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Math Olympics Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic 7. Evaluate the expression a ÷ b for a = 24 and b = 8. a. 192 b. 16 c. 3 d. 4 expression p ÷ 10 in words. a. the product of p and 10 p times 10 b. p subtracted from 10 p less than 10 c. the quotient of 10 and p 10 divided by p d. the quotient of p and 10 p divided by 10 2. 3. Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters Julia wrote. Mike scored 40 points in the first half of the basketball game, and he scored y points in the second half of the game. Write an expression to determine the number of points he scored in all Then, find the number of points he scored in all if he scored 2 points in the second half of the game. a. 40y; 42 points b. 40 – y; 38 points c. ; 38 points d. 40 + y; a. 14 42 points –y c. 14 +y d. Salvador’s class has collected 88 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in each bag. Write an expression to show how many cans there will be in each bag. a. 88x 4. b. 14y 8. b. 88 +x c. d. 88 9. –x Evaluate the expression m + o for m = 9 and o = 7. a. 15 b. 16 c. 2 d. 63 5. Evaluate the expression q – v for q = 5 and v = 1. a. 3 b. 4 c. 5 d. 6 6. Evaluate the expression xy for x = 6 and y = 3. a. 21 b. 24 c. 9 d. 18 Aaron has saved 72 sand dollars and wants to give them away equally to y friends. Write an expression to show how many sand dollars each of Aaron’s friends will receive. Then, find the total number of sand dollars each of Aaron’s friends will get if Aaron gives them to 12 friends. a. 72 – y; 60 sand dollars b. 72 + y; 60 sand dollars c. ; 6 sand dollars 10. d. 72y; 6 sand dollars Salvador reads 12 books from the library each month for n months in a row. Write an expression to show how many books Salvador read in all. Then, find the number of books Salvador read if he read for 7 months. a. 12 – n; 19 books c. 12 + n; 19 books books 12. 11. ; 84 books d. 12n; 84 b. Evaluate the expression and . a. 23 b. 25 c. 32 d. 18 for Subtract using a number line. –5 – (–3) – (–3) –5 –8 –7 a. –3 13. –6 –5 –4 b. 2 –3 –2 –1 c. –5 0 1 2 3 4 5 6 7 d. –2 Add. 34 + (–21) a. 55 b. 13 a. –34ºF d. –42ºF c. –55 d. –13 14. Evaluate x + (–9) for x = 35. a. –44 b. –26 c. 26 d. 44 15. Subtract. –5 – (–8) b. 13 a. –13 c. 3 Evaluate x – (–10) for x = 12. a. –22 b. 2 c. 22 d. –2 17. The highest temperature recorded in the town of Westgate this summer was 101ºF. Last winter, the lowest temperature recorded was –9ºF. Find the difference between these extremes. a. 92ºF b. –92ºF c. 110ºF d. –110ºF The temperature on the ground during a plane’s takeoff was 4ºF. At 38,000 feet in the air, the temperature outside the plane was –38ºF. Find the difference between these two temperatures. b. 42ºF c. 34ºF 19. The elevator in the a downtown skyscraper goes from the top floor down to the lowest level of the underground parking garage. If the building is 470 feet tall and the elevator descends 530 feet from top to bottom, how far underground does the parking garage go? a. 990 feet b. 60 feet c. 1,000 feet d. 50 feet 20. Multiply. –8 • 9 b. –72 a. 1 d. –3 16. 18. 8 c. –17 d. 72 21. Evaluate –5u for u = –4. a. –9 b. 25 c. –20 d. 20 22. Divide. –48 8 a. –384 b. 6 c. –56 d. –6 23. Evaluate k (–11) for k = –33. a. 363 b. 3 c. –22 d. –3 24. Divide. 32. 8 a. 6 21 25. 26. 27. 5 a. 3 8 c. 8 21 b. 4 7 d. 6 14 33. Divide. 0 ÷ 5.928 a. –5.928 d. 0 b. 5.928 Write 9 as a power of the base 3. c. undefined Carina hiked at Yosemite National Park for 1.75 hours. Her average speed was 3.5 mi/h. How many miles did she hike? a. 2 mi b. 20 mi c. 61.25 mi d. 6.125 mi b. c. d. Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 6 times brighter than the next lower category. For example, a day that is dazzling is 6 times brighter than a day that is radiant. How many times brighter is a dazzling day than an illuminated day? Sunlight Intensity Category Brightness Dim 2 Illuminated 3 Radiant 4 Dazzling 5 Write the power represented by the geometric model. a. 36 times brighter b. 2 times brighter c. 6 times brighter d. 216 times brighter 34. 5 a. 3 28. 29. 30. 31. 2 b. 5 3 Simplify . a. 27 b. 93 d. –12 c. –8 d. –16 . Simplify . 5 36 d. 12 c. 1 Simplify a. –2 b. 16 b. d. 2 c. 729 Simplify . a. –81 b. 81 a. 5 c. 5 c. 25 6 d. 25 36 If the population of an ant hill doubles every 10 days and there are currently 40 ants living in the ant hill, what will the ant hill population be in 20 days? a. 320 ants b. 160 ants c. 1,600 ants d. 80 ants 35. To cover the path, 7 bags of gravel are needed. b. The total area is 144 sq ft. The area of the vegetable garden is 110.25 sq ft, and the area of the path is 33.75 sq ft. To cover the path, 4 bags of gravel are needed. c. The total area is 144 sq ft. The area of the vegetable garden is 81 sq ft, and the area of the path is 63 sq ft. To cover the path, 7 bags of gravel are needed. d. The total area is 144 sq ft. The area of the vegetable garden is 72 sq ft, and the area of the path is 72 sq ft. To cover the path, 8 bags of gravel are needed. The design shows the layout of a vegetable garden and the surrounding path. The path is 1.5 feet wide. First, find the total area of the vegetable garden and path. Then, find the area of the vegetable garden and the area of the path. If one bag of gravel covers 10 square feet, how many bags of gravel are needed to cover the path? 12 ft 36. Find the square root. a. 14 12 ft a. The 38. 39. 37. b. 98 c. 38416 d. –14 The area of a square garden is 202 square feet. Estimate the side length of the garden. a. 16 ft b. 12 ft c. 17 ft d. 14 ft total area is 81 sq ft. The area of the vegetable garden is 144 sq ft, and the area of the path is 63 sq ft. Write all classifications that apply to the real number . a. rational number, terminating decimal b. rational number, repeating decimal c. irrational number d. rational number Write all classifications that apply to the real number . a. irrational number, integer b. irrational number c. rational number, terminating decimal, integer, whole number, natural number d. rational number, terminating decimal 40. A set of numbers is said to be closed under a certain operation if, when you perform the operation on any two numbers in the set, the result is also a number in the set. Is the set of irrational numbers closed under addition? Explain. closed under addition. For example, the sum of and is not an irrational number. d. No, the set of irrational numbers is not closed under addition. The result of adding any two irrational numbers is an irrational number. a. Yes, 42. 43. 45. the set of irrational numbers is closed under addition. For example, the sum of 0.121221222.. and 0.131331333.. is 0.252552555... which is an irrational number. b. Yes, the set of irrational numbers is closed under addition. The result of adding any two irrational numbers is an irrational number. c. No, the set of irrational numbers is not Simplify . a. 21 b. 75 c. 39 d. 93 Evaluate for x = 9. a. –68 b. 58 c. –5 d. 72 Simplify the expression a. 14 46. b. 23 c. 4 Simplify a. –1 b. 2 44. Evaluate 1 + x2 • 6 for x = 4. a. 102 b. 97 c. 94 d. 150 48. Use the numbers 2, 3, 5, and 8 to write an expression that has a value of . You may use any operations, and you must use each of the numbers at least once. d. 22 b. d. a. 47. c. 22 . d. 14 . Translate the word phrase, the product of 8.5 and the difference of –4 and –8, into a numerical expression. a. c. 41. Tatia has coins in pennies, nickels, dimes, and quarters. The total amount of money she has in dollars can be found using the expression (P + 5N + 10D + 25Q) ÷ 100. Use the table to find how much money Tatia has. P 20 a. $140.50 d. $1.90 N 16 D 4 b. $33.30 Q 2 b. c. d. 49. Simplify the expression . 5 a. 10 9 b. 10 5 c. 9 9 d. 9 50. Write 11 • 59 using the Distributive Property. Then simplify. a. 11 • 50 + 11 • 9; 649 b. (11 + 50)(11 + 9); 1,220 c. 11 • 59 + 11 • 9; 748 d. 11 • 5 + 11 • 9; 154 51. Write using the Distributive Property. Then simplify. c. $0.42 a. b. 60 52. 53. d. ; 130 ; 114 c. ; 168 ; b. a. c. d. Simplify by combining like terms. The table shows, step-by-step, how to simplify the algebraic expression . Justify Step 4. Step 1. 2. 3. 4. 5. 6. a. Multiply Procedure Justification Distributive Property b. Associative Property c. Combine like terms d. Commutative Property 54. Fill in the missing justifications. Procedure Justification Definition of subtraction ? ? ? Simplify Definition of subtraction a. Distributive Property; Associative Property; Commutative b. Associative Property; Commutative Property; Distributive c. Commutative Property; Distributive Property; Associative d. Commutative Property; Associative Property; Distributive 55. Graph the point (1, 4). Property Property Property Property a. 56. y 5 Name the quadrant where the point (–3, 2) is located. y 5 5 x –5 –5 –5 b. 5 x y 5 –5 a. Quadrant c. Quadrant 5 x –5 57. –5 c. III IV b. Quadrant I d. Quadrant II Name the quadrant where the point (3, 0) is located. y y 5 5 5 x –5 –5 5 x –5 d. y –5 5 b. No quadrant a. Quadrant III (y-axis) c. No quadrant (x-axis) d. Quadrant I 5 x –5 –5 58. 59. A phone company advertises a new plan in which the customer pays a fixed amount of $25 per month for unlimited calls in the country, and $0.10 per minute for international calls. Find a rule for the monthly payment a customer pays according to the new plan. Write ordered pairs for the monthly payment when the customer uses 90, 120, 145, and 150 international minutes in a month. a. ; (34, 90), (37, 120), (39.5, 145), (40, 150) b. ; (90, 34), (120, 37), (145, 39.5), (150, 40) c. ; (34, 90), (37, 120), (145, 39.5), (150, 40) d. ; (34, 90), (37, 120), (145, 39.5), (150, 40) The points form an S shape. b. Create a table of ordered pairs for the function using the values x = –2, –1, 0, 1, and 2. Graph the ordered pairs and describe the shape of the graph. a. The points form a straight line. c. The points form a U shape. 60. The coordinates of three vertices of , , a rectangle are and . Find the coordinates of the fourth vertex. Then, find the area of the rectangle. a. ; Area = 80 square units b. ; Area = 72 square units c. ; Area = 80 square units d. ; Area = 72 square units 61. Give two ways to write the algebraic expression 6p in words. a. the quotient of 6 and p 6 divided by p b. p subtracted from 6 p less than 6 c. 6 times p 6 groups of p d. p more than 6 p added to 6 The points form a V shape. d. 62. Add using a number line. 3+3 3 3 –8 –7 a. 0 63. 64. –6 –5 b. 6 Solve a. p = 22 d. p = –10 Solve –4 –3 –2 c. –6 –1 0 1 2 3 4 5 6 7 8 d. 3 . b. p = –22 a. s c. p = 52 = 54 = 10 65. . b. s = 42 Solve –14 + s = 32. c. s = 43 d. s a. s 66. = 46 b. s = 18 c. s = –46 d. s = –18 A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an equation to find the salaries for the second month if the first month’s salaries are $10,205. a. The salaries for the second month are $11,689. b. The salaries for the second month are $21,894. c. The salaries for the second month are $10,947. d. 67. The salaries for the second month are $32,099. The range of a set of scores is 23, 71. The time between a flash of lightning and the lowest score is 33. Write and the sound of its thunder can be and solve an equation to find the used to estimate the distance from a highest score. (Hint: In a data set, lightning strike. The distance from the range is the difference between the strike is the number of seconds the highest and the lowest values.) between seeing the flash and a. hearing the thunder divided by 5. Suppose you are 17 miles from a The highest score is 10. b. lightning strike. Write and solve an equation to find how many seconds The highest score is 56. c. there would be between the flash and thunder. The highest score is –10. d. The highest score is 79. 68. Solve a. q = 46 1 d. q = 8 5 69. 70. . b. q = 205 Solve d. , so t is about 85 seconds. b. , so t is about 3.4 seconds. 72. c. n = 45 If a. 3 d. n 73. . b. , so t is about 22 seconds. c. = 36 d. Solve 3n = 42. a. n = 39 b. n = 15 = 14 a. c. q a. , so t is about 0.3 seconds. , find the value of b. –5 c. 5 d. –3 Solve a. a = –29 d. a = –15 . b. a = 29 c. 74. Solve . c. a = 15 . a. d. 75. 80. 81. 82. 83. c. Solve a. d. 76. b. . b. If 8y – 8 = 24, find the value of 2y. a. 8 b. 11 c. 2 d. 24 78. The formula gives the profit p when a number of items n are each sold at a cost c and expenses e are subtracted. If , , and , what is the value of c? a. 0.80 b. 1.55 c. 1.25 d. 0.95 79. Solve c. Sara needs to take a taxi to get to the movies. The taxi charges $4.00 for the first mile, and then $2.75 for each mile after that. If the total charge is $20.50, then how far was Sara’s taxi ride to the movie? a. 6 miles b. 7 miles c. 5.1 miles d. 7.5 miles Solve 1 a. n = 1 2 77. . a. d. b. c. . b. n = −4 1 2 c. n = 3 12 d. n = −1 16 Solve . Tell whether the equation has infinitely many solutions or no solutions. a. Two solutions b. No solutions c. Infinitely many solutions d. Only one solution A video store charges a monthly 84. A professional cyclist is training for membership fee of $7.50, but the the Tour de France. What was his charge to rent each movie is only average speed in kilometers per $1.00 per movie. Another store has hour if he rode the 194 kilometers no membership fee, but it costs from Laval to Blois in 4.7 hours? Use $2.50 to rent each movie. How many the formula , and round your movies need to be rented each answer to the nearest tenth. month for the total fees to be the a. 189.3 kph b. 911.8 kph c. 115.3 same from either company? kph d. 41.3 kph a. 3 movies b. 5 movies c. 7 85. The formula for the resistance of a movies d. 9 movies conductor with voltage V and current Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer. a. 2, 3, 4 b. 4, 5, 6 c. 6, 7, 8 d. 8, 9, 10 I is a. I . Solve for V. = Vr b. c. V d. 86. Solve for x. = Ir a. b. c. 87. Solve 94. 