1.6 Limits of accuracy
Limits of accuracy
Everything on limits of accuracy that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
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A worked example
Error intervals · [2 marks]
A mass x is 28.2 kg, correct to 1 decimal place. Write down the error interval for x.
- B128.15 ≤ x
- B1x < 28.25
The exam skills (5)
Error intervals
- Find half of the unit it was rounded to, e.g. nearest whole number → 0.5.
- Lower bound = value − half. Upper bound = value + half.
- Write it as lower ≤ x < upper.
Watch out: Using ≤ on both sides. The upper bound itself would round up, so it gets <.
Truncation
- Truncating chops the digits off, it never rounds up.
- So the lower bound is the number itself.
- The upper bound is the next value up: write number ≤ x < next.
Watch out: Treating it like rounding and taking 0.5 off. Truncation only goes up from the number.
Upper and lower bounds
- Find the upper (or lower) bound of every measurement.
- Put those bounds into the formula.
- Work it out and include units.
Watch out: Using the measurements as given. Bounds questions need the bounds in the calculation.
Bounds with division
- Biggest answer from a division: biggest top ÷ smallest bottom.
- Smallest answer: smallest top ÷ biggest bottom.
- Write down both bounds you use, then divide.
Watch out: Using the upper bound of both. Dividing by a bigger number makes the answer smaller.
Bounds with subtraction
- Smallest difference: smallest first value − biggest second value.
- Biggest difference: biggest first − smallest second.
- Show both bounds you used.
Watch out: Subtracting lower bound − lower bound. That is neither the biggest nor the smallest.
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