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
The length of a shelf is 45 cm, correct to the nearest centimetre.

(a) Write down the lower bound of the length.

(b) Write down the upper bound of the length.
Level 3 · 2 marksTry it
2
The mass of a cat is $2.7$ kg, correct to $1$ decimal place.

(a) Write down the lower bound of the mass.

(b) Write down the upper bound of the mass.
Level 3 · 2 marksTry it
3
The side of a square is $5.4$ cm, correct to 1 decimal place.

(a) Write down the error interval for the side length, $s$ cm. (2 marks)

(b) Work out the lower bound for the perimeter of the square. (1 mark)
Level 3 · 3 marksTry it
4
A rectangle has length $8.4$ cm and width $5.6$ cm, each measured correct to 1 decimal place.

Work out the upper bound for the area of the rectangle. (3 marks)
Level 3 · 3 marksTry it
5
$x = 7.36$ correct to 2 decimal places. $y = 4.9$ correct to 1 decimal place.

(a) Write down the error interval for $y$ . [2]

(b) Work out the upper bound of $\dfrac{x}{y}$ . Give your answer correct to 3 significant figures. [3]
Level 3 · 5 marksTry it

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