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Chapter 7 Practice Paper: Set Language and Notation — question paper

QuizQuipPractice Series
QQ/S3EM/CH7

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 7 Practice Paper

Set Language and Notation

Duration: 40 minutes
Total: 30 marks
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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 7 (N8 Set Language and Notation: membership and subset notation, union, intersection, complement, Venn diagram counting).

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.

  1. 1

    The universal set is ξ = {1, 2, 3, …, 12}. A is the set of even numbers in ξ and B = {4, 8, 12}.

    1. (a)

      List the elements of A.

      [1]
    2. (b)

      State n(A).

      [1]
    3. (c)

      Explain why B ⊆ A.

      [1]
  2. 2

    A is the set of letters in the word MATH and B is the set of letters in the word STUDY.

    1. (a)

      List sets A and B.

      [1]
    2. (b)

      Find A ∩ B.

      [1]
    3. (c)

      Find n(A ∪ B).

      [1]
  3. 3

    Two sets satisfy n(A) = 18, n(B) = 13 and n(A ∩ B) = 7.

    1. (a)

      Find n(A ∪ B).

      [2]
    2. (b)

      Find n(A ∩ B′), the number of elements in A but not in B.

      [1]
    3. (c)

      Describe the four regions of the Venn diagram with their element counts.

      [1]
  4. 4

    In a sports group of 40 students, 28 play netball, 19 play tennis and 5 play neither.

    1. (a)

      Find the number who play at least one of the two sports.

      [2]
    2. (b)

      Find the number who play both sports.

      [2]
  5. 5

    The universal set is ξ = {1, 2, …, 15}. P = {prime numbers in ξ} and Q = {odd numbers in ξ}.

    1. (a)

      List P and Q.

      [2]
    2. (b)

      Find P ∩ Q.

      [1]
    3. (c)

      Find P′ (within ξ).

      [1]
    4. (d)

      Is P ⊆ Q? Give a reason.

      [1]
  6. 6

    Two sets satisfy n(A) = 3x, n(B) = 2x, n(A ∩ B) = x and n(A ∪ B) = 40.

    1. (a)

      Form an equation in x using the counting formula.

      [2]
    2. (b)

      Solve the equation.

      [1]
    3. (c)

      Hence write down the number of elements in A and in B.

      [2]
  7. 7

    In a survey of 60 people, 33 speak French (F), 27 speak Spanish (S) and 12 speak both languages.

    1. (a)

      State the number in each region of the Venn diagram.

      [4]
    2. (b)

      Find n(F ∩ S′).

      [1]
    3. (c)

      How many people speak at least one of the two languages?

      [1]

— End of paper —