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Bounds

Total questions: 70

Worksheet time: 53mins

Name

Class

Date

the weight of a potatoes is 25 kg correct to the nearest kG /write down the smallest possible weight of the of bag /and also in largest

smallest24.5/largest25.5

smallest23.6/largest29.5

smallest24.5/largest25.5kg

kjjnejneqovmqeo

find the upper and lower bounds in each case 305 (nearest 5)

300≤305<310

302.5≤305<307.5

find the upper and lower bounds in each case 700(nearst100)

600≤700<800

650≤700<850

What is the upper bound and lower bound of 390 grams, measured to the nearest 10 grams?

395 and 385

390.5 and 389.5

400 and 300

400 and 350

A bag of flour has a mass of 1500 g (to the nearest 10 g). Find the maximum mass of 10 bags of flour.

15050 g

15000.5 g

15000 g

15050 kg

A piece of A4 paper is 21.1 cm by 29.7 cm measured to the nearest 0.1cm. What are the lower and upper bounds of its area, in square centimetres, correct to 1 dp?

624.1325 and 629.2125

624.1 and 629.2

624.13 and 629.21

624 and 629

A cuboid measures 2 x 11 x 9 m measured to the nearest metre.

What is the least possible volume of the cuboid?

198.5

382.375

197.5

223.125

If $A\ =\ \frac{B}{C}$ what is the maximum and minimum value of A, if B is 100m correct to the nearest 5 m and C is 10 m correct to the nearest meter? $\$

10.79 $cm^2$ and 9.28 $cm^2$

10.78 $cm^2$ and 9.29 $cm^2$

10.79 $cm^2$ and 9.29 $cm^2$

10.78 $cm^2$ and 9.28 $cm^2$

Work out the upper bound and lower bound for 32 cm, measured to the nearest cm

32.5 and 31.5

31.5 and 32.5

35 and 30

33 and 31

10.

The length and width of a field have been measured as 78m and 35m to the nearest metre. Find the greatest possible amount of fencing needed to surround the field

228

226.5

228.5

11.

To 1 significant figure 80,000 people attended Manchester United's last game. What is the maximum number of people that could have actually attended the game?

85,000

84,900

84,990

84,999

12.

The horsepower of a car is measured at 351 bhp to the nearest integer. What are the limits of accuracy for the actual horsepower?

350.5≤x≤351.5

350.5<x<351.5

350.5<x≤351.5

350.5≤x<351.5

13.

A number, y, is rounded to 2 significant figures.

The result is 0.46

Write down the error interval for y.

0.445≤y<0.455

0.455≤y<0.465

0.45≤y<0.55

0.5≤y<0.6

14.

Dionne has 60 golf balls.

Each of these golf balls weighs 42 grams to the nearest gram.

Work out the greatest possible total weight of all 60 golf balls.

Give your answer in kilograms.

2550

2520

2544

2490

15.

A car is stopped for speeding travelling at 85mph to the nearest 5mph. What is the slowest speed it could have been doing?

84.5

82.5

16.

p = 5.37 correct to 2 decimal places.

s = 2.9 correct to 1 decimal place.

Which is the correct working to find the greatest possible value of m?

17.

a is 8.3 cm correct to the nearest mm

b is 6.1 cm correct to the nearest mm

Calculate the upper bound for c to 1 d.p.

You must show your working.

5.8

5.6

10.4

10.3

18.

Jarek uses the formula shown to work out the area of a triangle.

For this triangle,

a = 7.8 cm correct to the nearest mm.

b = 5.2 cm correct to the nearest mm.

C = 63° correct to the nearest degree.

Calculate the lower bound for the area of the triangle to 3 s.f.

18.4

17.7

19.

1. The length of a fence is 137 metres, correct to the nearest metre. Choose the upper and lower bound for the length of the fence.

136.5 m

141m

137.5m

132m

20.

Zoe’s weight is 62 kg, correct to the nearest kilogram. Anu’s weight is 85 kg, correct to the nearest kilogram.

(a) Write down the upper bound for the weight of Zoe.

(b) Write down the lower bound for the weight of Anu.

a) 61.5 kg

a) 62.5 kg

b) 84.5 kg

b) 85.5 kg

21.

Zoe’s weight is 62 kg, correct to the nearest kilogram. Anu’s weight is 85 kg, correct to the nearest kilogram.

Work out the upper bound for the difference between Zoe’s weight and Anu’s weight.

20 kg

23 kg

22 kg

24 kg

22.

y = 1.8 correct to 1 decimal place.

Calculate the lower bound for the value of 4y + 1.

10.2

6.2

23.

