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Date May Example question Marks available 2 Reference code EXM.2.AHL.TZ0.15
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number 15 Adapted from N/A

Question

The matrix A is defined by  A = ( 3 0 0 2 ) .

Pentagon, P, which has an area of 7 cm2, is transformed by A.

The matrix B is defined by  B = 1 2 ( 3 3 3 2 2 3 ) .

B represents the combined effect of the transformation represented by a matrix X, followed by the transformation represented by A.

Describe fully the geometrical transformation represented by A.

[5]
a.

Find the area of the image of P.

[2]
b.

Find the matrix X.

[3]
c.

Describe fully the geometrical transformation represented by X.

[2]
d.

Markscheme

stretch          A1

scale factor 3,          A1

y-axis invariant (condone parallel to the x-axis)          A1

and

stretch, scale factor 2,          A1

x-axis invariant (condone parallel to the y-axis)          A1

[5 marks]

a.

det ( A ) = 6         A1

7 × 6 = 42 c m 2          A1

[2 marks]

b.

B = A X         (A1)

X = A 1 B         (M1)

X = ( 0.866 0.5 0.5 0.866 ) ( = ( 3 2 1 2 1 2 3 2 ) )         A1

[3 marks]

c.

Rotation       A1

clockwise by 30° about the origin       A1

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.9—Matrix transformations
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Topic 3—Geometry and trigonometry

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