1. An arithmetic sequence is a list of numbers in which consecutive numbers share a common difference. Each number after the first is calculated by adding the common difference to the preceding number. For example, the arithmetic sequence 1, 4, 7, 10,... has 3 as its common difference. Identify the common difference in each arithmetic sequence that follows. a. 10, 12, 14, 16, 18,... b. 7, 8, 9, 10, 11,... c. 25, 30, 35, 40, 45,... a. The common difference of the arithmetic sequence 10, 12, 14, 16, 18,... is. b. The common difference of the arithmetic sequence 7, 8, 9, 10, 11,... is. c. The common difference of the arithmetic sequence 25, 30, 35, 40, 45,... is. ID: 1.2.3 2. A geometric sequence is a list of numbers in which consecutive numbers share a common ratio. Each number after the first is calculated by multiplying the preceding number by the common ratio. For example, 1, 3, 9, 27,... has 3 as its common ratio. Identify the common ratio in each geometric sequence that follows. a. 2, 6, 18, 54, 162,... b. 3, 6, 12, 24, 48,... a. The common ratio of the geometric sequence 2, 6, 18, 54, 162,... is. b. The common ratio of the geometric sequence 3, 6, 12, 24, 48,... is. ID: 1.2.4 3. Describe a relationship shared by consecutive numbers in the following sequence. 3, 9, 21, 45, 93,... Choose the mathematical steps that best illustrate the above sequence. A. Each number is generated by multiplying the preceding number by 2 and adding 3. B. Each number is generated by multiplying the preceding number by 2 and subtracting 3. C. Each number is generated by dividing the preceding number by 2 and adding 3. D. Each number is generated by dividing the preceding number by 2 and subtracting 3. ID: 1.2.5 4. Simplify. 8 6 + 4 ID: 1.3.1b 8 6 + 4 = (Simplify your answer.) 5. Evaluate. 17 ( 6 2) ID: 1.3.2a The answer is. (Simplify your answer.)
6. Evaluate the following expression. (4 + 2) 8 (4 + 2) 8 = ID: 1.3.3b 7. Simplify. 39 + 2 4 39 + 2 4 = ID: 1.3.4a 8. Simplify using order of operations. 3 1 + 3( 14 9 ) + 7 3 1 + 3( 14 9 ) + 7 = ID: 1.3.6f 9. Find the value of the expression. 41 2 4 + 2 41 2 4 + 2 = ID: 1.3.7c 10. Simplify. ( 5 + 3) 2 ( 5 + 3) 2 = ID: 1.3.8b 11. Find the value of the expression. 8 0 8 0 = ID: 1.HCIP1.3a 12. Evaluate. 3 6 = 6 3 ID: 1.HCIP1.3c
13. Evaluate 3 6. 3 6 = ID: 1.HCIP1.3d 14. Decide which property is illustrated by the given statement. 5 ( 11) = 11 8 5 8 5 5 Which property is illustrated by the equation ( 11) = 11? 8 8 A. distributive property B. associative property of addition C. commuatitive property of multiplication D. associative property of multiplication E. commuatitive property of addition ID: 1.HCIP1.7a 15. Decide whether the statement is an example of the commutative, associative, identity, inverse or distributive property. 5(x + y) = 5x + 5y Which property is illustrated by the equation 5(x + y) = 5x + 5y? A. commutative property of addition B. associative property of multiplication C. distributive property D. communtative property of multiplication E. associative property of addition ID: 1.HCIP1.7b 16. 7 Leo farms 256 acres of land. One year, he planted soybeans on of his land. How many acres did he plant with 16 soybeans? Leo planted (Simplify your answer.) acres with soybeans. ID: 1.4.1
