Mathematics for IGCSE & O level - Limits Of Accuracy (Section 2)
1
Find the upper and lower bounds of the floor area of a rectangular room, which is 7.6m by 5.2m to the nearest 10cm. What is the upper bound of the area?
Answer
(C)
39.70 m²
2
Calculate, to 3 significant figures, the lower bound of the average speed for those measured times and distances. The distance travelled is 106 m in 10.0 seconds (both values to 3 s.f.)
Answer
(A)
10.5 m/s
3
A measurement of 10 cm is given to the nearest 10 cm. Between what values must the actual measurement lie?
Answer
(B)
5 cm and 15 cm
4
A rectangle measures 12 cm by 5 cm, with both measurements correct to the nearest centimetre. What is the smallest possible area of the rectangle?
Answer
(C)
54.25 cm²
5
Por won the 200m race in a time of 24.2 seconds to the nearest tenth of a second. Which is the correct range of Por's time?
Answer
(B)
24.15 seconds and 24.25 seconds
6
Given that p = 5.1 and q = 8.6, both correct to 1 decimal place, calculate the largest possible value of p-q?
Answer
(A)
-3.6
7
The height of a person is given as 4.7 m to 1 decimal place. The height lies between which two measurements?
Answer
(B)
4.65 m and 4.75 m
8
Calculate, to 3 significant figures, the lower bound of the distance travelled for a speed of 1.54m/second for 8.20 seconds, both values to 3 s.f.
Answer
(B)
12.58 m
9
A piece of red string is 35.2 cm long to the nearest millimetre. The lower bound for the length is
Answer
(B)
35.15 cm
10
In calculating the density, if density = mass/volume, which calculation provides the largest possible density?
Answer
(C)
UB(mass) / LB(volume)
11
A volume is given as 468 ml to the nearest millilitre. Between which two values does the volume lie?
Answer
(B)
467.5 ml and 468.5 ml
12
Calculate, to 3 significant figures, the lower bound of the distance travelled for a speed of 57 km/h for 2.5 hours, both values being to 2 s.f.
Answer
(A)
140 km
13
A winning time is given as 34.91 seconds to the nearest hundredth of a second. Between which two times does the actual winning time lie?
Answer
(B)
34.905 seconds and 34.915 seconds
14
What is the minimum possible difference in length of two strings if one is measured at 20.0 cm and the other is 12.0 cm to the nearest mm?
Answer
(B)
7.95 cm
15
A mass is given as 57 kg to the nearest kilogram. Between which two values does this mass lie?
Answer
(B)
56.5 kg and 57.5 kg
16
Don Quarie ran 100 m in 9.9 s (correct to 1 d.p.). If the speed = distance/time, what is the lower bound of Quarie's speed?
Answer
(C)
10.00 s
17
A runner completes a race in 10.2 seconds to the nearest tenth of a second. What is the minimum possible time taken?
Answer
(A)
10.15 s
18
A town has a population of 108,000 to the nearest 1000. Its area is given as 129 km² to the nearest km². Calculate the upper bound of its population density, giving your answer to 3 significant figures.
Answer
(C)
845 / km²
19
For a quantity calculated as P = V/R. If V=6 and R=1, which bounds are required to give the largest possible value of P?
Answer
(A)
UB(V) and LB(R)
20
A runner completed a 100m race in 12.3 seconds. What is the upper bound of their average speed?
Answer
(D)
8.14 m/s
21
A piece of paper 21.0 cm long is taped onto the end of another piece 29.7 cm long. Both measurements are given to the nearest millimetre. What is the lower bound of the total length?
Answer
(B)
50.65 cm
22
A measurement of a length is given as 128 cm. What is the upper bound of this measurement?
Answer
(D)
128.5 cm
23
A winning time is given as 34.91 seconds to the nearest hundredth of a second. What is the upper bound of the possible time?
Answer
(B)
34.915 s
24
Given that $P = \frac{V}{R}$, and that V = 6 (correct to the nearest whole number), and R = 1 (correct to the nearest whole number), what is the lower bound of P?
Answer
(A)
5.0
25
Find the upper bound of the difference between 947 g and 1550 g, both to the nearest gram.
