Mathematics for IGCSE & O level - Limits Of Accuracy (Section 3)
1
A rectangular room measures 5.2 m by 3.69 m, both to the nearest centimeter. What is the upper bound of the perimeter of the room?
Answer
(D)
17.81 m
2
A volume is given as 468 ml to the nearest milliliter. What is the lower bound of this volume?
Answer
(B)
467.5 mL
3
A length of string is measured to be 27 cm to the nearest cm. Between which values must the actual length lie?
Answer
(B)
26.5 cm - 27.5 cm
4
A water tank measures 80 cm by 75 cm by 90 cm, to the nearest cm. What is the maximum volume of the tank?
Answer
(C)
551,487.375 cm³
5
A mass is given as 30 cm to the nearest 10 cm. What is the upper bound of this measurement?
Answer
(C)
35 cm
6
What is the lower bound of the area, for the given measurements; length is 17.8 cm to the nearest millimetre and width is 21.0 to 3 s.f?
Answer
(A)
373.595 cm²
7
The density of a bar of gold is 19.3 g/cm³, correct to the nearest 0.1 g/cm³. A bar of gold measures 8.6 cm by 4.1 cm by 2.4 cm, correct to the nearest mm. What is the smallest possible mass of the gold bar?
Answer
(D)
1697 g
8
What is the upper bound of the area for the measurements of 5.2m by 3.69 m, with both measurements to the nearest centimetre?
Answer
(C)
19.21 m²
9
What is the lower bound of the measurement 9.81 seconds, to the nearest hundredth of a second?
Answer
(B)
9.805 s
10
A rectangle measures 12 cm by 5 cm, with both measurements correct to the nearest cm. What is the greatest possible perimeter?
Answer
(C)
35.0 cm
11
The length of a rectangle is 19 cm (correct to the nearest cm) and its width is 27 cm (correct to the nearest cm). Which of the following is/are a possible area of this rectangle?
Answer
A
B
C
D
12
A height is given as 4.7 m to 1 decimal place. What is the lower bound of the actual height?
Answer
(B)
4.65 m
13
If the length of a paper is 21.0 cm and a piece of A4 paper is 29.7 cm. Both are to the nearest millimetre. What is the upper bound of the sum of the areas?
Answer
(D)
50.8 cm
14
If a speed is calculated by dividing distance (14.2 km to 3 s.f.) by time (46 minutes to the nearest minute), what should be done to work out the lower bound speed?
Answer
(A)
Divide 14.15 by 45.5
15
Two stages of a relay race have times of 14.07 seconds and 15.12 seconds, both to the nearest 0.01 second. What is the upper bound of the total time for these two stages?
Answer
(D)
29.22 s
16
Find the upper bound of the difference between 28.7 seconds and 31.4 seconds (both to 3 significant figures).
Answer
(C)
2.75 s
17
Two kitchen cupboards have widths of 300 mm and 500 mm, both correct to the nearest millimeter. What is the lower bound of their combined width when placed next to each other?
Answer
(C)
799.5 mm
18
Find the upper bound of the difference between 24.1 s and 19.8 s, both to the nearest 0.1 s.
Answer
(B)
4.3 s
19
Find the lower bound of the difference between 11.04 s and 13.46 s, both to the nearest hundredth of a second.
Answer
(B)
2.40 s
20
The area of a rectangle is found to be 30 cm² when measurements are rounded to the nearest cm. What would the possible area be?
Answer
(A)
29.5 cm² - 30.5 cm²
21
The area of a room is 21.0 cm² to 3 significant figures, the length is 17.8 cm to the nearest millimetre. To calculate the maximum value for the width, what values should be used?
Answer
(B)
20.95cm² and 17.85cm
22
Find the upper bound of the sum of 11.04 s and 13.46 s, both to the nearest hundredth of a second.
Answer
(D)
24.53 s
23
Find the lower bound of the sum of 11.04 s and 13.46 s (both to the nearest hundredth of a second)
Answer
(A)
24.48 s
24
What is the lower bound of the sum of 28.7 s and 31.4 s, with measurements to 3 significant figures?
