s2 ch 1 estimation and approximation q

8
1 Chapter 1 Estimation and Approximation Multiple Choice Questions 1. Correct 243.56 to the nearest unit. A. 240 B. 243 C. 243.6 D. 244 2. Correct 50.997 to 2 decimal places. A. 50.00 B. 50.10 C. 50.90 D. 51.00 3. Correct 0.037 48 m 2 to the nearest cm 2 . A. 3.748 cm 2 B. 3.75 cm 2 C. 37.5 cm 2 D. 375 cm 2 4. Find the length of line segment XV in the following figure, correct to the nearest cm. A. 10 cm B. 10.2 cm C. 10.5 cm D. 11 cm 5. Which of the following units is the most suitable for measuring the time required to travel from Hong Kong to U.S.A. by plane? A. second B. minute C. hour D. year 6. What is the precision of the following instrument? A. 5 mL B. 6 mL C. 10 mL D. 36 mL 7. Find the measured temperature and the precision of the thermometer shown below. A. Temperature = 24°C, precision = 0.5°C B. Temperature = 24°C, precision = 1°C C. Temperature = 24.5°C, precision = 0.5°C D. Temperature = 25°C, precision = 1°C 0 1 2 3 4 5 6 7 8 9 1 0 1 1 cm V X 30 24 18 12 6 mL 36 0 10 C 20 30 40

Upload: kenneth-wong

Post on 21-Dec-2015

19 views

Category:

Documents


0 download

DESCRIPTION

nothing

TRANSCRIPT

Page 1: S2 Ch 1 Estimation and Approximation Q

1

Chapter 1 Estimation and Approximation

Multiple Choice Questions

1. Correct 243.56 to the nearest unit.

A. 240 B. 243 C. 243.6 D. 244

2. Correct 50.997 to 2 decimal places.

A. 50.00 B. 50.10 C. 50.90 D. 51.00

3. Correct 0.037 48 m2 to the nearest cm

2.

A. 3.748 cm2 B. 3.75 cm

2 C. 37.5 cm

2 D. 375 cm

2

4.Find the length of line segment XV in the following figure, correct to the nearest cm.

A. 10 cm B. 10.2 cm C. 10.5 cm D. 11 cm

5.Which of the following units is the most sui table for measuring the time required to travel from

Hong Kong to U.S.A. by plane?

A. second B. minute C. hour D. year

6. What is the precision of the following instrument?

A. 5 mL B. 6 mL C. 10 mL D. 36 mL

7. Find the measured temperature and the precision of the thermometer shown below.

A. Temperature = 24°C, precision = 0.5°C

B. Temperature = 24°C, precision = 1°C

C. Temperature = 24.5°C, precision = 0.5°C

D. Temperature = 25°C, precision = 1°C

0 1

2 3 4 5 6 7 8 9 1 0 1 1 c m

V X

30

2418

126

mL

36

0 10C

20 30 40

Page 2: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

2

8. Estimate the size of x.

A. 90 B. 200 C. 240 D. 270

9. The capacity of a cup is 72 mL and that of a kettle is approximately equal to 4

310 times of

the cup. Estimate the capacity of the kettle.

A. 700 mL B. 770 mL C. 840 mL D. 890 mL

10. The height of Jenny is about 90 cm and her brother is taller than her by 5 heads’ length. If

the length of Jenny’s head is about 19 cm, estimate the height of her brother.

A. 135 cm B. 170 cm C. 175 cm D. 190 cm

11. The typing speed of Miss Lee is about 38 words per minute. If she needs to type 560 words,

estimate the time required.

A. 10 min B. 14 min C. 18 min D. 22 min

12. Trees are planted long the side of a road at regular intervals of approximately 20 m. Estimate

the number of trees to be planted along a road of 3.978 km long.

A. 160 B. 180 C. 200 D. 220

13. Estimate the area of the shaded region.

A. 1.8 cm2 B. 3.2 cm

2 C. 5 cm

2 D. 9 cm

2

14.The total weight of 40 students is 1 247 kg. If a boat can carry 250 kg only, estimate the

number of boats required to carry all the students.

A. 4 B. 5 C. 8 D. 16

15. The price of a pack of chocolate is $4.9. If Johnson has $70, estimate the number of packs of

chocolate he can buy.