95. Solve the proportion b. d. The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 7:19. There are 38 gallons of gasoline. How many ounces of oil are there? a. 103.1 ounces b. 20 ounces c. 14 ounces d. 3.5 ounces Ramon drives his car 150 miles in 3 hours. Find the unit rate. a. Ramon drives 50 miles per hour. b. Ramon drives 1 mile per 50 hours. c. Ramon drives 30 miles per hour. d. Ramon drives 150 miles per 3 hours. Find the value of MN if ABCD LMNO a. 22.4 91. for y. c. 89. The local school sponsored a mini-marathon and supplied 84 gallons of water per hour for the runners. What is the amount of water in quarts per hour? a. 672 qt/h b. 336 qt/h c. 168 qt/h d. 21 qt/h d. a. 88. 90. cm b. 12.6 cm a. x = d. x = cm b. x = 26 c. x = 0.03 92. An architect built a scale model of a shopping mall. On the model, a circular fountain is 20 inches tall and 22.5 inches in diameter. If the actual fountain is to be 8 feet tall, what is its diameter? a. 7 ft b. 7.1 ft c. 9 ft d. 10.5 ft 93. Complementary angles are two angles whose measures add to 90°. The ratio of the measures of two complementary angles is 4:11. What are the measures of the angles? a. 51.4°, 38.6° b. 26°, 64° c. 24°, 66° d. 24°, 114° cm, and cm. cm, c. 22.8 36 25 . d. 23.8 cm On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby eucalyptus tree is 35 feet long. Write and solve a proportion to find the height of the tree. ; 25 feet a. ; 49 feet b. ; 245 feet c. ; 175 feet d. 96. A right triangle has legs 15 inches and 12 inches. Every dimension is multiplied by to form a new right triangle with legs 5 inches and 4 inches. How is the ratio of the areas related to the ratio of corresponding sides? a. The ratio of the areas is the square of the ratio of the corresponding sides. b. The ratio of the areas is equal to the ratio of the corresponding sides. c. The ratio of the areas is the cube of the ratio of the corresponding sides. d. None of the above 97. Triangles C and D are similar. The . The area of triangle C is 47.6 base of triangle D is 6.72 in. Each dimension of D is the corresponding dimension of C. What is the height of D ? a. 20.4 in b. 17 in c. 5.6 in d. 57.12 in 98. Find 55% of 125. a. 227.27 b. 68.75 d. 6875 c. 70.25 99. What percent of 74 is 481? If necessary, round your answer to the nearest tenth of a percent. a. 6.5% b. 650% c. 550% d. 15.38% 100. 66 is 56% of what number? If necessary, round your answer to the nearest hundredth. a. 0.85 b. 117.86 c. 1.18 d. 36.96 101. A compound is made up of various elements totaling 80 ounces. If the total amount of lead in the compound weighs 15 ounces, what percent of the compound is made up of lead? If necessary, round your answer to the nearest hundredth of a percent. a. 81.25% b. 18.75% c. 5.33% d. 0.19% 102. 103. 104. 105. According to the United States Census Bureau, the United States population was projected to be 293,655,404 people on July 1, 2004. The two most populous states were California, with a population of 35,893,799, and Texas, with a population of 22,490,022. About what percent of the United States population lived in California or Texas? Round your answer to the nearest percent. a. 8% b. 12% c. 20% d. 37% Aaron works part time as a salesperson for an electronics store. He earns $6.75 per hour plus a percent commission on all of his sales. Last week Aaron worked 17 hours and earned a gross income of $290.63. Find Aaron’s percent commission if his total sales for the week were $3,350. If necessary, round your answer to the nearest hundredth of a percent. a. 1.03% b. 0.05% c. 5.25% d. 6% After 6 months the simple interest earned annually on an investment of $8000 was $975. Find the interest rate to the nearest tenth of a percent. a. 0.2 % b. 22.4% c. 0.244% d. 24.4% Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive? a. $14.00 d. $3.50 b. $84.00 c. $13.55 106. Hannah had dinner at her favorite restaurant. If the sales tax rate is 4% and the sales tax on the meal came to $1.25, what was the total cost of the meal, including sales tax and a 20% tip? a. $52.50 b. $45.63 c. $31.25 d. $38.75 107. Find the percent change from 52 to 390. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent. a. 650% decrease b. 87% decrease c. 650% increase d. 87% increase 108. Find the result when 28 is decreased by 25%. a. 21 b. 35 c. 7 d. 3 109. The price of a train ticket from Atlanta to Oklahoma City is normally $117.00. However, children under the age of 16 receive a 70% discount. Find the sale price for someone under the age of 16. a. $35.10 b. $198.90 c. $81.90 d. $49.14 110. A bookstore buys Algebra 1 books at a wholesale price of $16 each. It then marks up the price by 83%, and sells the Algebra 1 books. What is the amount of the markup? What is the selling price? a. The amount of the markup is $29.28, and the selling price is $13.28. b. The amount of the markup is $13.28, and the selling price is $29.28. c. The amount of the markup is $13.28, and the selling price is $2.72. d. The amount of the markup is $83, and the selling price is $99.00. 111. Mr. Chang sells holiday greeting cards in his gift shop. Before the holidays, he sells the cards at a 225% markup on the price he paid his supplier. After the holidays, he discounts the cards 60%. What is the post-holiday price of two cards he originally bought from his supplier for $1.50 and $2.00, respectively? a. $2.03; c. $2.93; 112. 113. Solve a. x = 1 $2.70 $3.9 b. $1.35; $1.80 d. $1.95; $2.60 Solve . a. x = 0 or x = –14 d. x = 7 or x = –21 b. x =7 c. x =0 . b. x = 11 6 c. No solution d. x 114. Describe the solutions of in words. a. The value of y is a number less than or equal to 3. b. The value of y is a number greater than 4. c. The value of y is a number equal to 3 d. The value of y is a number less than 4. = 8 3 a. –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 b. 115. Graph the inequality m < –3.4. c. d. 116. Write the inequality shown by the graph. –7 –6 a. m ≤ –3 –5 –4 –3 –2 b. m > –3 –1 0 1 2 c. m ≥ –3 3 4 5 6 7 m d. m < –3 117. To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution. a. 0 100 200 300 400 500 600 700 800 900 1000 n b. 0 100 200 300 400 500 600 700 800 900 1000 n 0 100 200 300 400 500 600 700 800 900 1000 n 0 100 200 300 400 500 600 700 800 900 1000 n c. d. 118. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality. a. ; s –500 –400 b. –300 –200 –100 0 100 200 300 400 500 300 400 500 300 400 500 300 400 500 ; s –500 –400 c. –300 –200 –100 0 100 200 ; s –500 –400 d. –300 –200 –100 0 100 200 ; s –500 –400 –300 –200 –100 0 100 119. Solve the inequality n + 6 < –1.5 and graph the solutions. a. n < 4.5 –10 –8 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 b. n < –7.5 –10 –8 c. n < –7.5 –10 –8 120. Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week. Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download. a. s > 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 b. s ≥ 3 –6 –4 –2 0 2 4 6 8 10 d. n < 4.5 –10 –8 200 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 c. s ≤ 3 –6 –4 –2 0 2 4 6 8 10 0 d. s < 3 0 1 2 3 4 5 6 7 8 9 10 11 –9 b. 121. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money Denise must save to reach her goal. Let d represent the amount of money in dollars Denise must save to reach her goal. a. ; b. ; c. ; d. ; 5 –9 c. 5 8 –3 0 3 6 9 12 15 18 21 –6 –3 0 3 6 9 12 15 18 21 –6 –3 0 3 6 9 12 15 18 21 –6 –3 0 3 6 9 12 15 18 21 2 5 –9 d. –6 2 5 1 5 122. Solve the inequality and graph the solution. –9 a. 1 85 > 3 and graph the solutions. 123. Solve the inequality a. x > 24 0 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 45 50 b. x > 24 0 c. x > 3 8 0 1 2 3 4 5 6 7 8 9 10 11 12 d. x > 24 0 5 10 15 20 25 30 35 40 124. Solve the inequality 2m ≤ 18 and graph the solutions. a. m ≤ 9 –1 0 1 2 3 4 5 6 7 8 9 10 11 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 b. m ≤ 36 0 c. m ≤ 36 0 d. m ≤ 9 –1 0 1 2 3 4 5 6 7 8 9 ≤ 2 and graph the 125. Solve the inequality solutions. a. z ≤ –8 10 11 129. Solve the inequality − n – 4 < 3 and graph the solutions. a. n < –7 –10 –8 –10 –8 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 b. z ≥ 8 c. z ≤ 8 d. z ≥ –8 126. Solve the inequality 2f ≥ –8 and graph the solutions. a. f ≥ –4 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 b. f ≤ –4 c. f ≤ 4 d. f ≥ 4 127. Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.50 each and he has $14.75 to spend, how many tickets can he buy? a. 0 tickets b. 5 tickets c. 6 tickets d. 4 tickets 128. What is the greatest possible integer solution of the inequality ? a. 5.33 b. 4 c. 6 d. 5 132. Solve and graph . 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 –6 –4 –2 0 2 4 6 8 10 d. z ≥ 1 –10 –8 –10 –8 6 c. z ≤ –3 –10 –8 –10 –8 4 b. z ≤ 1 –10 –8 –10 –8 2 130. Solve the inequality z + 8 + 3z ≤ –4 and graph the solutions. a. z ≥ –3 –10 –8 –10 –8 0 d. n < 1 –10 –8 –10 –8 –2 c. n > 1 –10 –8 –10 –8 –4 b. n > –7 –10 –8 –10 –8 –6 131. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the second day, they drove 190 miles. What is the least number of miles they drove on the third day if their average number of miles per day was at least 180? a. 540 mi b. 180 mi c. 201 mi d. 200 mi a. x > 5 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 b. x < 5 –13 –12 –11 –10 –9 c. x > 3 –13 –12 –11 –10 –9 d. x < –5 –13 –12 –11 –10 –9 133. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science Center charge less than the Dino Discovery Museum? a. 132 or more students b. 132 or fewer students c. More than 45 students d. Fewer than 45 students 134. Solve the inequality and graph the solution. a. –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 b. c. d. 135. Solve the inequality 7 9 a. z ≤ −2 16 b. z ≤ 3 16 d. no solutions 136. Solve a. . c. all real numbers b. . d. c. 137. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions. a. –250 b. –200 –150 –100 –50 0 50 100 150 200 250 –250 –200 –150 –100 –50 0 50 100 150 200 250 –250 –200 –150 –100 –50 0 50 100 150 200 250 –250 –200 –150 –100 –50 0 50 100 150 200 250 c. d. 138. Solve and graph the solutions of the compound inequality a. AND 0 b. 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 . AND 0 c. AND 0 d. AND 0 139. Solve and graph the compound inequality. OR a. OR –10 –9 b. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 s –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 s –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 s –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 s OR –10 –9 c. –8 OR –10 –9 d. –8 OR –10 –9 –8 140. Write the compound inequality shown by the graph. –10 –9 a. –8 –7 –6 AND –5 –4 –3 b. –2 –1 0 1 AND 141. Which of the following is a solution of a. 2 b. 14 c. 12 d. –6 2 3 4 5 6 c. AND 7 8 9 10 OR x d. ? OR 142. Solve the inequality a. and graph the solutions. Then write the solutions as a compound inequality. –27 –24 –21 –18 –15 –12 –9 –6 –3 0 3 6 9 12 15 18 21 24 27 30 –30 –27 –24 –21 –18 –15 –12 –9 –6 –3 0 3 6 9 12 15 18 21 24 27 30 –27 –24 –21 –18 –15 –12 –9 –6 –3 0 3 6 9 12 15 18 21 24 27 30 –30 –27 –24 –21 –18 –15 –12 –9 –6 –3 0 3 6 9 12 15 18 21 24 27 30 b. c. d. 143. Solve and graph the solutions of a. –9 < x < 21 –24 –22 –20 –18 –16 –14 –12 –10 –8 . Write the solutions as a compound inequality. –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 b. x < – 15 OR x > 15 –24 –22 –20 –18 –16 –14 –12 –10 –8 c. x > 21 –24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 d. x < – 9 OR x > 21 –24 –22 –20 –18 –16 –14 –12 –10 –8 Numeric Response 144. An architect charges $1800 for a first draft of a three-bedroom house. If the work takes longer than 8 hours, the architect charges $105 for each additional hour. What would be the total cost for a first draft that took 14 hours to complete? 145. The maximum speed of a greyhound is 153 miles per hour less than 3 times the maximum speed of a cheetah. If a greyhound’s maximum speed is 42 miles per hour, what is the maximum speed of a greyhound? Check to make sure your answer is reasonable. 146. A car rental company increases daily rental fees 15% in the summer to cover increased fuel costs. They then have a “25% off” promotion for the fall. If a car rented for $36.00 per day before the summer, what would the per-day rental cost be during the fall promotion? 147. What is the least possible integer solution of the inequality ? 148. A volleyball team scored 14 more points in its first game than in its third game. In the second game, the team scored 28 points. The total number of points scored was less than 80. What is the greatest number of points the team could have scored in its first game? Matching 149. 150. 151. 154. 