Answer
(B)
60.0 s
25
A measurement is given as 27 cm to the nearest centimeter. What interval describes the range of possible values for this measurement?
Answer
(B)
26.5 cm - 27.5 cm
26
The length of a sheet of paper is said to be 26 cm to the nearest cm. What does this mean regarding the accuracy of the measurement?
Answer
(D)
The actual length is between 25.5 cm and 26.5 cm.
27
A container will hold exactly 550 litres. It is measured to 80 cm by 75 cm and 90 cm, to the nearest cm. How does this affect its capacity?
Answer
(B)
The capacity could be less than 550L
28
Find the upper bound of the sum of 28.7 seconds and 31.4 seconds, both to 3 significant figures.
Answer
(C)
60.2 s
29
Find the lower bound of the sum of each of these pairs of measurements: 447 g and 1550 g (both to the nearest g).
Answer
(C)
1997 g
30
The density of gold is 19.3 g/cm³, correct to the nearest 0.1 g/cm³. A bar of gold measures 8.6 cm by 4.1 cm by 2.4 cm, all correct to the nearest mm. What is the greatest possible mass of the gold bar?
Answer
(B)
1700 g
31
A bar of gold is a cuboid. It is measured as 8.6 cm by 4.1 cm by 2.4 cm. All measurements are correct to the nearest millimeter. What is the largest possible volume of the bar of gold?
Answer
(D)
85.20 cm³
32
What is the lower bound of the difference in the lengths, given that 28.7 s is to 3 s.f, and 31.4 s is to 3 s.f?
Answer
(A)
2.6 s
33
A speed is calculated from a distance of 14.2 km (to 3 s.f.) and a time of 46 minutes (to the nearest minute). What is the greatest possible speed?
Answer
(D)
18.9 km/h
34
A piece of red string is 35.2 cm long to the nearest millimeter and a piece of blue string is 12.6 cm long to the nearest millimeter. What is the lower bound of the difference in their lengths (red - blue)?
Answer
(A)
22.55 cm
35
A mass is recorded as 30 cm to the nearest 10 cm. What could the actual mass be?
Answer
(B)
24.9 cm
36
The area of a rectangle is calculated using measurements of length and width. The length is 21.0 cm (to 3 significant figures) and the width is 17.8 cm (to the nearest mm). To calculate the greatest possible area, what values should be used?
Answer
(A)
21.05 cm and 17.85 cm
37
A piece of paper is 21.0 cm long and another is 29.7 cm long. Both measurements are given to the nearest millimetre. What is the upper bound of the total length?
Answer
(D)
50.80 cm
38
The area of a room is calculated using the measurements of 5.2m by 3.69 m, correct to the nearest centimeter. What should be used to calculate the maximum floor area?
Answer
(A)
5.205 m x 3.695 m
39
The length of a piece of paper is measured as 26 cm to the nearest centimeter. What is the lower bound of this measurement?
Answer
(B)
25.5 cm
40
A bar of gold is a cuboid and measures 8.6 cm by 4.1 cm by 2.4 cm. All the measurements are correct to the nearest millimetre. Calculate the greatest possible volume of the gold bar.
Answer
(D)
85.20 cm³
41
A height is given as 4.7 m to 1 decimal place. What is the greatest possible height?
Answer
(C)
4.74 m
42
A winning time is given as 34.91 seconds to the nearest hundredth of a second. What is the lower bound of this time?
Answer
(B)
34.905 s
43
A drain cleaner uses a pole made up of ten identical flexible pieces. Each piece is 1 meter long, measured to the nearest centimeter. What is the minimum length of the drain cleaner's pole?
Answer
(B)
9.95 m
44
If a length is given as 10 cm to the nearest 10 cm, which of the following could be the upper bound?
Answer
(C)
15.0 cm
45
A height is given as 4.7 m to 1 decimal place. Between what values must the actual height lie?
