1,001 Praxis® Core Practice Questions For Dummies®
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ISBN 978-1-119-26388-3 (pbk); ISBN 978-1-119-26395-1 (ebk); ISBN 978-1-119-26398-2 (ebk)
Welcome to 1,001 Praxis Core Practice Questions For Dummies. Don’t take the dummies thing literally — you’re obviously smart and capable. You’ve chosen to shape the minds of future generations through education. And on that quest, you will encounter obstacles. At least one of those is a Praxis exam.
This book is designed to give you lots of exposure to the kinds of questions you’ll see on the very first test for teachers: the Praxis Core Academic Skills for Educators exam (referred to as Praxis or Praxis Core from here on). To clear this hurdle, you need some practice and pointers on how best to answer the questions. This book provides that and more: It goes beyond providing relevant practice questions by showing simple and effective ways to solve challenging Praxis problems.
The Praxis Core practice problems in this book are divided into four chapters based on skills involving Math, Reading, Writing, and Essays. Questions are adjusted and repeated to give you practice and mastery. If you struggle with one question, you can find a group of similar questions to practice and hone your skills. This book serves as an effective standalone refresher of Praxis basics or as an excellent companion to the latest edition of Praxis Core For Dummies (Wiley). Either way, this book helps you identify subject areas you need to work on so you can practice them until you’re a pro and thus prepare for test day.
If you get a problem wrong, don’t just read the answer explanation and move on. Instead, come back to the problem and solve it again, this time avoiding the mistake you made the first time. This is how you improve your skills and figure out how to solve the problems correctly and easily.
Whatever you do, stay positive. The challenging problems in this book aren’t meant to discourage you; they’re meant to show you how to solve and master them.
The first part of this book gives you questions covering math, reading, and writing. All the answers and explanations are in the second part of the book.
The math subtest covers the following topics:
The reading questions in this book cover the following topics:
On the writing subtest, you find these types of questions:
As part of the writing subtest, you’ll also be required to demonstrate knowledge and research skills by writing two essays based on information presented. One is an argumentative essay; the other is an explanation of a topic.
Your purchase of this book gives you so much more than a thousand (and one) problems to work on to improve your skills with the Praxis Core. It also comes with a free, one-year subscription to hundreds of practice questions online. Not only can you access this digital content anytime you want, on whichever device is available to you, but you can also track your progress and view personalized reports that show which concepts you need to study the most.
The online practice that comes free with this book offers you the same questions and answers that are available here. Of course, the real beauty of the online problems is your ability to customize your practice. In other words, you get to choose the types of problems and the number of problems you want to tackle. The online program tracks how many questions you answer correctly or incorrectly so that you can get an immediate sense of which topics require more of your attention.
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The solutions to the practice problems in this book are meant to walk you through how to get the right answers; they’re not meant to teach the material. If certain concepts are unfamiliar to you, you can find help at www.dummies.com. Just type “1,001 Praxis Core” into the Search box to turn up a wealth of Praxis-related information.
If you need more detailed instruction, check out Praxis Core For Dummies, also by Carla Kirkland and Chan Cleveland.
Part 1
IN THIS PART …
Practice basic math, algebra, geometry, and statistics problems.
Read passages and answer reading comprehension questions.
Work through grammar and writing questions.
Answer research questions and write essays.
Chapter 1
The math test of the Praxis Core exam includes 56 questions in four major areas of math. This part of the book explores each of those areas and the general math topics that are covered on the test. In this chapter, you can gain further understanding of the skills you need and get perspective on an array of questions and approaches to various math topics.
Math questions may be multiple choice, fill-in, or select all that apply. When working through the questions in this chapter, be prepared to answer questions on these topics:
Various types of mistakes can occur when you’re working math problems. Be on the lookout for common errors such as these:
1. What is the value of the following sum?
(A) 24
(B) –10
(C) 4
(D) –24
(E) 18
2. What is the sum of –5, –10, 4, and –7?
(A) –18
(B) –26
(C) 18
(D) –4
(E) 26
3. Which of the following is the value of this product?
(A) 45
(B) –90
(C) –45
(D) 90
(E) 30
4. What is the value of 
?