155. Match each vocabulary term with its definition. a. algebraic expression b. numerical expression c. like terms d. absolute value e. evaluate f. variable g. constant a symbol used to represent a 152. a mathematical phrase that contains quantity that can change operations and numbers a value that does not change 153. to find the value of an algebraic expression by substituting a number an expression that contains at least for each variable and simplifying by one variable using the order of operations Match each vocabulary term with its definition. a. real numbers b. additive inverse c. opposites d. multiplicative inverse e. natural numbers f. reciprocal g. absolute value numbers that are the same distance 156. for any real number from zero on opposite sides of the 157. the distance from zero on a number number line line the opposite of a number 158. the reciprocal of the number Match each vocabulary term with its definition. a. coefficient b. variable c. d. e. f. g. 159. 160. 161. 164. 165. 166. 170. 171. power perfect square square root exponent base the number in a power that is used 162. an expression written with a base as a factor and an exponent or the value of such an expression a number that is multiplied to itself to form a product 163. the number that indicates how many times the base in a power is used as a number whose positive square a factor root is a whole number Match each vocabulary term with its definition. a. real numbers b. positive numbers c. negative numbers d. integers e. irrational numbers f. rational numbers g. natural numbers h. whole numbers the set of numbers that can be 167. the set of rational and irrational numbers written in the form , where a and b 168. the set of whole numbers and their are integers and opposites the set of counting numbers 169. the set of real numbers that cannot the set of natural numbers and zero be written as a ratio of integers Match each vocabulary term with its definition. a. repeating decimal b. terminating decimal c. reciprocal d. absolute value e. term f. coefficient g. like terms h. order of operations a rational number in decimal form 172. a part of an expression to be added that has a block of one or more or subtracted digits that repeats continuously 173. terms with the same variables raised to the same exponents a number multiplied by a variable 174. 176. 177. 178. 181. 182. Fourth, perform all addition and A rule for evaluating expressions: subtraction from left to right. First, perform operations in parentheses or other grouping 175. a rational number in decimal form symbols. that has a finite number of digits Second, evaluate powers and roots. after the decimal point Third, perform all multiplication and division from left to right. Match each vocabulary term with its definition. a. coordinate plane b. ordered pair c. origin d. quadrant e. y-axis f. x-axis g. axes the intersection of the x- and y-axes 179. the two perpendicular number lines, in a coordinate plane also known as the x-axis and the y-axis, used to define the location of the vertical axis in a coordinate a point in a coordinate plane plane 180. a pair of numbers that can be used the horizontal axis in a coordinate to locate a point on a coordinate plane plane Match each vocabulary term with its definition. a. x-axis b. x-coordinate c. y-coordinate d. input e. output f. y-axis g. quadrant h. coordinate plane the second number in an ordered 183. the result of substituting a value for a pair, which indicates the vertical variable in a function distance of a point from the origin on 184. a value that is substituted for the the coordinate plane independent variable in a relation or function the first number in an ordered pair, which indicates the horizontal 185. one of the four regions into which distance of a point from the origin on the x- and y-axis divide the the coordinate plane coordinate plane 186. 187. 188. 189. 193. 194. 195. a plane that is divided into four the x-axis and a vertical line called regions by a horizontal line called the y-axis Match each vocabulary term with its definition. a. expression b. solution of an equation c. contradiction d. identity e. formula f. inequality g. equation h. literal equation a mathematical sentence that shows 190. a value or values that make the that two expressions are equivalent equation or inequality true an equation that contains two or 191. a literal equation that states a rule more variables for a relationship among quantities an equation that is true for all values 192. an equation that is not true for any of the variables value of the variable Match each vocabulary term with its definition. a. proportion b. formula c. ratio d. unit rate e. identity f. conversion factor g. rate a rate in which the second quantity 196. an equation that states that two in the comparison is one unit ratios are equal the ratio of two equal quantities, 197. a comparison of two numbers by each measured in different units division a ratio that compares two quantities measured in different units Match each vocabulary term with its definition. a. conversion factor b. scale c. scale drawing d. scale factor e. scale model f. proportion g. similar 198. 199. 200. 203. 204. 205. 208. a drawing that uses a scale to 201. a three-dimensional model that uses represent an object as smaller or a scale to represent an object as larger than the original object smaller or larger than the actual object the ratio of any length in a drawing to the corresponding actual length 202. the ratio of two equal quantities, each measured in different units in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage Match each vocabulary term with its definition. a. proportion b. corresponding sides c. indirect measurement d. like terms e. cross products f. similar g. corresponding angles the product of the means bc and the 206. angles in the same relative position product of the extremes ad in the in two different polygons that have the same number of angles statement 207. a method of measuring an object by sides in the same relative position in using formulas, similar figures, two different polygons that have the and/or proportions same number of sides two figures that have the same shape, but not necessarily the same size Match each vocabulary term with its definition. a. commission b. interest c. rate d. sales tax e. markup f. principal g. tip an amount of money added to a bill 209. the amount of money charged for for service borrowing money or the amount of money earned when saving or investing money 210. 211. 213. 214. 215. 219. 220. 221. 222. 223. money paid to a person or company 212. an amount of money borrowed or for making a sale invested a percent of the cost of an item that is charged by governments to raise money Match each vocabulary term with its definition. a. rate b. markup c. percent change d. percent decrease e. ratio f. percent g. percent increase h. discount a decrease given as a percent of the 216. an increase or decrease given as a original amount percent of the original amount an increase given as a percent of 217. a ratio that compares a number to the original amount 100 an amount by which an original price 218. the amount by which a wholesale is reduced cost is increased Match each vocabulary term with its definition. a. compound inequality b. inequality c. intersection d. solution of an inequality e. union f. Venn diagram g. equation the set of all elements that are common to both sets, denoted by the set of all elements that are in either set, denoted by a statement that compares two expressions by using one of the following signs: <, >, , , or a value or values that make the inequality true two inequalities that are combined into one statement by the word and or or Math Olympics Answer Section MULTIPLE CHOICE 1. ANS: D The operation means “divided by” or “quotient”. p ÷ 10: the quotient of p and 10 p divided by 10 Feedback A B C D Check the operation in the algebraic expression. Check the operation in the algebraic expression. Check the order of the variable and constant. Correct! TOP: 1-1 Variables and Expressions 2. ANS: B y represents the number of letters Julia wrote. Think: y groups of 14 letters. 14y Feedback A B C D Think: how many groups of letters are there? Correct! Think: how many groups of letters are there? To translate words into an algebraic expression, look for words that indicate the action. TOP: 1-1 Variables and Expressions 3. ANS: C x represents the number of bags. Think: How many groups of 88 are in x? Feedback A B Think: how many groups of cans are in the number of bags? Think: how many groups of cans are in the number of bags? C D Correct! To translate words into an algebraic expression, look for words that indicate the action. TOP: 1-1 Variables and Expressions 4. ANS: B m+o 9+7 16 Substitute 9 for m and 7 for o. Simplify. Feedback A B C D Check your addition. Correct! This expression involves addition, not subtraction. This expression involves addition, not multiplication. TOP: 1-1 Variables and Expressions 5. ANS: B Substitute the values for q and v into the expression, and then subtract. Feedback A B C D Check your subtraction. Correct! This expression involves subtraction, not division. This expression involves subtraction, not addition. TOP: 1-1 Variables and Expressions 6. ANS: D Substitute the values for x and y into the expression, and then multiply. Feedback A B C D Check your multiplication. Check your multiplication. This expression involves multiplication, not addition. Correct! TOP: 1-1 Variables and Expressions 7. ANS: C Substitute the values for a and b into the expression, and then divide. Feedback A B C D This expression involves division, not multiplication. This expression involves division, not subtraction. Correct! Check your division. TOP: 1-1 Variables and Expressions 8. ANS: D The expression 40 + y models the number of points Mike scored in all Evaluate 40 + y for y = 2. 40 + 2 = 42 If Mike scored 2 points in the second half of the game, then he scored 42 points in all. Feedback A B C D Use a different operation. Use a different operation. Use a different operation instead of division. Correct! TOP: 1-1 Variables and Expressions 9. ANS: C The expression receive. Evaluate models the number of sand dollars each of Aaron’s friends will for y = 12. =6 If Aaron gives 72 sand dollars to 12 friends, each friend will get 6 sand dollars. Feedback A B C D Use a different operation. Use a different operation. Correct! Use a different operation instead of multiplication. TOP: 1-1 Variables and Expressions 10. ANS: D The expression 12n models the number books Salvador read in all. Evaluate 12n for n = 7. 12(7) = 84 If Salvador read for 7 months, then that means Salvador read 84 books. Feedback A B C D Use a different operation. Use a different operation. Use a different operation. Correct! TOP: 1-1 Variables and Expressions 11. ANS: A Substitute 7 for m and 9 for n. Simplify. Remember: means 2 times m. Feedback A B C D Correct! You switched the values of the variables. First, substitute the given values. Then, simplify the expression. When there is no operation sign between a number and a variable, it means it is multiplication. TOP: 1-1 Variables and Expressions 12. ANS: D The lower vector shows the minuend and the upper vector shows the subtrahend. The number at which the upper vector stops is the difference of the two integers. Feedback A B C D Move left on a number line to subtract a positive integer; move right to subtract a negative integer. Move left on a number line to subtract a positive integer; move right to subtract a negative integer. Move left on a number line to subtract a positive integer; move right to subtract a negative integer. Correct! TOP: 1-2 Adding and Subtracting Real Numbers 13. ANS: B To add two integers with the same sign, find the sum of their absolute values and use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values and use the sign of the integer with the greater absolute value. Feedback A B C D When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. Correct! When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. Check the sign of your answer. TOP: 1-2 Adding and Subtracting Real Numbers 14. ANS: C Substitute 35 for x, and then add the integers. To add two integers with the same sign, find the sum of their absolute values and use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values and use the sign of the integer with the greater absolute value. Feedback A B C D Substitute for x, and then add the integers. Check the sign of your answer. Correct! When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. TOP: 1-2 Adding and Subtracting Real Numbers 15. ANS: C Change the subtraction sign to an addition sign, and change the sign of the second number. Feedback A B Change the subtraction sign to an addition sign, and change the sign of the second number. Change the subtraction sign to an addition sign, and change C D the sign of the second number. Correct! Pay attention to the sign. TOP: 1-2 Adding and Subtracting Real Numbers 16. ANS: C Substitute 12 for x, and then subtract the integers. To subtract, change the subtraction sign to an addition sign, and change the sign of the second number. Feedback A B C D Pay attention to the sign. Change the subtraction