Blitzer, Thinking Mathematically, 8e Chapter 1 Test Item File SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find a counterexample to show that the statement is false. 1) No women have sat on the bench of the U.S. Supreme Court. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) If a number is multiplied by itself, the result is greater than 0. A) The number is 0.
B) The number is 0.1.
C) The number is 1.
D) The number is
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) All U.S. presidents have been one-term presidents. Objective: (1.1) Understand and Use Inductive Reasoning
4) All actors are Academy Award winners. Objective: (1.1) Understand and Use Inductive Reasoning
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify a pattern in the list of numbers. Then use this pattern to find the next number. 5) 2, 9, 16, 23, 30, ___ A) 37 B) 32 C) 44
D) 36
Objective: (1.1) Understand and Use Inductive Reasoning
6) 1, 12, 1, 18, 1, 24, 1, _____ A) 36
B) 30
C) 1
D) 32
C) 0
D) 2
C) -3,375
D) 3,375
C) -1/32
D) -1/64
Objective: (1.1) Understand and Use Inductive Reasoning
7) 31, 26, 21, 16, 11 A) 6
B) 5
Objective: (1.1) Understand and Use Inductive Reasoning
8) 3, -15, 75, -375, 1,875 A) 9,375
B) -9,375
Objective: (1.1) Understand and Use Inductive Reasoning
9) 1, -
1 1 1 1 , ,- , 8 16 2 4
A) 1/32
B) 1/64
Objective: (1.1) Understand and Use Inductive Reasoning
1
1 . 2
10) 1, 5, 2, 10, 4, 20 A) 30
B) 8
C) 6
D) 40
Objective: (1.1) Understand and Use Inductive Reasoning
Identify a pattern in the sequence of figures. Then use the pattern to find the next figure in the sequence. 11)
A)
________________ C)
B)
Objective: (1.1) Understand and Use Inductive Reasoning
12)
A)
B)
C)
D)
Objective: (1.1) Understand and Use Inductive Reasoning
2
D)
The problem describes procedures that are to be applied to numbers. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. 13) Select a number. Multiply the number by 16. Add 16 to the product. Divide this sum by 8. Subtract 2 from the quotient. A) The result is one more than the original number. B) The result is one more than double the original number. C) The result is double the original number. D) The result is the original number. Objective: (1.1) Understand and Use Inductive Reasoning
Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 14) 60 - 9 = 51 600 - 89 = 511 6,000 - 789 = 5,211
A) 60,000 - 6,789 = 593,211 C) 60,000 - 6,789 = 53,211
B) 6,000 - 6,789 = 53,211 D) 600,000 - 6,789 = 53,211
Objective: (1.1) Understand and Use Inductive Reasoning
15) 96 - 94 + 92 - 90 = 97 - 95 + 93 - 91 106 - 104 + 102 - 100 = 107 - 105 + 103 - 101 A) 116 + 114 - 112 - 110 = 117 + 115 - 113 + 111 C) 116 - 114 - 112 + 110 = 117 - 115 + 113 - 111
B) 116 + 114 - 112 + 110 = 117 + 115 - 113 + 111 D) 116 - 114 + 112 - 110 = 117 - 115 + 113 - 111
Objective: (1.1) Understand and Use Inductive Reasoning
16) 2 x 4 = 3 × 5 - 7 4 x 6 = 5 × 7 - 11 A) 6 × 8 = 7 × 9 + 13
B) 6 × 8 = 7 × 9 - 13
C) 6 × 8 = 7 × 9 - 15
D) 6 × 8 = 9 × 11 - 15
Objective: (1.1) Understand and Use Inductive Reasoning
17) 3 × 3 = 9 33 × 33 = 1,089 333 × 333 = 110,889 A) 3,333 × 3,333 = 112,889 C) 3,333 × 3,333 = 111,889
B) 3,333 × 3,333 = 11,108,889 D) 333 × 3,333 = 11,108,889
Objective: (1.1) Understand and Use Inductive Reasoning
18) 20 × 21 = 22 × 23 - (20 + 21 + 22 + 23) 21 × 22 = 23 × 24 - (21 + 22 + 23 + 24) A) 23 × 24 = 25 × 26 - (23 + 24 + 25 + 26) C) 23 × 24 = 25 × 26 - (22 + 21 + 20 + 19)
B) 22 × 23 = 24 × 25 - (20 + 21 + 22 + 23 + 24 + 25) D) 22 × 23 = 24 × 25 - (22 + 23 + 24 + 25)
Objective: (1.1) Understand and Use Inductive Reasoning
3
19) (1 × 9) - 9 = 0 (21 × 9) - 9 = 180 (321 × 9) - 9 = 2,880 A) (4321 × 9) - 9 = 3,879 C) (4321 × 9) - 9 = 28,880
B) (4321 × 9) - 9 = 38,880 D) (432 × 9) - 9 = 38,880
Objective: (1.1) Understand and Use Inductive Reasoning
20) (4 × 1) × (2 × 1) = 8 (4 × 10) × (2 × 2) = 160 (4 × 100) × (2 × 3) = 2,400 A) (4 × 1000) × (2 × 4) = 36,000 C) (4 × 1000) × (2 × 4) = 32,000
B) (4 × 1000) × (2 × 4) = 28,000 D) (4 × 1000) × (2 × 4) = 3,200
Objective: (1.1) Understand and Use Inductive Reasoning
21) 37,037 × 3 = 111,111 37,037 × 6 = 222,222 37,037 × 9 = 333,333 37,037 × 12 = 444,444 A) 111,111 × 15 = 1,666,665 C) 37,037 × 18 = 666,666
B) 37,037 × 13 = 481,481 D) 37,037 × 15 = 555,555
Objective: (1.1) Understand and Use Inductive Reasoning
1 1 1 = 13 2 3
22)
1 1 1 1 + = 13 9 2 9 1 1 1 1 1 = 1+ + 27 3 9 27 2 1 1 1 1 1 1 = 1+ + + 81 3 9 27 81 2
A)
1 1 1 1 1 1 1 = 1+ + + + 729 3 9 27 81 729 2
B)
1 1 1 1 1 1 1 = 1+ + + + 243 3 9 27 81 243 3
C)
1 1 1 1 1 1 1 + + + + = 1243 3 9 27 81 243 2
D)
1 1 1 1 1 1 1 + + + + = 1162 3 9 27 81 162 2
Objective: (1.1) Understand and Use Inductive Reasoning
4
23)
8(5) = 10(5 - 1) 8(5) + 8(25) = 10(25 - 1) 8(5) + 8(25) + 8(125) = 10(125 - 1) 8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)
A) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 8(3125 - 1) B) 8(5) + 8(25) + 8(125) + 8(625) + 8(1250) = 10(1250 - 1) C) 8(5) + 8(25) + 8(125) + 8(625) + 8(5000) = 10(5000 - 1) D) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 10(3125 - 1) Objective: (1.1) Understand and Use Inductive Reasoning
The following table relates an adult's body weight, in pounds, to his or her dosage of a certain medication, in milligrams. 24) Weight 100 125 150 175 200 225 Dosage 20 25 30 a. Use inductive reasoning to fill in the missing portions of the table. b. What would be the dosage of a person who weighs 375 pounds?
A) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 95 115
B) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 39 40
b. 80 mg
b. 70 mg
C) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 35 35
D) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 40 45
b. 65 mg
b. 75 mg
Objective: (1.1) Understand and Use Inductive Reasoning
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem using inductive reasoning. 25) Write the next three "square" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
26) Write the next three "triangular" figurate numbers.