(A) 379
(B) 1
(C) –379
(D) –1
(E) 378
5. Which of the following is a factor of 63?
(A) 31
(B) 21
(C) 13
(D) 16
(E) 6
6. Which of the following is NOT a factor of 42?
(A) 7
(B) 6
(C) 14
(D) 21
(E) 18
7. All of the following are multiples of 53 EXCEPT
(A) 106
(B) 265
(C) 370
(D) 159
(E) 318
8. Ninety is NOT a multiple of which of the following?
(A) 30
(B) 5
(C) 15
(D) 23
(E) 3
9. What number is the greatest common factor of 28 and 72?
(A) 4
(B) 1
(C) 7
(D) 2
(E) 14
10. Which of the following is NOT a common factor of 84 and 144?
(A) 12
(B) 6
(C) 1
(D) 24
(E) 21
11. What is the least common multiple of 18 and 24?
(A) 48
(B) 72
(C) 144
(D) 432
(E) 6
12. Twenty-four is the least common multiple of 8 and which of the following numbers?
(A) 12
(B) 36
(C) 4
(D) 16
(E) 2
13. What is the cube of 5?
(A) 25
(B) 15
(C) 625
(D) 125
(E) 50
14. Which of the following numbers to the 4th power is 81?
(A) 27
(B) 3
(C) 9
(D) 36
(E) 13
15. What is the square root of 576?
(A) 34
(B) 56
(C) 24
(D) 44
(E) 26
16. If the cube root of 64 is multiplied by the greatest common factor of 20 and 45, what is the result?
(A) 100
(B) 20
(C) 80
(D) 60
(E) 40
17. What is half the square of the least common multiple of 14 and 21?
(A) 882
(B) 98
(C) 1,764
(D) 220.5
(E) 196
18. Which of the following is the value of this expression?
(A) 8
(B) 16
(C) 32
(D) 72
(E) 64
19. What is the greatest common factor of the square of 6 and the least common multiple of 8 and 9?
(A) 72
(B) 6
(C) 24
(D) 36
(E) 18
20. Which of the following is a counterexample to this statement?
With the exception of 1, the common factors of 24 and 120 are even.
(A) 3
(B) 12
(C) 10
(D) 9
(E) 6
21. Which of the following is the simplified form of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
22. What is 
in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
23. The fraction 
is the simplified form of which of the following fractions?
(A) 
(B) 
(C) 
(D) 
(E) 
24. If 
of the songs played on a radio station in a year were rock and roll songs, which of the following also represents the portion of rock and roll songs that were played on the station?
(A) 
(B) 
(C) 
(D) 
(E) 
25. Which of the following is 
in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
26. Is 
equal to 
?
(A) Yes
(B) No
27. Which of the following fractions is equal to 
?
(A) 
(B) 
(C) 
(D) 
(E) 
28. What is 
in simplified fraction form? Write your answer.
29. What fraction is the simplified form of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
30. Which of the following mixed numbers is equal to 
?
(A) 
(B) 
(C) 
(D) 
(E) 
31. Which of the following is equal to 
?
(A) 
(B) 
(C) 
(D) 
(E) 
32. The fraction 
is equal to which of the following?
(A) 
(B) 
(C) 7
(D) 
(E) 
33. Which of the following is the sum of 
and 
?
(A) 
(B) 
(C) 4
(D) 
(E) 
34. Which of the following equals the value of this expression?
(A) 
(B) 
(C) 
(D) –2
(E) 
35. What is the product of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
36. What is the quotient?
(A) 
(B) 
(C) 
(D) 
(E) 
37. What is the value of 
divided by 
?
38. Which of the following is 
in decimal form?
(A) 0.8
(B) 0.4
(C) 0.5
(D) 0.1
(E) 0.2
39. Which of the following is equal to 
?
(A) 0.2
(B) 0.8
(C) 0.7
(D) 0.125
(E) 0.15
40. Which of the following is 0.34 expressed as a fraction in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
41. The number 0.75 can be expressed as which percent?
(A) 0.075%
(B) 750%
(C) 0.75%
(D) 0.0075%
(E) 75%
42. The fraction 
can be represented as what percent?
(A) 2.5%
(B) 0.25%
(C) 250%
(D) 25%
(E) 0.025%
43. Which of the following is 42% in simplest fraction form?
(A) 
(B) 
(C) 
(D) 
(E) 
44. What is 34.848% in decimal form?
(A) 34.848
(B) 3,484.8
(C) 3.4848
(D) 348.48
(E) 0.34848
45. Which of the following is 496.032% expressed as a decimal number?
(A) 496032.0
(B) 49.6032
(C) 49,603.2
(D) 496.032
(E) 4.96032
46. What is 
in decimal form?
(A) –2.125
(B) –2.25
(C) –2.1
(D) –2.8
(E) –2.012
47. Which of the following is 
expressed as a percent?
(A) 8.2%
(B) 8.4%
(C) 0.08%
(D) 80.4%
(E) 840%
48. What is the sum of 
and 3.178, rounded to the nearest thousandth?
(A) 3.3
(B) 3.26
(C) 3.262
(D) 3.026
(E) 3.261
49. Which of the following is the sum of this expression, rounded to the nearest tenth?
(A) 15.54123
(B) 15.6
(C) 4,704.4
(D) 15.5
(E) 4,704.3
50. Which of the following is the product of 
and –14.4?
(A) 2.16
(B) –2
(C) –2.16
(D) 2
(E) –2.07
51. Which of these numbers is greater?
(A) 
(B) 0.76
52. Which of these numbers has the greatest value?
(A) 
(B) 
(C) 3.1
(D) 3.11
(E) 
53. Which of these numbers has the lowest absolute value?
(A) 
(B) 
(C) –0.47
(D) 0.471
(E) 
54. Which of the following is the correct order of these numbers from least to greatest?
(A) 
, 1.36, 134%, 1.36, 
(B) 
, 
, 1.36, 134%, 
(C) 134%, 
, 1.36, 
, 1
(D) 
, 
, 134%, 1.36, 
(E) 1
, 
, 1.36, 
, 134%
55. Which of the following is the correct order of these numbers from greatest to least?
(A) 409%, 4.1, 
, 
, 
(B) 
, 
, 4.1, 
, 409%
(C) 409%, 4.1, 
, 
, 
(D) 
, 409%, 
, 
, 4.1
(E) 
, 
, 
, 4.1, 409%
56. Which of the following numbers has a greater magnitude than 
?
