\begin{smallmatrix} 4 & 0\\ 0 & 1 \end{smallmatrix}\right) \left(\begin{smallmatrix} -\frac{\sqrt3}{2} & -\frac12\\ \frac12 & -\frac{\sqrt3}{2} \end{smallmatrix}\right)$ $C= \left(\begin{smallmatrix} -2\sqrt3 & -2\\ \frac12 & -\frac{\sqrt3}{2} \end{smallmatrix}\right)$

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Edexcel A-Level Mathematics AS Fp1 6 3 Combinations of Transformations Questions question 1

Question (a)

Question (b)