Write down the upper bound for the length of AB & BC

AB = 19.5

AB = 15

BC = 8.25

BC= 8.35

24.

Calculate the lower bound of the area of the triangle.

(a)

25.

Glass A contains 122 millilitres of water, correct to the nearest millilitre. Glass B contains 168 millilitres of water, correct to the nearest millilitre.

Calculate the upper bound of the difference, in millilitres, between the volume of water in glass A and the volume of water in glass B.

26.

An athlete runs 400 metres, correct to the nearest metre. The athlete takes 50.2 seconds, correct to the nearest 0.1 of a second.

Work out the upper bound of the athlete’s average speed.

Give your answer correct to 3 significant figures

(a)

27.

Some cases have to be lifted by the crane. Each case has a mass of 68 kg , correct to 2 significant figures.

Write down the upper bound of the mass of a case.

(a)

28.

Some cases have to be lifted by the crane. Each case has a mass of 68 kg , correct to 2 significant figures.

A crane can lift safely a load of 1200 kg, correct to 2 significant figures.

Find the greatest number of cases that the crane can lift safely in one load.

(a)

29.

The length of a side of a square is 6.81cm, correct to 3 significant figures.

Work out the lower bound for the perimeter of the square

(a)

30.

What is the upper bound and lower bound of 390 grams, measured to the nearest 10 grams?

395 and 385

390.5 and 389.5

400 and 300

400 and 350

31.

What is 89,555 rounded to the nearest 10, 100 and 1,000?

89560 89500 and 89000

89550 89600 and 89600

89560 89600 and 90000

89560. 89600. and 89000

32.

Round 248.561 to 1 decimal place

248.5

249

248.56

248.6

33.

Round 53,879 to 2 significant figures.

53,800

53,900

53,88

54,000

34.

A bag of flour has a mass of 1500 g (to the nearest 10 g). Find the maximum mass of 10 bags of flour.

15050 g

15000.5 g

15000 g

15050 kg

35.

A piece of A4 paper is 21.1 cm by 29.7 cm measured to the nearest 0.1cm. What are the lower and upper bounds of its area, in square centimetres, correct to 1 dp?

624.1325 and 629.2125

624.1 and 629.2

624.13 and 629.21

624 and 629

36.

A cuboid measures 2 x 11 x 9 m measured to the nearest metre.

What is the least possible volume of the cuboid?

198.5

382.375

197.5

223.125

37.

A formula describing the driving force,F, in Newtons of a vehicle is given by $f\ =\ \frac{P}{v}$ whereP is the power in Watts, and v is the velocity in $\frac{m}{s}$

$P=145\ to\ 3\ sf$
$v=23.4\ to\ 1\ dp$
$Work\ out\ the\ lower\ bound\ for\ the\ driving\ force\ of\ the\ car.\$
$Give\ your\ answer\ to\ a\ suitable\ \deg ree\ of\ accuracy.$

6.23

6.16

6.25

6.17

38.

$v\ =\ \sqrt{\frac{a}{b}}$
a = 6.43 correct to 2 decimal places
b = 5.514 correct to 3 decimal places.
By considering bounds, work out the value of v to a suitable degree of accuracy.

1.079

1.0799

1.08

1.0795

39.

If $A\ =\ \frac{B}{C}$ what is the maximum and minimum value of A, if B is 100m correct to the nearest 5 m and C is 10 m correct to the nearest meter? $\$

10.79 $cm^2$ and 9.28 $cm^2$

10.78 $cm^2$ and 9.29 $cm^2$

10.79 $cm^2$ and 9.29 $cm^2$

10.78 $cm^2$ and 9.28 $cm^2$

40.

The horsepower of a car is measured at 351 bhp to the nearest integer. What are the limits of accuracy for the actual horsepower?

350.5≤x≤351.5

350.5<x<351.5

350.5<x≤351.5

350.5≤x<351.5

41.

1. The length of a fence is 137 metres, correct to the nearest metre. Choose the upper and lower bound for the length of the fence.

136.5 m

141m

137.5m

132m

42.

Zoe’s weight is 62 kg, correct to the nearest kilogram. Anu’s weight is 85 kg, correct to the nearest kilogram.

(a) Write down the upper bound for the weight of Zoe.

(b) Write down the lower bound for the weight of Anu.

a) 61.5 kg

a) 62.5 kg

b) 84.5 kg

b) 85.5 kg

43.

Zoe’s weight is 62 kg, correct to the nearest kilogram. Anu’s weight is 85 kg, correct to the nearest kilogram.

Work out the upper bound for the difference between Zoe’s weight and Anu’s weight.

20 kg

23 kg

22 kg

24 kg

44.

y = 1.8 correct to 1 decimal place.