Answer
(C)
604 g
26
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 lower bound of the total length?
Answer
(B)
50.70 cm
27
Calculate, to 3 significant figures, the minimum width of a rectangle with these dimensions: Area = 21.0 cm² to 3 significant figures, Length = 17.8 cm to the nearest millimetre.
Answer
(A)
1.17 cm
28
A mass is 9.81s. What is the upper and lower bound of 9.81s?
Answer
(B)
9.805 s and 9.815 s
29
Find the upper bound of the sum of 86mm and 98mm (both to the nearest mm).
Answer
(B)
183.5 mm
30
What is the upper bound of the measurement 10.62 seconds, to the nearest hundredth of a second?
Answer
(C)
10.625 s
31
A water tank measures 80 cm by 75 cm by 90 cm, to the nearest cm. The tank is used to fill how many 550 liter containers? Which of the following statements are correct?
Answer
A
C
D
32
A rectangle measures 12 cm by 5 cm, with both measurements correct to the nearest centimeter. What is the smallest possible area of the rectangle?
Answer
(B)
50.25 cm²
33
The sides of a triangle are 7 cm, 8 cm and 10 cm. They are measured to the nearest centimetre. What is the smallest possible perimeter?
Answer
(A)
24 cm
34
Can cycles 14.2km (to 3 significant figures) in a time of 46 minutes (to the nearest minute). What is the lower bound of their average speed in kilometers per hour?
Answer
(A)
18.3 km/h
35
Two stages of a relay race are run in times of 14.07 seconds and 15.12 seconds, both to the nearest 0.01 second. What is the lower bound of the difference between the times for those two stages?
Answer
(A)
1.03 s
36
A triangle has sides of length 7 cm, 8 cm and 10 cm. All measurements are correct to the nearest centimeter. What is the upper bound of the perimeter of the triangle?
Answer
(C)
25.5 cm
37
A volume is given as 468 mL to the nearest millilitre. What is the upper bound of this volume?
Answer
(D)
468.5 mL
38
A runner completes a 200m race in 24.2 seconds to the nearest tenth of a second. What are the upper and lower bounds of the runner's time?
Answer
(B)
24.15 s - 24.25 s
39
A sheet of paper is measured to be 26 cm long to the nearest centimeter. Which of the following ranges represents the possible length of the paper?
Answer
(B)
25.5 cm ≤ length < 26.5 cm
40
Two stages of a relay race are run in 14.07 seconds and 15.12 seconds. Both were measured to the nearest 0.01 second. What is the upper bound of the difference in those times?
Answer
(A)
1.03 s
41
Pencils have a width of 8 mm, to the nearest millimetre. What is the smallest total width of 10 pencils?
Answer
(C)
70.5 mm
42
A water tank measures 80 cm by 75 cm by 90 cm, to the nearest cm. What is the minimum volume of the tank?
Answer
(B)
506,250 cm³
43
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)
24.52 s
44
Find the lower bound of the difference between 16.4 cm and 9.8 cm (both to the nearest mm).
Answer
(A)
6.5 cm
45
A mass is given as 57 kg to the nearest kilogram. What is the upper bound of this measurement?
Answer
(D)
57.5 kg
46
A mass is given as 0.634 kg to the nearest gram. What is the upper bound of this measurement?
Answer
(C)
0.6345 kg
47
The population of a town is 108,000 to the nearest 1000. The area is 129 km² to the nearest km². What is the upper bound for the population density?
Answer
(B)
837.3 km⁻²
48
The population of a town is 108,000 to the nearest 1000. Its area is given as 129 km² to the nearest km². Calculate the lower bound of its population density, giving your answer to 3 significant figures.
Answer
(B)
829 km⁻²
49
Find the upper bound of the difference between 16.4 cm and 9.8 cm, both to the nearest mm.
Answer
(B)
6.6 cm
50
In a race, Don Quarrie ran 100 m in 9.9 s (correct to 1 d.p.). In 1983, Calvin Smith ran it in 9.93 s (correct to 2 d.p.). What can we say about the difference in the running times?