sign to an addition sign, and change the sign of the second number. Correct! Change the subtraction sign to an addition sign, and change the sign of the second number. TOP: 1-2 Adding and Subtracting Real Numbers 17. ANS: C Subtract the negative temperature from the positive temperature to calculate the difference in the two readings. Feedback A B C D Check the signs. Check the signs. Correct! Subtract the lower temperature from the higher one. TOP: 1-2 Adding and Subtracting Real Numbers 18. ANS: B Subtract the lower temperature from the higher temperature to calculate the difference in the two readings. Feedback A B C D Subtract the lower temperature from the higher temperature. Correct! Subtract the lower temperature from the higher temperature. Check the signs. TOP: 1-2 Adding and Subtracting Real Numbers 19. ANS: B Subtract the height of the building from the height of the elevator. The difference represents how far underground the parking garage goes. Feedback A B C D Check your subtraction. Correct! Subtract the numbers instead of adding them. Check your subtraction. TOP: 1-2 Adding and Subtracting Real Numbers 20. ANS: B Multiply the two integers. If the signs are the same, the product is positive; if the signs are different, the product is negative. Feedback A B C D Multiply the integers, not add. Correct! Be sure to multiply the integers. If the signs of the two integers are the same, the product will be positive. If the signs are different, the product will be negative. TOP: 1-3 Multiplying and Dividing Real Numbers 21. ANS: D Substitute –4 for u. Then multiply. Feedback A B C D Substitute the value in the variable, and then multiply. Check your multiplication. If the signs of the two integers are the same, the product will be positive; if they are different, the product will be negative. Correct! TOP: 1-3 Multiplying and Dividing Real Numbers 22. ANS: D Divide the two integers. If the signs are the same, the quotient is positive; if the signs are different, the quotient is negative. Feedback A B This expression involves division, not multiplication. If the signs of the two integers are the same, the quotient will be positive. If the signs are different, the quotient will be C D negative. This expression involves division, not subtraction. Correct! TOP: 1-3 Multiplying and Dividing Real Numbers 23. ANS: B Substitute –33 for k in the expression. Then divide the integers. If the signs are the same, the quotient is positive; if the signs are different, the quotient is negative. Feedback A B C D This expression involves division, not multiplication. Correct! This expression involves division, not subtraction. If the signs of the two integers are the same, the product will be positive. If the signs are different, the product will be negative. TOP: 1-3 Multiplying and Dividing Real Numbers 24. ANS: C Write as an improper fraction. To divide by Multiply. 8 218 multiply by . Simplify. Feedback A B C D First convert the mixed number to an improper fraction. Multiply by the reciprocal. Correct! First convert the mixed number to an improper fraction. Then multiply by the reciprocal. TOP: 1-3 Multiplying and Dividing Real Numbers 25. ANS: D The quotient of 0 and any nonzero number is 0. Feedback A B C D Multiply or divide by 0. Multiply or divide by 0. Only division by 0 is undefined. Correct! TOP: 1-3 Multiplying and Dividing Real Numbers 26. ANS: D Distance = rate time Distance = Substitute 3.5 for rate and 1.75 for time. Multiply to find the distance. Feedback A B C D To find distance, multiply rate by time. To find distance, multiply rate by time. Then estimate to check if your answer is reasonable. The decimal point is not in the correct place. Use estimation to check if your answer is reasonable. Correct! TOP: 1-3 Multiplying and Dividing Real Numbers 27. ANS: C The figure is 5 cubes tall, 5 cubes wide, and 5 cubes long. The factor 5 is used 3 times. Feedback A B C D The length, width, and height of the figure is 5. Is the figure 2-dimensional or 3-dimensional? Correct! The length, width, and height of the figure is 5. TOP: 1-4 Powers and Exponents 28. ANS: C The exponent tells the number of times to multiply the base number by itself. Multiply 9 by itself 3 times. Feedback A B Multiply the base number by itself as many times as the exponent tells you. Multiply using the base. The exponent just tells how many C D times to multiply the base by itself. Correct! Multiply the number by itself rather than adding two different numbers. TOP: 1-4 Powers and Exponents 29. ANS: A The exponent tells the number of times to multiply the base number by itself. The negative sign in front of the expression multiplies the expression by –1. Multiply 3 by itself 4 times, and then multiply your answer by –1. Feedback A B C D Correct! Think of the negative sign in front as multiplying the expression by -1. Multiply the base number by itself rather than adding. Multiply the base number by itself. The exponent tells how many times to multiply the base by itself. TOP: 1-4 Powers and Exponents 30. ANS: B The exponent tells the number of times to multiply the base number by itself. Multiply –4 by itself 2 times. Feedback A B C D Multiply the base number by itself rather than adding. Correct! This is the product of the base and the exponent. The exponent tells how many times to multiply the base by itself. Check the sign of your answer. The product of an even number of negative factors is positive; the product of an odd number of negative factors is negative. TOP: 1-4 Powers and Exponents 31. ANS: D The exponent tells how many times to multiply the fraction by itself. Multiply by itself 2 times. Feedback A The exponent tells how many times to multiply the fraction by itself. B C D Raise both the numerator and denominator to the exponent. Raise both the numerator and denominator to the exponent. Correct! TOP: 1-4 Powers and Exponents 32. ANS: B The number given as a base should be multiplied by itself a certain number of times in order to represent the value of the whole number given. The product of two 3’s is 9. Feedback A B C D An exponent is written as a small number raised slightly above the base number. Correct! The exponent tells how many times to multiply the base by itself. The number given as a base should be multiplied by itself a certain number of times in order to represent the value of the whole number given. TOP: 1-4 Powers and Exponents 33. ANS: A If each category represents sunlight that is 6 times brighter than the category before, then a dazzling day would be 36 times brighter than an illuminated day because: a dazzling day is 6 times brighter than a radiant day, a radiant day is 6 times brighter than an illuminated day, and an illuminated day is 6 times brighter than a dim day. Feedback A B C D Correct! The brightness number is just for identifying the category. You need to use the number of times brighter as a factor. You need to use the number of times brighter as a factor one more time. Check to see whether you used the number of times brighter as a factor too many times. TOP: 1-4 Powers and Exponents 34. ANS: C If the population of the ant hill is 40 ants and it doubles every 10 days, then to find its population in 20 days, make a chart to see what the population is after a certain number of days. In 10 days, the population is 40 ants. In 2 • 10 days, the population is 402 ants. In 3 • 10 days, the population is 403 ants. In 4 • 10 days, the population is 404 ants. Feedback A B C D Make a chart to see what the population is after a certain number of days. Make a chart to see what the population is after a certain number of days. Correct! Make sure that the ant population doubles. TOP: 1-4 Powers and Exponents 35. ANS: C Step 1 Find the total area of the vegetable garden and path. Step 2 Find the area of the vegetable garden and the area of the path. Find the side length of the vegetable garden. Find the area of the vegetable garden. To find the area of the path, subtract the area of the vegetable garden from the total area. Step 3 Find the number of gravel bags needed to cover the path. So, 7 bags of gravel are needed to cover the path. Feedback A B C D You switched the area of the vegetable garden and the area of the path. To find the area of the path, subtract the area of the vegetable garden from the total area. Correct! To find the area of the path, subtract the area of the vegetable garden from the total area. TOP: 1-4 Powers and Exponents 36. ANS: A 196 = What number squared equals 196? = 14 The sign to the left of the radical determines whether the square root is positive or negative. Feedback A B C D Correct! This is half of the number. The square root of a number, multiplied by itself, equals that number. Find the square root of the number under the radical sign, not the square of that number. The + or - sign to the left of the radical is the sign of the square root. TOP: 1-5 Square Roots and Real Numbers 37. ANS: D 202 is between 196 and 225. Since 202 is closer to 196, the best estimate for the side length is 14 ft. Feedback A B C D Find the two perfect squares that the area is between. Find the two perfect squares that the area is between. Of the two perfect squares that the area is between, which is closer to the area? Correct! TOP: 1-5 Square Roots and Real Numbers 38. ANS: B Any number that can be written as a fraction is a rational number. Rational numbers include terminating decimals and repeating decimals. If a rational number simplifies to a whole number or its opposite, it is also an integer. If a rational number simplifies to a nonzero whole number, it is also a natural number. Feedback A B C D To check whether the number is a terminating or repeating decimal, divide the numerator by the denominator. Correct! Since this number can be written as a fraction, it is not an irrational number. There are more ways to classify the number. Check to see whether it is a terminating or repeating decimal. TOP: 1-5 Square Roots and Real Numbers 39. ANS: D A rational number can be written as a fraction. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. An irrational number cannot be expressed as either a terminating decimal or repeating decimal. Feedback A B C D A rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. A rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. A rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. Correct! TOP: 1-5 Square Roots and Real Numbers 40. ANS: C If there is an example of two irrational numbers whose sum is not an irrational number, then the set of irrational numbers is not closed under addition. Add the following irrational numbers: 0.121121112... 0.212212221... The result is 0.33333... which is equal to , and is a rational number. Another example is and . The sum is 0 which is a rational number. Feedback A B C D Find an example of two irrational numbers whose sum is not an irrational number. If there is an example of two irrational numbers whose sum is not an irrational number, then the set of irrational numbers is not closed under addition. Correct! The set of irrational numbers being closed under addition means that when you add any two irrational numbers, the sum is also an irrational number. TOP: 1-5 Square Roots and Real Numbers 41. ANS: D Use the order of operations: 1. Perform operations in parentheses. 2. Evaluate powers. 2. Multiply or divide from left to right. 3. Add or subtract from left to right. Feedback A B C D The exponent tells how many times to use the base as a factor with itself. The order of operations is correct, but check your signs. After evaluating the exponents and evaluating within parentheses, multiplication must be performed before addition or subtraction. Correct! TOP: 1-6 Order of Operations 42. ANS: D Use the order of operations: 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. Add or subtract from left to right. Feedback A B C D Use the order of operations. Perform operations in parentheses first. Divide before you add. Correct! TOP: 1-6 Order of Operations 43. ANS: C Substitute 9 for x in the expression. Then use the order of operations to evaluate the expression. 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. Add or subtract from left to right. Feedback A B C D Use the order of operations. Multiply before adding or subtracting. Use the order of operations. Multiply before adding or subtracting. Correct! Use the order of operations. Multiply before adding or subtracting. TOP: 1-6 Order of Operations 44. ANS: B Substitute 4 for x in the expression. Then use the order of operations to evaluate the expression. 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. Add or subtract from left to right. Feedback A B C D Use the order of operations. Evaluate powers before multiplying or adding. Correct! Use the order of operations. Evaluate powers before multiplying or adding. Use the order of operations. Evaluate powers before multiplying or adding. TOP: 1-6 Order of Operations 45. ANS: A First, simplify the numerator of the fraction, and then divide the numerator by the denominator. Next, subtract the terms in the absolute value, and then find the absolute value. = Finally, add the two terms. = 14 Feedback A B C D Correct! Only square the value that has an exponent, not both numbers in the numerator. Subtract within the absolute value bars before taking the absolute value. Simplify the numerator before dividing by the denominator. TOP: 1-6 Order of Operations 46. ANS: D Use parentheses so that the difference is evaluated first. Product means multiplication. Feedback A B C D "Product" indicates multiplication. Use parentheses so the difference is evaluated first. When finding a difference, subtract the second number from the first. Correct! TOP: 1-6 Order of Operations 47. ANS: D Use the formula (P + 5N + 10D + 25Q) ÷ 100. Substitute the values from the table. 