Pearson Edexcel GCSE (9-1) Mathematics revision notes
Measures and accuracy Revision Notes
Review revision notes for Measures and accuracy in Edexcel Mathematics.
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Measures and accuracy
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Bounds for combined quantities Revision Notes
Constructing bounds
For a value rounded to the nearest unit, use ±0.5 unit; for the nearest tenth, use ±0.05. Thus 6.4 cm correct to the nearest 0.1 cm has bounds 6.35 cm ≤ length < 6.45 cm. The stated value is not automatically an exact value.
Choosing endpoints
For positive multiplication, the minimum product comes from both lower bounds and the maximum from both upper bounds. For division, use lower numerator with upper denominator for the minimum, and upper numerator with lower denominator for the maximum.
Addition and subtraction
For a sum, add all lower bounds to obtain the minimum and all upper bounds to obtain the maximum. For a difference A − B, use lower A − upper B for the minimum and upper A − lower B for the maximum. Keep units consistent before calculating.
Estimating and checking calculations Revision Notes
Making a useful estimate
Round each number to a convenient value before calculating. Choose rounding that makes the arithmetic manageable while keeping the size of the answer clear. For example, 48.7 × 19.6 can be estimated as 50 × 20 = 1000.
Checking an answer
Compare the calculated result with the estimate. A result close in size to the estimate is plausible, although it may not be exact. A result that is much larger or smaller should prompt a check of the operation, signs, decimal places and numbers entered.
Using technology responsibly
A calculator can produce a precise-looking result, but it does not guarantee that the correct numbers or operation were entered. Estimate first or afterwards, then compare the calculator result with the expected size before accepting it.
Limits of Accuracy Revision Notes
Finding bounds
For a value rounded to the nearest whole unit, use half a unit on either side. For a value rounded to the nearest 0.1, use 0.05 on either side; for the nearest 0.01, use 0.005. Write the lower bound with an inclusive inequality and the upper bound with a strict inequality.
Interpreting ranges
A recorded value does not usually identify the exact original value. It identifies an interval of possible values. Check the rounding unit carefully, calculate the half-unit adjustment, and state whether the question asks for a lower bound, an upper bound, or the complete interval.
Combining measured values
When adding rounded measurements, combine their lower bounds to obtain the lower bound for the total. Combine their upper-bound values to identify the limiting upper value, remembering that the actual total is normally less than that value. Show the adjustments and arithmetic clearly.
Rounding and error intervals Revision Notes
Rounding to a stated accuracy
Identify the place value or unit required, then inspect the next digit. A next digit of 5 or more rounds the retained digit up; a next digit below 5 leaves it unchanged. For example, 7.846 rounded to 2 decimal places is 7.85.
Writing error intervals
If a positive number is rounded to the nearest unit u and displayed as r, its interval is r − u/2 ≤ x < r + u/2. The lower boundary is included because it rounds to r, while the upper boundary belongs to the next rounded value.
Truncation intervals
For a positive number truncated to a unit u and displayed as t, the interval is t ≤ x < t + u. The displayed value is included, but the upper boundary is excluded because a value at that boundary would truncate to the next value.
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