Lesson 5.4

5.4 Combination of transformations Quiz: AQA Further Maths, Unit 5

20 questions

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Lesson 5.4, Combination of transformations: 20 multiple choice questions for the AQA GCSE Further Maths (8365), Unit 5: Matrix Transformations, written with Revision Ninja.

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The 20 questions

  1. If transformation A is applied first and then B, what is the combined matrix?

    • A + B
    • BA
    • AB
    • B - A

  2. What single transformation is equivalent to a reflection in x = 0 followed by y = 0?

    • Reflection in y = x
    • 90° rotation
    • 180° rotation
    • Identity transformation

  3. Which single transformation equals a reflection in y = x followed by reflection in y = -x?

    • 180° rotation
    • Reflection in x-axis
    • Reflection in y-axis
    • 90° rotation

  4. Compute [[1, 0], [0, -1]] x [[0, -1], [1, 0]].

    • [[0, -1], [-1, 0]]
    • [[-1, 0], [0, 1]]
    • [[0, 1], [1, 0]]
    • [[1, 0], [0, -1]]

  5. Enlargement by factor 2 is followed by reflection in the x-axis. What is the combined matrix?

    • [[0, 2], [-2, 0]]
    • [[2, 0], [0, -2]]
    • [[-2, 0], [0, 2]]
    • [[2, 0], [0, 2]]

  6. Point (1, 0) is rotated 90 degrees anticlockwise, then reflected in the x-axis. What is the image?

    • (0, 1)
    • (-1, 0)
    • (1, 0)
    • (0, -1)

  7. Enlargement by factor 3 then 90 degree anticlockwise rotation: what is the combined matrix?

    • [[3, 0], [0, 3]]
    • [[0, 3], [-3, 0]]
    • [[0, -3], [-3, 0]]
    • [[0, -3], [3, 0]]

  8. Matrix multiplication for combining transformations is not generally what?

    • Associative
    • Commutative
    • Distributive
    • Invertible

  9. Reflection in y = -x followed by reflection in x = 0 has what combined matrix?

    • [[0, -1], [1, 0]]
    • [[0, -1], [-1, 0]]
    • [[1, 0], [0, -1]]
    • [[0, 1], [-1, 0]]

  10. Three steps: enlargement by 2, then 180 degree rotation, then reflection in the x-axis. What is the combined matrix?

    • [[-2, 0], [0, 2]]
    • [[2, 0], [0, -2]]
    • [[2, 0], [0, 2]]
    • [[-2, 0], [0, -2]]

  11. Using M = [[0, 1], [1, 0]] then N = [[2, 0], [0, 2]], where does (2, 1) go?

    • (2, 4)
    • (4, 2)
    • (2, 1)
    • (1, 2)

  12. Combine a 90 degree anticlockwise rotation with a reflection in x = 0 (rotation applied first). What is the matrix?

    • [[0, -1], [-1, 0]]
    • [[0, -1], [1, 0]]
    • [[1, 0], [0, -1]]
    • [[0, 1], [1, 0]]

  13. Under enlargement by factor 2 then reflection in y = x, what is the image of (1, 1)?

    • (2, 2)
    • (1, 1)
    • (-2, -2)
    • (2, -2)

  14. An enlargement by factor 2 then a 90 degree rotation: by what area factor is the unit square scaled?

    • 2
    • 8
    • 1
    • 4

  15. What is the combined matrix for an enlargement by factor 3 then a 180 degree rotation?

    • [[0, -3], [3, 0]]
    • [[3, 0], [0, 3]]
    • [[-1, 0], [0, -1]]
    • [[-3, 0], [0, -3]]

  16. A point P is reflected in y = x, then rotated 90 degrees anticlockwise, giving (1, -2). What is P?

    • (-2, -1)
    • (-1, -2)
    • (1, -2)
    • (2, 1)

  17. A 90 degree anticlockwise rotation is followed by a 90 degree clockwise rotation. What is the result?

    • The zero matrix
    • A 180 degree rotation
    • The identity
    • A reflection in y = x

  18. What is [[0, -1], [1, 0]] squared?

    • [[0, 1], [-1, 0]]
    • [[0, -1], [1, 0]]
    • I
    • [[-1, 0], [0, -1]]

  19. If transformation M is followed by an enlargement of scale factor 3, what is the combined matrix?

    • M + 3
    • M³
    • 3M
    • M / 3

  20. If an enlargement by factor 2 is applied after N and the total is [[4, 0], [0, 6]], what is N?

    • [[2, 0], [0, 3]]
    • [[4, 0], [0, 6]]
    • [[2, 0], [0, 6]]
    • [[1, 0], [0, 3]]

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