100 Total 100 100 Tatia has $1.90. Feedback A B C D First perform operations inside parentheses, and then divide. Multiply before you add. Multiply the number of coins of each type by its coin value before performing the addition. Correct! TOP: 1-6 Order of Operations 48. ANS: C You must use each of the numbers at least once, and you may use any operations. Pay attention to the order of operations. Feedback A B C D Evaluate powers before performing subtraction. Perform multiplication before subtraction. Correct! The number 8 must be used also. TOP: 1-6 Order of Operations 49. ANS: B Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. Simplify. Feedback A B C D The sum of two mixed numbers is the sum of the whole parts plus the sum of the fractional parts. Correct! To add two fractions, first find a common denominator and then add the numerators. The sum of the fractional parts is greater than 1. TOP: 1-7 Simplifying Expressions 50. ANS: A Rewrite 59 as 50 + 9. Then multiply each term by 11 and add the products. Feedback A B C D Correct! Multiply the first number by each digit in the second number, then add the two products. Multiply the first number by each digit in the second number, then add the two products. Multiply the first number by each digit in the second number, then add the two products. TOP: 1-7 Simplifying Expressions 51. ANS: B Notice that 19 is very close to 20. . Then use the Distributive Property. Rewrite 19 as 20 + Feedback A B C D You've reversed multiplication and addition. Look at the Distributive Property again. Correct! Use mental math. Notice that the two-digit factor is close to a multiple of 10. Use mental math. Notice that the two-digit factor is close to a multiple of 10. TOP: 1-7 Simplifying Expressions 52. ANS: A Group like terms. Add or subtract the coefficients. Feedback A B C D Correct! Combine only like terms. Check the signs of all the coefficients. First, group like terms. Then, add or subtract the coefficients. TOP: 1-7 Simplifying Expressions 53. ANS: D The Commutative Property allows for you to add or subtract terms in any order. Feedback A B C D Multiplication is used in Step 3. The Associative Property is used in Step 5. Like terms are combined in Step 6. Correct! TOP: 1-7 Simplifying Expressions 54. ANS: D Procedure Justification Definition of subtraction Commutative Property Associative Property Distributive Property Simplify Definition of subtraction Feedback A B C D What is the difference between the Commutative Property and the Distributive Property? The Associative Property involves grouping of numbers. What does the Commutative Property state? What is the difference between the Associative Property and the Distributive Property? Correct! TOP: 1-7 Simplifying Expressions 55. ANS: C The x-coordinate of the ordered pair tells how many units to move left or right from the origin. The y-coordinate of the ordered pair tells how many units to move up or down from the origin. Feedback A B The first number in the ordered pair tells whether to move left or right from (0, 0). The second number tells whether to move up or down. The first number in the ordered pair tells whether to move left or right from (0, 0). The second number tells whether to move up or down. Correct! The first number in the ordered pair tells whether to move left or right from (0, 0). The second number tells whether to move up or down. C D TOP: 1-8 Introduction to Functions 56. ANS: D If both x and y are positive, the point is in Quadrant I. If x is negative and y is positive, the point is in Quadrant II. If both x and y are negative, the point is in Quadrant III. If x is positive and y is negative, the point is in Quadrant IV. y 5 Quadrant II Quadrant I –5 5 Quadrant III x Quadrant IV –5 Feedback A B C D The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. Correct! TOP: 1-8 Introduction to Functions 57. ANS: C If x = 0, the point is on the y-axis. If y = 0, the point is on the x-axis. Feedback A B C D The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x = 0, the point is on the y-axis. If y = 0, the point is on the x-axis. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x = 0, the point is on the y-axis. If y = 0, the point is on the x-axis. Correct! The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x = 0, the point is on the y-axis. If y = 0, the point is on the x-axis. TOP: 1-8 Introduction to Functions 58. ANS: B Let y represent the monthly payment and x represent the number of minutes of international calls. monthly is $25 plus $0.10 for international payment each minute = 25 + 0.10 y x Number of international minutes x (input) 90 120 145 150 Rule Monthly payment Ordered pair y (output) $34.00 $37.00 $39.50 $40.00 (x, y) (90, 34) (120, 37) (145, 39.5) (150, 40) Feedback A B C The monthly payment is determined by the number of international minutes, so the number of international minutes is the input and the monthly payment is the output. Correct! The monthly payment is determined by the number of international minutes, so the number of international minutes is D the input and the monthly payment is the output. The monthly payment is $25 plus $0.10 for each international minute. TOP: 1-8 Introduction to Functions 59. ANS: D Make a table to find values of (x, y) for x y (x, y) –2 (–2, 6) –1 (–1, 0) 0 (0, –2) 1 (1, 0) 2 (2, 6) . The points form a U shape. Feedback A B C D This is a cubic function. Use the given values for x to get the values for y. This is a linear function. Use the given values for x to get the values for y. This is an absolute value function. Use the given values for x to get the values for y. Correct! TOP: 1-8 Introduction to Functions 60. ANS: B Step 1 Plot the points. y 5 4 B 3 C 2 1 1 –1 2 3 4 5 6 7 8 9 10 x –2 –3 –4 A –5 Step 2 Find the fourth vertex. The fourth vertex will have the same x-coordinate as C(10,3) and the same y-coordinate as A(1, –5). x-coordinate: 10 y-coordinate: –5 The fourth vertex is D(10, –5). y 5 4 C B 3 2 1 1 –1 2 3 4 5 6 7 8 9 10 x –2 –3 –4 –5 A D Step 3 Find the area of the rectangle. square units Feedback A B C The fourth vertex will have the same x-coordinate as point C and the same y-coordinate as point A. Correct! First, plot the points. Then, use the formula for the area of the D rectangle. The fourth vertex will have the same x-coordinate as point C and the same y-coordinate as point A. TOP: 1-8 Introduction to Functions 61. ANS: C The operation means “times”, “multiplied by”, “product”, or “each groups of”. 6p: 6 times p 6 groups of p Feedback A B C D The algebraic expression does not show division. Check the operation in the algebraic expression. Correct! Check the operation in the algebraic expression. TOP: 1-1 Variables and Expressions 62. ANS: B The lower vector shows the first addend, and the upper vector shows the second addend. The number at which the upper vector stops is the sum of the two integers. Feedback A B C D Move right on a number line to add a positive integer; move left to add a negative integer. Correct! Move right on a number line to add a positive integer; move left to add a negative integer. Move right on a number line to add a positive integer; move left to add a negative integer. TOP: 1-2 Adding and Subtracting Real Numbers 63. ANS: A Since 6 is subtracted from p, add 6 to both sides to undo the subtraction. Check: To check your solution, substitute 22 for p in the original equation. Feedback A B C D Correct! Check the ones place. Is subtraction the correct operation for solving this equation? Check the tens place. TOP: 2-1 Solving Equations by Adding or Subtracting 64. ANS: B Since 6 is added to s, subtract 6 from both sides to undo the addition. Check: To check your solution, substitute 42 for s in the original equation. Feedback A B C D Check the tens place. Correct! Check the ones place. Is addition the correct operation for solving this equation? TOP: 2-1 Solving Equations by Adding or Subtracting 65. ANS: A When something is added to the variable, add its opposite to both sides of the equation to isolate the variable. Here, –14 is added to the variable, so add 14 to both sides of the equation to isolate s. Feedback A B Correct! Add the number that will isolate the variable. C D Add the opposite to isolate the variable. Add the number that will isolate the variable. TOP: 2-1 Solving Equations by Adding or Subtracting 66. ANS: A First month salaries Added to b + b + x = 21,894 10,205 + x = 21,894 –10,205 –10,205 Second month salaries x is 21,894 = 21,894 Write an equation to represent the relationship. Substitute 10,205 for b. Since 10,205 is added to x, subtract 10,205 from both sides to undo the addition. The salaries for the second month are $11,689. Feedback A B C D Correct! Subtract the same number from both sides of the equation. Check your answer. Use the same operation on both sides of the equation. TOP: 2-1 Solving Equations by Adding or Subtracting 67. ANS: B highest score h minus – lowest score l equals score range = 23 Write an equation to represent the relationship. Substitute 33 for l. Solve the equation. Feedback A The sum of the lowest value and the range is the highest B C D value. Correct! The range is the difference between the highest and the lowest values, not the sum. The range is the difference between the highest and the lowest values, not the average. TOP: 2-1 Solving Equations by Adding or Subtracting 68. ANS: B Since q is divided by 5, multiply both sides by 5 to undo the division. q = 205 Check: To check your solution, substitute 205 for q in the original equation. Feedback A B C D If the variable is connected to the number by division, then use multiplication to solve for it. Correct! Instead of subtracting, multiply both sides by the denominator. Multiply on both sides of the equation to isolate the variable. TOP: 2-2 Solving Equations by Multiplying or Dividing 69. ANS: D 3n = 42 Since n is multiplied by 3, divide both sides by 3 to undo the multiplication. Check: 3n = 42 To check your solution, substitute 14 for n in the original equation. Feedback A B C D Since the variable is multiplied, divide on both sides to undo the multiplication. Check your solution by substituting the variable in the original equation. To undo multiplication, use division. Correct! TOP: 2-2 Solving Equations by Multiplying or Dividing 70. ANS: A The reciprocal of multiplied by is . Since is , multiply both sides by Feedback A B C D Correct! Multiply both sides of the equation by the reciprocal of the fraction. Multiply both sides of the equation by the reciprocal of the fraction. Multiply both sides of the equation by the reciprocal of the fraction. TOP: 2-2 Solving Equations by Multiplying or Dividing 71. ANS: A Seconds divided by 5 equals distance. Write an equation. Let d = distance from the lightning strike in miles and t = number of seconds between flash and thunder. Substitute 17 for d, the distance from the lightning strike. Multiply both sides of the equation by 5 to undo the division. . The number of seconds between flash and thunder is about 85 seconds. Feedback A B C D Correct! Divide the distance from the lightning strike by 5. Divide the distance from the lightning strike by 5. Divide the distance from the lightning strike by 5. TOP: 2-2 Solving Equations by Multiplying or Dividing 72. ANS: B Solve the equation. Substitute 8 for x and simplify. Feedback A B C D Find the value of x by solving the equation. Then substitute it for x in the given expression and simplify. Correct! Subtract the terms in the right order. Find the value of x by solving the equation. Then substitute it for x in the given expression and simplify. TOP: 2-2 Solving Equations by Multiplying or Dividing 73. ANS: D First x is multiplied by –2. Then 14 is added. Work backward: Subtract 14 from both sides. Since x is multiplied by –2, divide both sides by –2 to undo the multiplication. Feedback A B To solve for the variable, work backward. Substitute the solution in the original equation to check your answer. C D Check the signs. Correct! TOP: 2-3 Solving Two-Step and Multi-Step Equations 74. ANS: C Since is subtracted from , add both sides to undo the subtraction. to Since f is divided by 45, multiply both sides by 45 to undo the division. Simplify. Feedback A B C D First, add to undo the subtraction. Then, multiply to undo the division. Check your signs. Correct! First, add to undo the subtraction. Then, multiply to undo the division. TOP: 2-3 Solving Two-Step and Multi-Step Equations 75. ANS: A Use the Commutative Property of Addition. Combine like terms. Since 10 is added to 17a, subtract 10 from both sides to undo the