TEAS VI  Math  2017 (1)
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TEAS MATH PRACTICE EXAM...
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Practice Test for the TEAS VI Mathematics
__________________________________________ Published by Tests.com LLC PO Box 232 Lititz, PA 17543 www.Tests.com ISBN: 9781938967412 Copyright © 20132017 Tests.com LLC All rights reserved. No part of this publication may be reproduced, distributed or transmitted in any form or by any means without the prior written permission of Tests.com LLC. Published in electronic format in the United States of America. Contributing Authors: Adel Arshaghi is a mathematics instructor who has taught mathematics at both the high school and college levels for over 10 years. He has his Master of Science degree in Mathematics Education from East Tennessee State University. Curriculum Management Group is a company specializing in mathematics and science educational publishing. Lydia Wieberg is a high school math teacher in Emporia, Kansas. She also teaches math to nursing students at Allen Community College. She holds Bachelors degrees in mathematics and secondary education from Kansas State University.
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Table of Contents Review of the TEAS VI .................................................................................................................... 1 Practice Exam Questions Section 1 – Numbers and Operations .................................................................................... 8 Section 2 – Algebra ............................................................................................................... 51 Section 3 – Data Interpretation ............................................................................................ 64 Section 4 – Measurements ................................................................................................... 81 Section 5 – Geometry .......................................................................................................... 90 Practice Exam Answers ................................................................................................................ 97 Practice Exam Questions with Answers .................................................................................... 135 Test Preparation and Test Taking Tips ...................................................................................... 261 Bubble Sheet .............................................................................................................................. 264
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Review of the TEAS VI A career choice to become a registered or practical nurse may be right for you. Nursing professionals are consistently listed as one of the most respected and trusted professions in the country. And, importantly, job security is rarely an issue for a nurse. In most areas of the country, there are reports of nursing shortages. To become a nurse, one must go to nursing school and pass a professional exam. Many nursing schools require their applicants to take the Test of Essential Academic Skills (TEAS). As of August 31, 2016, the TEAS will be based on the Sixth Edition of TEAS Study Manual. This review discusses the requirements of the TEAS VI. Education for initial licensure as a registered nurse is provided through diploma programs, such as community/or junior colleges offering an associate degree in nursing (ADN) and colleges offering a bachelors degree in nursing (BSN). Most colleges require students who apply for admission to registered nursing, practical nursing and dental hygiene programs to participate in preadmission testing prior to the admissions deadline for the respective program. The TEAS is an aptitude test. It is a fourpart assessment developed by Assessment Technologies Institute LLC (ATI). It includes reading comprehension, mathematics, science and English exam sections. The exam is calibrated to the 10th grade  12th grade level. Nursing programs use the TEAS as a tool to evaluate the academic readiness of candidates prior to admission into the nursing program. Test results are used in admission determinations. The exam assesses the candidate’s ability to respond and apply knowledge to new situations and to
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understand complex technical material and relationships. The results also provide documentation useful for counseling and advisement. Some nursing schools also use the TEAS as a placement exam. The exam can identify students who struggle in certain areas but have the potential to be excellent nurses. Students can receive remediation in their weak areas to improve their skill level and increase the chance of success in nursing school. 1. Exam Background and Scoring The TEAS consists of a total of 170 multiple choice questions and approximately 3 ½ hours is given to complete the test. Only 150 of the questions are scored and 20 are unscored pretest items. The TEAS is administered in either a computer based format or a paper and pencil based format. The TEAS is not a pass or fail test. Students completing the TEAS exam are encouraged to earn a proficient score or higher in the ATI Academic Preparedness Category if applying to nursing. Each school has their own cut off scores. The TEAS score report does not indicate whether a candidate has passed or failed the exam. That means there is no passing score determined by ATI. Nursing schools have their individual cutoff scores for admission purposes and to maintain their standards. You will have to check with the nursing schools to find out their cutoff score. The TEAS score report gives a detailed description of a testtakers performance on the test. The following scores are given in ATI’s TEAS score report: 1. Adjusted Individual Score 2. National mean TOP
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3. Program mean 4. Percentile rank – National 5. Percentile rank – Program
The scores for all the content areas of the four test sections are also given. Hence, the score report of TEAS is extremely descriptive. It gives nursing schools a chance to view your overall performance in relation to others. Whether a certain score is sufficient varies from one nursing school to another. As stated above, nursing schools set their own cutoff TEAS scores for admissions. Most schools have their cutoffs set around 70% for English, math and science and around 80% for reading comprehension. However, the weight given to each subject score can vary for each nursing school. Some nursing schools lay more emphasis on the national percentiles while others give more weight to the scores in science and math. The TEAS score report makes it possible to judge the applicant from various angles. Nursing schools may not publically disclose how they weigh the scores. Therefore, it is essential to score well in all sections of the test. 2. Exam Content The TEAS has four sections: English, math, science and reading comprehension. Each section will be discussed in some detail. English and Language Usage The English subtest measures knowledge of grammar, sentence structure, punctuation, contextual words and spelling. The time given to take this section is 28 minutes. It has a total of 28 testing items, 24 of which are scored. TOP
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It is imperative to test the language skills of students since it is the most common medium of exchange of ideas not only in education but also in your profession. In order to succeed in the coursework it is most essential to understand the language in which the instruction is carried out. Moreover, the study and the profession involve a great amount of interaction among many people. A good understanding of grammar and proper usage of English makes the journey smoother since it facilitates understanding and results in effective communication. The English section is essential to judge the basic communication skills of candidates aspiring to undertake nursing studies. Mathematics The math subtest covers rational numbers, metric conversions, fractions and decimals, algebraic equations, percentages, ratio/proportions and geometry. This section of TEAS has 36 testing items, 32 of which are scored. The section must be completed in 54 minutes. These questions test the basic mathematical skills possessed by students. It is essential to evaluate these skills since the work of nurses involves the use of math and requires precision and accuracy. The math problems on the test do not involve difficult concepts; instead only basic knowledge is required. The testing center will provide a fourfunction calculator. Science The science portion of the exam covers human anatomy and physiology, the life and physical sciences and scientific reasoning. There are 53 testing items, of which 47 are scored. The time given to complete the test is 63 minutes.
