GCSE · Rounding & bounds

Upper and lower boundsExam-style questions

Why a rounded value hides half a unit of uncertainty each way, why the upper bound is a strict "less than", how truncation differs, and how to pick the right bounds when calculating — the ÷ and − traps included.

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23 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A runner covers a distance of $d = 84$ m, correct to the nearest metre, in a time of $t = 6.2$ s, correct to 1 decimal place.

Work out the upper bound of the average speed $\dfrac{d}{t}$ . Give your answer to 2 decimal places.
Level 5 · 3 marksTry it
2
$k = \dfrac{a}{b}$ , where $a = 5.4$ and $b = 1.8$ , each correct to 1 decimal place.

By considering bounds, work out the value of $k$ to a suitable degree of accuracy. You must show all your working and give a reason for your answer.
Level 5 · 4 marksTry it
3
$x = 7.2$ and $y = 4.5$ , each correct to 1 decimal place.

Work out the lower bound of $x - y$ .
Level 5 · 3 marksTry it
4
A cyclist covers a distance of $d = 150$ m, correct to the nearest $10$ m, in a time of $t = 12.4$ s, correct to $1$ decimal place.

Work out the lower bound of the cyclist's average speed. Give your answer correct to 3 significant figures.
Level 5 · 3 marksTry it
5
$v = \dfrac{x}{y}$ , where $x = 9.6$ and $y = 3.2$ , each correct to $1$ decimal place.

By considering bounds, work out the value of $v$ to a suitable degree of accuracy. You must show your working and give a reason for your answer.
Level 5 · 4 marksTry it

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