addition. Since a is multiplied by 17, divide both sides by 17 to undo the multiplication. Feedback A B C Correct! Check your signs. Combine like terms, and then solve. D Combine like terms, and then solve. TOP: 2-3 Solving Two-Step and Multi-Step Equations 76. ANS: B Let d be the distance (in miles) to the movies, then is the number of miles after the first mile. So a formula for the total charge could be first mile + charge 4.00 + rate after first mile 2.75 = 2.75 = 2.75 = = total charge 20.50 20.50 4.00 16.5 Subtract 4.00 from each side. Divide both sides by 2.75. = d d = 6 = = 6+1 7 Add 1 to both sides. Feedback A B C D Add one for the first mile. Correct! The mileage rate is the charge for each mile after the first mile. Subtract the charge for the first mile. TOP: 2-3 Solving Two-Step and Multi-Step Equations 77. ANS: A 8y – 8 = 24 +8 +8 8y = 32 8y = 8 y= 2(4) = 32 8 4 8 Add 8 to both sides of the equation. Divide both sides by 8. Apply 4 to 2y. Feedback A B C D Correct! Add before multiplying. To undo subtraction, add to both sides. To undo multiplication, divide. TOP: 2-3 Solving Two-Step and Multi-Step Equations 78. ANS: B Substitute 3750 for p, 3000 for n, and 900 for e. Add 900 to both sides of the equation. Divide both sides by 3000. Feedback A B C D Divide both sides of the equation by the coefficient of c. Correct! Add the same number to both sides of the equation. Add the same number to both sides of the equation. TOP: 2-3 Solving Two-Step and Multi-Step Equations 79. ANS: D To collect the variable terms on one side, subtract 50q from both sides. Since 81 is subtracted from 2q, add 81 to both sides to undo the subtraction. Since q is multiplied by 2, divide both sides by 2 to undo the multiplication. Feedback A B Check your signs. After adding to undo the subtraction, divide to undo the C D multiplication. First, collect the variable terms on one side. Then, add to undo the subtraction. Correct! TOP: 2-4 Solving Equations with Variables on Both Sides 80. ANS: A Combine like terms. Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the multiplication. n = 1 12 Feedback A B C D Correct! Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the multiplication. Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the multiplication. Combine like terms, and then solve. TOP: 2-4 Solving Equations with Variables on Both Sides 81. ANS: C Combine like terms on each side of the equation before collecting variable terms on one side. If you get an equation that is always true, the original equation is an identity, and it has infinitely many solutions. If you get a false equation, the original equation is a contradiction, and it has no solutions. Feedback A B First, combine like terms on each side of the equation. Then collect variable terms on one side. Now, if you get an equation that is always true, it means that the original equation has infinitely many solutions. If you get a false equation, the original equation has no solutions. If you get an equation that is always true, the original equation is an identity, and it has infinitely many solutions. If you get a C D false equation, the original equation is a contradiction and it has no solutions. Correct! If you get an equation that is always true, the original equation is an identity, and it has infinitely many solutions. If you get a false equation, the original equation is a contradiction and it has no solutions. TOP: 2-4 Solving Equations with Variables on Both Sides 82. ANS: B Let m represent the number of movies rented each month. Here are the costs for each company (in dollars). 7.5 + m = 2.5m To collect the variable terms on one side, subtract m from both sides. 7.5 – m = 2.5m – m 7.5 = 1.5 m Divide both sides by 1.5. = m 5 = m Feedback A B C D You divided $7.50 by $2.50. Before dividing by 2.50, subtract the $1.00 charge from the $2.50. Correct! You divided $7.50 by $1.00. Subtract the $1.00 charge from the $2.50 and then divide. Set up this equation 7.5 + m = 2.5m, where m is the number of movies. TOP: 2-4 Solving Equations with Variables on Both Sides 83. ANS: C Let g represent the greatest integer. The expressions for the three consecutive integers from least to greatest: , g. twice the greatest 3 times the least integer integer g ( ) , To create an equation, use the additional data that 2g is 2 less than . Solve the equation. g 8 The three consecutive numbers are 6, 7, and 8. Feedback A B C D If an expression is x less than a second expression, add x to the first expression to make it equal to the second one. If the variable represents the least number, add 2 to the variable value to find the greatest number. Add 1 to find the second number. Correct! If the variable represents the greatest number, subtract 2 from the variable value to find the least number. Subtract 1 to find the second number. TOP: 2-4 Solving Equations with Variables on Both Sides 84. ANS: D Divide both sides by t. Substitute the known values. Simplify. Round to the nearest tenth. Feedback A B C D Solve the equation Solve the equation Solve the equation Correct! . . . TOP: 2-5 Solving for a Variable 85. ANS: C Locate V in the equation. Since V is divided by I, multiply both sides by I to undo the division. Feedback A B C D Multiply both sides by I to isolate r. Multiply both sides by I to isolate r. Correct! Multiply both sides by I to isolate r. TOP: 2-5 Solving for a Variable 86. ANS: D Add z to both sides. Divide both sides by 4. Feedback A B C D To undo subtraction, add to both sides. Both terms need to be divided by the coefficient of x. To undo multiplication, divide. Correct! TOP: 2-5 Solving for a Variable 87. ANS: B Subtract 2 from both sides. Subtract the Rewrite 3.8 as Multiply by Distribute. Simplify. Feedback . term from both sides. . A B C D Divide all terms by 3.8. Correct! Multiply by the reciprocal of 3.8. Keep the x term in the equation. TOP: 2-5 Solving for a Variable 88. ANS: C Write a ratio comparing ounces of oil to gallons of gasoline. Write a proportion. Let x be the amount of oil in ounces. Since x is divided by 38, multiply both sides of the equation by 38. There are 14 ounces of oil. Feedback A B C D Set up a proportion, and use cross products. First, set up two ratios that compare the ounces of oil to the gallons of gasoline. Then, solve for the unknown amount of oil. Correct! Write a proportion, and use cross products. TOP: 2-6 Rates Ratios and Proportions 89. ANS: A Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is . Ramon drives 50 miles per hour. Feedback A Correct! B C D Divide miles by hours, not hours by miles. Check that you divided correctly when finding the unit rate. This is not a unit rate. TOP: 2-6 Rates Ratios and Proportions 90. ANS: B • To convert the first quantity in a rate, multiply by a conversion factor with that unit in the first quantity. 336 quarts per hour Feedback A B C D There are 4 quarts in a gallon. Correct! There are 4 quarts in a gallon. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the first quantity. TOP: 2-6 Rates Ratios and Proportions 91. ANS: D Use cross products. Divide both sides by 6. Feedback A B C D Use cross products to solve. Cross multiply. Multiply the numerator of one fraction by the denominator of the other fraction. Correct! TOP: 2-6 Rates Ratios and Proportions 92. ANS: C Write the scale as a fraction. Let x be the actual diameter. Use cross products to solve. Feedback A B C D Use cross products to solve. Use the proportion (model height)/(actual height) = (model diameter)/(actual diameter). Correct! Set up a proportion and solve. TOP: 2-6 Rates Ratios and Proportions 93. ANS: C Let a represent the measure of one of the complementary angles and represent the measure of the second angle. ratio of the measures of the angles is 4:11 = Solve . Use cross products. Distribute. Add 4a to both sides. Simplify. Solve the equation. Substitute 24 for a to find the measure of the second angle. The measures of the complementary angles are 24° and 66°. Feedback A B Check if the signs of all the terms in the equation are correct when you simplify. Write an equation that uses the given ratio and the sum of the C D angles' measures. Correct! Subtract the measure of the angle you found from 90 to get the second angle. TOP: 2-6 Rates Ratios and Proportions 94. ANS: A A corresponds to L, B corresponds to M, C corresponds to N, and D corresponds to O. Use cross products. Since x is multiplied by 21, divide both sides by 21 to undo the multiplication. _MN is 22.4 cm. Feedback A B C D Correct! Set up a proportion, and solve for the missing length. Set up a proportion, and solve for the missing length. Set up a proportion, and solve for the missing length. TOP: 2-7 Applications of Proportions 95. ANS: A Use cross products. Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. The tree is 25 feet tall. Feedback A B C D Correct! Check that the proportion is set up correctly. Set up a proportion and solve. Divide the cross products by the length of the kangaroo's shadow. TOP: 2-7 Applications of Proportions 96. ANS: A Find the areas of the two right triangles: , Then, find the ratio of the sides and the ratio of the corresponding areas. ratio of the sides: ratio of the areas: The ratio of the areas is the square of the ratio of the corresponding sides. Feedback A B C D Correct! First, find the ratio of the corresponding sides and the ratio of the areas. Then, compare the two ratios. First, find the ratio of the corresponding sides. Then, find the ratio of the areas. How is the second number you found related to the first number? First, find the ratio of the corresponding sides and the ratio of the areas. Then, compare the two ratios. TOP: 2-7 Applications of Proportions 97. ANS: A Step 1 Find the base of C. Base C Base D 6.72 (6.72) 5.6 Base C Base C Base C Step 2 Find the height of C. Area C (Base C)(Height C) Substitute 6.72 for the base of D. Multiply by . 47.6 47.6 17 (5.6)(Height C) (2.8)(Height C) Height C Substitute 5.6 for the base of C. Multiply. Divide by 2.8. Step 3 Find the height of D. Height D Height C Height D Height D (17) 20.4 Substitute 17 for the height of D. Feedback A B C D Correct! This is the height of C. Now find the height of D. This is the base of C. Use this to find the height of C, and then the height of D. Find the base of C, then the height of C, then the height of D. TOP: 2-7 Applications of Proportions 98. ANS: B Method 1 Use a proportion. Use the percent proportion. Let x represent the part. Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. _55% of 125 is 68.75. Method 2 Use an equation. Write an equation. Let x represent the part. Write the percent as a decimal and multiply. 55% of 125 is 68.75. Feedback A B C D Divide the percent by 100, and then multiply. Correct! First, write the percent as a decimal. Then, multiply. Divide the percent by 100, and then multiply. TOP: 2-8 Percents 99. ANS: B Method 1 Use a proportion. Use the percent proportion. Let x represent the percent. Find the cross products. Since x is multiplied by 74, divide both sides by 74 to undo the multiplication. _481 is 650% of 74. Method 2 Use an equation. Write an equation. Let x represent the percent. Since x is multiplied by 74, divide both sides by 74 to undo the multiplication. The answer is a decimal. Write the decimal as a percent. _481 is 650% of 74. Feedback A B C D Set up an equation where the percent is a variable, "of" means to multiply, and "is" means "=". Then, solve for the variable. Correct! Use the percent proportion: part is to whole as percent is to 100. Then, find the cross products. Use the percent proportion: part is to whole as percent is to 100. Then, find the cross products. TOP: 2-8 Percents 100. ANS: B Method 1 Use a proportion. Use the percent proportion. Let x represent the whole. Find the cross products. Since x is multiplied by 56, divide both sides by 56 to undo the multiplication. _56% of 66 is 117.86. Method 2 Use an equation. Write an equation. Let x represent the whole. Write the percent as a decimal. Since x is multiplied by 0.56, divide both sides by 0.56 to undo the multiplication. _56% of 66 is 117.86. Feedback A B C D Use the percent proportion: part is to whole as percent is to 100. Then, find the cross products. Correct! Set up an equation where the percent is a variable, "of" means to multiply, and "is" means "=". Then, solve for the variable. Set up an equation where the percent is a variable, "of" means to multiply, and "is" means "=". Then, solve for the variable. TOP: 2-8 Percents 101. ANS: B Use the percent proportion. Let x represent the percent. Find the cross products. Since x is multiplied by 80, divide both sides by 80 to undo the multiplication. 