Printable · GCSE Higher · ages 14-16

Limits of accuracy and bounds worksheet — GCSE Higher

Fifteen questions on "limits of accuracy and bounds" — DfE statement N16. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Limits of accuracy and bounds worksheet — GCSE Higher

Maths · GCSE Higher · N16 · Limits of accuracy and bounds · 15 questions

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1.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.
(a)93.375
(b)93.9975
(c)92.0075
(d)93
2.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.
(a)Yes, the true mass is at least 847.5 kg and at most 850 kg
(b)No, the true mass could be as high as 852.5 kg
(c)Yes, the display reads 850 kg, which is not above the limit
(d)No, 850 kg on the display rounds up to 855 kg
3.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?
(a)1,850
(b)1,799
(c)1,760
(d)1,750
4.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?
(a)They cannot both be describing the same path
(b)Jon's measurement must be wrong
(c)Mia's measurement must be wrong
(d)They must both be describing the same path
5.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?
(a)1.4 ≤ m < 1.6
(b)1.45 ≤ m < 1.55
(c)1.45 < m ≤ 1.55
(d)1.45 ≤ m ≤ 1.55
6.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.
(a)The tape can only give the length to the nearest centimetre
(b)A length in metres must be written to 2 decimal places
(c)A length in metres must be rounded to the nearest metre
(d)The tape can only give the length to the nearest millimetre
7.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.
(a)18.5 ≤ T ≤ 18.7
(b)18.5 ≤ T < 18.7
(c)18.4 ≤ T < 18.8
(d)18.6 ≤ T < 18.8
8.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.
(a)14
(b)10
(c)18
(d)12.9
9.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.
(a)37.5
(b)27.5
(c)36.5
(d)26.5
10.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.
(a)19.5
(b)20
(c)18
(d)21
11.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.
(a)49 km/h
(b)48.54 km/h
(c)52 km/h
(d)50 km/h
12.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.
(a)Yes — Priya's jump could have been up to 3.9 m
(b)No — their possible jump lengths do not overlap
(c)Yes — both jumps could have been 3.85 m
(d)No — a recorded jump is exactly the length jumped
13.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?
(a)£4.55
(b)£4.50
(c)£4.65
(d)£4.80
14.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.
(a)13
(b)13.52
(c)12.44
(d)12.52
15.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.
(a)33.5 mph
(b)33 mph
(c)34.5 mph
(d)34 mph

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