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Topic 14 Practice Paper: Transformations and vectors — question paper

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QQ/IGCSE-MATHS/T14

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 14 Practice Paper

Transformations and vectors

Duration: 40 minutes
Total: 30 marks
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 14: reflections, rotations, translations and enlargements including negative scale factors, column vectors, vector arithmetic, magnitudes, and vector routes in parallelogram diagrams.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    Reflecting (4, 7) in the x-axis gives

    1. A(−4, 7)
    2. B(4, −7)
    3. C(−4, −7)
    4. D(7, 4)
    ( )
  2. 2

    Reflecting (2, 8) in the line y = x gives

    1. A(−2, −8)
    2. B(2, −8)
    3. C(8, 2)
    4. D(−8, −2)
    ( )
  3. 3

    A 90° anticlockwise rotation about O maps (5, 3) to

    1. A(−3, 5)
    2. B(3, −5)
    3. C(−5, −3)
    4. D(5, 3)
    ( )
  4. 4

    After a translation of four units left and six units up, the point (7, 1) lands on

    1. A(11, 7)
    2. B(11, −5)
    3. C(3, −5)
    4. D(3, 7)
    ( )
  5. 5

    Enlarging about the origin with scale factor 3 sends the point (2, −1) to

    1. A(−6, 3)
    2. B(6, −3)
    3. C(5, −4)
    4. D(2, −3)
    ( )
  6. 6

    Halving its distance from the origin, the point (10, −6) is mapped to

    1. A(−10, 6)
    2. B(20, −12)
    3. C(5, −3)
    4. D(−5, 3)
    ( )
  7. 7

    A half-turn about the origin carries the point (3, 5) to

    1. A(−3, −5)
    2. B(3, 5)
    3. C(5, 3)
    4. D(−5, −3)
    ( )
  8. 8

    How long is the vector (8, 15)? (Extended)

    1. A23
    2. B161
    3. C13
    4. D17
    ( )
  9. 9

    Adding the vectors (2, 3) and (5, −1) gives (Extended)

    1. A(−3, 4)
    2. B(3, −4)
    3. C(7, 2)
    4. D(−7, −2)
    ( )
  10. 10

    PQ joins P(2, 5) to Q(6, 8). As a column vector, PQ is (Extended)

    1. A(−4, −3)
    2. B(4, 3)
    3. C(8, 13)
    4. D(3, 4)
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    Describe each single transformation.

    1. (a)

      The transformation (x, y) → (x − 3, y + 4).

      [2]
    2. (b)

      The transformation (x, y) → (−y, −x).

      [3]
  2. 12

    Turning points about the origin.

    1. (a)

      The point (6, −2) is turned through half a revolution about O. Write down its image.

      [2]
    2. (b)

      The same point is then turned through a quarter-turn clockwise about O. Write down its image.

      [3]
  3. 13

    p = (3, −4) and q = (1, 2). (Extended)

    1. (a)

      Find p + q.

      [1]
    2. (b)

      Find 3p − 2q.

      [2]
    3. (c)

      Find |p|.

      [2]
  4. 14

    The parallelogram PQRS has PQ = p and PS = q. M divides PQ so that PM = ½p. (Extended)

    1. (a)

      Write down, in terms of p and q, the vector QS.

      [2]
    2. (b)

      Show that MS = q − ½p.

      [2]
    3. (c)

      With p = (6, 0) and q = (2, 8), write MS as a column vector.

      [1]

— End of paper —