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Candidates are required to have a basic knowledge in science since many of the courses a nursing student will face involve science. The profession of nursing involves study of such subjects as well as keeping in touch with the latest developments in the field. Reading Comprehension The reading comprehension subtest covers passage comprehension, craft and structure and the integration of knowledge and ideas. The reading section of TEAS contains 53 multiplechoice questions, of which 47 are scored. You will have 64 minutes to complete this section of the test. This section is composed of many different types of written communication and requires the student to answer questions based on a reading and analysis of the material. The material will be presented various forms, such as in paragraph format or classified ads, blog entries and opinion pieces. It may incorporate graphs and illustrations. The test requires students to understand a given text in different ways. Some questions will deal with literal understanding. Other questions will require students to draw inferences and form conclusions using their logical reasoning abilities. Students will be asked to differentiate between fact and opinion, strong and weak arguments and to integrate data from various sources to form conclusions about the author’s purpose and perspective. Students should bear in mind that they have to answer the questions only according to the information given in the passage and not by referring to any information outside the exam. 3. Applying for the Exam Students must register with ATI prior to scheduling to take the TEAS. Scheduling is not permitted without preregistering. Log on to www.atitesting.com. Click Create New Account TOP
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and complete the user information page. The TEAS is given at PSI testing centers across the country. You must register for the exam keeping in mind the time required for the results to reach the schools you are applying to. There could be specific deadlines declared by the schools; check with the schools before you register. The retesting conditions are also decided by the schools you apply to and you should weigh your retest options also before you register for TEAS. Early registration is recommended as test centers tend to get booked quickly. 4. How to use Tests.com to Study Start early and schedule your studying over the days, weeks and months during which you plan to study. If you have a detailed study schedule, you can reach your goal in time. Taking the practice test is the first part of the study plan. You should also review reference books, and text books, class notes, study guides and flashcards in your study regimen. Use either Tests.com’s online interactive platform (TESTSIM) or the ebook (PDF) to take the practice test. If you are using the ebook make copies of the bubble sheet that is found at the end of the test so that you can conveniently track your answers. The TESTSIM online platform allows you to fashion a simulated test as to time and number of questions, so you can get similar testing conditions that you will face on test day. Taking the Tests.com practice test will allow you to assess your strengths and weaknesses as well as determine how much of the material you are familiar with. It’s important to vary the methods you use in studying so that the process keeps you engaged and interested. This includes practicing your test taking skills. Limit yourself to a certain time period for a certain number of questions randomly selected. It’s
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recommended you do this a few times throughout your preparation period. A few days before the actual test, retake the practice test to evaluate your grasp of the material. 5. Planning for Exam Day You should plan to arrive at least a half hour prior to testing time to allow for check in. You need to go to www.atitesting.com and register as a user. You must bring your User Name and Password that you have chosen to be able to take the computerbased exam. A picture ID with your signature is now required. (Acceptable ID's are an unexpired drivers license or passport). You will need to know or bring your social security number. You will need to bring two #2 pencils if you are taking the paper formatted exam. Calculators are not allowed. All cell phones or any other electronic device is not allowed. 6. After the Exam
Your official test scores will be available upon completion of the test. You can access your test scores via the ATI Testing Web site (www.atitesting.com) at any time after the exam. You can request that copies of your TEAS scores be sent to other universities. 7. Conclusion
Taking the TEAS is the first step towards a promising career in nursing. It is important to study for the test to do well. The test content deals with subjects candidates may not have seen since 10th grade. Therefore, a refresher course is necessary. The Tests.com practice test is engineered to provide a thorough study of the subjects tested on the TEAS. If you start studying for the exam well in advance of the test., follow a study plan and work hard to prepare yourself, you will do well.
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TEAS Practice Exam – Math  Section 1 Numbers and Operations 1.
1/4 + 2/8 = a. b. c. d.
2.
4 x 3/7 = a. b. c. d.
3.