A. 10 B. 14 C. 15 D. 18

16. The following is the price list of some food and drink. If Ken wants to buy two boxes of

lemon tea, 1 chicken leg and 3 sandwiches, estimate the total price.

x

0.6 cm

0.6 cm

Page 3: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

3

Item Dim-sum Sandwich Potato Chips Chicken Leg Lemon Tea

Price

(per unit) $4.7 $15.9 $6.8 $10.7 $7.8

A. $60 B. $65 C. $69 D. $75

17. Using the strategy of reformulation, round off each number in the following expression to the

nearest unit. 0.849 + 5.77 3.44

A. 0 + 6 3 B. 1 + 6 3 C. 0.8 + 5 3 D. 0.9 + 6 3

18. Write down the third significant figure in 5.004 87.

A. 0 B. 4 C. 7 D. 8

19. What is the number of significant figures in 0.004 411?

A. 2 B. 4 C. 6 D. 7

20. Change

660

11 into a decimal number, correct to 3 significant figures.

A. 0.016 B. 0.017 C. 0.016 6 D. 0.016 7

21. A motor cycle can travel 0.55 km in a minute. Find the speed of the motor cycle in m/s.

(Correct your answer to 3 significant figures.)

A. 0.55 m/s B. 0.917 m/s C. 9.17 m/s D. 550 m/s

22. John spent 11.06 s (correct to 4 significant figures) to complete a 100 m race. Find the

maximum absolute error of John’s record.

A. 0.005 s B. 0.01 s C. 0.05 s D. 0.5 s

23. The weight of a steak should be 442 g (correct to the nearest g) in order to fulfill the quality

control requirement. Which of the following weights is not acceptable?

A. 441.49 g B. 441.59 g C. 442.3 g D. 442.45 g

24. Peter spends 16.2 minutes (correct to the nearest 0.1 minute) on the Internet everyday. Find

the percentage error. (Correct your answer to 2 decimal places.)

A. 0.31% B. 0.62% C. 3.1% D. 6.2%

25. The weight of a bean is 0.35 g with a percentage error of 6%. Find the maximum absolute

error of this measurement.

A. 0.012 g B. 0.021 g C. 0.171 g D. 5.833 g

26. The length of a side of a square tile is 10.42 cm, correct to the nearest 0.01 cm. Find the

range of the true length of the square tile.

A. Between 10.405 cm and 10.435 cm

B. Between 10.415 cm and 10.425 cm

C. Between 10.42 cm and 10.43 cm

D. Between 10.37 cm and 10.47 cm

Page 4: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

4

Level 1

1. Choose the suitable units from the brackets for the following measurements.

(mm, cm, m, km)

(a) The length of a (b) The length of a (c) The distance between the

photo album basketball field Kwun Tong station and the

Tsuen Wan station

Kwun Tong

Tsuen Wan

2. Choose the suitable units from the brackets for the following measurements. (mg, g, kg)

(a) The weight of a nail (b) The weight of an adult (c) The weight of a battery

3. Write down the precision of each of the following instruments.

(a) (b)

0 1 2 3 4 5 cm

0 1 2 3 4 5 cm

4.Write down the precision of each of the following instruments.

(a) (b)

5.Find the length of the pencil in the following figure, correct to the nearest

(a) cm. (b) 0.5 cm. (c) 0.1 cm.

Page 5: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

5

0 1 2 3 4 5 6 7 8 9 10cm

6.Find the volume of water in the cylinder, correct to the nearest

(a) 10 cm3. (b) 5 cm

3. (c) cm

3.

20

25

30

35 cm3

30

25

7.Measure the length of the line segment AB, correct to the nearest

(a) 0.5 cm. (b) 0.1 cm.

BA

8.Correct the following numbers to 2 significant figures.

(a) 94 675 (b) 28.48 (c) 104.59 (d) 0.498 1

9.Correct the following numbers to 3 significant figures.

(a) 237 821 (b) 599.58 (c) 0.001 428 (d) 0.058 39

10. Estimate the values of the following expressions and st ate the estimation strategies used.

(a) 68 + 52 + 98 + 58 + 12 + 31 + 43

(b) 5.97 + 3.21 + 6.09 + 4.89 + 8.81 + 9.19 + 2.51

11. Estimate the values of the following expressions and state the estimation strategies used.

(a) 159.59 0.45 (b) 27.66 3.58 + 119.57 6.29

12. The population of City A is 376 894. Find the population, correct to

(a) 1 significant figure. (b) 2 significant figures. (c) 4 significant figures.

13. Write down the number of significant figures in each of the following numbers.

(a) 4.57 (b) 2.090 (c) 5 870 (d) 28 900

14. The length, width and height of a train compartment are 42.5 m, 2.5 m and 3.0 m respectively.

If the length, width and height of a cargo container are 13.3 m, 2.3 m and 2.7 m respectively,

estimate the number of cargo containers that a train compartment can carry.