Objective: (1.1) Understand and Use Inductive Reasoning
5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which reasoning process is shown in the following example? 27) We examine the genetic blueprints of 100 people. No two individuals from this group of people have identical genetic blueprints. We conclude that for all people, no two people have identical genetic blueprints. A) reasoning by counterexample B) deductive reasoning C) theoretical reasoning D) inductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
28) If Mary goes to the mall, she gets ice cream. Mary did not get ice cream. We conclude Mary did not go to the mall. A) inductive reasoning B) reasoning by counterexample C) theoretical reasoning D) deductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning
The problem describes procedures that are to be applied to numbers. Represent the original number as n and use deductive reasoning to prove a conjecture that relates the result of the process to the number n. 29) Select a number. Multiply the number by 24. Add 24 to the product. Divide this sum by 12. Subtract two from the quotient. 24n + 24 24n + 24 - 2 = 2n + 2 - 2 = 2n -2=n+1-2=n-1 A) B) 12 24
C)
24n + 24 -1=n+1-1=n 24
D)
24n + 12 - 2 = 2n + 1 - 2 = 2n - 1 12
Objective: (1.1) Understand and Use Deductive Reasoning
Solve the problem. 30) Study the pattern, or trend, shown by the data. Then select the expression that best describes the number of tickets sold, in thousands, n years after Year 1.
A) 2.5 - 0.2n
B) 2.5 - 1.02n
C) 2.5 + 0.2n
D) 2.5 + 1.02n
Objective: (1.1) Understand and Use Deductive Reasoning
Round the number to the given place value. 31) In the past year, a company spent $693,749,312 on advertising. Round the advertising figure to the nearest hundred thousand. A) $693,800,000 B) $700,000,000 C) $693,700,000 D) $600,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
6
32) A publishing company sold 16,267,591 books last year. Round the number of books sold to the nearest ten million. A) 16,270,000 B) 20,000,000 C) 16,000,000 D) 10,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
33) In a town in Nebraska, the average consumption of soft drinks per day per elementary school student is 14.189 ounces. Round this value to the nearest tenth. A) 14.2 ounces B) 15 ounces C) 14.3 ounces D) 14.1 ounces Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
34) According to his ultra-precise scale, Jeremy gained 3.558 pounds in a three-month period. Round this amount to the nearest hundredth. A) 3.57 pounds B) 0.56 pounds C) 4 pounds D) 3.56 pounds Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
35) In a laboratory course in veterinary biology, fleas gathered from Alexander, a volunteered pet dog, averaged 0.168209 inch in length. Round this amount to the nearest thousandth. A) 0.169 inch B) 0.168 inch C) 1 inch D) 0.167 inch Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
Solve the problem with estimation, but do not use a calculator. Use rounding to make the resulting calculations simple. 36) Estimate the cost to buy a refrigerator for $999, a stove for $459, and a dishwasher for $349. A) $1,800 B) $1,600 C) $1,900 D) $1,700 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
37) Estimate the cost of 101 shirts at $19.95 each. A) $1995 B) $2000
C) $2,014.95
D) $200
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
38) If a person earns $29.90 per hour, estimate that person's annual salary. A) $70,000 B) $60,000 C) $50,000
D) $40,000
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
39) Find an estimate of A) 36
0.245 × 72 . 0.538
B) 144
C) 9
D) 18
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
40) Estimate the number of seconds in a day. A) 3,600 seconds B) 72,000 seconds
C) 1,400 seconds
D) 600,000 seconds
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
41) If a person earns $19,500 per year, estimate that person's hourly salary. A) $10 B) $50 C) $100
D) $40
Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
42) You rented an apartment for $815 per month for 4 years. What is the total amount you paid in rent? A) $9600 B) $4,800 C) $38,400 D) $3,200 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
7
43) You spend $40.24 for a meal. If you want to leave a 15% tip, estimate the amount of the tip. A) $4 B) $6 C) $10 D) $8 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 44) Four people share the use of a cable modem service that costs $49.95 a month. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
45) If Jessica can type 48 words per minute, estimate the number of words she can type in one hour. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The map shows main roads between various towns in a certain county. Use the map to answer the question. 46)
90 a. Estimate the distance from State City to Capitol Park. b. If a vehicle travels at an average of 30 miles per hour, estimate the traveling time from State City to Capitol Park. A) a. 360 miles B) a. 180 miles C) a. 270 miles D) a. 90 miles b. 12 hours b. 6 hours b. 9 hours b. 3 hours Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem
8
The circle graph shows the number of times a group of survey respondents watched the news in the past week. Use the chart to answer the question.
47) If the number of respondents in the study was approximately 44,779, estimate how many stated that they watched the news 5-6 times in the last week. A) 8000 respondents B) 12,000 respondents C) 6000 respondents D) 10,000 respondents Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar graph below represents various colors of cars sold. Use the graph to answer the question(s).
48) Estimate the number of tan cars sold. A) 30,000 B) 35,000
C) 40,000
D) 25,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
49) Estimate the number of white cars sold. A) 50,000 B) 47,000
C) 40,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
9
D) 52,000
50) Which color sold over 50,000 cars? A) White B) Tan
C) Silver
D) Red
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
51) Which color sold under 20,000 cars? A) White B) Black
C) Tan
D) Yellow
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
52) Estimate how many more black cars were sold than silver cars. A) 21,000 B) 11,000 C) 14,000
D) 31,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
53) Estimate how many more white cars were sold than tan cars. A) 22,000 B) 17,000 C) 7,000
D) 27,000
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar graph shows the percentages of health clubs in a large city that offer the service listed on the left. Use the graph to answer the question.
54) Estimate the percentage of health clubs in this city that offer Pilates. A) 19% B) 26% C) 29%
D) 23%
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
55) Which services are offered at at least 20% of this city's health clubs and at most 45% of the clubs? A) massage, Pilates and nutritional counseling B) Pilates and nutritional counseling C) Pilates, nutritional counseling, and body fat testing D) massage, Pilates, nutritional counseling, and body fat testing Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
10
The bar graph shows the amount of scholarship money available to student athletes at State University in four consecutive years. Use the graph to answer the question.
56) Estimate the amount of scholarship money available to female student athletes at State University in year 1. A) $16,000 B) $11,000 C) $1,900 D) $7,000 Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The line graph below shows the price of a stock over the course of the day. Use the graph to answer the question(s). 10 9 8 7 Stock Price 6 (in dollars) 5 4 3 2 1 9AM 10AM 11AM 12PM 1PM
2PM
3PM
4PM
57) At what time was the stock price highest? A) 12 PM B) 2 PM
5PM 6PM
C) 9 AM
D) 1 PM
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
58) At what time was the stock price the lowest? A) 6 PM B) 10 AM
C) 1 PM
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
11
D) 9 AM
The line graph shows the pollution rate for a certain lake over six decades. Use the graph to answer the question.
59) Find an estimate for the pollution rate of the lake at the beginning of decade 6. A) 2.5% B) 3% C) 1.5%
D) 1%
Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs
The bar-graph shows the average living expenses of an undergraduate student. Provide an appropriate response.
