Mathematics for IGCSE & O level - Limits Of Accuracy (Section 1)
1
Pencils have a width of 8mm, to the nearest millimetre. What is the smallest total width of 10 pencils?
Answer
(C)
75.5 mm
2
A piece of blue string is 12.6 cm long to the nearest millimetre. What is the upper bound of the length?
Answer
(D)
12.65 cm
3
A mass is given as 0.634 kg to the nearest gram. Between which two values does the mass lie?
Answer
(B)
0.6335 kg and 0.6345 kg
4
A rectangular room measures 5.26m by 3.69m to the nearest centimetre. What is the upper bound of the floor area?
Answer
(B)
19.41 m²
5
A piece of red string is 35.2 cm long to the nearest millimetre, and a piece of blue string is 12.6 cm long to the nearest millimetre. What is the minimum total length of the two pieces laid end to end?
Answer
(A)
47.7 cm
6
Calculate, to 3 significant figures, the upper bound of the distance travelled for a speed of 92.4km/second for 12.3 seconds, both values to 3 s.f.
Answer
(D)
1133 km
7
What is the smallest perimeter of a triangle whose sides are 7 cm, 8 cm, and 10 cm, to the nearest cm?
Answer
(C)
23 cm
8
Calculate the lower bound of the distance travelled for a speed of 5.61m/second for 2.08 seconds (both values to 3 s.f.).
Answer
(B)
11.676
9
Find the lower bound of the sum of 1.248 kg and 0.498 kg (both to the nearest gram)
Answer
(B)
1.7455 kg
10
The lower bound of a sum is found by?
Answer
(B)
Adding the lower bounds
11
Can cycles 14.2 km (to 3 significant figures) in a time of 46 minutes (to the nearest minute). What is the lower bound of his average speed in kilometers per hour?
Answer
(A)
18.3 km/h
12
A piece of paper is measured to be 21.0 cm by 29.7 cm to the nearest millimetre. What is the upper bound of the area?
Answer
(D)
626.2575 cm²
13
What is the relationship between upper and lower bounds and the actual value of a measurement?
Answer
(C)
The actual value lies between the lower and upper bounds, inclusive of the bounds.
14
Given that the area of a rectangle is 21.0 cm² to 3 significant figures, and the length is 17.8 cm to the nearest millimetre. The minimum width is (in cm)
Answer
(D)
1.185 cm
15
Calculate, to 3 significant figures, the upper bound of the distance travelled for a speed of 57km/h for 2.5 hours (both values to 2 s.f.)
Answer
(C)
143 km
16
What is the maximum combined width of two objects, one with a width of 20.0 cm (to 1 d.p.) and another with a width of 30.0 cm (to 1 d.p.)?
Answer
(D)
50.1 cm
17
Calculate, to 3 significant figures, the lower bound of the average speed for those measured times and distances. The distance travelled is 6.4 cm in 1.2 seconds, both values to 2 s.f.
Answer
(A)
4.83 cm/s
18
A piece of paper is measured to be 21.0 cm and 29.7 cm, both to the nearest millimetre. What is the lower bound of the perimeter?
Answer
(D)
100.9 cm
19
Find the upper bound of the sum of 6.42m and 5.97m (both to the nearest centimetre)
Answer
(C)
12.395 m
20
A measurement of 30 cm is given to the nearest 10cm. Which of the following could be the actual measurement?
Answer
(D)
36 cm
21
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 upper bound of the total time for these two stages?
Answer
(D)
29.21 s
22
A measurement is given as 26 cm to the nearest centimetre. What is the lower bound of the interval?
Answer
(B)
25.5 cm
23
The width of a book is measured as 27 cm to the nearest cm. What are the upper and lower bounds of the width?
Answer
(B)
26.5 cm and 27.5 cm
24
What is the lower bound of the difference between the widths of two kitchen cupboards, one with a width of 300 mm and the other with a width of 500 mm, both to the nearest millimetre?
Answer
(A)
199 mm
25
The measurements of a piece of A4 paper are given as 21.0 cm and 29.7 cm to the nearest millimetre. What is the lower bound of the area of this piece of paper?
