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Topic 1 Practice Paper: Number and types of number — question paper

QuizQuipPractice Series
QQ/IGCSE-MATHS/T1

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

Topic 1 Practice Paper

Number and types of number

Duration: 40 minutes
Total: 30 marks
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Class:
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Date:

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 1: types of number, prime factors, HCF and LCM, set notation and Venn diagrams, powers, roots and reciprocals, and ordering exact values.

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

    Which of these is a prime number?

    1. A35
    2. B41
    3. C51
    4. D57
    ( )
  2. 2

    The highest common factor of 30 and 45 is

    1. A5
    2. B10
    3. C15
    4. D90
    ( )
  3. 3

    Which of these numbers is irrational?

    1. A√50
    2. B0.625
    3. C√49
    4. D22/7
    ( )
  4. 4

    Work out (−4)² − (−4)³.

    1. A48
    2. B−48
    3. C0
    4. D80
    ( )
  5. 5

    The reciprocal of 5/8 is

    1. A−5/8
    2. B8/5
    3. C5/8
    4. D−8/5
    ( )
  6. 6

    Set A = {prime numbers less than 11}. n(A) =

    1. A4
    2. B5
    3. C6
    4. D7
    ( )
  7. 7

    A = {multiples of 3} and B = {multiples of 4}. Which list is A ∩ B?

    1. A{4, 8, 16, 20}
    2. B{3, 9, 15, 21}
    3. C{12, 24, 36}
    4. D{1, 2, 3, 4}
    ( )
  8. 8

    ³√216 =

    1. A3
    2. B36
    3. C72
    4. D6
    ( )
  9. 9

    2⁻³ written as a fraction is

    1. A−8
    2. B1/8
    3. C−1/8
    4. D1/6
    ( )
  10. 10

    Which list is in ascending order?

    1. A−3, −1, 0, 2
    2. B−1, −3, 0, 2
    3. C2, 0, −1, −3
    4. D0, −1, 2, −3
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Use prime factorisation in this question.

    1. (a)

      Write 180 as a product of prime factors, showing your method.

      [2]
    2. (b)

      Given that 84 = 2² × 3 × 7, find the highest common factor of 180 and 84.

      [2]
    3. (c)

      Hence find the smallest number that is a multiple of both 180 and 84.

      [2]
  2. 12

    Of 60 students, 35 study French, 27 study Spanish and 12 study both.

    1. (a)

      Find the number of students who study neither language.

      [2]
    2. (b)

      Find n(F′).

      [1]
    3. (c)

      One student is chosen at random. Find the probability that they study Spanish but not French. Give your answer as a fraction.

      [2]
    4. (d)

      Write down n(F ∪ S) and state what it represents.

      [2]
  3. 13

    Answer this question without a calculator.

    1. (a)

      Write down the value of √225.

      [1]
    2. (b)

      Work out 4³.

      [1]
    3. (c)

      Write 5⁻² as a fraction.

      [1]
    4. (d)

      Write 2⅖ as an improper fraction, then write down its reciprocal.

      [2]
    5. (e)

      Write these in ascending order: 7.05, √50, 43/6. Show your working.

      [2]

— End of paper —