Number 5
4 marks · NormalA milk bottle is filled to 1.25 litres, measured to the nearest 0.05 litre.
Write down the lower and upper bounds for the volume of the milk bottle.
If you pour out 0.30 litres (measured to the nearest 0.01 litre), what is the greatest possible amount of milk left in the bottle?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Lower bound: 1.225 litres, Upper bound: 1.275 litres
(b) 1.275 - 0.29 = 0.985 litres
Common mistakes: Incorrect application of bounds (e.g. not halving the accuracy)
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Lower bound: 1.25 - 0.025 = 1.225 litres.
B2 (a) · 1 mark · Upper bound: 1.25 + 0.025 = 1.275 litres.
M1 (b) · 1 mark · Recognises upper bound of bottle and lower bound of amount poured out.
A1 (b) · 1 mark · Correct calculation of greatest possible amount: 1.275 - 0.29 = 0.985 litres.
Worked solution
a) Lower bound = 1.25 - 0.025 = 1.225 litres. Upper bound = 1.25 + 0.025 = 1.275 litres. b) Greatest possible amount left = upper bound of volume - lower bound of poured: 1.275 - 0.29 = 0.985 litres.