60) Estimate the yearly increase in living expenses. A) $750 B) $500
C) $450
D) $650
Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
61) Write a mathematical model that estimates the average living expenses, E, of an undergraduate student for x years after 2000. A) E = 5000 + 750x B) E = 5000 + 450x C) E = 5000 + 500x D) E = 5000 + 650x Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
62) Use a mathematical model to predict the average living expenses of an undergraduate student in 2015 A) $12,500 B) $11,750 C) $14,750 D) $16,250 Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables
12
State the necessary piece of information that is missing which prevents you from solving the problem. 63) A car traveled at an average rate of 55 miles per hour and then reduced its speed to 49 miles per hour for the rest of the trip. If the trip took 4 hours, determine how long the car traveled at each rate. A) the destination B) the time of day C) the time at each rate D) the distance of the trip Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem. Then identify the piece of information that is unnecessary to solve the problem. 64) A rental car company that rents cars for local-only use charges $30 plus $0.30 for each mile the rental car is driven. If a customer gives the rental attendant $100 for a charge of $54, how many miles did the customer drive? A) 40 miles unnecessary information: the $54 charge B) 79 miles unnecessary information: the $0.30 per-mile charge C) 180 miles unnecessary information: the $30 flat charge D) 80 miles unnecessary information: giving $100 to attendant Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Use the four-step method in problem solving to solve the problem. 65) City A has an elevation of 3,189 feet above sea level while city B has an elevation of 77 feet below sea level. How much higher is City A than City B? A) -3,012 feet B) -3,112 feet C) 3,266 feet D) 3,366 feet Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
66) Ashley owns 16 acres of land which she rents to a timber grower for $3,886 per acre per year. Her property taxes are $776 per acre per year. How much profit does she make on the land each year? A) $49,760 B) $62,952 C) $74,592 D) $61,400 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
67) At the beginning of the year, the odometer on an SUV read 37,587 miles. At the end of the year, it read 51,847 miles. If the car averaged 23 miles per gallon, how many gallons of gasoline did it use during the year? A) 620 gallons B) 14,260 gallons C) 62 gallons D) 327,980 gallons Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
68) A couch sells for $820. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $60 a month for 12 months. How much is saved by paying the total amount at the time of purchase? A) $960 B) $300 C) $100 D) $30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
69) CD's were purchased at $55 per dozen and sold at $40 for four CD's. Find the profit on 7 dozen CD's. A) $15 B) $65 C) $105 D) $455 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
13
70) A college cafeteria pays student cashiers $7.50 per hour. Cashiers earn an additional $1.70 per hour for each hour worked over 35 hours per week. A cashier worked 37 hours one week and 42 hours the second week. How much did this cashier earn in this two-week period? A) $726.80 B) $607.80 C) $592.50 D) $540.30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
71) A car rents for $230 per week plus $0.25 per mile. Find the rental cost for a three-week trip of 700 miles. A) $175.00 B) $865.00 C) $1,215.00 D) $405.00 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
72) An accountant receives a salary of $261,500 per year. During the year, he plans to spend $91,000 on his mortgage, $58,000 on food, $32,000 on clothing, $43,000 on household expenses, and $29,000 on other expenses. With the money that is left, he expects to buy as many shares of stock at $250 per share as possible. How many shares will he be able to buy? A) 33 shares B) 34 shares C) 31 shares D) 36 shares Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
73) Andrea decided to rollerblade to her mother's house. Six blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining eight blocks to her mother's. She could not repair her skate and had to walk all the way back home. How many more blocks did Andrea walk than she skated? A) 14 blocks B) 22 blocks C) 16 blocks D) 28 blocks Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
74) A store received 200 containers of milk to be sold by February 1. Each container cost the store $0.81 and sold for $1.57. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 180 containers were sold by February 1, how much profit did the store make? A) $120.60 B) $130.60 C) $145.80 D) $136.80 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem using the strategy of making a list or using a diagram. 75) How many matches will be required to determine the champion in a single-elimination tennis tournament that starts with 58 players? A) 58 matches B) 48 matches C) 57 matches D) 29 matches Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
76) A coin is tossed four times. How many ways can it come up heads 3 times and tails once? A) 4 B) 2 C) 3 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
14
D) 1
Solve the problem using the strategy of your choice. 77) Can you place the digits 1 through 9 into a 3 x 3 square so that each row, column, and diagonal add up to the same total? Four digits have been inserted. ( ) 1 ( ) 3 ( )( ) 4 ( ) 2 A) B) C) D) 8 1 9 8 1 6 6 1 8 8 1 7 3 5 7 3 5 7 3 5 7 3 5 6 4 6 2 4 9 2 4 9 2 4 9 2 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 78) Some numbers in the printing of a division problem have become illegible. They are designated below by *. Fill in the blanks. 1 * * * * 5 * * * 3 6 * 7 2 * * * * ** * * * 0 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 79) Three people have telephone prefixes whose three digits have the same sum. One of the prefixes is 448. None of the prefixes contains a digit that is in one of the other prefixes. None of the prefixes has a first digit of 6 or 1. One of the prefixes begins with 5. Another ends with 2. What is the prefix that ends with 2? A) 372 B) 772 C) 962 D) 592 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
80) Find the number of squares in the figure.
A) 30
B) 55
C) 26
Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
15
D) 25
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. This exercise involves problems encountered in everyday life. Write seven or more short solutions that might be effective in solving the problem. 81) Your younger brother has just graduated college. You allow him to live in your house, rent-free, under the condition that he does all the household chores. However, after two months of living with you, your brother has not done any chores. What actions can you take to remedy this situation? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
Solve the problem. 82) A certain Internet provider charges $16.95 for 150 hours of online usage per month and $0.95 for each additional hour. If Marc was online for 200 hours last month, what was his bill for that month? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process
16
Answer Key Testname: UNTITLED1
1) Answers may vary. Sandra Day O'Connor is one possible answer. 2) A 3) Answers may vary. Sample answer: George Washington was elected to two terms. 4) Answers may vary. Sample answer: Actor Jim Carrey is not an Academy Award winner. 5) A 6) B 7) A 8) B 9) C 10) B 11) D 12) A 13) C 14) C 15) D 16) C 17) B 18) D 19) B 20) C 21) D 22) C 23) D 24) D 25) 16, 25, 36 26) 10, 15, 21 27) D 28) D 29) A 30) A 31) C 32) B 33) A 34) D 35) B 36) A 37) B 38) B 39) A
40) B 41) A 42) C 43) B 44) $50 ÷ 4 = $12.50 45) 50 × 60 = 3000 46) C 47) A 48) A 49) B 50) D 51) D 52) A 53) B 54) D 55) B 56) D 57) D 58) D 59) C 60) D 61) D 62) C 63) D 64) D 65) C 66) A 67) A 68) B 69) D 70) B 71) B 72) B 73) C 74) B 75) C 76) A 77) B 148 78) 36 5328 36
81) Answers may vary. Possible answers may include: 1. I could kick my brother out of my house. 2. I could start charging my brother rent. 3. I could make a list or schedule of chores that I want him to perform, in hopes of motivating him. 4. I could offer my brother an additional incentive for each chore he performs. 5. I could relentlessly follow my brother around the house to ensure that he performs his chores. 6. I can throw out the agreement completely and allow him to live in my house for free. 7. I could hire a maid and make my brother pay for it. 8. I could change all the locks on the doors. 82) $64.45
172 144 288 288 0
79) B 80) B 17
Blitzer, Thinking Mathematically, 8e Chapter 2 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the collection is not well defined and therefore not a set. 1) The collection of frogs and toads currently in tanks at a nature center A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not
2) The collection of beautiful oil paintings currently on display at an art gallery A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not
Write a word description of the set. 3) {January, February, March, April, May, June, July, August, September, October, November, December} A) seasons of the year B) days of the year C) days of the week D) months of the year Objective: (2.1) Use Three Methods to Represent Sets
4) {2, 4, 6, 8, ..., 100} A) odd numbers from 2 to 100 C) even numbers from 2 to 100
B) numbers from 2 to 100 D) all even numbers
Objective: (2.1) Use Three Methods to Represent Sets
5) {March, May} A) the set of months in the year C) the set of months that begin with M
B) the set of months in the Spring D) the set of months that are warm
Objective: (2.1) Use Three Methods to Represent Sets
6) {10, 11, 12, 13, ...} A) the set of natural numbers less than 14 C) the set of natural numbers
B) the set of two-digit natural numbers D) the set of natural numbers greater than 9
Objective: (2.1) Use Three Methods to Represent Sets
Express the set using the roster method. 7) the set of natural numbers less than or equal to 7 A) {0, 1, 2, 3, . . . , 6} B) {1, 2, 3, . . . , 7}
C) {1, 2, 3, . . . , 6}
D) {0, 1, 2, 3, . . . , 7}
C) {2, 4, 6, . . . , 14}
D) {1, 3, 5, . . . , 15}
C) {10,11,12,...}
D) {10,11,12}
Objective: (2.1) Use Roster Method
8) the set of odd natural numbers less than 15 A) {1, 3, 5, . . . , 13} B) {0, 1, 3, 5, . . . , 13} Objective: (2.1) Use Roster Method
9) {x | x % N and x is greater than 9} A) {9,10,11,...} B) {10,12,14,...} Objective: (2.1) Use Roster Method
1
10) {x | x % N and x lies between 0 and 4} A) {1, 2, 3, 4} B) {0, 1, 2, 3}
C) {0, 1, 2, 3, 4}
Objective: (2.1) Use Roster Method
List the elements in the set. 11) The set of the days of the week A) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} B) {Saturday, Sunday} C) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} D) {Tuesday, Thursday} Objective: (2.1) Use Roster Method
Determine if the set is the empty set. 12) {0, +} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
13) {x|x is a living U.S. president born after 1700} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
14) {x|x is the number of living U.S presidents born before 1700} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set
15) {x|x is a day of the week whose name begins with the letter Y} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set
16) {x|x < 2 and x > 6} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
17) {x|x % Ν and 10 < x < 14} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
18) {x|x is a number less than 6 or greater than 10} A) Yes, it is the empty set.