18.75% of the compound is made up of lead. Feedback A B C D Use the percent proportion: part is to whole as percent is to 100. Then, find the cross products. Correct! Use the percent proportion: part is to whole as percent is to 100. Then, cross multiply. In your final answer, convert the decimal to a percent. TOP: 2-8 Percents 102. ANS: C Feedback A B C D This is the percent of the population who lived in Texas. Find the percent of the population who lived in both California and Texas. This is the percent of the population who lived in California. Find the percent of the population who lived in both California and Texas. Correct! Find the total in California and Texas, and then divide that by the total population. TOP: 2-8 Percents 103. ANS: C Write the formula for gross income. gross income (income number of hours) Write the formula for commission. commission gross income (income number of hours) % of total sales Substitute value given in the problem. Let x represent the percent commission. Multiply Subtract. Since x is multiplied by 3,350, divide both sides by 3,350 to undo the multiplication. The answer is a decimal. _5.25% = x Write the decimal as a percent. _Aaron’s percent commission is 5.25%. Feedback A B C D Use the formula for gross income: gross income = (income * number of hours) + commission, and solve for the percent commission. In your final answer, convert the decimal to a percent. Correct! The percent commission is the percent of the total sales. TOP: 2-9 Applications of Percents 104. ANS: D I=Prt 975 = (8000)(r) Write the formula for simple interest. Substitute the given values. 975 = 4000r Multiply (8000) . Since r is multiplied by 3500, divide both sides by 3500 to undo the multiplication. 0.244 = r The interest rate is 24.4%. Feedback A Use the formula for simple interest, I = Prt. B C D Use the formula for simple interest, I = Prt. Use the formula for simple interest, I = Prt. Correct! TOP: 2-9 Applications of Percents 105. ANS: A Round $69.98 to $70.00. 20% = 10% + 10% 10% of $70 = $7.00 10% of $70 = $7.00 $7.00 + $7.00 = $14.00 Feedback A B C D Correct! First, round the amount to the nearest dollar. Then, multiply to find 10% of that amount. First, round the amount to the nearest dollar. Then, multiply to find 10% of that amount. First, round the amount to the nearest dollar. Then, multiply to find 10% of that amount. TOP: 2-9 Applications of Percents 106. ANS: D Step 1 Find the cost of the meal before the tip and sales tax. Write the formula for the sales tax. Substitute known values. Solve for c, the cost of the meal. Step 2 Find the total cost of the meal, including tip and sales tax. Write the formula for the total cost. Substitute the known values. Feedback A B C D First, calculate the cost of the meal before sales tax and tip. Then, find the total cost including sales tax and tip. First, calculate the cost of the meal before sales tax and tip. Then, find the total cost including sales tax and tip. This is the cost of the meal before sales tax and tip. You need to include the sales tax and tip. Correct! TOP: 2-9 Applications of Percents 107. ANS: C Substitute the given values. If the first number is less than the second number, there is a percent of increase. If the first number is greater than the second number, there is a percent of decrease. Feedback A B C D If the first number is less than the second number, there is a percent of increase. If the first number is greater than the second number, there is a percent of decrease. The percent change is the amount of increase or decrease divided by the original amount. Correct! The percent change is the amount of increase or decrease divided by the original amount. TOP: 2-10 Percent Increase and Decrease 108. ANS: A To find the amount of decrease, multiply 28 by 0.25. Then, subtract the decrease from 28 to find the result of the decrease. Feedback A B Correct! For a percent increase, add the percent change to the original amount. For a percent decrease, subtract the percent change C D from the original amount. To find the result, add the percent change to or subtract the percent change from the original amount. First, calculate the percent change. Then, add it to or subtract it from the original amount. TOP: 2-10 Percent Increase and Decrease 109. ANS: A Method 1 A discount is percent decrease. So find $117.00 decreased by 70%. Find 70% of $117.00. This is the amount of the discount. Subtract 81.90 from 117.00. This is the sale price for children under the age of 16. Method 2 Subtract percent discount from 100%. Children under the age of 16 pay 30% of the regular price, $117.00. Find 30% of 117.00. This is the sale price for children under the age of 16. Feedback A B C D Correct! Check that the price is an increase or decrease. Find the discounted price, not the discount. Start by determining the discount. TOP: 2-10 Percent Increase and Decrease 110. ANS: B A markup is a percent increase. So find $16 increased by 83%. Find 83% of 16. This is the amount of the markup. Add to 16. This is the selling price. The amount of the markup is $13.28, and the selling price is $29.28. Feedback A B C You reversed the order of the numbers. A markup is an amount by which a wholesale cost is increased. Correct! A markup is an amount by which a wholesale cost is D increased. It's not a discount. To find the amount of the markup, you need to multiply the markup percent by the wholesale amount. TOP: 2-10 Percent Increase and Decrease 111. ANS: D Step 1 Calculate the pre-holiday price. Supplier’s price + markup = The selling price before the selling price holidays is 325% of the supplier’s price. For each card, find 325% of the supplier’s price. This is the pre-holiday price. First card: Second card: Step 2 Calculate the post-holiday price. The selling price after the holidays is 40% of the pre-holiday price. For each card, find 40% of the pre-holiday price. This is the post-holiday price. First card: Second card: Feedback A B C D To find the pre-holiday price, find the markup percent of the supplier's price and add it to the supplier's price. To find the pre-holiday price, find the markup percent of the supplier's price and add it to the supplier's price. To find the post-holiday price, subtract the discount percent from 100% and multiply the result by the pre-holiday price. Correct! TOP: 2-10 Percent Increase and Decrease 112. ANS: A Divide both sides by 2. What numbers are 7 units from 0? Case 1: x+7=7 Case 2: Rewrite the equation as two cases. x + 7 = The solutions are x = 0 or x = –14. –7 Feedback A B C D Correct! Divide before you add or subtract. There are two cases to solve. Absolute value means distance from zero. Solve the second case when the number inside the absolute value is negative. Divide before you add or subtract. TOP: 2-Ext Solving Absolute-Value Equations 113. ANS: C First, isolate the absolute value expression. Subtract 8 from both sides. The absolute value expression is equal to a negative number, which is impossible. The equation has no solution. Feedback A B C D An absolute value must be greater than or equal to 0. Isolate the absolute value by subtracting the term outside absolute value bars. Correct! Subtract the term outside the absolute value bars. TOP: 2-Ext Solving Absolute-Value Equations 114. ANS: D Test values of y that are positive, negative, and 0. When the value of y is a number less than 4, the value of When the value of y is 4, the value of is equal to 10. When the value of y is a number greater than 4, the value of It appears that the solutions of is less than 10. are numbers less than 4. is greater than 10. Feedback A B C D Test the value you found with the equal sign. Do you get a true statement? Test some values and find out if you get a true statement. Then, check the inequality symbol. Is this the only solution? Test some more values, including fractions. Correct! TOP: 3-1 Graphing and Writing Inequalities 115. ANS: B The graph should start at the given value. A > or < graph has an empty circle at that value. A or graph has a solid circle at that value. A > or graph has an arrow to the right, and a < or graph has an arrow to the left. Feedback A B C D Check the direction the arrow should be pointing. Correct! Check the direction the arrow should be pointing. A "greater than" or "less than" graph has an empty circle. A "greater than or equal to" or "less than or equal to" graph has a solid circle. TOP: 3-1 Graphing and Writing Inequalities 116. ANS: C Use the variable m. The arrow points to the right, so use either > or ≥. The solid circle at –3 means that –3 is a solution, so use ≥. Feedback A B C D The arrow should point in the same direction as the inequality symbol. The endpoint is not a solution. Correct! The endpoint is not a solution. TOP: 3-1 Graphing and Writing Inequalities 117. ANS: D The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line. Feedback A B C D The number of yards must be greater than or equal to 500, not less than 500. The number of yards must be greater than or equal to 500, not less than 500. The number 500 should be included in the solution. Correct! TOP: 3-1 Graphing and Writing Inequalities 118. ANS: C Sam has $450, but must save $180 of that for his camping trip. If s is the amount he can spend on music, then So, . s –500 –400 –300 –200 –100 0 100 200 300 400 500 Feedback A B The amount Sam can spend on music cannot be more than the amount he earned. The amount Sam can spend on music cannot be more than what he saved after his camping trip. Correct! Sam has $450, but must save $180 for his trip. The remaining amount is how much he can spend on music. C D TOP: 3-1 Graphing and Writing Inequalities 119. ANS: C n + 6 < –1.5 –6 –6 Subtract 6 on both sides to isolate n. n < –7.5 –10 –8 –6 –4 –2 0 2 4 6 8 10 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. Feedback A Use a solid circle for a "greater than or equal to" or "less than or equal to" graph. Use an empty circle for a "greater than" or "less than" graph. Check that the arrow is pointing in the correct direction. Correct! Check that you used the correct inverse operation. B C D TOP: 3-2 Solving Inequalities by Adding and Subtracting 120. ANS: C number already downloaded + additional songs ≤ 8 + s ≤ Subtract 8 from both sides to undo the addition. s ≤ weekly limit 11 3 Since you can only download whole songs, graph the nonnegative integers less than or equal to 3. 0 1 2 3 4 5 6 7 8 9 10 11 Feedback A B C D Check the inequality symbol. Check the graph, as it not reasonable to have a fractional number of songs. Correct! Check the graph, as it not reasonable to have a fractional number of songs. TOP: 3-2 Solving Inequalities by Adding and Subtracting 121. ANS: A Let d represent the amount of money in dollars Denise must save to reach her goal. $365 plus additional amount of money is at least $635 in dollars 365 + d 635 Since 365 is added to d, subtract 365 from both sides to undo the addition. 365 365 Check the endpoint 270 and a number that is greater than the endpoint. Feedback A B C D Correct! You should be solving an inequality, not an equation. Subtract from both sides of the inequality. Check the endpoint to see if you get a true statement. TOP: 3-2 Solving Inequalities by Adding and Subtracting 122. ANS: B Step 1: Rewrite both mixed numbers as improper fractions. and Step 2: Solve the inequality. Rewrite the inequality. Subtract from both sides. Rewrite the fractions with a common denominator. 2 = 55 Simplify. Step 3: Graph the inequality. –9 –6 –3 0 3 6 9 12 15 18 21 Feedback A B C D To solve the inequality, subtract the first mixed number from both sides of the inequality. Correct! Check the direction of the inequality. To solve the inequality, subtract the first mixed number from both sides of the inequality. TOP: 3-2 Solving Inequalities by Adding and Subtracting 123. ANS: A >3 Multiply both sides by 8 to isolate x. > 3(8) x > 24 0 5 10 15 20 25 30 35 40 45 50 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. Feedback A B Correct! Use a solid circle when the value is included in the graph. Use an empty circle when the value is not included. To solve the inequality, use multiplication to undo the division. Check that the arrow is pointing in the correct direction. C D TOP: 3-3 Solving Inequalities by Multiplying and Dividing 124. ANS: D 2m ≤ 18 ≤ Divide both sides by 2 to isolate m. m≤9 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. –1 0 1 2 3 4 5 6 7 8 9 10 11 Feedback A B C D Check that the arrow is pointing in the correct direction. To solve the inequality, use division to undo the multiplication. Use a solid circle when the value is included in the graph. Use an empty circle when the value is not included. Correct! TOP: 3-3 Solving Inequalities by Multiplying and Dividing 125. ANS: D ≤2 Multiply both sides by –4 to isolate z. When you multiply by a negative number, reverse the inequality symbol. ≥ 2(–4) z ≥ –8 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. –10 –8 –6 –4 –2 0 2 4 6 8 10 Feedback A B C D When multiplying by a negative number, reverse the inequality symbol. Check the signs. Check the signs. Correct! TOP: 3-3 Solving Inequalities by Multiplying and Dividing 126. ANS: A 2f ≥ –8 ≥ Divide both sides by 2 to isolate f. f ≥ –4 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. –10 –8 –6 –4 –2 0 2 4 6 8 10 Feedback A B C D Correct! When dividing by a positive number, keep the same inequality symbol. When dividing by a negative number, reverse the inequality symbol. Check the signs. Check the signs. TOP: 3-3 Solving Inequalities by Multiplying and Dividing 127. ANS: B Divide both sides by the ticket price. The inequality symbol does not change. Simplify. 