Unit 3: Geometry and Trigonometry
Topic 3.9: Matrix transformations (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 3.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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A unit square (area 1) is transformed by a matrix with det = −7. Its image has area:
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If det A = 4 and det B = 3, then det(AB) equals:
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To enlarge a triangle about the origin, you transform:
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The matrix is applied to the point P(2, 1). Find the image P′.
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A 90° clockwise rotation about the origin has matrix:
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A logo is rotated 90° anticlockwise about the origin. Write down the transformation matrix and find the image of the point Q(3, 5).
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A square has vertices O(0,0), A(1,0), B(1,1), C(0,1). The matrix is applied. Find the images of A, B and C.
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A region of area 7 m² is transformed by . Find the area of the image and comment on its orientation.
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A triangle of area 5 is transformed by . Find the image area and state what the sign of the determinant indicates.
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A motif is rotated by and then enlarged by .
(a) Find the single matrix that does 'rotate then enlarge'.
(b) The motif's area is 4 units². Find its image area.
(a) Find the single matrix that does 'rotate then enlarge'.
(b) The motif's area is 4 units². Find its image area.
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A transformation matrix has determinant 0. This means:
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Which statement about composing transformations is TRUE?
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Find the single matrix that applies first and then .
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Describe fully the single transformation represented by .
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A navigation system rotates a heading vector by 30° anticlockwise about the origin using a matrix R.
(a) Write down R, giving entries to 3 s.f.
(b) Find the image of the unit vector (1, 0).
(a) Write down R, giving entries to 3 s.f.
(b) Find the image of the unit vector (1, 0).
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