Page 6: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

6

15. The electricity charge of the Chan’s family is $689.56 this month. If the electricity charge

per unit is $0.38, find the number of units of electricity the Chan’s family consumed this

month.

16. To which digits are the following measurements corrected? Then find the maximum absolute

error, upper limit and lower limit of each measurement.

(a) 149 km (b) 25.6 cm

(c) 0.28 mm (d) 2.718 2 m

17. In an experiment, the temperature of a glass of solution is 48.5C (corrected to the nearest

0.1C). Find the maximum absolute error, upper limit and lower limit of the temperature.

18. In a 100 m race, the record made by May was 14.24 seconds, correct to the nearest 0.01

second. Find the maximum absolute error and the relative error of this record.

19. The length of the classroom is measured to be 18.8 m, correct to 3 significant figures. Find

the maximum absolute error and the percentage error of the measu rement.

(Correct your answer to 3 significant figures.)

20. David uses 7

22 as the estimation of and then find the percentage error. Firstly, he changes

7

22 into a decimal number and the answer is corrected to 5 significant figures. Then he uses

3.141 6 as the true value of . Find the percentage error in David’s estimation.

(Correct your answer to 4 significant figures.)

Level 2

21. The number of pages of a book is about 200. If there is approximately 26 words in a certain

line of a certain page, and there is about 60 lines in that page, estimate the number of words

in the book.

22. In the following figures, the same volume of water is put into cylinders A, B and C

respectively.

Page 7: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

7

100

cm3

20

30

50

60

100

10

40

70

80

90

20

1020

40

60

80

30

40

50

60

70

80

90

100cm3

cm3

A

B

C

(a) Which cylinder is the most precise?

(b) (i) Find the volume of water in cylinder A.

(ii) Find the volume of water in cylinder B.

(iii) Find the volume of water in cylinder C.

23. In Figure A, the area of each square is 1 cm2, and in Figure B, each square has an area of

0.25 cm2.

Figure A Figure B

(a) Find the approximate area of the figure in Figure A.

(b) Find the approximate area of the figure in Figure B.

(c) Which one gives a more precise result?

24. Find the approximate area of the figure by using two pieces of square paper A and B. Which

one gives a more precise result?

Square paper A Square paper B

Area of each square = 1 cm2

Area of each square = 0.25 cm2

25. Estimate the values of the following expressions and state the estimation strategies used.

(a) 48.92 +50.01 + 121.99 + 98.84 + 42.13 + 89.48 + 31.82

(b) 3.09 × 4.21 + 1 871 51

26. The height of Denny is 4 feet 8 inches. If 1 feet 12 inches and 1 inch 2.54 cm, find the

height of Denny in cm. (Correct your answer to 3 significant figures.)

Page 8: S2 Ch 1 Estimation and Approximation Q

Chapter 1 Estimation and Approximation

8

27. The weight of a box of candies is 785 g. If the relative error of the measurement is

0002

1,

find the maximum absolute error of this measurement. (Correct your answer to 3 significant

figures.)

28. The length of the equator of the earth is measured to be 12 756 km. If the percentage error is

0.1%, find the maximum absolute error of this measurement.

(Correct your answer to 2 significant figures.)

29. The distance between the earth and the moon is measured to be 385 000 km. If the

percentage error is 2%, find the range of the true distance.

30. Mary measured the weight of 50 $1 coins and the measurement is 350 g, correct to the

nearest g.

(a) Find the percentage error of this measurement.

(b) If Mary uses the weight of 50 $1 coins to estimate the weight of each $1 coin, find the

maximum absolute error of the weight of each $1 coin.

(c) If the true weight of each $1 coin is 7.02 g, using the result of (b), find the percentage

error of the weight of each $1 coin.

(Correct your answer to 2 significant figures if necessary. )

31. Sammy measures the length of a rope and the measurement is corrected to the neares t 0.1 cm.

(a) Find the maximum absolute error of the measurement.

(b) If the percentage error of the measurement is 1.4%, find the measured length of the rope.

(Correct your answer to 2 significant figures. )

(c) Find the range of the true length of the rope.

Level 3

32. The approximate values of x and y are 7.5 and 3.5 respectively, correct to 2 significant

figures.

(a) Find the upper limits and lower limits of x and y respectively.

(b) Find the upper limit and lower limit of x + y.

(c) Find the upper limit and lower limit of x y.

33. The base and the height of a parallelogram are 12.3 cm and 5.6 cm respectively.

(a) Find the upper limits and lower limits of the base and the height of the parallelogram

respectively.

(b) Find the upper limit and lower limit of the area of the parallelogram.

(Correct your answer to 3 significant figures. )