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Chapter 4 Practice Paper: Estimation, rounding and bounds — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH4

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

Chapter 4 Practice Paper

Estimation, rounding and bounds

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.
  • Where a question asks for an estimate, show your rounded calculation.
  • 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 4: rounding to d.p. and s.f., estimating with 1 s.f., error intervals for rounding and truncation, standard units with decimals, and upper and lower bounds of sums, products, quotients and speeds (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

    Round 5.271 to 1 decimal place.

    1. A5.3
    2. B5.2
    3. C5.27
    4. D5.0
    ( )
  2. 2

    Round 8264 to 2 significant figures.

    1. A8200
    2. B8260
    3. C8300
    4. D8000
    ( )
  3. 3

    Round 0.02068 to 2 significant figures.

    1. A0.02
    2. B0.021
    3. C0.0207
    4. D0.020
    ( )
  4. 4

    Using 1 s.f. rounding, 41.2 × 8.7 is approximately

    1. A40 × 9 = 360
    2. B41 × 8 = 328
    3. C40 × 8 = 320
    4. D42 × 9 = 378
    ( )
  5. 5

    A number v is 12, rounded to 2 significant figures. Its error interval is

    1. A11.5 ≤ v < 12.5
    2. B11.95 ≤ v < 12.05
    3. C12 ≤ v < 12.5
    4. D10 ≤ v < 14
    ( )
  6. 6

    A number is truncated to 1 d.p. and shows 6.3. The error interval is

    1. A6.25 ≤ x < 6.35
    2. B6.3 ≤ x ≤ 6.4
    3. C6.25 < x ≤ 6.35
    4. D6.3 ≤ x < 6.4
    ( )
  7. 7

    Write 90 minutes in hours as a decimal.

    1. A0.9 hours
    2. B1.5 hours
    3. C1.05 hours
    4. D90 hours
    ( )
  8. 8

    The lower bound of m = 3.6 to 1 d.p. is

    1. A3.6
    2. B3.56
    3. C3.65
    4. D3.55
    ( )
  9. 9

    With a = 5.2 and b = 1.4 (both to 1 d.p.), the upper bound of a × b is

    1. A7.28
    2. B7.2
    3. C7.6125
    4. D6.9525
    ( )
  10. 10

    A runner covers 400 m (nearest metre) in 50 s (nearest second). The maximum speed is

    1. A8 m/s
    2. B8.17 m/s
    3. C7.84 m/s
    4. D8.1 m/s
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Rounding in context.

    1. (a)

      A pencil is 17.86 cm long. Round this to 1 decimal place and to 2 significant figures.

      [2]
    2. (b)

      A town’s population is 128 500. Round this to 3 significant figures.

      [2]
  2. 12

    Estimation.

    1. (a)

      By rounding each number to 1 significant figure, estimate the value of (58.3 × 6.9) ÷ 21.4.

      [3]
    2. (b)

      Is the exact answer larger or smaller than your estimate? Give a reason.

      [1]
  3. 13

    Intervals of possible values.

    1. (a)

      A ladder is 4.2 m long to 1 d.p. Write an error interval for its length, l.

      [2]
    2. (b)

      A different measurement, 2.8 m, was truncated to 1 d.p. Write an error interval for it.

      [2]
  4. 14

    Combined uncertainty. (Higher)

    1. (a)

      j = 6.1 and k = 3.4, both to 1 d.p. Find the bounds of j + k and j × k.

      [3]
    2. (b)

      Work out the upper and lower bounds of the quotient j ÷ k, giving your answers to 3 significant figures.

      [2]
  5. 15

    The weight limit decision. (Higher)

    1. (a)

      A lift’s safe load is 400 kg. Six boxes each weigh 68 kg to 2 s.f. Can the lift be certain the boxes together are under the limit? Show your bounds.

      [3]

— End of paper —