(A) 1,250%
(B) 
(C) 
(D) –12.51
(E) 
57. What is the correct order of absolute value for these numbers, from greatest to least?
(A) 
, 5.14, 
(B) 
, 5.14, 
(C) 
, 
, 5.14
(D) 5.14, 
, 
(E) 
, 
, 5.14
58. The distance from one labeled coordinate to the next on the number line is the same in every case. What is the value of y?
© John Wiley & Sons, Inc.
(A) 17.5
(B) 18.5
(C) 17
(D) 16
(E) 18
59. For the number line, if D is halfway between C and E, what is the coordinate of D?
© John Wiley & Sons, Inc.
(A) 2.2
(B) 2.4
(C) 1.2
(D) 1.6
(E) 1.1
60. For this number line, the distance from P to Q is half the distance from Q to R, and that distance is half the distance from R to S. The coordinate of P is 4, and the coordinate of R is 10. What is the coordinate of S?
© John Wiley & Sons, Inc.
(A) 18
(B) 16
(C) 20
(D) 24
(E) 14
61. A number line contains the points A, B, C, and D. C is half the distance from B to D, and B is half the distance from A to C. Which of the following statements is true?
(A) The distance from A to B is greater than the distance from C to D.
(B) The distance from A to B is less than the distance from C to D.
(C) The distance from B to D is greater than the distance from A to C.
(D) The distance from B to D is equal to the distance from A to B.
(E) The distance from A to B is equal to the distance from C to D.
62. For this number line, T is halfway between M and W. What is the coordinate of T?
© John Wiley & Sons, Inc.
(A) 3.5
(B) 3
(C) 4
(D) 3.25
(E) 3.75
63. What is the seventh term of this sequence?
5, 9, 13, 17, …
(A) 21
(B) 20
(C) 29
(D) 24
(E) 33
64. What term belongs in the blank in this sequence?
14, 17, __, 23, …
(A) 18
(B) 20
(C) 26
(D) 22
(E) 29
65. What is the first term in this sequence?
__, 6, 12, 24, …
(A) 5
(B) 2
(C) 4
(D) 3
(E) 1
66. The first term of a geometric sequence is 1. The fifth term is 81. How many times greater is each term, after the first term, than the preceding term?
(A) 2
(B) 9
(C) 4
(D) 18
(E) 3
67. Is this sequence arithmetic or geometric?
10, 15, 20, 25, 30, …
(A) Arithmetic
(B) Geometric
68. What is the value of this expression?
(A) 25
(B) 20
(C) 21
(D) 15
(E) 24
69. Which of the following is the first operation that should be performed in evaluating the expression?
(A) Multiplying 5 by 2
(B) Adding 3 and 5
(C) Subtracting 2 from 7
(D) Squaring 2
(E) Multiplying 2 by 3
70. Which of the following is the value of this expression?
(A) 11
(B) –143
(C) 5
(D) 0
(E) –3
71. What is the value of this expression?
(A) –14
(B) 12
(C) –30
(D) 1
(E) –3
72. What is the value of this expression?
(A) 2
(B) 4
(C) 
(D) 8
(E) 
73. What number results from a correct evaluation of this expression?
(A) 16
(B) 13
(C) 3
(D) 26
(E) 21
74. What is the value of this expression?
(A) 15
(B) 
(C) 12.5
(D) 
(E) 3
75. Evaluate this expression.
(A) 
(B) 
(C) 
(D) 
(E) 
76. Evaluate this expression.
(A) 
(B) 
(C) 
(D) 
(E) 
77. What is the value of this expression?
(A) –5
(B) 4
(C) –12
(D) –10
(E) 7
78. At a school, 110 of the students are boys and 122 of the students are girls. What percent, rounded to the nearest hundredth, of the students are girls?
(A) 92.423%
(B) 52.59%
(C) 90.16%
(D) 190.16%
(E) 52.586%
79. The number of records in Joe’s record collection went from 400 to 408. By what percent did Joe’s record collection increase?
(A) 16%
(B) 8%
(C) 5%
(D) 4%
(E) 2%
80. The number of cookies in a box went from 40 to 30. Which of the following accurately describes the change in the number of cookies in the box?
(A) 1.33% increase
(B) 0.25% increase
(C) 25% decrease
(D) 0.25% decrease
(E) 2.5% increase
81. If 
of the flowers in a garden are daisies, what percent of the flowers in the garden are daisies?
(A) 40%
(B) 4%
(C) 2%
(D) 20%
(E) 50%
82. At a police department, 14% of the officers are rookies. What is the ratio, in simplest form, of officers who are rookies to the total number of officers?
