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Chapter 1 Practice Paper: Number: structure and calculation — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH1

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 1 Practice Paper

Number: structure and calculation

Duration: 40 minutes
Total: 30 marks
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Class:
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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.
  • You may use a ruler and graph paper, but not a calculator.
  • 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 for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 1: ordering and place value, the four operations with integers, decimals and fractions, order of operations and reciprocals, prime factorisation with HCF and LCM, systematic listing and the product rule for counting, powers and roots, and estimating roots (Higher).

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

    Work out −3 + 8 − 4.

    1. A−9
    2. B−1
    3. C1
    4. D9
    ( )
  2. 2

    The greatest number that divides exactly into both 24 and 36 is

    1. A12
    2. B6
    3. C72
    4. D864
    ( )
  3. 3

    Work out 2⁴.

    1. A8
    2. B6
    3. C24
    4. D16
    ( )
  4. 4

    0.6 written as a fraction in its simplest form is

    1. A6⁄10
    2. B3⁄5
    3. C3⁄10
    4. D60⁄100
    ( )
  5. 5

    Which list starts with the smallest number?

    1. A−2, −5, 0, 3
    2. B0, −2, −5, 3
    3. C−5, −2, 0, 3
    4. D−2, 0, −5, 3
    ( )
  6. 6

    An outfit is one top with one skirt. There are 5 tops and 3 skirts. How many outfits are there?

    1. A15
    2. B8
    3. C30
    4. D125
    ( )
  7. 7

    Work out √144 + ∛8.

    1. A20
    2. B6
    3. C146
    4. D14
    ( )
  8. 8

    Two bells ring every 9 minutes and every 12 minutes. After how many minutes do they next ring together?

    1. A3
    2. B36
    3. C108
    4. D18
    ( )
  9. 9

    Work out 5³.

    1. A15
    2. B243
    3. C125
    4. D35
    ( )
  10. 10

    Work out 3.08 × 100.

    1. A308
    2. B30.8
    3. C3080
    4. D0.0308
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer.

  1. 11

    This question is about fractions and reciprocals.

    1. (a)

      Add 3⅘ and 2¼, giving your answer as a mixed number in its simplest form.

      [3]
    2. (b)

      Write down the reciprocal of ⅗.

      [1]
  2. 12

    Here are two numbers: 72 and 48.

    1. (a)

      Write 72 as a product of primes, using index notation.

      [2]
    2. (b)

      Given that 48 = 2⁴ × 3, find the smallest number that is a multiple of both 72 and 48.

      [2]
  3. 13

    This question is about the order of operations.

    1. (a)

      Work out 4 × (3 + 2²) − 6 ÷ 2.

      [3]
    2. (b)

      Insert one pair of brackets in 20 + 4 × 3 − 1 to make the statement 20 + 4 × 3 − 1 = 71 correct.

      [1]
  4. 14

    A school uses codes made from digits.

    1. (a)

      A login code is three digits long, and each digit is chosen from 1 to 5. A digit cannot appear twice in the same code. Work out the number of possible codes.

      [2]
    2. (b)

      A different lock allows digits to appear more than once. Work out the number of possible three-digit codes from the digits 1 to 5.

      [2]
  5. 15

    Answer this question without a calculator. (Higher)

    1. (a)

      By considering 8² and 9², explain why √70 must lie between 8 and 9.

      [2]
    2. (b)

      Find an estimate of √70 correct to one decimal place, showing the trial squares you use.

      [2]

— End of paper —