B) No, it is not the empty set.
Objective: (2.1) Define and Recognize the Empty Set
Determine whether the statement is true or false. 19) 9 % {1, 3, 5, 7, 9} A) True
B) False
Objective: (2.1) Use the Symbols % and '
2
D) {1, 2, 3}
20) 7 % {1, 2, 3, ..., 15} A) True
B) False
Objective: (2.1) Use the Symbols % and '
21) 19 % {2, 4, 6, ..., 20} A) True
B) False
Objective: (2.1) Use the Symbols % and '
22) 14 ' {1, 2, 3, ..., 10} A) True
B) False
Objective: (2.1) Use the Symbols % and '
23) 11 ' {1, 2, 3, ..., 40} A) True
B) False
Objective: (2.1) Use the Symbols % and '
24) 3 ' {x|x % N and x is odd} A) True
B) False
Objective: (2.1) Use the Symbols % and '
25) 22 ' {x|x % N and 15 < x K 25} A) True
B) False
Objective: (2.1) Use the Symbols % and '
26) -5 ' N A) True
B) False
Objective: (2.1) Use the Symbols % and '
Find the cardinal number for the set. 27) {33, 35, 37, 39, 41} A) 4
B) 33
C) 6
D) 5
C) 60
D) 30
C) 3
D) 1
Objective: (2.1) Find the Cardinal Number for Each Set
28) {10, 12, 14, . . . , 68} A) 20
B) 15
Objective: (2.1) Find the Cardinal Number for Each Set
29) {x | x is a day of the week that begins with the letter N} A) 0 B) 2 Objective: (2.1) Find the Cardinal Number for Each Set
30) Determine the cardinal number of the set {x | x is a letter of the alphabet} A) 25 B) 26 C) 30
D) 23
Objective: (2.1) Find the Cardinal Number for Each Set
31) D = {seven} A) 1
B) 7
C) 0
Objective: (2.1) Find the Cardinal Number for Each Set
3
D) 5
32) B = {x|x % N and 1 K x < 9} A) 7
B) 9
C) 8
D) 10
C) 9
D) 16
Objective: (2.1) Find the Cardinal Number for Each Set
33) C = {x|x K 4 and x L 12} A) 0
B) 8
Objective: (2.1) Find the Cardinal Number for Each Set
Are the sets equivalent? 34) A is the set of residents age 45 or older living in the United States B is the set of residents age 45 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equivalent Sets
35) A = {11, 12, 13, 14, 15} B = {10, 11, 12, 13, 14} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
36) A = {13, 15, 17, 19, 21} B = {14, 16, 18, 20, 22} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
37) A = {11, 12, 12, 13, 13, 13, 14, 14, 14, 14} B = {14, 13, 12, 11} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
38) A = {Larry, Moe, Curly. Shemp} B = {Posh, Sporty, Baby, Scary} A) Yes
B) No
Objective: (2.1) Recognize Equivalent Sets
Are the sets equal? 39) {p, q, r, s} = {q, s, r, p} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
40) {20, 22, 24, 26, 28} = {22, 24, 26, 28} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
41) {7, 7, 11, 11, 16} = {7, 11, 16} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
4
42) A is the set of residents age 53 or older living in the United States B is the set of residents age 53 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equal Sets
43) A = {20, 21, 22, 23, 24} B = {19, 20, 21, 22, 23} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
44) A = {21, 23, 25, 27, 29} B = {22, 24, 26, 28, 30} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
45) A = {14, 15, 15, 16, 16, 16, 17, 17, 17, 17} B = {17, 16, 15, 14} A) Yes
B) No
Objective: (2.1) Recognize Equal Sets
Determine whether the set is finite or infinite. 46) {x | x % N and x L 100} A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
47) {x | x % N and x K 1,000} A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
48) The set of natural numbers less than 50 A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
49) The set of natural numbers less than 1 A) Finite
B) Infinite
Objective: (2.1) Distinguish Between Finite and Infinite sets
Express the set using set-builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. 50) A = {14, 15, 16, 17, 18,...} A) {x | x % N and x K 14} B) {x | x % N and x L 14} C) {x | x % N and x > 14} D) {x | x % N and x L 18} Objective: (2.1) Apply Set Notation to Sets of Natural Numbers
51) A = {600, 601, 602, . . ., 6,000} A) {x | x % N and 600 K x K 6,000} C) {x | x % N and x L 600 }
B) {x | 600 < x < 6,000} D) {x | x % N and x K 6,000}
Objective: (2.1) Apply Set Notation to Sets of Natural Numbers
5
The bar graph shows the percentage of adults that use the Internet for specific tasks. Use the graph to represent the given set using the roster method. 52)
34 29
25 18 13
the set of tasks in which usage exceeds 23% A) {e-mail, information searches} C) {e-mail, information searches, news}
B) {e-mail, information searches, news, job} D) {job, school}
Objective: (2.1) Solve Applications
53)
33 28
24 17 12 {x | x is a task in which usage lies between 14% and 32%} A) {news, job} C) {email, information searches, news, job, school} Objective: (2.1) Solve Applications
6
B) {information searches, news, job} D) {news}
The line graph shows the percentage of obese adults in a certain city by age. Based on the information in the graph, represent the set using the roster method. 54)
30 25 20 15 10 5
{x | x is an age at which 20% of adults in city X are obese} A) {30} B) {40}
C) {60}
Objective: (2.1) Solve Applications
Write 5 or * in the blank so that the resulting statement is true. 55) {4, 6, 8} {3, 4, 5, 6, 8} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
56) {3, 40, 45} A) 5
{9, 40, 45, 55} B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
57) {red, blue, green} _____ {blue, green, yellow, black} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
58) {x | x is a tree} _____ {x | x is a spruce tree} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
59) {c, a, n, d, i, d, a, t, e} _____ {a, c, d, e, i, t, a, n, d} A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
60)
8 3 11 7 , _____ , 11 7 8 3
A) 5
B) *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
7
D) {50}
Use 5, *, 2, or both 2 and 5 to make a true statement. 61) {a, b} {z, a, y, b, x, c} A) * B) 2 and 5
C) 2
D) 5
C) 5
D) 2 and *
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
62) {6, 7, 8} A) *
{6, 7, 8} B) 2
Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
63) {x | x is a male who is registered with Selective Service} _____ {x | x is a male who is in the Army} A) 2 B) 5 and 2 C) * D) 5 Objective: (2.2) Recognize Subsets and Use the Notation 2, 5
Determine whether the statement is true or false. 64) Alice 5 {Bob, Carol, Ted, Alice} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
65) {Ted} 5 {Bob, Carol, Ted, Alice} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
66) +5 {France, Germany, Switzerland} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
67) {2, 9} * {9, 2} A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
68) {1} * + A) True
B) False
Objective: (2.2) Determine Whether Each statement is True or False
List all the subsets of the given set. 69) {Siamese, domestic shorthair} A) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, B) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } C) {Siamese, domestic shorthair}, {domestic shorthair}, { } D) {Siamese}, {domestic shorthair}, { } Objective: (2.2) Determine the Number of Subsets of a Set
70) {12} A) {12}
B) { }
C) {0}, {12}, { }
Objective: (2.2) Determine the Number of Subsets of a Set
8
D) {12}, { }
71) + A) +
B) no subsets
C) { }, {0}
D) {+}
Objective: (2.2) Determine the Number of Subsets of a Set
Calculate the number of subsets and the number of proper subsets for the set. 1 1 1 1 , , , 72) 6 7 8 9 A) 15; 14
B) 14; 15
C) 15; 16
D) 16; 15
C) 64; 63
D) 63; 64
C) 510; 511
D) 511; 512
C) 16; 15
D) 8; 7
C) 64; 65
D) 128; 127
Objective: (2.2) Determine the Number of Subsets of a Set
73) {1, 3, 5, 7, 9, 11} A) 63; 62
B) 62; 63
Objective: (2.2) Determine the Number of Subsets of a Set
74) the set of natural numbers less than 10 A) 512; 511 B) 511; 510 Objective: (2.2) Determine the Number of Subsets of a Set
75) the set of words describing the colors on a stoplight A) 15; 16 B) 7; 8 Objective: (2.2) Determine the Number of Subsets of a Set
76) {x | x is a day of the week} A) 127; 126
B) 128; 129
Objective: (2.2) Determine the Number of Subsets of a Set
Provide an appropriate response. 77) If set A is equivalent to the set of natural numbers, then n(A) < E0 . A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
78) If set A is equivalent to the set of odd natural numbers, then n(A) = E0 . A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
79) The set {1, 2, 3, ..., 100} has 2 100 proper subsets. A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
80) {x|x % N and 45 < x < 70} 5 {x|x % N and 45 K x K 70} A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
81) +* {+ } A) True
B) False
Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets
9
Consider below the branching tree diagram based on the number per 3000 American adults.