(A) 
(B) 
(C) 
(D) 
(E) 
83. Sebastian ran 42 miles in a week. The next week, he ran 48 miles. Which of the following accurately represents the ratio of the number of miles Sebastian ran the first week to the number of miles he ran the second week?
(A) 
(B) 
(C) 
(D) 
(E) 
84. Two U.S. states are not on the country’s mainland. The U.S. has a total of 50 states. What is the ratio of U.S. states NOT on its mainland to U.S. states that are on the country’s mainland?
(A) 
(B) 
(C) 
(D) 
(E) 
85. Luca is 12 years old, and Dave is 66 years old. What is the ratio of Dave’s age to Luca’s age, in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
86. In a game of golf, Johnny scored 78. The next day, Johnny played another game of golf and scored 72. What is the ratio of Johnny’s golf score on the first day to his score on the second day, in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
87. Trace’s video collection includes 132 comedy videos and 144 drama videos. What is the ratio of comedy videos to drama videos in the collection?
(A) 
(B) 
(C) 
(D) 
(E) 
88. In a classroom, 8 of the 30 students are football players. In another classroom, 3 of the 10 students are football players. What is the sum of the ratios of football players to students who do not play football for the two classrooms?
(A) 
(B) 
(C) 
(D) 
(E) 
89. The ratio of cashews to other nuts in Jar 1 is 
. The ratio of cashews to other nuts in Jar 2 is 
. How much greater is the ratio of cashews to other nuts in Jar 2 than the ratio of cashews to other nuts in Jar 1?
(A) 
(B) 
(C) 
(D) 
(E) 
90. In a town with a population of 2,400, 41% of the residents drive trucks. How many of the residents drive trucks?
(A) 1,124
(B) 984
(C) 1,492
(D) 432
(E) 587
91. On a track team, 11 of the 22 members are honor roll students. What percent of the members of the track team are honor roll students?
(A) 200%
(B) 50%
(C) 25%
(D) 75%
(E) 2%
92. What number results from tripling the sum of 4 and 7?
(A) 11
(B) 3
(C) 22
(D) 19
(E) 33
93. If 17 is decreased by 8 and the difference is multiplied by 2 more than itself, what is the result?
(A) 72
(B) 11
(C) 20
(D) 99
(E) 20
94. A group of 400 people went camping for a weekend. On Saturday, each camper engaged in one of the activities listed in the table. The table shows the percentages of campers who engaged in each activity. According to the table, which of the following statements is true?
|
ACTIVITY |
PERCENT |
|
Canoeing |
34% |
|
Hiking |
21% |
|
Rock Climbing |
38% |
|
Birdwatching |
17% |
(A) Sixty-eight campers went canoeing.
(B) Twice as many campers went birdwatching as the number that went canoeing.
(C) Eighty-two campers went hiking.
(D) Sixteen more campers went rock climbing than canoeing.
(E) Twenty-one more campers went rock climbing than birdwatching.
95. The table shows the percentages of political party affiliation at a college for eccentric students. The number of students attending the college is 2,850. How many more students are in a political party NOT listed in the table than students in a political party that is listed in the table?
|
POLITICAL PARTY MEMBERSHIP |
PERCENT |
|
People’s Party of Utopia |
22% |
|
Anarchist Party of Not Voting |
16% |
|
Party of Free Market Communism |
8% |
|
Other |
54% |
(A) 8
(B) 1,539
(C) 627
(D) 228
(E) 1,311
96. An island had a population of 824 penguins. One-fourth of the island’s penguin population moved to another island. The remaining population increased by 
and has remained the same since then. How many penguins are now on the island?
(A) 927
(B) 824
(C) 618
(D) 206
(E) 309
97. A bakery had 42 rolls on a shelf. A customer bought 
of the rolls on the shelf. How many rolls did the customer buy?
(A) 42
(B) 7
(C) 16
(D) 24
(E) 32
98. Karen read 
of the pages in a book the day she bought it. The next day, she read another 
of the book. What portion of the book had Karen read by the end of the day after she bought it?
(A) 
(B) 
(C) 
(D) 
(E) 
99. A soccer team has a uniform design with 5 stripes on the shirt. Each stripe has 4 stars. The team has 34 members. If every member of the team stands in the same room, how many uniform stars are in the room?
(A) 43
(B) 680
(C) 54
(D) 720
(E) 870
100. In an organization, 
of the members are from Texas. Three-sevenths of those members are women. Of those women, 
ride a bus to work. What portion of the members of the organization are women from Texas who ride a bus to work?
(A) 
(B) 
(C) 
(D) 
(E) 
101. The number of customers in a grocery store at 4:15 p.m. was 37. An hour later, the number of customers was 5 times as many. At the decoration store across the street, the number of customers in the store at 4:15 p.m. on the same day was 12. An hour later, the number of customers in the decoration store was 
times as many. At 5:15 p.m. on that day, what was the sum of the number of customers in the grocery store and the decoration store?
(A) 185
(B) 42
(C) 188
(D) 240
(E) 227
102. Edward opened a savings account and put $500 in it. The interest on the account is 12% per year. If no money is deposited in or taken out of the account, how much money will Edward have in the account exactly a year after he put in $500?
