Bounds worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
Ben writes down three measurements.
The length of a table is 260 cm, correct to the nearest 10 cm.
The mass of a book is 1.2 kg, correct to 1 decimal place.
The capacity of a bottle is 850 ml, correct to the nearest 50 ml.
(a)Write down the upper bound of the length of the table.
(b)Write down the lower bound of the mass of the book.
(c)Write down the upper bound of the capacity of the bottle.
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6 marks
Amara weighs two parcels.
Parcel A has a mass of 7.1 kg, correct to 1 decimal place.
Parcel B has a mass of 5.4 kg, correct to 1 decimal place.
(a)Calculate the upper bound of the total mass of the two parcels.
(b)Calculate the upper bound of the difference between the two masses.
(c)Calculate the lower bound of the difference between the two masses.
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6 marks
A rectangular tile has a length of 24 cm and a width of 19 cm.
Both measurements are correct to the nearest centimetre.
(a)Calculate the upper bound of the area of the tile.
(b)Calculate the lower bound of the area of the tile.
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5 marks
A cyclist cycles 510 m, correct to the nearest 10 m.
It takes 77.2 seconds, correct to the nearest 0.1 seconds.
\(\text{average speed} = \text{distance} \div \text{time}\)
(a)Work out the upper bound of the average speed.
Give your answer in m/s correct to 3 significant figures.
(b)Work out the lower bound of the average speed.
Give your answer in m/s correct to 3 significant figures.
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6 marks
\(x = \dfrac{ a }{ b }\)
\(a = 48.5\) correct to 1 decimal place.
\(b = 17.1\) correct to 1 decimal place.
(a)Find the upper bound of \(x\).
Give your answer to 4 significant figures.
(b)Find the lower bound of \(x\).
Give your answer to 4 significant figures.
(c)Use your answers to parts (a) and (b) to write down the value of \(x\) to a suitable degree of accuracy.
Explain your answer.
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4 marks
A storage tank holds 160 litres of water, correct to the nearest 10 litres.
Each flask holds 1.7 litres, correct to the nearest 0.1 litres.
Work out the greatest number of flasks that can definitely be filled completely from the storage tank.
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3 marks
Amara writes down three measurements.
The length of a table is 200 cm, correct to the nearest 10 cm.
The mass of a book is 1.9 kg, correct to 1 decimal place.
The capacity of a bottle is 550 ml, correct to the nearest 50 ml.
(a)State the upper bound of the length of the table.
(b)State the lower bound of the mass of the book.
(c)State the upper bound of the capacity of the bottle.
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6 marks
Idris weighs two parcels.
Parcel A has a mass of 4.2 kg, correct to 1 decimal place.
Parcel B has a mass of 3.5 kg, correct to 1 decimal place.
(a)Work out the upper bound of the total mass of the two parcels.
(b)Work out the upper bound of the difference between the two masses.
(c)Work out the lower bound of the difference between the two masses.
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6 marks
A rectangular mirror has a length of 26 cm and a width of 14 cm.
Both measurements are correct to the nearest centimetre.
(a)Calculate the upper bound of the area of the mirror.
(b)Calculate the lower bound of the area of the mirror.
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5 marks
A remote-controlled car travels 530 m, correct to the nearest 10 m.
It takes 97.5 seconds, correct to the nearest 0.1 seconds.
\(\text{average speed} = \text{distance} \div \text{time}\)
(a)Calculate the upper bound of the average speed.
Give your answer in m/s correct to 3 significant figures.
(b)Calculate the lower bound of the average speed.
Give your answer in m/s correct to 3 significant figures.
Answers
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(a) \(265\ \text{cm}\)
(b) \(1.15\ \text{kg}\)
(c) \(875\ \text{ml}\) -
(a) \(12.6\ \text{kg}\)
(b) \(1.8\ \text{kg}\)
(c) \(1.6\ \text{kg}\) -
(a) \(477.75\ \text{cm}^2\)
(b) \(434.75\ \text{cm}^2\) -
(a) \(6.68\ \text{m/s}\)
(b) \(6.54\ \text{m/s}\) -
(a) \(2.848\)
(b) \(2.825\)
(c) \(x = 2.8\) to 2 significant figures, because the upper bound 2.848 and the lower bound 2.825 both round to 2.8 to 2 significant figures but differ at the third figure. - \(88\ \text{flasks}\)
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(a) \(205\ \text{cm}\)
(b) \(1.85\ \text{kg}\)
(c) \(575\ \text{ml}\) -
(a) \(7.8\ \text{kg}\)
(b) \(0.8\ \text{kg}\)
(c) \(0.6\ \text{kg}\) -
(a) \(384.25\ \text{cm}^2\)
(b) \(344.25\ \text{cm}^2\) -
(a) \(5.49\ \text{m/s}\)
(b) \(5.38\ \text{m/s}\)