Let T = the set of Americans who like classical music R = the set of Republicans who like classical music D = the set of Democrats who like classical music I = the set of Independents who like classical music Determine whether the statement is true or false. 82) R % T A) True
B) False
Objective: (2.2) Solve Applications
83) D 2 T A) True
B) False
Objective: (2.2) Solve Applications
84) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music W 2T A) True B) False Objective: (2.2) Solve Applications
85) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music If x %D, then x %M. A) True B) False Objective: (2.2) Solve Applications
86) Let M = the set of Republican men who like classical music W = the set of Republican women who like classical music If x %W, then x %R. A) True B) False Objective: (2.2) Solve Applications
87) If x %R, then x'I. A) True
B) False
Objective: (2.2) Solve Applications
10
88) Let M = the set of Independent men who like classical music W = the set of Independent women who like classical music The set of elements in M and W combined is equal to set I. A) True B) False Objective: (2.2) Solve Applications
Use the formula for the number of subsets of a set with n elements to solve the problem. 89) Pasta comes with tomato sauce and can be ordered with some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? A) 128 B) 255 C) 127 D) 256 Objective: (2.2) Solve Applications
90) A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation, no engines, one engine, two engines, three engines, or all four engines can be sent to a fire. How many options does the dispatcher have for sending the fire engines to the scene of the caller? A) 15 B) 8 C) 7 D) 16 Objective: (2.2) Solve Applications
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Describe a universal set U that includes all elements in the given sets. Answers may vary. 91) A = {Copeland, Gershwin, Bernstein} B = {Strauss, Mendlssohn} Objective: (2.3) Understand the Meaning of a Universal Set
92) A = {fruit juice, coffee} B = {tea, spring water} Objective: (2.3) Understand the Meaning of a Universal Set
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 93) A = {2, 4, b, d} A) {1, 5, a, c, e} B) {1, 5, a, e} C) {1, 2, 4, 5, a, b, c, d, e} D) {1, 3, 5, a, c, e} Objective: (2.3) Understand the Meaning of a Universal Set
Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}. Use the roster method to write the following set. 94) A' A) A' = {21, 22, 23, . . . , 40} B) A' = {26, 28, 30, . . . , 40} C) A' = {27, 29, 31, . . . , 39} D) A' = {26, 27, 28, . . . , 40} Objective: (2.3) Understand the Meaning of a Universal Set
11
Let U = {21, 22, 23, 24, ...}, A = {21, 22, 23, 24, ..., 40}, B = {21, 22, 23, 24, ..., 50}, C = {22, 24, 26, 28, ...}, and D = {21, 23, 25, 27, ...}. Use the roster method to write the following set. 95) C' A) C' = {21, 23, 25, 27, ..., 39} B) C' = {21, 22, 23, 24, ...} C) C' = {21, 23, 25, 27, ...} D) C' = {22, 24, 26, 28, ...} Objective: (2.3) Understand the Meaning of a Universal Set
Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 96) (A 1 B)' A) {r, t, v, x} B) {s, u, w}
C) {r, s, t, u, v, w, x, z}
D) {t, v, x}
C) {s, u, w}
D) {q, s, t, u, v, w, x, y}
C) {q, s, u, v, w, x, y, z}
D) {w, y}
Objective: (2.3) Perform Operations with Sets
97) A' 1 B A) {r, s, t, u, v, w, x, z}
B) {q, r, s, t, v, x, y, z}
Objective: (2.3) Perform Operations with Sets
98) C' 1 A' A) {q, r, s, t, u, v, x, z}
B) {s, t}
Objective: (2.3) Perform Operations with Sets
99) B 1 C A) {q, s, u, w, y} C) {q, s, v, w, x, y, z}
B) {v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
100) C 1 + A) {v, w, x, y, z}
B) {q, s, y, z}
C) { }
D) {q, s, u, w, y}
Objective: (2.3) Perform Operations with Sets
101) B 1 U A) {q, s, y, z} C) {q, r, s, t, u, v, w, x, y, z}
B) {q, s, u, w, y} D) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
102) A . B' A) {u, w}
B) {r, s, t, u, v, w, x, z}
C) {t, v, x}
D) {q, s, t, u, v, w, x, y}
C) {r, s, t, u, v, w, x, z}
D) {t, v, x}
C) {t, v, x}
D) {q, s, t, u, v, w, x, y}
Objective: (2.3) Perform Operations with Sets
103) (A 1 B)' A) {s, u, w}
B) {r, t, v, x}
Objective: (2.3) Perform Operations with Sets
104) (A . B)' A) {r, t, u, v, w, x, z}
B) {s, u, w}
Objective: (2.3) Perform Operations with Sets
12
105) A' 1 B A) {q, r, s, t, v, x, y, z}
B) {r, s, t, u, v, w, x, z}
C) {q, s, t, u, v, w, x, y}
D) {s, u, w}
C) {w, y}
D) {q, r, s, t, u, v, x, z}
C) {w, y}
D) {r, t}
C) {q, s, u, w, y, z}
D) {q, s, y}
Objective: (2.3) Perform Operations with Sets
106) C' 1 A' A) {s, t}
B) {q, s, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
107) C' . A' A) {q, r, s, t, u, v, x, z}
B) {q, s, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
108) A . B A) {r, t, u, v, w, x, z}
B) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
109) B 1 C A) {v, w, x, y, z} C) {q, s, u, w, y}
B) {q, s, v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
110) A' A) {r, t, v, x, z} C) {q, r, s, t, u, v, w, x, y, z}
B) {s, u, w, y} D) {q, s, y, z}
Objective: (2.3) Perform Operations with Sets
111) (A . C)' A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}
B) {w, y} D) {q, r, s, t, u, v, x, z}
Objective: (2.3) Perform Operations with Sets
112) C 1 + A) {q, s, u, w, y}
B) {q, s, y, z}
C) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
113) B 1 U A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}
B) {q, s, u, w, y} D) {v, w, x, y, z}
Objective: (2.3) Perform Operations with Sets
13
D) { }
Use the Venn diagram to determine the set or cardinality. 114) A
A) {12, 15, 16}
B) {11, 13, 14, 17}
C) {11, 12, 13}
D) {13, 17}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
115) B
A) {12, 13, 15, 16, 17}
B) {14, 16, 17}
C) {11, 14}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
116) U
A) {12, 15, 16} C) {11, 12, 13, 14, 15, 16, 17, 18, 19}
B) {13, 17} D) {11, 14}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
14
D) {13, 17}
117) A . B
A) {%, @, &, one, six}
B) {@, &}
C) {%, one, six}
D) {77, 95}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
118) n(A 1 B)
A) 5
B) {%, @, &, one, six}
C) 2
D) {@, &}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
119) n(1) - n(B)
A) {%, 77, 95}
B) 4
C) 3
D) {%, @, &, 77, 95}
Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets
Use the formula for the cardinal number of the union of two sets to solve the problem. 120) Set A contains 4 elements, set B contains 9 elements, and 2 elements are common to sets A and B. How many elements are in A 1 B? A) 11 B) 13 C) 12 D) 10 Objective: (2.3) Use the Formula for n(A 1 B)
121) Set A contains 8 letters and 12 numbers. Set B contains 12 letters and 8 numbers. Two letters and 5 numbers are common to both sets A and B. Find the number of elements in set A or set B. A) 40 B) 33 C) 27 D) 47 Objective: (2.3) Use the Formula for n(A 1 B)
