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Midterm Review

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MATH 121

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PRACTICE MIDTERM

1. Express in simplest form: 10 + 72 / 6 x 4
2. Rewrite using the distributive property: 12(6 + 4 + 20)
3. Translate and simplify: The sum of the squares of three and seven.
4. If you spend \$3.70 each day in tolls, how much money would be spent in 25 days?
5. Write 124/10 as a mixed number.
6. Write 11 and 4/5 as an improper fraction.
7. Change 9 and 1/8 to decimal form.
8. Round \$58.195 to the nearest cent.
9. Write 176, 000, 000 in scientific notation.
10. Write 7.35 x 10^(-7) without exponents.
11. Reduce the fraction 1600/3640 to its simplest form.
12. Simplify (3/10) + (1/18) – (2/15) and express your answer in simplest form.
13. Simplify 17 ¾ – (10 and 8/9).
14. Simplify (6 and 5/7) x (9 and 6/11)
15. Simplify (32/17) / (8/34).
16. Simplify (2/5)[(23/8) – (5/8) x 2]
17. Write 174/11 as a decimal in simplest form.
18. If you join a movie club and you agree to buy 24 movies for \$18.63 each and
\$3.44 postage and handling for each movie, what is the total cost to fulfill this agreement? 19. A recipe calls for 2 and 4/5 lb of light brown sugar and 4 ½ lb of dark brown sugar. How many pounds of sugar are needed for this recipe?

20. Each time a rubber rebounds, it bounces to a height tat is ¾ the height of the previous bounce. If the ball is dropped from 256 feet, approximately how high would it bounce after its third bounce.
21. If D = {-3, -2, 1} , find the values for 87 – x^2.
22. Evaluate y^2 – 3yz + z^2 if y = -5 and z = 3.
23. Evaluate | 11 – 16|.
24. Simplify: 12 + (-21)
25. On a number line, start at 5 and move -7 units. Then move 10 followed by 8, and then 9. What is the ending point?
26. Simplify: -22 – (-51)
27. Simplify: -50 – 53
28. Simplify: -11^2
29. Simplify: 518/(-14)
30. Simplify: (74 – 204) / (122 – 122)
31. Simplify: 14 – (-8)(-3)
32. Simplify: [16(-7) + 8] / 4
33. Simplify: 3(-14) + (30/-6)
34. Find the average of: -4, 10, -1, -6, -9, and 1 and round your answer to the nearest hundredth. 35. Find sqrt(8100).
36. Evaluate: -k^2 –m^2 for k= -3 and m = -9
37. Write a mathematical statement to express the following: The product of a number and 19.

38. Determine the length of the missing side of the right triangle below. Round to the nearest tenth of a foot.

59 ft

24 ft

39. Determine the length of the missing side of the right triangle below. Round to the nearest tenth of an inch.

24 in

15in
40. A 15 ft ladder is placed against a building so that the base of the ladder is 3 feet away form the building. How high up, rounded to the nearest foot, does the ladder reach? 41. Translate the following into an algebraic expression: Ten times a number added to four.
42. The temperature of the planet Pluto ranges from -218 degrees to 237 degrees.
What is the difference between the temperatures?

43. A person leaves her home and walks 730 feet due north, then she walks 620 feet east, then she walks 650 feet north and 900 feet east. How far, to the nearest tenth of a foot, is she from her starting point?
44. A rectangular field (such as the one that is shown below) measures 260 feet by
410 feet. If you wish to go from point A to point B, how much shorter is the trip if you walk along the diagonal rather than the edges? Round to the nearest tenth of a foot. B

A
Simplify the following expressions.
45. (x + 4) + (7x – 7)
46. (7x^2 – 7x + 4) + (3x^2 – 5x – 8)
47. 3(x + 2) – 5(x^2 – 6x + 7) + 3(x – 6)
48. (x + 4) (x + 6)
49. (3a + 7)(2a + 7)
50. (x + 3)^2
51. (x – 3)(4x – 5) – (x + 5)(x – 5)
52. (8x + 7) + (4x – 1)
53. (11c^2 + 9c + 4) + (13c^2 + 4c + 3)
54. (v^2)(v^5)