17. A student rents an apartment for the academic year (two semesters) with three friends. The rent for the entire academic year is $ 10,080. Each semester, the student receives a bill for his share of the rent. If he and his friends divide the rent equally, how much must he pay each semester? The student pays $ for rent each semester. (Simplify your answer.) ID: 1.4.2 18. Kathryn, a college student, works part time at a coffee house. Last week, she worked 4 5 hours on Monday, 5 1 on 12 2 Tuesday, 2 3 on Wednesday, and 6 1 on Thursday. How many hours did she work last week? 4 4 Kathryn worked hours last week. (Simplify your answer. Type a whole number, proper fraction, or mixed number.) ID: 1.4.4 19. 1 A serving of filet mignon is generally considered to be about lb. How many servings can be prepared from 3 1 lb of 4 3 filets? ID: 1.4.5 servings (Simplify your answer. Type a mixed numeral, if possible. Otherwise, type a whole number or a fraction.) 20. Kathryn, a college student, works part time at a coffee house. Last week, she worked 4 7 hours on Monday, 6 1 on 16 2 Tuesday, 3 3 on Wednesday, and 2 1 on Thursday. How many hours did she work last week? 4 4 Kathryn worked hours last week. (Simplify your answer. Type a whole number, proper fraction, or mixed number.) ID: 1.4.6 21. Subtract. 19 1 5 3 5 10 19 1 5 3 5 10 = (Type an integer, fraction, or mixed number. Simplify your answer.) ID: 1.4.8a
22. Find the sum and write it in lowest terms. 1 2 3 + 2 1 6 1 2 3 + 2 1 6 = (Simplify your answer. Type a whole number, fraction, or a mixed number.) ID: 1.4.8b 23. Perform the indicated operation. 7 1 1 12 ID: 1.4.8c 7 13 7 7 1 1 12 13 = (Type a whole number, proper fraction, or mixed number.) 24. Divide as indicated. Write the answer in lowest terms. 1 5 2 6 1 5 2 6 = ID: 1.4.8e 25. Suppose that a student took the courses in the table below, with the given amount of credits and got the corresponding grades. If a student withdraws from a course, he or she receives a W. The W appears on the transcript, but is not included in the grade point average. Suppose that instead of a C + in economics, the student received a W. Use this to recalculate the new GPA. Course Letter Grade Numerical Equivalent Credit Hours Weight Contribution to GPA Psychology A 4.00 4 4 18 4 18 4.00 = 0.889 Economics C + 2.33 4 4 18 0.518 Chemistry B 2.67 3 3 18 0.445 English C + 2.33 4 4 18 0.518 Mathematics B 2.67 3 3 18 0.445 The new GPA would be. (Type a whole number or decimal rounded to three decimal places as needed.) ID: 1.5.1
26. Suppose that a student took the courses in the table below, with the given amount of credits and got the corresponding grades. If a student withdraws from a course, he or she receives a W. The W appears on the transcript, but is not included in the grade point average. Suppose that instead of a C + in economics, the student received a W. Use this to recalculate the new GPA. Course Letter Grade Numerical Equivalent Credit Hours Weight Contribution to GPA Psychology A 4.00 4 4 18 4 18 4.00 = 0.889 Economics C + 2.33 4 4 18 0.518 Chemistry B 3.00 3 3 18 0.500 English C + 2.33 4 4 18 0.518 Mathematics B 2.67 3 3 18 0.445 The new GPA would be. (Type a whole number or decimal rounded to three decimal places as needed.) ID: 1.5.3b 27. The following prices per pound of meat were found at five grocery stores. Find the mean. $ 3.29, $ 3.50, $ 3.26, $ 3.59, $ 3.21 The mean price is $. ID: 1.5.4a 28. To get a B in math, Alexandria Pappas must average 80 on five tests. Scores on the first four tests were 83, 75, 82, and 78. What is the lowest score that she can get on the last test and still get a B? The lowest possible score for getting a B is. ID: 1.5.4b 29. Suppose you took 17 credit courses last semester. You earned an A in English ( 3 hours), a C + in mathematics ( 3 hours), a B in chemistry ( 4 hours), a C + in health ( 4 hours), and a B in history ( 3 hours). Calculate your GPA for the semester. Course ID: 1.5.5 Letter Grade Numerical Equivalent English A 3.67 3 3 17 Math C + 2.33 3 3 17 Chemistry B 2.67 4 4 17 Health C + 2.33 4 4 17 History B 3.00 3 3 17 GPA Credit Hours Weight Weight Num. Equiv. (Type whole numbers or decimals rounded to three decimal places as needed.)