15
122) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A 1 B) then how many elements are in (A . B)? A) 13 B) 8 C) 17 D) 5 Objective: (2.3) Use the Formula for n(A 1 B)
In the exercise below, let U = {x|x % N and x < 10} A = {x|x is an odd natural number and x < 10} B = {x|x is an even natural number and x < 10} C = {x|x % N and 3 < x < 5} Find the set. 123) A 1 B A) {1, 3, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}
B) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) B or {2, 4, 6, 8}
Objective: (2.3) Find Each of the Given Sets
124) B . U A) U or {1, 2, 3, 4, 5, 6, 7, 8, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B) B or {2, 4, 6, 8} D) B or {2, 4, 6, 8, 10}
Objective: (2.3) Find Each of the Given Sets
125) B . C' A) B or {2, 4, 6, 8, 10}
B) C or {4}
C) B or {2, 4, 6, 8}
Objective: (2.3) Find Each of the Given Sets
126) (A . C)' A) {1, 3, 4, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B) {1, 2, 3, 5, 6, 7, 8, 9} D) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}
Objective: (2.3) Find Each of the Given Sets
Use the Venn diagram to list the elements of the set in roster form. 127)
A 1B A) {11, 12, 13, 14, 15, 16, 17, 18, 19} C) {13, 17}
B) {11, 12, 14, 15, 16} D) {11, 12, 13, 14, 15, 16, 17}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
16
D) {2, 6, 8}
128)
A .B A) {13, 17} C) {11, 12, 13, 14, 15, 16, 17}
B) {11, 12, 13, 14, 15, 16, 17, 18, 19} D) {11, 12, 14, 15, 16}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
129)
A'
A) {12, 15, 16, 18, 19}
B) {11, 13, 14, 17}
C) {11, 14, 18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
130)
B'
A) {11, 14} C) {12, 15, 16, 18, 19}
B) {11, 14, 18, 19} D) {11, 13, 14, 17, 18, 19}
Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram
17
D) {12, 15, 16}
Solve the problem. 99) An experiment calls for cooling a mixture to -14°F, then increasing the temperature 80 degrees. What is the final temperature the experiment is to obtain? A) -94°F B) 94°F C) 66°F D) -66°F Objective: (5.2) Use the Order of Operations Agreement
100) A hill is at 534 feet above sea level, and a crater next to it is at 265 feet below sea level. What is the difference in height between the hill and the crater? A) 269 ft B) -799 ft C) -269 ft D) 799 ft Objective: (5.2) Use the Order of Operations Agreement
101) The temperature at the South pole was °F at 8 am. At 3 pm, it was -47°F. By how many degrees did the temperature drop? A) by -83°F B) by 83°F C) by -11°F D) by 11°F Objective: (5.2) Use the Order of Operations Agreement
Express the sentence as a single numerical expression. Then use the order of operations to simplify the expression. 102) Cube -5. Subtract this exponential expression from -50. A) B) 175 C) -75 D) -175 Objective: (5.2) Use the Order of Operations Agreement
103) Subtract 10 from 7. Multiply this difference by 3. Raise this product to the fourth power. A) 1,296 B) -6,561 C) -729
D) 6,561
Objective: (5.2) Use the Order of Operations Agreement
Solve the problem. 104) The bar graph shows the combined benefits /deficits of a company for six consecutive years.
-430
-394
-460 -511 -672 -798
Find the difference between the Year 2 combined amount and the Year 6 combined amount. A) $338,000 B) $404,000 C) -$338,000 D) -$404,000 Objective: (5.2) Use the Order of Operations Agreement
11
105) The bar graph shows the combined benefits /deficits of a company for six consecutive years.
-419
-395
-451 -511 -665 -807
By how much did the Year 6 combined amount exceed twice the Year 3 combined amount? A) -$95,000 B) $95,000 C) -$356,000 D) -$712,000 Objective: (5.2) Use the Order of Operations Agreement
106) The bar graph shows the combined benefits /deficits of a company for six consecutive years.
-426
-396
-453 -515 -678 -799
Find the average combined amount for Year 5 and Year 6. A) -$1,477,000 B) -$738,400
C) -$738,600
D) -$738,500
Objective: (5.2) Use the Order of Operations Agreement
Provide an appropriate response. 107) The set of rational numbers is the set of all numbers which can be expressed in the form are integers and
is not equal to 0.
A) a · b; a
B)
a ;b b
C)
Objective: (5.3) Define the Rational Numbers
12
a ;a b
, where a and b
D) a · b; b
Reduce the rational number to its lowest terms. 10 108) 12 A)
10 12
B)
5 6
C)
5 2
D)
2 6
C)
44 77
D)
4 11
C)
13 19
D)
13 5
C)
16 13
D)
11 16
C)
25 5
D)
25 2
D)
180 17
Objective: (5.3) Reduce Rational Numbers
109)
44 77
A)
4 7
B)
11 7
Objective: (5.3) Reduce Rational Numbers
110)
65 95
A)
5 19
B)
65 95
Objective: (5.3) Reduce Rational Numbers
111)
176 208
A)
176 208
B)
11 13
Objective: (5.3) Reduce Rational Numbers
Convert the mixed number to an improper fraction. 2 112) 5 5 A)
27 5
B)
27 2
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
113) 18
10 17
A)
316 10
B)
476 10
C)
316 17
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
114) -5
4 7
A) -
39 7
B) -
39 4
C) -
35 4
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
13
D) -
35 7
Convert the improper fraction to a mixed number. 22 115) 3 A) 7
1 3
B)
1 3
C) 6
1 7
D) 8
1 3
D) 7
1 5
D) 6
1 2
D) 1
7 9
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
116)
36 5
A) 6
1 5
B) 7
1 7
C) 8
1 5
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
117)
15 2
A) 7
1 7
B) 7
1 2
C) 8
1 2
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
118)
16 9
A) 16
9 16
B)
9 16
C) 16
16 9
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
119)
216 7
A)
7 216
B) 216
7 216
216 7
D) 30
6 7
4 5
D) -7
4 5
C) 216
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
120) -
34 5
A) -6
4 7
B) -5
4 5
C) -6
Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions
Express the rational number as a decimal. 15 121) 16 A) 0.9375
B) 0.9375
C) 0.9375
Objective: (5.3) Express Rational Numbers as Decimals
14
D) 0.9375
122)
7 20
A) 0.35
B) 0.355
C) 0.35
D) 0.35
C) 0.09
D) 0.09
C) 0.375
D) 0.125
C) 1.6
D) 0.8
C) 0.35
D) 0.7
C) 0.81
D) 0.181
C) 1.4
D) 1.14
Objective: (5.3) Express Rational Numbers as Decimals
123)
1 11
A) 0.09
B) 0.090
Objective: (5.3) Express Rational Numbers as Decimals
124)
3 8
A) 0.1375
B) 3.125
Objective: (5.3) Express Rational Numbers as Decimals
125)
4 5
A) 1
B) 0.1
Objective: (5.3) Express Rational Numbers as Decimals
126)
7 20
A) 3.2
B) 0.3
Objective: (5.3) Express Rational Numbers as Decimals
127)
9 11
A) 0.81
B) 0.181
Objective: (5.3) Express Rational Numbers as Decimals
128)
13 9
A) 1.14
B) 1.4
Objective: (5.3) Express Rational Numbers as Decimals
Express the rational number as a decimal. Then insert either < or > between the rational number to make the statement true. 4 5 129) 11 12
A) >
B) <