Calculate the lower bound for the value of 4y + 1.

10.2

6.2

45.

Write down the upper bound for the length of AB & BC

AB = 19.5

AB = 15

BC = 8.25

BC= 8.35

46.

Calculate the lower bound of the area of the triangle.

(a)

47.

Glass A contains 122 millilitres of water, correct to the nearest millilitre. Glass B contains 168 millilitres of water, correct to the nearest millilitre.

Calculate the upper bound of the difference, in millilitres, between the volume of water in glass A and the volume of water in glass B.

48.

An athlete runs 400 metres, correct to the nearest metre. The athlete takes 50.2 seconds, correct to the nearest 0.1 of a second.

Work out the upper bound of the athlete’s average speed.

Give your answer correct to 3 significant figures

(a)

49.

Some cases have to be lifted by the crane. Each case has a mass of 68 kg , correct to 2 significant figures.

Write down the upper bound of the mass of a case.

(a)

50.

Some cases have to be lifted by the crane. Each case has a mass of 68 kg , correct to 2 significant figures.

A crane can lift safely a load of 1200 kg, correct to 2 significant figures.

Find the greatest number of cases that the crane can lift safely in one load.

(a)

51.

The length of a side of a square is 6.81cm, correct to 3 significant figures.

Work out the lower bound for the perimeter of the square

(a)

52.

The number 10 has been rounded to the nearest whole number. Find its lower and upper bounds

9 ≤ 10 < 10

9.5  ≤ 10  < 10.5

9 ≤ 10 < 11

53.

The number 1000 has been rounded to the nearest 100. Find its lower and upper bounds

950  ≤ 1000  < 1050

950 ≤ 1000 < 1050.1

950 ≤ 1000 < 1051

54.

The number 51.2 has been rounded to the nearest 1 decimal place. Find its lower and upper bound

51.1 ≤ 51.2 < 51.2

51.15  ≤ 51.2  < 51.25

51 ≤ 51 < 51

55.

The number 43.4 has been rounded to the nearest tenth. Find its lower and upper bounds.

42 ≤ 43 < 44

43.3 ≤ 43.4 < 43.4

43.35  ≤ 43.4  < 43.45

56.

The number 10 has been rounded to the nearest whole number. Find its lower and upper bounds

9 ≤ 10 < 10

9.5  ≤ 10  < 10.5

9 ≤ 10 < 11

57.

The number 1000 has been rounded to the nearest 100. Find its lower and upper bounds

950  ≤ 1000  < 1050

950 ≤ 1000 < 1050.1

950 ≤ 1000 < 1051

58.

The number 51.2 has been rounded to the nearest 1 decimal place. Find its lower and upper bound

51.1 ≤ 51.2 < 51.2

51.15  ≤ 51.2  < 51.25

51 ≤ 51 < 51

59.

The number 43.4 has been rounded to the nearest tenth. Find its lower and upper bounds.

42 ≤ 43 < 44

43.3 ≤ 43.4 < 43.4

43.35  ≤ 43.4  < 43.45

60.

The number 60 has been rounded to 1 significant figure. Find its lower and upper bounds.

55< 60 < 65

55.25 ≤ 60 < 65.25

55  ≤ 60  < 65

61.

What is the upper bound and lower bound of 390 grams, measured to the nearest 10 grams?

395 and 385

390.5 and 389.5

400 and 300

400 and 350

62.

The following number has been rounded to 1 significant figure.

800

Find the upper bound...

850

750

849

749

63.

The following number has been rounded to 1 significant figure.

8000

Find the lower bound...

8500

7500

8490

7490

64.

The following number has been rounded to the nearest 5 metres.

125m

Find the upper bound...

125.5m

127.5m

122.5m

125.05m

65.

The following number has been rounded to the nearest 5 metres.

260m

Find the lower bound...

262.5m

257.5m

260.6m

259.5

66.

The length and width of a field have been measured as 78m and 35m to the nearest metre. Find the upper bound of fencing needed to surround the field.

228

226.5

228.5

67.

The sides of the rectangle are measured to the nearest cm. What is the largest area of the rectangle?

15 cm²

19.3 cm

19.25 cm²

11.25 cm²

68.

If $A\ =\ \frac{B}{C}$ what is the maximum value of A, if B is 100m correct to the nearest 5 m and C is 10 m correct to the nearest meter?

(Give your final answer in 2 decimal places)

(a)

69.

A metal rod has a length of 2 cm to the nearest cm.

What is the greatest possible length of the rod?

(a)

70.

Write down the lower bound of 60kg rounded to the nearest kg.

59.5

60.5

100 %

Bounds

Total questions: 70

Worksheet time: 53mins

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