Answer
(A)
620.95 cm²
26
A value is given to a certain unit of accuracy. How is the upper bound calculated?
Answer
(B)
The value plus half the given unit.
27
The height of a door is given as 2.10 m to 2 decimal places. Between what two values does the height lie?
Answer
(B)
2.095 m and 2.105 m
28
A measurement of 27 cm is given to the nearest centimetre. What is the upper bound of this measurement?
Answer
(D)
27.5 cm
29
A drain cleaner uses a pole made up of ten identical flexible pieces. Each piece is 1 metre long, measured to the nearest centimetre. What is the minimum possible length of drain the cleaner could reach?
Answer
(B)
9.95 m
30
Given that p = 5.1 and q = 8.6, both correct to 1 decimal place, work out the largest possible value of p + q.
Answer
(D)
13.8
31
What is the upper bound of the difference between the lengths of the two strings, where a piece of red string is 35.2 cm long and a piece of blue string is 12.6 cm long, both measured to the nearest millimetre?
Answer
(C)
22.65 cm
32
A rectangle has sides of 86 mm and 98 mm, both measured to the nearest millimetre. What is the lower bound of the sum of the lengths?
Answer
(B)
183.5 mm
33
The measurement of a piece of paper is given as 21.0 cm by 29.7 cm, both to the nearest millimetre. What is the lower bound of the area of this piece of paper?
Answer
(A)
620.95 cm²
34
Fab is fitting a new kitchen. She has an oven which is 595 mm wide, to the nearest millimetre. Will it definitely fit in a gap which is 60 cm wide, to the nearest centimetre?
Answer
(B)
No
35
Two kitchen cupboards have widths of 300 mm and 500 mm correct to the nearest millimetre. What is the upper bound of the combined width of the cupboards?
Answer
(C)
800.5 mm
36
Find the upper bound of the difference between 24.1 s and 19.8s (both to the nearest 0.1 second)
Answer
(B)
4.25 s
37
What is the upper bound of the sum of 29.7 seconds and 31.4 seconds, both to 3 significant figures?
Answer
(D)
61.2 s
38
When multiplying measurements to find the upper bound, which values should you use?
Answer
(B)
The upper bounds of the measurements.
39
Given that p = 5.1 and q = 8.6, both correct to 1 decimal place, work out the smallest possible value of p - q.
Answer
(D)
-3.65
40
A measurement of 128 cm is given to the nearest centimetre. Which two measurements are the boundaries of this interval?
Answer
(B)
127.5 cm and 128.5 cm
41
What is the maximum possible length of the drain cleaner if each piece is 1.0 m long measured to the nearest 0.01 m and there are 10 pieces?
Answer
(C)
10.05 m
42
A rectangle measures 12.0 cm by 5.0 cm, with both measurements correct to 1 decimal place. What is the greatest possible area?
Answer
(C)
60.75 cm²
43
A rectangular field measures 12 cm by 5 cm, with both measurements correct to the nearest centimetre. Calculate the greatest possible perimeter of the rectangle.
Answer
(D)
34.5 cm
44
Which of the following statements are true when calculating the upper bound of a calculation?
Answer
A
C
D
45
A triangle has sides of length 7 cm, 8 cm and 10 cm. All measurements are correct to the nearest centimetre. What is the lower bound of the perimeter of the triangle?
Answer
(B)
24.0 cm
46
If the speed is found by dividing the distance by the time taken, which formula should be used to find the upper bound of the speed of an object?
Answer
(C)
UB(distance) / LB(time)
47
The population density of a town is calculated by dividing the population by its area. Which bounds of the population and area are needed to calculate the upper bound of the population density?
Answer
A
D
48
The length of a table is measured as 1.8 meters to the nearest tenth of a meter. What is the upper bound of this measurement?
Answer
(C)
1.85 m
49
What is the correct way to calculate the upper bound of a difference, when calculating with two values, A and B, each given to a unit of accuracy?
Answer
(A)
U(A) - L(B)
50
Find the lower bound of the sum of 11.04s and 13.46s (both to the nearest hundredth of a second).