5 is the largest whole number less than 5.9. Feedback A B C D Divide the total amount by the ticket price and round down to the nearest whole number. Correct! Round down, not up, to the nearest whole number. Divide the total amount by the ticket price and round down to the nearest whole number. TOP: 3-3 Solving Inequalities by Multiplying and Dividing 128. ANS: D 2.847 is about 3, and 15.168 about 15. With estimation, becomes . So, the greatest possible integer solution is 5. Feedback A The solution needs to be an integer. B C D Round the numbers in the inequality to the nearest integer, and then divide. Round the numbers in the inequality to the nearest integer, and then divide. Correct! TOP: 3-3 Solving Inequalities by Multiplying and Dividing 129. ANS: B Use inverse operations to undo the operations in the inequality one at a time. −n – 4 < 3 n > –7 –10 –8 –6 –4 –2 0 2 4 6 8 10 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. Feedback A B C D If you divide both sides of the inequality by a negative number, reverse the inequality symbol. If you divide by a positive number, do not reverse the inequality symbol. Correct! Use inverse operations to undo the operations in the inequality one at a time. Check your calculations when using inverse operations to isolate the variable. TOP: 3-4 Solving Two-Step and Multi-Step Inequalities 130. ANS: C z + 8 + 3z ≤ –4 Combine like terms. 4z + 8 ≤ –4 Subtract 8 from both sides. 4z ≤ –12 Divide both sides by 4. When you divide by a negative number, reverse the inequality symbol. When you divide by a positive z ≤ –3 number, keep the same inequality symbol. –10 –8 –6 –4 –2 0 2 4 6 8 10 Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value is not included, such as with > or <. Feedback A B C D If you divide both sides of the inequality by a negative number, reverse the inequality symbol. If you divide by a positive number, keep the same inequality symbol. Use inverse operations to isolate the variable. Correct! Check your calculations. TOP: 3-4 Solving Two-Step and Multi-Step Inequalities 131. ANS: D Let d represent the distance the family drove on the third day. The average number of miles is the sum of the miles of each day divided by 3. ( 150 plus 190 plus d) divided 3 is at 180 by least ( 150 + 190 + d) ÷ 3 180 Since is divided by 3, multiply both sides by 3 to undo the division. Combine like terms. Since 340 is added to d, subtract 340 from both sides to undo the addition. The least number of miles the family drove on the third day is 200. Feedback A B C D First, set up an inequality where the average number of miles is the sum of the miles of each day divided by 3. Then, solve the inequality. First, set up an inequality where the average number of miles is the sum of the miles of each day divided by 3. Then, solve the inequality. First, set up an inequality where the average number of miles is the sum of the miles of each day divided by 3. Then, solve the inequality. Correct! TOP: 3-4 Solving Two-Step and Multi-Step Inequalities 132. ANS: B Subtract 3x from both sides to collect the x terms on one side of the inequality symbol. Divide both sides by 3. 3x < 15 x<5 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Feedback A B C D Only change < to > when you divide or multiply by a negative number. Correct! Check your calculations. Check your positive and negative signs. TOP: 3-5 Solving Inequalities with Variables on Both Sides 133. ANS: C Science plus $3 per student is less Center fee than $135 + $3 s < 135 + 3s < 6s – 3s – 3s 135 < 3s < $12 $6 per student s 45 < s If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students. Feedback A B C D The per-student fees need to be multiplied by the number of students. The per-student fees need to be multiplied by the number of students. Correct! This is the number of students where the Dino Discovery Museum charges less. TOP: 3-5 Solving Inequalities with Variables on Both Sides 134. ANS: B On the left side, combine the two terms. On the right side, distribute 1.5. ≤ ≤ Subtract the 1.5x from both sides of the inequality. 6 ≤ Divide both sides of the inequality by 3 . Reverse the inequality symbol. Feedback A B C D Check your signs. When you subtract 1.5 from both sides you should have a negative coefficient. Correct! Check your signs. When you subtract 1.5 from both sides you should have a negative coefficient. When multiplying or dividing by a negative number, reverse the inequality symbol. Reverse the inequality symbol when multiplying or dividing both sides of an inequality by a negative number. TOP: 3-5 Solving Inequalities with Variables on Both Sides 135. ANS: C When the inequality is simplified, if the result is a statement that is always true, then the solution set includes all real numbers. If the result is a statement that is always false, then there are no solutions to the inequality. Feedback A B C D Check that you have simplified the inequality correctly. Check that you have simplified the inequality correctly. Correct! Check whether any real number will make the inequality true or whether no real numbers will make the inequality true. TOP: 3-5 Solving Inequalities with Variables on Both Sides 136. ANS: D Combine like terms. Simplify. Divide both sides by 0.5. Feedback A B C D The inequality symbol will only change if you multiply or divide by a negative number. Combine only like terms. When moving a term from one side of the inequality to the other side, subtract from both sides. Correct! TOP: 3-5 Solving Inequalities with Variables on Both Sides 137. ANS: A Let n represent the possible number of people in the flight. 100 is less than or equal to n is less than or equal to 100 n –250 –200 –150 –100 –50 0 50 100 150 240 240 200 250 Feedback A B C D Correct! The phrase "at least" means the number 100 is included in the solution. Check your inequality symbols. Is it possible for a number to be less than or equal to 100 AND greater than or equal to 240? A compound inequality is the result of combining two simple inequalities into one statement by the words AND or OR. TOP: 3-6 Solving Compound Inequalities 138. ANS: C AND Write the compound inequality using AND. Solve each simple inequality. Divide to undo the multiplication. AND First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two graphs overlap. Feedback A B C D Check the endpoints to see whether they are included in the solutions. Check the endpoints to see whether they are included in the solutions. Correct! Check the inequality symbols. A number cannot be less than 1 AND greater than or equal to 4. TOP: 3-6 Solving Compound Inequalities 139. ANS: D First solve each simple inequality to obtain of the graph of and the graph of –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 OR . The graph of the compound inequality is the union . Find the union by combining the two regions. 2 3 4 5 6 7 8 9 s 10 Feedback A B C D Use a solid circle if and only if the endpoint is contained in the solution set. Find the union of the two regions. Use a solid circle if and only if the endpoint is contained in the solution set. Find the union of the two regions. Correct! TOP: 3-6 Solving Compound Inequalities 140. ANS: C –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 x ≤ –5 The numbers to the left of –5 are shaded. A solid circle is used. This part of the inequality uses ≤. 0 1 2 3 4 5 6 OR The shaded area is not between two numbers so the compound inequality uses OR. 7 8 9 10 x x>3 The numbers to the right of 3 are shaded. An empty circle is used. This part of the inequality uses >. Feedback A B C D The shaded portion is not between two numbers. The shaded portion is not between two numbers. Correct! There is a closed dot at –5. TOP: 3-6 Solving Compound Inequalities 141. ANS: A Test each value to see which is a solution of AND . If x = 14, then AND . The first inequality is false, so the compound inequality is false. If x = 12, then AND . The first inequality is false, so the compound inequality is false. If x = –6, then AND . The second inequality is false, so the compound inequality is false. If x = 2, then AND . Both inequalities are true, so the compound inequality is true. Feedback A B C D Correct! Substitute the solution into the inequalities to check that the compound inequality is true. Check the inequality symbols. As the compound inequality is an "AND" statement, check that both inequalities are true. TOP: 3-6 Solving Compound Inequalities 142. ANS: C Add 9 to isolate the absolute-value expression. Think: What numbers have an absolute value less than 8? is between –8 and 8, inclusive. Solve the two inequalities. Write the solution as a compound inequality. AND AND –27 –24 –21 –18 –15 –12 –9 –6 –3 0 3 6 9 12 15 18 21 24 27 30 Feedback A B C D Isolate the variable to find the solution of the original inequality. Check the inequality symbols. Correct! The inequality contains an absolute-value expression, so the solution should be a compound inequality. TOP: 3-Ext Solving Absolute-Value Inequalities 143. ANS: D x – 6 < –15 OR x – 6 > 15 x < – 9 OR x > 21 Add 3 to both sides to undo the subtraction and isolate the absolute value. Think: “What numbers have an absolute value less than –15 or greater than 15?” Solve the two inequalities. –26 –24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 16 18 Feedback A B C D First, isolate the absolute value. Then, solve two separate inequalities. First, isolate the absolute value. Then, solve two separate inequalities. First, isolate the absolute value. Then, solve two separate inequalities. Correct! TOP: 3-Ext Solving Absolute-Value Inequalities NUMERIC RESPONSE 144. ANS: $2430 TOP: 1-3 Multiplying and Dividing Real Numbers 145. ANS: 65 20 22 24 26 TOP: 2-3 Solving Two-Step and Multi-Step Equations 146. ANS: $31.05 147. ANS: 5 TOP: 3-3 Solving Inequalities by Multiplying and Dividing 148. ANS: 18 TOP: 3-4 Solving Two-Step and Multi-Step Inequalities MATCHING 149. 150. 151. 152. 153. ANS: ANS: ANS: ANS: ANS: F G A B E TOP: TOP: TOP: TOP: TOP: 1-1 Variables and Expressions 1-1 Variables and Expressions 1-1 Variables and Expressions 1-1 Variables and Expressions 1-1 Variables and Expressions 154. 155. 156. 157. 158. ANS: ANS: ANS: ANS: ANS: C B F G D TOP: TOP: TOP: TOP: TOP: 1-2 Adding and Subtracting Real Numbers 1-2 Adding and Subtracting Real Numbers 1-3 Multiplying and Dividing Real Numbers 1-2 Adding and Subtracting Real Numbers 1-3 Multiplying and Dividing Real Numbers 159. 160. 161. 162. 163. ANS: ANS: ANS: ANS: ANS: G E D C F TOP: TOP: TOP: TOP: TOP: 1-4 Powers and Exponents 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 1-4 Powers and Exponents 1-4 Powers and Exponents 164. 165. 166. 167. 168. 169. ANS: ANS: ANS: ANS: ANS: ANS: F G H A D E TOP: TOP: TOP: TOP: TOP: TOP: 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 1-5 Square Roots and Real Numbers 170. 171. 172. 173. 174. 175. ANS: ANS: ANS: ANS: ANS: ANS: A F E G H B TOP: TOP: TOP: TOP: TOP: TOP: 1-5 Square Roots and Real Numbers 1-7 Simplifying Expressions 1-7 Simplifying Expressions 1-7 Simplifying Expressions 1-6 Order of Operations 1-5 Square Roots and Real Numbers 176. 177. 178. 179. ANS: ANS: ANS: ANS: C E F G TOP: TOP: TOP: TOP: 1-8 Introduction to Functions 1-8 Introduction to Functions 1-8 Introduction to Functions 1-8 Introduction to Functions 180. ANS: B TOP: 1-8 Introduction to Functions 181. 182. 183. 184. 185. 186. ANS: ANS: ANS: ANS: ANS: ANS: C B E D G H TOP: TOP: TOP: TOP: TOP: 1-8 Introduction to Functions 1-8 Introduction to Functions 1-8 Introduction to Functions 1-8 Introduction to Functions 1-8 Introduction to Functions 187. 188. 189. 190. 191. 192. ANS: ANS: ANS: ANS: ANS: ANS: G H D B E C TOP: TOP: TOP: TOP: TOP: TOP: 2-1 Solving Equations by Adding or Subtracting 2-5 Solving for a Variable 2-4 Solving Equations with Variables on Both Sides 2-1 Solving Equations by Adding or Subtracting 2-5 Solving for a Variable 2-4 Solving Equations with Variables on Both Sides 193. 194. 195. 196. 197. ANS: ANS: ANS: ANS: ANS: D F G A C TOP: TOP: TOP: TOP: TOP: 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 198. 199. 200. 201. 202. ANS: ANS: ANS: ANS: ANS: C B D E A TOP: TOP: TOP: TOP: TOP: 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 2-7 Applications of Proportions 2-6 Rates Ratios and Proportions 2-6 Rates Ratios and Proportions 203. 204. 205. 206. 207. ANS: ANS: ANS: ANS: ANS: E B F G C TOP: TOP: TOP: TOP: TOP: 2-6 Rates Ratios and Proportions 2-7 Applications of Proportions 2-7 Applications of Proportions 2-7 Applications of Proportions 2-7 Applications of Proportions 208. 209. 210. 211. 212. ANS: ANS: ANS: ANS: ANS: G B A D F TOP: TOP: TOP: TOP: TOP: 2-9 Applications of Percents 2-9 Applications of Percents 2-9 Applications of Percents 2-9 Applications of Percents 2-9 Applications of Percents 213. 214. 215. 216. 217. 218. ANS: ANS: ANS: ANS: ANS: ANS: D G H C F B TOP: TOP: TOP: TOP: TOP: TOP: 2-10 Percent Increase and Decrease 2-10 Percent Increase and Decrease 2-10 Percent Increase and Decrease 2-10 Percent Increase and Decrease 2-8 Percents 2-10 Percent Increase and Decrease 219. ANS: C TOP: 3-6 Solving Compound Inequalities 220. 221. 222. 223. ANS: ANS: ANS: ANS: E B D A TOP: TOP: TOP: TOP: 3-6 Solving Compound Inequalities 3-1 Graphing and Writing Inequalities 3-1 Graphing and Writing Inequalities 3-6 Solving Compound Inequalities