30. Complete the table by representing each ratio in all four formats. Round decimals to the thousandths place and percents to the tenths place. Verbal 1 out of 2 14 out of 80 13 out of 10 30 out of 10 Reduced fraction Decimal Percent Verbal 1 out of 2 14 out of 80 13 out of 10 30 out of 10 Reduced fraction Decimal Percent % % % % ID: 1.6.1 31. Of 500 people who used the Internet to find pet information, 270 said they used it when buying a pet. What portion used the Internet when buying a pet? ID: 1.6.8 % used the Internet when buying a pet. (Simplify your answer. Type a whole number or a decimal.) 32. The customary tip on waiter service in New York City restaurants is approximately 20% of the food and beverage cost. This means that your server is counting on a tip of $0.20 for each dollar you spend on your meal. What is the expected tip on a dinner for two costing $ 80? The tip on a dinner for two costing $ 80 is $. ID: 1.7.5 33. The sales tax on the purchase of a used truck is $ 750. If the tax rate is 5%, find the purchase price of the truck. The purchase price is $. ID: 1.7.6 34. In a medical study of pregnant women with ' poor' diets, 40 women, or 8%, had babies in good or excellent health. How many women were in the original study? There were women were in the original study. ID: 1.7.7
35. In a very disappointing season, a softball team won only 20% of the games it played this year. If it won 12 games, how many games did it play? How many games did it lose? The softball team played The softball team lost games. games. ID: 1.7.11 36. You are purchasing a new car. The price you negotiated with a car dealer is $ 18,808, excluding sales tax. The sales tax rate is 8.125%. a. What growth factor is associated with sales tax rate? b. Use the growth factor to determine the total cost of the car. a. The growth factor associated with sales tax rate is. b. The total price of the car is $. (Round to the nearest cent as needed.) ID: 1.9.2 37. You decide to invest $ 5000 in a 1 year certificate of deposit (CD) that earns an annual percentage yield (APY) of 7.08%. How much will your investment be worth in a year? The investment will be worth $. ID: 1.9.8 38. John is taking a photography class at the local community college and needs to purchase a digital camera. The college bookstore is having a big sale on digital cameras. After a 50% price reduction, he purchased a digital camera for $ 280. What was the price of the camera before the reduction? The price of the camera before the reduction is $. ID: 1.9.21 (Simplify your answer. Type a whole number.) 39. A $ 300 leather jacket is on sale for 30% off. You present a coupon at the cash register for an additional 10% off. a. Determine the decay factor corresponding to each percent decrease. b. Use these decay factors to determine the price you paid for the jacket. a. What is the decay factor corresponding to 30% off? (Simplify your answer. Type an integer or a decimal.) What is the decay factor corresponding to 10% off? (Simplify your answer. Type an integer or a decimal.) b. What is the price paid for the jacket? (Simplify your answer. Type an integer or a decimal.) ID: 1.10.3
40. You had anticipated a large demand for a popular toy and increased your inventory of 2400 by 15%. You were able to sell 75% of your inventory. How many toys remain? The remaining inventory is toys. ID: 1.10.5 41. A digital camera with an original price tag of $ 500 was marked down by 30%. You have a coupon good for an additional 20% off. a. What is the effective decay factor? (Simplify your answer. Type an integer or a decimal.) b. What is the final cost of the camera? (Simplify your answer. Type an integer or a decimal.) c. What is the effective percent discount? % (Simplify your answer. Type an integer or a decimal.) ID: 1.10.8 42. Write 39% as a decimal. 39% = ID: 1.HCIP3.1a 43. Write 54.4% as a decimal. 54.4% = ID: 1.HCIP3.1b 44. Express the given percent as a decimal. 294% ID: 1.HCIP3.1e 45. On three consecutive passes, a football team gains 6 yards, loses 39 yards, and gains 12 yards. What number represents the total net yardage? The total net yardage is yards. (Type a negative number with a negative sign, or type a positive number with no sign.) ID: 1.12.4