(A) $560
(B) $60
(C) $6,000
(D) $440
(E) $620
103. Virgie buys a hat for $56. If the tax on the hat is 8%, what is the total price of the hat?
(A) $4.48
(B) $51.52
(C) $60.48
(D) $62.58
(E) $58.72
104. A governor wants 
of a state construction project finished by the end of the month. The construction supervisor wants 
of the project finished by the end of the month. Do the governor and the construction supervisor want the same portion of the project finished by the end of the month?
(A) Yes
(B) No
105. How many meters are in 14.8 centimeters?
(A) 14
(B) 1.4
(C) 0.014
(D) 140
(E) 0.148
106. How many deciliters are in 0.571 hectoliters?
(A) 5.71
(B) 571
(C) 57.1
(D) 5,710
(E) 0.571
107. A rock has a mass of 4.9327 dekagrams. What is the mass of the rock in centigrams?
(A) 4,932.7
(B) 49.327
(C) 0.49327
(D) 0.049327
(E) 493.27
108. Alexia drove 54 kilometers on the Natchez Trace. How many millimeters did she drive?
(A) 540
(B) 5,400
(C) 0.000054
(D) 0.00054
(E) 54,000,000
109. The amount of rainwater in a bucket is 0.38 liters. How many kiloliters of rain water are in the bucket?
(A) 380
(B) 0.00038
(C) 0.038
(D) 3,800
(E) 3.8
110. How many inches are in 4 feet?
(A) 
(B) 3
(C) 8
(D) 48
(E) 12
111. How many feet are in 4 inches?
(A) 
(B) 3
(C) 8
(D) 48
(E) 12
112. How many cups are in 4.5 gallons?
(A) 0.28125
(B) 3.56
(C) 20.5
(D) 72
(E) 11.5
113. How many gallons are in 4.5 cups?
(A) 0.28125
(B) 3.56
(C) 20.5
(D) 72
(E) 11.5
114. Simon walked 3 kilometers down a trail. He then got on another trail and walked 456 meters. What is the total distance Simon walked, in kilometers?
(A) 3.456
(B) 3,456
(C) 459
(D) 34.56
(E) 345.6
115. Dr. Richard has 5.382 kiloliters of a chemical in a drum. He pours out 42.79 hectoliters of the chemical. How much of the chemical remains in the drum?
(A) 48.172 kL
(B) 1.103 kL
(C) 4.8172 kL
(D) 4.9541 kL
(E) 374.08 kL
116. A baby frog had a mass of 4.07 decigrams. It now has an extra 0.08 kilograms of mass. Which of the following correctly represents the mass of the frog?
(A) 4.15 decigrams
(B) 804.07 decigrams
(C) 399 decigrams
(D) 0.080407 decigrams
(E) 1,207 decigrams
117. The height of a tower is 15 feet plus another 7 yards. Which of the following is a true representation of the height of the tower?
(A) 22 feet
(B) 66 feet
(C) 36 feet
(D) 52 feet
(E) 24 feet
118. A snail moved 2,088 inches north and then turned around and moved 72 yards south. Which of the following correctly represents the position of the snail in relation to its starting point?
(A) 42 feet north
(B) 58 feet north
(C) 42 feet south
(D) 58 feet south
(E) 2,016 feet north
119. Jake has 3.5 gallons of water in a jug for his football team. Each player has a 2-pint bottle. How many 2-pint bottles can be filled by the water in the jug?
(A) 28
(B) 56
(C) 14
(D) 7
(E) 112
120. Stefan ran 15 miles at a constant speed in 3 hours. What was his speed?
(A) 45 miles per hour
(B) 15 miles per hour
(C) 5 miles per hour
(D) 3 miles per hour
(E) 
mile per hour
121. Two trains start at the same place and move in opposite directions. One train moves at a constant speed of 56 kilometers per hour, and the other train moves at a constant speed of 72 kilometers per hour. How many hours will it take for the trains to be 729.6 kilometers apart?
(A) 10.13
(B) 13
(C) 601.6
(D) 5.7
(E) 0.175
122. What is 41 yards per minute expressed in inches per second?
(A) 24.6 inches per second
(B) 1,476 inches per second
(C) 123 inches per second
(D) 2.05 inches per second
(E) 8.2 inches per second
123. Herschel ran 40 yards in 4.2 seconds. What was his average speed in feet per minute, rounded to the nearest hundredth?
(A) 28.57 feet per minute
(B) 571.43 feet per minute
(C) 8.40 feet per minute
(D) 9.52 feet per minute
(E) 1,714.29 feet per minute
124. What is the sum of 12xy and 14xy?
(A) 
(B) 26xy
(C) 2xy
(D) 26
(E) 
125. Which of the following is the product of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
126. If a represents 2 pounds and b represents 4 ounces, which of the following represents 8 pounds and 12 ounces?
(A) 
(B) 
(C) 
(D) 
(E) 
127. Which of the following is the sum of 
and 
?
(A) 
(B) 
(C) –4
(D) 
(E) 
128. Which of the following is equal to 
?
