Estimation & error intervals
AQA GCSE Maths revision on Estimation & error intervals. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A length is measured as 12 cm, rounded to the nearest centimetre. What is the lower bound of this measurement?
- A) 11.5 cm
- B) 11.0 cm
- C) 12.5 cm
- D) 11.9 cm
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Answer: 11.5 cm
When a value is rounded to the nearest unit, the interval is defined by adding and subtracting half of that unit. Since the measurement is to the nearest 1 cm, we subtract 0.5 cm from 12 cm to find the lower bound. This creates an error interval of 11.5 <= x < 12.5.
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Question 2
If a value x is rounded to 2 decimal places, which inequality correctly represents the error interval?
- A) x < 0.005
- B) lower bound <= x < upper bound
- C) lower bound < x <= upper bound
- D) x > 0.01
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Answer: lower bound <= x < upper bound
By convention, when rounding, we include the lower bound because it rounds up to the stated value. We exclude the upper bound because it would round up to the next possible value. This notation is the standard mathematical way to define the range of possible values for a rounded number.
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Question 3
When estimating the result of a complex calculation, why is it usually better to round values to 1 significant figure rather than 2?
- A) It is always more accurate
- B) It simplifies mental arithmetic
- C) It eliminates all rounding error
- D) It makes the answer larger
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Answer: It simplifies mental arithmetic
The primary purpose of estimation is to find a quick, manageable value that is close to the true answer. Using 1 significant figure reduces the complexity of the numbers involved, making mental calculations significantly faster. While less precise than using 2 significant figures, it serves the goal of checking for order-of-magnitude errors.
Want to test yourself on the remaining cards for this topic?
13 more questions on Estimation & error intervals — plus mistakes tracking and spaced repetition across the whole Maths spec.