C3-C4 Linear transformations and invariant points Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Which matrix represents reflection in the x-axis?

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

2. Which matrix represents rotation of 90 degrees anticlockwise about the origin?

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

3. What is the matrix for a stretch with scale factor 3 parallel to the x-axis?

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

4. What is an invariant point of a linear transformation?

   • A point that is reflected in the line y = x
   • A point that maps to itself
   • A point that maps to the origin
   • A point whose image is at infinity

5. Under M = [[2, 1], [1, 2]], what is the image of (1, 1)?

   • (3, 3)
   • (1, 3)
   • (0, 0)
   • (2, 1)

6. Which lines through the origin are invariant under M = [[2, 1], [1, 2]]?

   • y = x and y = -x
   • x = 0 only
   • y = x only
   • y = 2x and y = x/2

7. Which set describes the invariant points of [[1, 2], [0, 3]]?

   • No invariant points, since the matrix moves every non-zero point away
   • All points on the y-axis, since the matrix fixes every point with x = 0
   • Only the origin (0, 0), since it is the only point fixed by the matrix
   • All points on the x-axis, (x, 0)

8. Which points are invariant under the transformation with matrix [[0, 1], [1, 0]]?

   • No points at all
   • All points on the line y = x
   • All points on the line y = -x
   • Only the origin

9. What is the area scale factor of the transformation [[3, 0], [0, 2]]?

   • 3
   • 1
   • 5
   • 6

10. Which points are invariant under a rotation of 90 degrees about the origin?

    • Only the origin (0, 0)
    • All points on the y-axis
    • Every point of the plane
    • All points on the x-axis

11. What is the matrix of a reflection in the x-axis followed by a rotation of 90 degrees anticlockwise?

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

12. A transformation maps (1, 0) to (2, 1) and (0, 1) to (1, 2). What is its matrix?

    • [[1, 2], [2, 1]]
    • [[2, 0], [1, 2]]
    • [[2, 2], [1, 1]]
    • [[2, 1], [1, 2]]

13. What is the image of (1, 2) under M^2 where M = [[0, 1], [-1, 0]]?

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

14. Which describes the invariant points of [[3, 1], [0, 2]]?

    • The whole line y = -2x
    • Every point on the x-axis
    • Only the origin
    • The line y = 2x

15. Which matrix represents a reflection in the line y = x?

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

16. Which matrix represents an enlargement of scale factor 2 about the origin?

    • [[0, 2], [2, 0]]
    • [[2, 0], [0, 2]]
    • [[1, 2], [2, 1]]
    • [[2, 0], [0, 1]]

17. Which matrix represents the shear (x, y) to (x + y, y)?

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

18. What is the image of (3, -2) under [[0, 1], [1, 0]]?

    • (-2, 3)
    • (2, -3)
    • (3, -2)
    • (-3, 2)

19. Which matrix represents rotation of 180 degrees about the origin?

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

20. Which points are invariant under the identity transformation [[1, 0], [0, 1]]?

    • Only points on the x-axis
    • Only the origin
    • No points
    • Every point of the plane

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