(A) 
(B) 
(C) 
(D) 
(E) 
129. All of the following are like terms to 
EXCEPT
(A) 
(B) 
(C) 
(D) 
(E) 
130. What is the product of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
131. Which of the following is equal to this expression?
(A) 
(B) 
(C) 
(D) 
(E) 
132. If j, k, and m are consecutive integers, listed in order from least to greatest, what is one-third of their sum?
(A) 
(B) k
(C) 
(D) 
(E) 3j
133. Bill’s age is represented by xy, and Michael’s age is represented by xyz. Which of the following represents the product of Bill and Michael’s ages?
(A) 2xyz
(B) 
(C) 4xyz
(D) 
(E) y
134. Which of the following binomials can be multiplied by 
to get a product of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
135. Which of the following is equal to the product of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
136. If the ratio 
is equal to the ratio 
, which of the following is true?
(A) 
(B) 
(C) 
(D) 
(E) 
137. Which of the following terms is equal to this expression?
(A) 9m
(B) 6m
(C) 4m
(D) –9m
(E) 2m
138. If j is an even number and k is an odd number, which of the following represents an odd number?
(A) 
(B) 
(C) 
(D) 
(E) 
139. Which of the following is the complete factorization of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
140. Which of the following is the full factorization of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
141. What is the greatest common factor of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
142. Which of the following is the full factorization of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
143. Which of the following is NOT a factor of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
144. 
is the full factorization of what expression?
145. Which of the following is the full factorization of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
146. 6xy is the greatest common factor of 
and which of the following terms?
(A) 
(B) 
(C) 
(D) 
(E) 
147. 
is the product of 
and what binomial?
(A) 
(B) 
(C) 
(D) 
(E) 
148. If 
is factored out of 
, by which of the following binomials will it be multiplied?
(A) 
(B) 
(C) 
(D) 
(E) 
149. 
is the full factorization of which of the following trinomials?
(A) 
(B) 
(C) 
(D) 
(E) 
150. Which of the following terms is a factor of 
?
Select all that apply.
(A) 
(B) 
(C) 
(D) 
(E) 
151. The trinomial 
is the square of which of the following binomials?
(A) 
(B) 
(C) 
(D) 
(E) 
152. What is the greatest common factor of 
and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
153. Which of the following binomials is a factor of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
154. Which of the following is NOT a factor of 
?
(A) 1
(B) 
(C) 
(D) 
(E) 2
155. Which of the following is the simplified form of this expression?
(A) 
(B) 
(C) 
(D) 
(E) 
156. Which of the following is the simplified form of the expression 
?
(A) 
(B) 
(C) 
(D) 
(E) 
157. Which of the following is the simplified form of this rational expression?
(A) 
(B) 
(C) 
(D) 
(E) 
158. Which of the following is equal to this rational expression?
(A) 
(B) 
(C) 
(D) 
(E) 
159. Which of the following is the simplified form of this expression?
(A) 
(B) 2
(C) 16pq
(D) –2
(E) 2pq
160. Which of the following represents this expression in simplified form?
(A) 
(B) 
(C) 
(D) 
(E) 
161. Which of the following is the simplified form of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
162. Which of the following is this expression in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
163. Which of the following is the value of this expression?
(A) –1
(B) 1
(C) 
(D) 
(E) 
164. Which of the following has the same value as 
?
(A) 
(B) 
(C) 
(D) 
(E) 
165. Which of the following is the rational expression 
in simplest form?
(A) 
(B) 
(C) p + 2
(D) 
(E) 
166. Which of the following is the simplified form of this rational expression?
(A) 
(B) 
(C) 3mn
(D) 
(E) 3n
167. Which of the following is the simplified form of this expression?
(A) 
(B) 
(C) 
(D) 
(E) 
168. Which of the following is this expression in simplest form?
(A) 
(B) 
(C) 
(D) 
(E) 
169. Which of the following is the value of the expression 
?
(A) 7ab
(B) 7a
(C) 
(D) 7b
(E) 
170. What is the value of 
if 
?
(A) –5
(B) 1
(C) 2a
(D) –1
(E) 5
171. What is the value of this expression if 
, 
, and 
?
(A) –8
(B) 103
(C) 64
(D) 36
(E) –71
172. What is the value of 
if 
and 
?
(A) 72
(B) –12
(C) 54
(D) 68
(E) –45
173. If 
, 
, and 
, what is the value of 
?
(A) 42
(B) 24
(C) –34
(D) 7
(E) 17
174. What is the value of this expression if 
, 
, 
, and 
?
(A) 
(B) 
(C) 
(D) 26
(E) 
175. What is the value of this expression if 
, 
, and 
?
(A) 24
(B) 15
(C) –2
(D) 28
(E) –31
176. If 
, 
, and 
, what is the value of 
?
(A) 45
(B) 40
(C) 58
(D) 19
(E) 34
177. If 
and 
, what is the value of 
?
(A) 
(B) 
(C) 
(D) 1
(E) 
178. What is the value of this expression if 
, 
, and 
?
(A) 
(B) 
(C) 
(D) 
(E) 
179. What is the value of 
if 
, 
, and 
?
(A) 40
(B) 20
(C) 10
(D) 50
(E) 60
180. What is the value of x if 
?
