Practise Upper and lower bounds. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
The capacity of a bottle is 520 ml, correct to the nearest 10 ml.
(a) Write down the lower bound for the capacity of the bottle.[1]
(b) Write down the upper bound for the capacity of the bottle.[1]
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(a)Answer: 515 ml
B1 for 515
Worked solution: Half of the unit of accuracy is 5, so the lower bound is \(520 - 5 = 515\)
(b)Answer: 525 ml
B1 for 525
Worked solution: \(520 + 5 = 525\)
Question 2Medium2 marks
A rectangle has length 8 cm and width 5 cm. Both measurements are correct to the nearest centimetre. Work out the upper bound for the perimeter of the rectangle.[2]
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Answer: 28 cm
M1 for using 8.5 or 5.5
A1 for 28
Worked solution: The upper bounds are 8.5 cm and 5.5 cm. \(2 \times (8.5 + 5.5) = 28\) cm
Question 3Hard3 marks
A lift has a sign that says 'Maximum load 630 kg'. The 630 kg is correct to the nearest 10 kg. Eight people want to use the lift together. Each person has a mass of 78 kg, correct to the nearest kilogram.
Can you be sure that the total mass of the eight people is less than the maximum load? You must show all your working.[3]
Show the answer and mark scheme
Answer: No: the people could have a total mass of up to \(8 \times 78.5 = 628\) kg, but the maximum load could be as low as 625 kg.
B1 for 78.5 or 625 seen
M1 for \(8 \times 78.5\) (= 628)
C1 for 'no' (cannot be sure) with a correct comparison of 628 and 625
Worked solution: Upper bound of one person's mass = 78.5 kg, so the total could be up to \(8 \times 78.5 = 628\) kg. Lower bound of the maximum load = 625 kg. 628 > 625, so it is possible that the people are over the limit: you cannot be sure.