Objective: (5.3) Express Rational Numbers as Decimals
130)
24 37
23 36
A) >
B) <
Objective: (5.3) Express Rational Numbers as Decimals
15
131) -
5 6
-
1 3
A) >
B) <
Objective: (5.3) Express Rational Numbers as Decimals
Express the terminating decimal as a quotient of integers. If possible, reduce to lowest terms. 132) 0.1 1 1 1 A) B) C) 9 10 99
D)
1 100
Objective: (5.3) Express Decimals in the Form a/b
133) 0.34 A)
17 5
B)
34 9
C)
17 50
D)
34 99
C)
267 500
D)
178 333
C)
2326 999
D)
2326 9999
Objective: (5.3) Express Decimals in the Form a/b
134) 0.534 A)
178 3333
B)
267 5000
Objective: (5.3) Express Decimals in the Form a/b
135) 0.2326 1163 A) 500
B)
1163 5000
Objective: (5.3) Express Decimals in the Form a/b
Express the repeating decimal as a quotient of integers. If possible, reduce to lowest terms. 136) 0.1 A)
1 10
B)
1 9
C)
1 100
D)
1 99
C)
65 99
D)
13 200
C)
119 5000
D)
119 500
Objective: (5.3) Express Decimals in the Form a/b
137) 0.65 A)
13 20
B)
65 999
Objective: (5.3) Express Decimals in the Form a/b
138) 0.238 A)
238 9999
B)
238 999
Objective: (5.3) Express Decimals in the Form a/b
16
Perform the indicated operation(s). Where possible, reduce the answer to lowest terms. 5 1 139) · 7 8 A)
2 5
B)
56 5
C)
7 40
D)
5 56
6 5
D)
6 5
Objective: (5.3) Multiply and Divide Rational Numbers
140) - 1 -
6 5
A) -
7 5
B)
5 6
C) -
Objective: (5.3) Multiply and Divide Rational Numbers
141) 1
2 2 5 3 5
A) 9
B) 5
C) 8
D) 3
Objective: (5.3) Multiply and Divide Rational Numbers
142) -
2 1 9 12
A) -
1 36
B) -
1 7
C)
1 54
D)
2 21
C)
16 35
D)
7 120
D)
21 8
D)
2 9
Objective: (5.3) Multiply and Divide Rational Numbers
143)
6 7 ÷ 15 8
A)
13 23
B)
120 7
Objective: (5.3) Multiply and Divide Rational Numbers
144) -
7 8 ÷ 3 9
A) -
56 27
B)
56 27
C) -
21 8
Objective: (5.3) Multiply and Divide Rational Numbers
145)
2 3 ÷ 15 5
A) -
2 25
B) -
2 9
C)
Objective: (5.3) Multiply and Divide Rational Numbers
17
9 2
146) -
5 9 ÷ 6 10
A) -
3 4
B) -
27 25
C)
25 27
D)
27 25
C)
2 9
D)
4 81
C)
4 7
D)
56 45
Objective: (5.3) Multiply and Divide Rational Numbers
147)
1 3 + 9 9
A)
4 9
B) 0
Objective: (5.3) Add and Subtract Rational Numbers
148)
4 4 + 5 9
A)
8 45
B)
1 6
Objective: (5.3) Add and Subtract Rational Numbers
149)
9 1 11 11
A)
10 11
B)
8 11
C) -
9 11
D) 0
Objective: (5.3) Add and Subtract Rational Numbers
150)
3 1 - 13 13
A)
2 13
B)
4 13
C)
1 13
D) -
4 13
C)
3 16
D)
1 8
C)
1 3
D)
11 7
Objective: (5.3) Add and Subtract Rational Numbers
151)
2 1 8 8
A)
1 4
B)
1 2
Objective: (5.3) Add and Subtract Rational Numbers
152)
6 5 - 21 21
A)
1 2
B)
11 21
Objective: (5.3) Add and Subtract Rational Numbers
18
153)
5 6 25 22
A)
7 25
B)
7 550
C)
1 550
D)
1 25
C)
9 88
D) 0
C)
43 24
D)
4 3
D)
1 10
D)
55 56
Objective: (5.3) Add and Subtract Rational Numbers
154)
1 1 8 ÷ 5 6 9
A) -
9 88
B)
3 80
Objective: (5.3) Add and Subtract Rational Numbers
155)
1 1 1 1 + ÷ + 2 3 2 8
A) 2
B)
31 24
Objective: (5.3) Add and Subtract Rational Numbers
Perform the indicated operations. If possible, reduce the answer to its lowest terms. 1 1 1 + · 156) 5 10 2 A)
3 20
B)
3 40
C)
3 5
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
157)
11 8 8 ÷ + 7 5 15
A)
55 64
B)
165 224
C)
15 224
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
158)
5 1 2 2 ÷ 6 3 3 5
A)
11 15
B) 1
5 6
C) 2
7 30
D) 12
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
159)
2 1 4 1 - ÷ 3 6 5 2
A)
1 9
B)
1 8
C)
5 3
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
19
D)
1 24
1 2
160)
1 4 2 1 + ÷ 4 5 3 6
A)
10 21
B)
10 63
C)
14 5
D)
32 63
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
161)
32 49 3 -5 7
A)
÷
1 5 7 4
1 4
B) -
1 4
C) -
9 4
D) -
9 2
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
Perform the indicated operations. Leave denominators in prime factorization form. 1 1 1 + 162) 4 2 3 2 2 · 112 2 · 5 · 11 2 · 5 A)
-4,671 3 2 · 5 4 · 112
B)
5,009 4 2 · 5 3 · 112
C)
-4,671 4 2 · 5 3 · 112
D)
5,009 3 2 · 5 4 · 112
Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers
Find the rational number halfway between the two numbers in each pair. 1 1 163) and 2 4 A)
3 4
B)
1 8
C)
3 8
D)
1 4
C)
13 4
D)
13 2
Objective: (5.3) Apply the Density Property of Rational Numbers
164) -
3 and -5 2
A) -
13 4
B) -
13 2
Objective: (5.3) Apply the Density Property of Rational Numbers
Solve the problem. 165) Of the 621 people polled about gardening, 207 replied that they plant a garden. What fractional part of those polled, expressed in lowest terms, plant a garden? 1 1 2 1 A) B) C) D) 3 2 3 4 Objective: (5.3) Solve Problems Involving Rational Numbers
166) Of the 500 urban residents polled about gardening, 108 replied that they plant a garden. What fractional part of those polled, expresses in lowest terms, plant a garden? 1 1 98 27 A) B) C) D) 500 125 125 5 Objective: (5.3) Solve Problems Involving Rational Numbers
20
167) Of the 300 suburban residents polled about gardening, garden? A) 180 residents
12 replied that they plant a garden. How many plant a 20
B) 300 residents
C) 60 residents
D) 15 residents
Objective: (5.3) Solve Problems Involving Rational Numbers
168) A recipe calls for A)
1 cup of butter. How much is needed to double the recipe? 4
2 c 3
B)
1 c 8
C)
1 c 6
D)
1 c 2
Objective: (5.3) Solve Problems Involving Rational Numbers
169) A recipe calls for 7 ounces of unsweetened chocolate for 16 brownies. How much of unsweetened chocolate is needed to make 30 brownies? 7 56 105 oz oz oz A) B) 210 oz C) D) 16 15 8 Objective: (5.3) Solve Problems Involving Rational Numbers
170) A recipe calls for 1 1 A) 43 c 5
1 cups of sugar for 8 brownies. How much of sugar is needed to make 36 brownies? 5
B) 5
2 c 5
C)
4 c 15
D)
3 c 20
Objective: (5.3) Solve Problems Involving Rational Numbers
171) Jerry caught a fish that weighed 10
1 3 pounds. Pat caught a fish that weighed 7 pounds. How much more did 7 7
Jerry's fish weigh than Pat's fish? 5 4 A) 2 lb B) 2 lb 7 7
C) 17
5 lb 7
D) 16
5 lb 7
Objective: (5.3) Solve Problems Involving Rational Numbers
172) In most societies, men say they prefer women who are younger. In country A, the preferred age in a mate for men 4 6 is 14 years younger than self. In country B, the preferred age in a mate for men is 8 years younger than self. 7 7 What is the difference between the preferred age in a mate for men in country A and men in country B? 5 4 5 5 A) 22 yr B) 5 yr C) 5 yr D) 21 yr 7 7 7 7 Objective: (5.3) Solve Problems Involving Rational Numbers
173) A business is owned by three people. The first owns
7 1 of the business and the second owns of the business. 12 6
What fractional part of the business is owned by the third person? 1 1 3 A) B) C) 3 4 4 Objective: (5.3) Solve Problems Involving Rational Numbers
21
D)
5 12
174) If a person walks A)
4 mi 13