(A) 
(B) 3
(C) 15
(D) 5
(E) 4
181. Which of the following is a solution to this equation?
Select all that apply.
(A) 5
(B) 10
(C) 20
(D) –5
(E) –10
182. If 
and 
, what is the value of y?
(A) 10
(B) –2
(C) 8
(D) 4
(E) –11
183. If 
, what is the value of 
?
(A) 8w
(B) 
(C) 1
(D) 8
(E) y
184. If 
and 
, which of the following could be the value of b?
Select all that apply.
(A) 49
(B) 7
(C) –7
(D) –49
(E) 14
185. What is the value of p in this equation?
(A) –15
(B) 11
(C) 15
(D) 22
(E) –11
186. If 
, what is 7 less than 
?
(A) 27
(B) 34
(C) 45
(D) 14
(E) 20
187. What is the value of w in this proportion?
(A) 2
(B) 4
(C) 20
(D) 40
(E) 5
188. What is the solution to this equation?
(A) 3.5
(B) 2
(C) 0.5
(D) –3.5
(E) 3
189. If 
and 
, which of the following is true?
(A) 
(B) 
(C) 
(D) 
(E) 
190. What is the value of u in this equation?
(A) 4
(B) 1
(C) 7
(D) 3
(E) 0
191. If 
, what is the value of 
?
(A) 41
(B) –22
(C) 16
(D) 15
(E) –33
192. If 
and 
, what is the value of 
?
(A) –10
(B) 22
(C) 6
(D) –3
(E) 14
193. If 
and 
, what is the value of 
?
(A) 25
(B) 8
(C) 12
(D) 17
(E) 10
194. If 
, what value could x have?
Select all that apply.
(A) 18
(B) 0
(C) 9
(D) –9
(E) –18
195. If 
, which of the following is equal to the value of p?
(A) 
(B) 
(C) 
(D) 
(E) 2qr
196. If 
and 
, what is the solution to the system of equations?
(A) (8, 5)
(B) (5, 3)
(C) (–8, 5)
(D) (4, –3)
(E) (5, 8)
197. If 
, what is the value of 
?
(A) 0
(B) –17
(C) 17
(D) 15
(E) –8
198. What is the value of h in this equation?
(A) 
(B) 
(C) 
(D) 
(E) 
199. If 
and 
, which of the following numbers is NOT between the values of x and y?
(A) 6
(B) 8
(C) 5
(D) 3
(E) 7
200. If 
, what is the value of a in the equation 
?
(A) 
(B) 
(C) 
(D) 
(E) 
201. What is the solution of this inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
202. If 
, which of the following could be the value of w?
(A) 4
(B) 2
(C) 3
(D) 1
(E) 6
203. What is the solution to this inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
204. What is the solution to the following inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
205. If 
, which of the following CANNOT be the value of j?
(A) 6
(B) 7
(C) 5
(D) 9
(E) 8
206. Which of the following graphs represents the inequality 
?
(A) 
(B) 
(C) 
(D) 
(E) 
© John Wiley & Sons, Inc.
207. What is the solution to the following inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
208. Which of the following is the solution to this inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
209. If 
, then 
would have to be less than which number?
(A) 5
(B) 15
(C) –15
(D) –20
(E) 20
210. What is the solution to the following inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
211. Which inequality does the following graph represent?
© John Wiley & Sons, Inc.
(A) 
(B) 
(C) 
(D) 
(E) 
212. If 
is added to the left side of this inequality and 
is added to the right side, and a true inequality is the result, which of the following could NOT be a value of q?
(A) 1
(B) –2
(C) 0
(D) –1
(E) –4
213. If 
, which of the following could be a value of x?
(A) 0
(B) –1
(C) 
(D) 
(E) 
214. What is the solution to the following inequality?
(A) 
(B) 
(C) 
(D) 
(E) 
215. If 
, then m could NOT be equal to which of the following?
(A) –0.7125
(B) 0
(C) –0.7625
(D) 0.5626
(E) –0.51
216. Two consecutive integers have a sum of 15. What is the greater of the two integers?
(A) 1
(B) 8
(C) 15
(D) 0
(E) 7
217. Two consecutive odd integers have a sum of 28. What is the lower of the two integers?
(A) 13
(B) 15
(C) 28
(D) 2
(E) 17
218. Two consecutive even integers have a sum of 18. What is the product of the two integers?
(A) 10
(B) 100
(C) 80
(D) 8
(E) 18
219. Four more than twice a number is 12 less than 3 times the number. What is the number?
(A) 36
(B) 8
(C) 3
(D) 16
(E) 18
220. If 7 is taken from 5 times a number, the result is 21 more than the number. Which of the following is 11 more than 6 times the number?
(A) 5
(B) 14
(C) 53
(D) 7
(E) 28
221. Fourteen more than twice the sum of a number and 10 is at least 2 more than 10 times the number. Which of the following could be the number?
Select all that apply.
