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Bounds practice questions with answers

Higher · Grade 7 · Calculator

A second set of bounds questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Give the lower bound of a length measured as 12 cm to the nearest cm.

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Answer: 11.5

  1. Half unit is 0.5.
  2. 12 - 0.5 = 11.5.
  • Method (1): Half unit is 0.5.
  • Accuracy (1): 12 - 0.5 = 11.5.

Question 2 Easy

Give the upper bound of a length measured as 12 cm to the nearest cm.

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Answer: 12.5

  1. Half unit is 0.5.
  2. 12 + 0.5 = 12.5.
  • Method (1): Half unit is 0.5.
  • Accuracy (1): 12 + 0.5 = 12.5.

Question 3 Medium

Give the upper bound of the area of a 7 cm by 4 cm rectangle measured to the nearest cm.

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Answer: 33.75

  1. Upper bounds: 7.5 and 4.5.
  2. 7.5 × 4.5 = 33.75.
  • Method (1): Upper bounds: 7.5 and 4.5.
  • Accuracy (1): 7.5 × 4.5 = 33.75.

Question 4 Medium

Give the lower bound of the area of a 7 cm by 4 cm rectangle measured to the nearest cm.

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Answer: 22.75

  1. Lower bounds: 6.5 and 3.5.
  2. 6.5 × 3.5 = 22.75.
  • Method (1): Lower bounds: 6.5 and 3.5.
  • Accuracy (1): 6.5 × 3.5 = 22.75.

Question 5 Hard

Distance is 8 m to the nearest metre and time is 2 s to the nearest second. Find the lower bound of speed.

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Answer: 3

  1. Lower distance 7.5, upper time 2.5.
  2. 7.5 ÷ 2.5 = 3.
  • Method (1): Lower distance 7.5, upper time 2.5.
  • Accuracy (1): 7.5 ÷ 2.5 = 3.

Question 6 Hard

Distance is 13 m to the nearest metre and time is 2 s to the nearest second. Find the lower bound of speed.

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Answer: 5

  1. Lower distance 12.5, upper time 2.5.
  2. 12.5 ÷ 2.5 = 5.
  • Method (1): Lower distance 12.5, upper time 2.5.
  • Accuracy (1): 12.5 ÷ 2.5 = 5.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A rectangle is 12 cm by 3 cm. Both lengths are measured to the nearest cm. Work out the upper bound of the area of the rectangle.

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Answer: 43.75

  1. Find upper bound of length: 12 + 0.5 = 12.5.
  2. Find upper bound of width: 3 + 0.5 = 3.5.
  3. Multiply upper bounds: 12.5 × 3.5.
  4. 12.5 × 3.5 = 43.75.
  5. State upper bound of area is 43.75 cm².
  • Method (1): 12.5 × 3.5
  • Accuracy (1): 43.75

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What is the lower bound of 7 cm to the nearest cm?

  1. 11.5 cm
  2. 6.5 cm
  3. 38.25 cm²
Show answer

6.5 cm Subtract half the unit: 7 - 0.5 = 6.5 cm.

Check 2

What is the upper bound of 7 cm to the nearest cm?

  1. 20.5 cm
  2. 26.25 cm²
  3. 7.5 cm
Show answer

7.5 cm Add half the unit: 7 + 0.5 = 7.5 cm.

Check 3

How far can a nearest-centimetre reading be wrong?

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Up to half a centimetre either side. Up to half a centimetre either side.

Check 4

Lower bound of 12 cm to the nearest cm?

  1. 26.25 cm²
  2. 11.5 cm
  3. 6.5 cm
Show answer

11.5 cm 12 - 0.5 = 11.5 cm.

Check 5

Upper bound of 20 cm to the nearest cm?

  1. 11.5 cm
  2. 26.25 cm²
  3. 20.5 cm
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20.5 cm 20 + 0.5 = 20.5 cm.

Check 6

Which bounds give the greatest area?

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Multiply upper bound by upper bound. Multiply upper bound by upper bound.

Check 7

Which bounds give the least area?

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Multiply lower bound by lower bound. Multiply lower bound by lower bound.

Check 8

Upper area of an 8 cm by 4 cm rectangle to the nearest cm?

  1. 11.5 cm
  2. 20.5 cm
  3. 38.25 cm²
Show answer

38.25 cm² 8.5 × 4.5 = 38.25 cm².

Check 9

Lower area of an 8 cm by 4 cm rectangle to the nearest cm?

  1. 7.5 cm
  2. 26.25 cm²
  3. 20.5 cm
Show answer

26.25 cm² 7.5 × 3.5 = 26.25 cm².

Check 10

Why not use 8 × 4.5 as the upper area?

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Both dimensions must be at their upper bounds. Both dimensions must be at their upper bounds.

Check 11

Upper area of a 10 cm by 6 cm rectangle to the nearest cm?

  1. 7.5 cm
  2. 68.25 cm²
  3. 6.5 cm
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68.25 cm² 10.5 × 6.5 = 68.25 cm².

Check 12

Upper bound of a quotient uses which combination?

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Upper numerator divided by lower denominator. Upper numerator divided by lower denominator.

Check 13

Lower bound of a quotient uses which combination?

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Lower numerator divided by upper denominator. Lower numerator divided by upper denominator.

Check 14

What is 9.5 × 5.5?

  1. 52.25
  2. 53.25
  3. 9.5
Show answer

52.25 52.25, the lower area of 10 cm by 6 cm.

Check 15

A student adds 1 cm for the upper bound. What is the error?

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The half-unit error has been doubled. The half-unit error has been doubled.

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