Matrix transformations: IB Mathematics: Applications & Interpretation questions with answers
Free Matrix transformations questions for IB Mathematics: Applications & Interpretation (SL & HL), HL only, part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.
Let R be the matrix representing an anticlockwise rotation of 90° about the origin, and E the matrix representing an enlargement, scale factor 2, centre the origin.
(a)
Write down R and E.
[2]
(b)
Find the single matrix representing the rotation followed by the enlargement.
[2]
(c)
A triangle of area 6 units2 is transformed by this matrix. Find the area of its image.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
R = 0 −11 0, E = 2 00 2
R = 0 −11 0A1 E = 2 00 2A1
2
(b)
0 −22 0
ER (order matters) (M1) 0 −22 0A1
2
(c)
24
|det| = 4 (M1) 24 A1
2
Question 2Structured · 5 marks
The matrix T = 0 −11 0 represents a transformation.
(a)
Describe the transformation.
[2]
(b)
The matrix S = 2 00 2. Find ST and describe the combined transformation.
[2]
(c)
A triangle has area 5 units². Find the area of its image under ST.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
rotation 90° anticlockwise about the origin
rotation A1 90° anticlockwise about O A1
2
(b)
enlargement scale factor 2 with rotation
ST correct A1 rotation 90° then enlargement scale factor 2 A1
2
(c)
20
20 A1
1
Question 3Structured · 6 marks
Let R be the matrix representing an anticlockwise rotation of 90° about the origin, and E the matrix representing an enlargement, scale factor 2, centre the origin.
(a)
Write down R and E.
[2]
(b)
Find the single matrix representing the rotation followed by the enlargement.
[2]
(c)
A triangle of area 8 units2 is transformed by this matrix. Find the area of its image.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
R = 0 −11 0, E = 2 00 2
R = 0 −11 0A1 E = 2 00 2A1
2
(b)
0 −22 0
ER (order matters) (M1) 0 −22 0A1
2
(c)
32
|det| = 4 (M1) 32 A1
2
Question 4Structured · 5 marks
The matrix T = 0 −11 0 represents a transformation.
(a)
Describe the transformation.
[2]
(b)
The matrix S = 3 00 3. Find ST and describe the combined transformation.
[2]
(c)
A triangle has area 5 units². Find the area of its image under ST.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
rotation 90° anticlockwise about the origin
rotation A1 90° anticlockwise about O A1
2
(b)
enlargement scale factor 3 with rotation
ST correct A1 rotation 90° then enlargement scale factor 3 A1
2
(c)
45
45 A1
1
Question 5Structured · 6 marks
Let R be the matrix representing an anticlockwise rotation of 270° about the origin, and E the matrix representing an enlargement, scale factor 3, centre the origin.
(a)
Write down R and E.
[2]
(b)
Find the single matrix representing the rotation followed by the enlargement.
[2]
(c)
A triangle of area 12 units2 is transformed by this matrix. Find the area of its image.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
R = 0 1−1 0, E = 3 00 3
R = 0 1−1 0A1 E = 3 00 3A1
2
(b)
0 3−3 0
ER (order matters) (M1) 0 3−3 0A1
2
(c)
108
|det| = 9 (M1) 108 A1
2
Question 6Structured · 6 marks
Let R be the matrix representing an anticlockwise rotation of 180° about the origin, and E the matrix representing an enlargement, scale factor 2, centre the origin.
(a)
Write down R and E.
[2]
(b)
Find the single matrix representing the rotation followed by the enlargement.
[2]
(c)
A triangle of area 8 units2 is transformed by this matrix. Find the area of its image.
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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in