3 1 mile, then jogs mile, what is the total distance covered? 8 5
B)
23 mi 40
C)
7 mi 40
D)
1 mi 10
Objective: (5.3) Solve Problems Involving Rational Numbers
175) Some companies pay people extra when they work more than a regular 40-hour week. The overtime rate is often 1 3 1 , or , times the regular hourly rate. A clerical job pays $10 an hour and offers time and a half for hours worked 2 2 over 40. If a clerk works 44 hours during one week, what is the clerk's total pay before taxes? A) $460 B) $60 C) $440 D) $660 Objective: (5.3) Solve Problems Involving Rational Numbers
176) A will states that
2 1 of the estate is to be divided among the relatives. Of the remaining estate, goes to a certain 3 6
charity. What fractional part of the estate goes to the charity? 1 1 1 A) B) C) 9 6 18
D)
11 18
Objective: (5.3) Solve Problems Involving Rational Numbers
177) On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 5 miles. Find the length of a trail 1 represented by a line that is 9 centimeters long on the map. 2 A)
10 mi 19
B) 484
1 mi 2
C) 1
9 mi 10
D) 47
1 mi 2
Objective: (5.3) Solve Problems Involving Rational Numbers
Provide an appropriate response. 178) Which of the following decimal numbers is an irrational number? Explain your answer. A) 1.73205080757... is irrational because it neither terminates nor repeats. B) 0.53 is irrational because it is a repeating decimal. C) 1.16 is irrational because it does not terminate. D) 0.0089372432 is irrational because it extends past the millionths place. Objective: (5.4) Define the Irrational Numbers
Evaluate the expression. 179) 16 A) 2
B) 4
C) 8
D) 16
Objective: (5.4) Simplify Square Roots
Use a calculator with a square root key to find a decimal approximation for the square root. Round the number displayed as indicated. 180) 888 to the nearest thousandth A) 888.000 B) 29.799 C) 29.796 D) 29.804 Objective: (5.4) Simplify Square Roots
22
181)
4,951 to the nearest hundredth A) 70.36 B) 70.4
C) 70.363
D) 70
C) 5.1
D) 15.9
Objective: (5.4) Simplify Square Roots
182)
9π to the nearest tenth A) 15.7
B) 5.3
Objective: (5.4) Simplify Square Roots
Simplify the square root. 183) 112 A) 10.583 C) 16 7
B) 4 7 D) This expression is already simplified.
Objective: (5.4) Simplify Square Roots
184)
72 A) 2 23 C) 3 8
B) 6 2 D) This expression is already simplified.
Objective: (5.4) Simplify Square Roots
185) 2 192 A) 4 12 C) 16 3
B) 4 48 D) This expression is already simplified.
Objective: (5.4) Simplify Square Roots
Perform the indicated operation. Simplify the answer when possible. 186) 3 · 2 A) 3 + 2 B) 6 C)
5
D)
6
Objective: (5.4) Perform Operations with Square Roots
187)
7 · 16 A) 28
B)
112
C) 4 7
D) 4
Objective: (5.4) Perform Operations with Square Roots
188)
5· 5 A) 2 5 · 12
B) 5
C)
10
D)
25
C)
2
D)
6 3
Objective: (5.4) Perform Operations with Square Roots
189)
6 3
A) 6
B)
3
Objective: (5.4) Perform Operations with Square Roots
23
54 6
190)
B) 3 6
A) 6
3 6
D) 3
C) -1 19
D)
C) 52 186
D) 9 3
C) 36
D) 6
C) 4 10
D) 2 10
C) 3 2
D) 8
C) 5 3
D)
C) 14 3
D) 87
3 5
D)
C)
Objective: (5.4) Perform Operations with Square Roots
191) 17 19 + 18 19 A) -36 19
B) 35 19
19
Objective: (5.4) Perform Operations with Square Roots
3 + 3 75 + 6 108 A) 9 186
192)
B) 52 3
Objective: (5.4) Perform Operations with Square Roots
6+ 6 A) 2 6
193)
B) 72
Objective: (5.4) Perform Operations with Square Roots
194) 2 10 + 3 10 A) 5 10
10
B) 6 10
Objective: (5.4) Perform Operations with Square Roots
2+ 8 A) 4
195)
B) 5 2
Objective: (5.4) Perform Operations with Square Roots
27 - 12 A) 2 3
196)
3
B)
15
Objective: (5.4) Perform Operations with Square Roots
197) 2 12 + 5 12 A) 399
B) 7 87
Objective: (5.4) Perform Operations with Square Roots
198)
1 5
12 +
A)
1 15
1 10
12
60
B)
2 5
3
C)
3
2 15
Objective: (5.4) Perform Operations with Square Roots
199)
7 · 21 - 5 3 3 A)
B) -5(
21 + 3 7 )
Objective: (5.4) Perform Operations with Square Roots
24
C) 44 3
D) 7 3
12
200) 8 125 + 8 63 + 5 175 A) 191 5 + 197 7
45
B) 197 5 + 149 7
C) 37 5 + 49 7
D) 31 5 + 97 7
Objective: (5.4) Perform Operations with Square Roots
Solve the problem. 201) When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the h ground is given by the equation t = , where t is measured in seconds. If an object falls 19.6 meters before it 4.9 hits the ground, find the time it took for the object to fall. A) 5 sec B) 2 sec
C) 3 sec
D) 4 sec
Objective: (5.4) Perform Operations with Square Roots
202) The maximum number of volts, E, that can be placed across a resistor is given by the formula E = PR, where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. Find E if P = 2 watts and R = 50 ohms. A) 10 V B) 20 V C) 100 V D) 5 V Objective: (5.4) Perform Operations with Square Roots
203) The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 25 months of age and a child 16 months of age? A) 2.9 in. B) 14.5 in. C) 4.9 in. D) 43.1 in. Objective: (5.4) Perform Operations with Square Roots
204) The square root expression Rf 1 -
v 2 gives the aging rate of an astronaut relative to the aging rate of a friend on c
Earth, Rf, where v is the astronaut's speed and c is the speed of light. An astronaut is moving at 60% of the speed of light. Substitute 0.6c in the expression above. What is his aging rate, correct to two decimal places if necessary, relative to a friend on Earth? A) 0.8 B) 0.8Rf C) 0.63R f D) 1.17R f Objective: (5.4) Perform Operations with Square Roots
205) The square root expression Rf 1 -
v 2 gives the aging rate of an astronaut relative to the aging rate of a friend on c
Earth, Rf, where v is the astronaut's speed and c is the speed of light. An astronaut is moving at 70% of the speed of light. Substitute 0.7c in the expression above. If 50 weeks have passed for his friend, how long, to the nearest week, was he gone? A) 1 weeks B) 27 weeks C) 61 weeks D) 36 weeks Objective: (5.4) Perform Operations with Square Roots
Rationalize the denominator. 9 206) 7 A)
81 7 7
B)
9 7 7
C) 58
Objective: (5.4) Rationalize Denominators
25
D) 9 7
207)
9 5
A) 9
B)
9 5
C) 9 5
D)
9 5 5
Objective: (5.4) Rationalize Denominators
208)
19 18
A)
19 6
18
B) 57 2
C)
19 6
C)
3 5
D)
15 5
C)
8 4 35
D)
46 4 35
C)
8 15
D)
8
2
D) 57 18
Objective: (5.4) Rationalize Denominators
209)
3 5
B) 3 5
A) 3
Objective: (5.4) Rationalize Denominators
Perform the indicated operation. Simplify the answer when possible. 36 100 + 210) 5 7 A)
23 4 6
B)
92 4 35
Objective: (5.4) Rationalize Denominators
211)
3 + 5
5 3
A)
8 3+
5
B)
8 15 15
Objective: (5.4) Rationalize Denominators
List all numbers from the set that are natural numbers. 1 212) {-3, - , 0, 0.14, 15, 9.8, 9} 3 A) { 9} C) {-3,
B) {0,
9}
D) {-3, -
9}
Objective: (5.5) Recognize Subsets of the Real Numbers
26
1 , 0, 0.14, 9.8, 3
9}