Solve the following equations and inequalities:
55. x – 4 = 10

56. x + 8 = 2
57. 18 + c = 10
58. x – 1 = -35
59. z + 6 = -14
60. p/8 = -15
61. 7 = x/-8
62. w/-9 = 0
63. –t = 5
64. 13x = -234
65. 2y = 0
66. 4x – 3 =77
67. (z/3) – 1 9 = 47
68. 3 + (-a) = 15
69. 18 – p = 31
70. (x/5) – 12 =53
71. 6 + (p/2) = -10
72. 6 – 5z = 26
73. 2x + 1 = 3x + 8
74. 5x – 8 = 3x + 2
75. 5x – 3 = 7x + 5
76. 6x – 5 = 5(x – 1)
77. 3(x – 2) = 2(x + 5)
78. 189(x – 2) = 4(x + 1) - 12
79. 5(W + 3) – 6(W + 12) = 0
80. x + 5 > 1

81. –t < -6
82. 2 < 2s + 10
83. 3 – x > 3x + 15
84. Suppose that seven times a number is added to 21 and the result is positive.
What are the possible numbers?
85. With summer approaching, the number of air conditioners sold is expected to be double that of stoves and refrigerators combined. Stoves sell for \$200, refrigerators for \$300, and air conditioners for \$350, and sales of \$76,000 are expected. If stoves and refrigerators sell in equal numbers, how many of each appliance should be stocked?
86. What is the correct term classification of the following polynomial? 5x^4 +
8x^3 – 2s
87. What is the correct term classification of the following polynomial? 8x^2 – 4
88. Find the degree of the following polynomial: 6x^4 +5x^8 – 2x + 9
89. A particular car gets 28 miles per gallon and a fuel tank capacity of 9.46 gallons. What is the estimated cruising range (distance) on a full tank of gasoline? Round to the nearest mile.
90. If you subtract 98 from ten times a number and the result is equal to -338, what is the number?
91. Suppose that the odometer read 83,238.1 at the start of your vacation and
85,712.6 at the end. If your trip required 101 gallons of gasoline, what was the car’s average miles per gallon for this trip?
92. Young’s Rule for calculating a child’s dosage for medication is
Child’s dose = [(age of child)/(age of child + 12)](adult dose)
If a 12 year old child’s dose of a particular medication is 15mg, what is the adult’s dose?
93. Express 400 to 900 as a reduced ratio.
94. What are the means in the proportion (g/m) = (p/z)? (the division symbols are light on the screen)
95. What are the extremes in the proportion (g/f) =(p/v)? (the division symbols are light on the screen)
96. Change 155.3% to a decimal.

97. Determine what number is 49% of 160.
98. If the ratio of miles to gallons is 224 to 21, what is this as a reduced ratio?
99.. Solve the proportion (11/9) = (176/x). (the division symbols are light on the screen) 100. Solve the proportion (4/25) = (80/x). (the division symbols are light on the screen) 101. What percent of 803 is 642.4?
102. 918 is 90% of what number?
103. 304.5 is 35% of what number?
104. Write 76% as a fraction in simplest form.
105. Twelve apartments use 70,842 gallons of water per month. Determine the approximate number of gallons of water that would be needed for 272 apartments.
Round to the nearest hundredth of a gallon.
106. In order to produce 90 widgets, it takes 7290 person-hours of labor. Howmany person-hours would be needed to produce 1046 widgets? Round your answer to the nearest person-hour.
107. Suppose you get 28 correct out of 54 on a test. What is your score expressed as a percent/ Round to the nearest percent.
108. In a city of 765,000 people, the average monthly megawatt usage is 1,669,230.
What would you expect the average monthly megawatt usage to be for a city of
2,704,000 people?
109. If you received 24% on a test consisting of 25 questions, how many questions did you get correct?
110. If the sales tax on a \$98 item is 5.5%, what is the total price including tax?
111, If the property tax on a \$570,000 home is \$1995, what is the tax rate?
112. The price of an item including sales tax is \$844. If the price without tax was
\$800, what is the sales tax rate?
113. Change the fraction 1/7 to a decimal. (the division symbol is light on the screen) 114. Change 11/16 to a percent. (the division symbol is light on the screen)
115. Write 5% as a fraction in simplest form.

116. Write 37.5% as a fraction in simplest form.

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