46. Add. 7 + ( 1) 7 + ( 1 ) = ID: 1.12.5c 47. Subtract. 7 13 ID: 1.12.5i 7 13 = (Simplify your answer. Type an integer.) 48. Subtract the following. 15 ( 15) The answer is. ID: 1.12.5n 49. Add and simplify. 7 5 + 14 14 ID: 1.12.5u 7 5 + 14 14 = (Simplify your answer. Type a fraction.) 50. Subtract. 3.9 8.8 3.9 8.8 = ID: 1.12.5v 51. The lowest temperature ever recorded in Sundance was 29 F. The highest recorded temperature in Sundance was 140 F higher than the record low temperature. Find Sundance's highest recorded temperature. Sundance's highest recorded temperature is F. ID: 1.12.6 52. One day the temperature started at 9 F and dropped 16 by the end of the day. What was the temperature at the end of the day? ID: 1.12.7 At the end of the day, the temperature was F. 53. A temperature recorded in Antarctica was 117 F. The temperature recorded in the Sahara Desert was 130 F. How many degrees warmer is 130 F than 117 F? F ID: 1.12.8
54. Use either < or > to make this a true statement. 18 16 18 16 ID: 1.12.10a 55. Use either < or > to make this a true statement. 13 3 13 3 ID: 1.12.10b 56. Use either < or > for to write a true sentence. 6 17 1 6 6 17 1 6 ID: 1.12.10f 57. The lowest point in a country is a lake at an elevation of 17 m. The highest point is a mountain at an elevation of 2330 m. What is the difference in elevation between the mountain and the lake. The difference in elevation is m. ID: 1.12.18c 58. The bar graph to the right shows the yearly net income (in thousands of dollars) for Dynamo Co. What was the net income (in dollars) for Dynamo Co. in 2000? Thousands of Dollars Net Income for Dynamo Co. 8000 7122 4000 2252 0 1055 4000 4477 8000 1999 2000 2001 2002 Year The net income was dollars. ID: 1.12.20 59. Multiply. ( 10)( 15) ( 10)( 15 ) = ID: 1.13.1b
60. Find the quotient. 16 ( 4) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 16 ( 4 ) = (Simplify your answer.) B. The quotient is undefined. ID: 1.13.1j 61. Multiply. 5 6 6 19 5 6 6 19 = (Type an integer or a simplified fraction.) ID: 1.13.2g 62. Evaluate 5 1 7 3 35. Use a calculator to verify answer. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 5 3 A. 1 (Type an integer or an improper fraction.) 7 35 = B. The expression is undefined. ID: 1.13.2h 63. 4 5 A cold front moves through town in January, dropping the temperature an average of per day for days. What is the change in temperature over a 5 day period? Write your answer as a signed number. The change in temperature over a 5 day period is. ID: 1.13.5 64. In 3 days, the value of a share of stock dropped by a total of 7 1 points. Use a signed number to express the average daily 8 loss. ID: 1.13.7 points per day (Type a mixed number.)
65. Stock values are reported daily in some newspapers. Reports usually state the values at both the opening and the closing of a business day. Suppose you own 215 shares of a stock. At the highest point today, your stock is worth $ 26.05 per share, but by the close of the Stock Exchange, it had dropped to $ 24.27 per share. What is the total change in the value of your 215 shares from the highest point of the day to the close of business? Today the value of your shares of stock dropped $ from the highest point to the end of the day. ID: 1.13.9a 66. Find the average of the list of numbers. 