(A) 4
(B) 3
(C) 9
(D) 6
(E) 7
222. Twice the sum of a number and 6 is no more than 3 times the number. Which of the following CANNOT be the number?
(A) 12
(B) 11
(C) 13
(D) 16
(E) 15
223. Jason is 3 years older than Bethany. The sum of their ages is 81. What is Jason’s age?
(A) 39
(B) 42
(C) 31
(D) 40
(E) 28
224. Casey’s age is 7 years less than twice Kellie’s age. In 12 years, Kellie’s age will be 10 greater than Casey’s current age. How old was Kellie 8 years ago?
(A) 1
(B) 9
(C) 11
(D) 2
(E) 12
225. If half a number is increased by twice the number, the result is 6 more than 2 times half the number. Which of the following is 8 less than 5 times the number?
(A) 4
(B) 28
(C) 2
(D) 27
(E) 12
226. If 11 less than a number is not as much as 3 less than a third of the number, which of the following could NOT have a value that is 26 higher than the number?
(A) 37
(B) 39
(C) 35
(D) 28
(E) 24
227. The product of two numbers is 15. The sum of one of the numbers and 14 is 2 more than 5 times the number. What is the other number?
(A) 3
(B) 5
(C) 15
(D) 12
(E) 2
228. Two numbers are opposites. Their product is –81. The higher number is 3 more than twice y. What is the value of y?
(A) –3
(B) 9
(C) –6
(D) –243
(E) 3
229. Which of the following is a counterexample to this statement?
If four less than the square of a number is more than five, the number is greater than three.
(A) –2
(B) 1
(C) –4
(D) 0
(E) –1
230. John has 8 less than twice as many four-wheeler wheels attached to his four wheelers as Elizabeth has to hers. However, they have the same number of four wheelers. How many four wheelers does John have?
(A) 16
(B) 4
(C) 2
(D) 8
(E) 3
231. Two numbers have a sum of 17. The greater number minus the smaller number is 7. What is the greater number?
(A) 12
(B) 24
(C) 5
(D) 22
(E) 10
232. A classroom with 28 students has 4 more boys than girls. How many girls are in the classroom?
(A) 12
(B) 16
(C) 4
(D) 28
(E) 24
233. The price of student tickets to a school play is $3, and the price of non-student tickets is $5. David sold 61 tickets for a total price of $251. How many student tickets did David sell?
(A) 34
(B) 22
(C) 17
(D) 27
(E) 81
234. Alex has only $10 and $20 bills in his wallet. The total number of bills in his wallet is 18, and the amount of money in the wallet is $290. How many $20 bills does Alex have?
(A) 4
(B) 220
(C) 70
(D) 7
(E) 11
235. In 17 years, Danforth’s age will be 1 more than three times what it is now. How old will Danforth be in 30 years?
(A) 12
(B) 42
(C) 38
(D) 35
(E) 8
236. Is the relation {(2, 5), (3, 7), (4, 1), (8, 1)} a function?
(A) The relation is a function because no element of the range is paired with more than one element of the domain.
(B) The relation is a function because no element of the domain is paired with more than one element of the range.
(C) The relation is NOT a function because 1 is paired with both 4 and 8.
(D) The relation is NOT a function because no element of the domain is paired with more than one element of the range.
(E) The relation is NOT a function because 2 is paired only with 5.
237. Does the following table represent a function?
|
x |
y |
|
–8 |
7 |
|
–2 |
4 |
|
3 |
8 |
|
–2 |
14 |
(A) Yes
(B) No
238. Which of the following relations is a function?
(A) {(–8, 7), (–3, 1), (7, 6), (7, 8)}
(B) {(1, 2), (3, 4), (5, 6)}
(C) {(0, 0), (2, 2), (0, 2), (2, 0)}
(D) {(1, 2), (1, 3)}
(E) {(0, 1), (1, 2), (1, 3)}
239. Which of the following relations is NOT a function?
(A) {(–1, –3), (2, 4), (5, 10)}
(B) {(0, 1), (1, 2), (2, 3), (3, 4)}
(C) {(5, 5)}
(D) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}
(E) {(–4, 5), (2, 6), (8, 3), (2, 7), (5, 10)}
240. Does the following mapping represent a function?
(A) It does represent a function because each number in the domain is paired with at least one number in the range.
(B) It does represent a function because each number in the range is paired with at least one number in the domain.
(C) It does NOT represent a function because 2 is paired with both 1 and 12.
(D) It does NOT represent a function because 5 is paired with both 7 and 10.
(E) It does represent a function because no number is listed more than once in the left column.
241. If 
, what is the value of 
?
(A) 1
(B) 4
(C) 3
(D) 0
(E) 2
242. For the following function, what is the value of 
?
(A) 7
(B) 77
(C) 63
(D) 35
(E) 49
243. If 
, what is the value of 
?
(A) –29
(B) –32
(C) 29
(D) 2
(E) 32
244. If 
and 
, what is the value of 
?
(A) 15
(B) 26
(C) –11
(D) 4
(E) 9
245. If 
and 
, what is the product of 
and 
?
(A) 19
(B) –270
(C) –874
(D) –46
(E) 471
246. For the two following functions, what is the value of 
?
(A) 508
(B) 415
(C) 29
(D) 580
(E) 18