Error Intervals 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.

10 questions 26 marks Sheet 1

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2 marks
A garden cane is 79 cm long, correct to the nearest centimetre.

Its length is \(x\) cm.

Write down the error interval for \(x\).
2 marks
1700 people went to a football match, correct to the nearest 100.

(a)
State the least possible number of people.

(b)
State the greatest possible number of people.
2 marks
A jug has a capacity of 5.8 litres, correct to 1 decimal place.

The capacity is \(x\) litres.

Write down the error interval for \(x\).
4 marks
A garden hose is measured as 54 cm. Its true length is \(x\) cm.

(a)
The measurement has been rounded to the nearest centimetre.

Write down the error interval for \(x\).

(b)
The measurement has instead been truncated to 54 cm.

Write down the error interval for \(x\).
2 marks
A number \(n\) is 2200 correct to 2 significant figures.

Write down the error interval for \(n\).
4 marks
A rectangle has a length of 28 cm and a width of 19 cm.

Both measurements are correct to the nearest centimetre.

(a)
Work out the lower bound of the perimeter of the rectangle.

(b)
Work out the upper bound of the perimeter of the rectangle.
2 marks
A wooden batten is 42 cm long, correct to the nearest centimetre.

Its length is \(x\) cm.

Write down the error interval for \(x\).
2 marks
1900 people went to a football match, correct to the nearest 100.

(a)
State the least possible number of people.

(b)
State the greatest possible number of people.
2 marks
A cat has a mass of 1.6 kg, correct to 1 decimal place.

The mass is \(x\) kg.

Write down the error interval for \(x\).
4 marks
A plank of wood is measured as 13 cm. Its true length is \(x\) cm.

(a)
The measurement has been rounded to the nearest centimetre.

Write down the error interval for \(x\).

(b)
The measurement has instead been truncated to 13 cm.

Write down the error interval for \(x\).

Answers

\(78.5 \leq x < 79.5\)
(a) \(1650\)
(b) \(1749\)
\(5.75 \leq x < 5.85\)
(a) \(53.5 \leq x < 54.5\)
(b) \(54 \leq x < 55\)
\(2150 \leq n < 2250\)
(a) \(92\ \text{cm}\)
(b) \(96\ \text{cm}\)
\(41.5 \leq x < 42.5\)
(a) \(1850\)
(b) \(1949\)
\(1.55 \leq x < 1.65\)
(a) \(12.5 \leq x < 13.5\)
(b) \(13 \leq x < 14\)

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