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

MathsUKwww.geekhero.co.uk

1.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
2.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.
(a)62 ≤ r < 63
(b)62.35 ≤ r ≤ 62.45
(c)62.35 ≤ r < 62.45
(d)62.3 ≤ r < 62.5
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 triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.
(a)20.000
(b)46.750
(c)23.375
(d)16.875
5.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.
(a)14.5 < l < 15.5
(b)14.5 ≤ l < 15.5
(c)14 ≤ l < 16
(d)14.5 ≤ l ≤ 15.5
6.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.
(a)33.2
(b)31.2
(c)32.2
(d)10.2
7.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.
(a)No — the actual mass is exactly 1,000 g
(b)Yes — the actual mass could be as low as 995 g
(c)Yes — the actual mass could be as low as 990 g
(d)No — the actual mass is at least 999.5 g
8.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
9.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
10.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
11.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
12.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
13.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
14.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.
(a)the nearest whole number
(b)it cannot be given to any degree of accuracy
(c)the nearest 0.1
(d)the nearest 10
15.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

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