8, 10, 12, 15, 15, 7, 3 The average is. ID: 1.13.14 67. To discourage random guessing on a multiple choice exam, the professor assigns 6 points for a correct response, deducts 3 points for an incorrect answer, and gives 0 points for leaving the question blank. What is the student's score on a 36 question exam if he has 20 correct answers and 16 incorrect? The student's score on the exam is points. ID: 1.14.1a 68. While remodeling a room, a developer decides to install molding around the base of each wall. The molding needs to go all the way around the room except for a 37 inch gap at the doorway. The dimensions of the room are 8 1 feet by 12 3 feet. 3 4 The number of feet of molding needed is determined by evaluating the expression below. How much molding does the developer need? 1 3 1 2 8 + 12 3 3 4 12 The developer needs (Simplify your answer.) feet of molding. ID: 1.14.2 69. Simplify. 8 + 6( 9 15) 8 + 6( 9 15 ) = (Type an integer or a fraction.) ID: 1.14.4b 70. Evaluate the following expression. 2 2 2 3 + 25 2 2 2 3 + 25 = (Simplify your answer.) ID: 1.14.4c
71. Evaluate the following expression. 3.6 (2.4 + 3.6) 2 3.6 (2.4 + 3.6) 2 = (Simplify your answer.) ID: 1.14.4d 72. Evaluate the given expression. 2 6 ( 7) 2 2 6 ( 7) 2 = ID: 1.14.4h 73. Evaluate this expression. 5 2 5 2 = (Simplify your answer. Type an integer or a fraction.) ID: 1.14.6a 74. Evaluate the expression. ( 4) 4 ( 4) 4 = ID: 1.14.6b 75. Evaluate. 5 2 5 2 = ID: 1.14.6c 76. Simplify the following expression. ( 3) 4 ( 3) 4 = (Type a simplified fraction.) ID: 1.14.6d 77. Express the number 0.000721 in scientific notation. 0.000721 = (Use scientific notation. Use the multiplication symbol in the math palette as needed.) ID: 1.14.7a
78. Write the number in scientific notation. 670,000 (Use scientific notation. Use the multiplication symbol in the math palette as needed.) ID: 1.14.7d 79. Convert to decimal notation. 5.228 10 8 ID: 1.14.8b 5.228 10 8 = (Simplify your answer. Type an integer or a decimal.) 80. Write the number without exponents. 6.381 10 7 6.381 10 7 = ID: 1.14.8c 81. A ray has a wavelength of 0.000000862 millimeters. Write 0.000000862 in scientific notation. 0.000000862 = (Use scientific notation. Use the multiplication symbol in the math palette as needed.) ID: 1.14.9 82. Jennifer owes $ 199 to a credit card company. She makes a $11 purchase with the card, and then pays $90 on the account. What is her current balance? What is her balance? $ (Type your answer as a signed number.) ID: 1.HCIP4.36 83. Find the difference in altitude between a mountain that has an altitude of 2265 feet and a desert valley that is 416 feet below sea level. The difference in altitude is feet. ID: 1.HCIP4.38 84. One day the temperature started at 6 F and dropped 20 by the end of the day. What was the temperature at the end of the day? ID: 1.HCIP4.39b At the end of the day, the temperature was F.
85. The number of credit unions in a midwestern state in the years 1998 2002 is given in the adjacent table Year Number of Credit Unions 1998 4907 1999 5221 2000 6860 2001 7100 2002 7266 The average number of credit unions operating in the years 1998 2002 is. (Round to the nearest whole number.) ID: 1.HCIP4.41b
1. 2 1 5 2. 3 2 3. A. Each number is generated by multiplying the preceding number by 2 and adding 3. 4. 52 5. 68 6. 48 7. 47 8. 25 9. 35 10. 64 11. 1 12. 216 13. 729 14. C. commuatitive property of multiplication 15. C. distributive property 16. 112 17. 1260
18. 18 11 12 19. 13 1 3 20. 16 15 16 21. 15 7 10 22. 3 5 6 23. 2 17 39 24. 3 5 25. 2.953 26. 3.024 27. 3.37 28. 82 29. 0.648 0.411 0.628 0.548 0.529 2.764
30. 1 2 0.5 50 7 40 0.175 17.5 13 10 1.3 130 3 3 300 31. 54 32. 16 33. 15,000 34. 500 35. 60 48 36. 1.08125 20,336.15 37. 5354.00 38. 560 39. 0.7 0.9 189
40. 690 41. 0.56 280 44 42. 0.39 43. 0.544 44. 2.94 45. 21 46. 6 47. 20 48. 30 49. 1 7 50. 4.9 51. 111 52. 25 53. 247 54. > 55. < 56. >
57. 2347 58. 1,055,000 59. 150 60. A. 16 ( 4 ) = 4 (Simplify your answer.) 61. 5 19 5 3 62. A. 1 (Type an integer or an improper fraction.) 7 35 = 20 63. 20 64. 2 3 8 65. 382.70 66. 2 67. 72 68. 39 1 12 69. 44 70. 11 71. 32.4 72. 13 73. 1 25
74. 256 75. 25 76. 1 81 77. 7.21 10 4 78. 6.7 10 5 79. 0.00000005228 80. 63810000 81. 8.62 10 7 82. 120 83. 2681 84. 26 85. 6271