A rounded value has a range
A value given to a degree of accuracy could really be anything in a range half a unit either side of it.
Pick bounds for max or min result
For a sum/product use both upper (or both lower); for a difference/quotient mix them: UB(a−b)=UB(a)−LB(b), UB(a÷b)=UB(a)÷LB(b).
Drawn from real examiner reports.
Using 28.499… instead of 28.5
The upper bound is the exact halfway value (28.5), not a string of 9s like 28.499 — terminating decimals just below it are not accepted.
Penalised on Nov 2024 Paper 1H (Q21).
Mixing upper and lower bounds in one formula
Substituting a mixture (e.g. an upper bound for one quantity and the rounded value for another) loses marks.
Seen on Nov 2024 Paper 1H (Q21).
Substituting the rounded values
Putting the given (rounded) numbers into the formula and then "finding bounds" of the result scores nothing.
Seen on Nov 2024 Paper 1H (Q21).
Wrong bound for a subtraction or division
To MAXIMISE or , take the upper bound of but the LOWER bound of : . Using makes the result too small. Difference and quotient mix the bounds; sum and product do not.
(general exam technique)
Halving the wrong unit
The bound is half of the rounding UNIT, not half the value. To the nearest m, m gives (half of ); to d.p., go either side. Using whatever the stated accuracy is a frequent slip.
(general exam technique)
Give the answer to the accuracy asked
If asked for an answer to 3 s.f., round at the end — don't leave 12.750… unrounded.
Write both bounds before substituting
List and for every quantity first, e.g. . With both written down, choosing the right combination for the largest or smallest result becomes mechanical instead of guesswork.
Decide max or min before you start
Read whether the question wants the greatest or least value, then set each bound accordingly: the biggest result needs the biggest top and the smallest bottom. Deciding the direction first stops you mixing bounds mid-calculation.
A measurement rounded to the nearest lies within of the stated value:
12 cm to the nearest cm — bounds?
A length cm, measured to the nearest centimetre. Write down the lower and upper bounds of .