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Chapter 2 Practice Paper: Vectors in Two Dimensions — question paper

QuizQuipPractice Series
QQ/S4EM/CH2

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 2 Practice Paper

Vectors in Two Dimensions

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 2 (G7 Vectors in Two Dimensions: notation, translation, arithmetic, magnitude, position vectors, geometric problems).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

  1. 1

    The points A(2, 3) and B(7, 15) are given.

    1. (a)

      Write AB as a column vector.

      [2]
    2. (b)

      Find |AB|.

      [1]
  2. 2

    Given u = (4, −2) and v = (−1, 5), find

    1. (a)

      u + v.

      [2]
    2. (b)

      2u − v.

      [2]
  3. 3

    Triangle T has vertices A(1, 1), B(4, 1) and C(1, 3). It undergoes a translation by (3, −2).

    1. (a)

      Find the coordinates of the image T′.

      [2]
    2. (b)

      Explain why triangle T′ is congruent to triangle T.

      [2]
  4. 4

    The points P(2, 5) and Q(8, 1) are given, and M is the midpoint of PQ.

    1. (a)

      Write down the position vector of M.

      [2]
    2. (b)

      Find |OM|, correct to 3 significant figures.

      [2]
  5. 5

    OABC is a parallelogram with O the origin, OA = (3, 1) and OC = (1, 4).

    1. (a)

      Write down the coordinates of A and C.

      [1]
    2. (b)

      Explain why OB = OA + OC, and hence find B.

      [2]
    3. (c)

      Find |OB|, correct to 3 significant figures.

      [2]
  6. 6

    The points P(1, 2), Q(5, 4) and R(7, 8) are given.

    1. (a)

      Write PQ and QR as column vectors.

      [2]
    2. (b)

      Explain why P, Q and R do not lie on a straight line.

      [3]
  7. 7

    The position vectors of A and B are a = (6, 2) and b = (2, 4).

    1. (a)

      Express AB in terms of a and b, and as a column vector.

      [2]
    2. (b)

      Find |AB|, correct to 3 significant figures.

      [2]
    3. (c)

      M is the midpoint of AB. Write down OM as a column vector.

      [1]

— End of paper —