48 58 68 74
8–3x4+9= a. b. c. d.
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5/8 8/10 15/10 None of the above.
348 ÷ 6 = a. b. c. d.
5.
1 3/7 1 5/7 12/28
5/6 x 3/4 = a. b. c. d.
4.
3/12 3/4 5/4 1/2
5 5 65  65
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6.
18 – 23 + 99 ÷ 3 = a. b. c. d.
7.
28 285 105 37.3
– 33 – 5 x 1 = a. b. c. d.
39 38  38 1
8. 2/3 ÷ 4/5 = a. b. c. d. 9.
3/5 5/6 6/8 None of the above.
36 ÷ .4 = a. b. c. d.
9 40 90 144
10. .08 + 7 x 9 = a. b. c. d. 11.
Which of the following is equivalent to 425%? a. b. c. d.
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63.08 62.73 63.72 62.37
.425 4.25 42.5 425
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12.
Terry has a basket full of various fruits. There are 12 pieces of fruit, and of those, two are bananas. What fraction of fruits is bananas? Express in simplest form. a. b. c. d.
13.
What decimal is equivalent to ¾? a. b. c. d.
14.
1/6 3/5 6/100 6/60
Three friends have some money in their pockets. Anna has $1.24, Sara has $12.40, and Timmy has $2.42. Later in the day, Anna found 3 dimes on the ground and Timmy’s dad gave him a dollar bill and a quarter. Sara paid for ice cream for the 3 of them and spent $9.24. Who has the most money at the end of the day? a. b. c. d.
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50% .5 3/6 All of the above
Which of the following is equivalent to .6? a. b. c. d.
16.
.34 3.4 .75 1.25
Which of the following is equivalent to ½? a. b. c. d.
15.
1/6 2/12 1/4 1/3
Anna Sara Timmy Cannot be determined
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17.
In Science Hill High School, 45% of students are female. What fraction of the students is male?
a. b. c. d. 18.
Two fifths of the members of a Literature Club are published writers. What percent of the members are not published writers? a. b. c. d.
19.
3
of A?
$78.97 $87.79 $97.58 $99.85
John’s annual salary in the year 2010 was $48,560.45 and in the year 2011 was $48,321.55. What is the difference between his monthly salary in years 20102011, to the nearest hundredth? a. b. c. d.
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124 128 142 122
2
Barbara purchased three shirts each for $12.54, and two pairs of shoes each for $29.98. How much did she pay in total for these items? a. b. c. d.
21.
25% 40% 60% 65%
If 25% of A is equal to 48, then what is a. b. c. d.
20.
11 25 13 20 11 20 9 20
$19.19 $19.91 $91.19 $29.91
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22.
Which of the following is a correct statement? a. b. c. d.
23.
Select the correct ordering of the numbers in increasing order. a. b. c. d.
24.
3, 3, .3, .3 .3, 3, 3, .3 3, .3, .3, 3 3, .3, .3, 3
Select the correct ordering of the numbers in decreasing order. a. b. c. d.
25.
5.26 > 25.6 12.124 < 12.214
.41, .23, .203, .198 .198, .203, .23, .41 .198, .203, .41, .23 .203, .198, .23, .41
Tommy and Dillon each ordered a pizza. Tommy ate onehalf of his pizza, and Dillon ate onethird of his pizza.
Tommy
Dillon
Which inequality represents who ate more pizza?
a. b. c. d. TOP
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26.
Lily has to give her daughter 8 mL of cough syrup at 9:30 a.m. each morning. The doctor prescribed her a bottle of 120 mL. How many days will Lily be able to give her the cough syrup before needing a refill? a. b. c. d.
27.
Tammy is trying to figure out her bank account balance by filling in her check register. On Monday, she spent $12.87 going out to lunch, and then another $2.79 for ice cream. On Wednesday, she deposited a check for $25 dollars. Finally, this morning, she filled up her gas tank for $28.35. If her bank account had $129.23 Sunday night, what is her account balance now? a. b. c. d.
28.
2 8 .5714 28
A light bulb factory produces 1 defective light bulb for every 1,500 light bulbs. In one week, the factory produces 30,000 light bulbs. How many are expected to be defective? a. b. c. d.
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$142.67 $133.33 $100.00 $400.00
A softball player hits 2 out of every 7 times at bat. At this rate, how many times will she get a hit if she went up to bat 28 times? a. b. c. d.
30.
$19.01 $110.22 $69.01 $19.01
There is a big sale at the computer store. The computer that Tom has been wanting is on sale for 25% off. If he paid $107.00 after tax, what was the original price? Tax is 7%. a. b. c. d.
29.
13 days 14 days 15 days 16 days
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31.
A newspaper reported that 15% of high school students are in band. A local school district has 1,825 students in the elementary, 1,230 in the middle school and1,680 students in the high school. How many students are expected to be in the band? a. b. c. d.
32.
Micah runs 3 hours every 4 days. At that rate, how many hours will Micah run in 2 weeks? a. b. c. d.
33.
3:1 12:7 1:3 2:3
If 24% of the expression (m + 2n) is 48, then what is 25% of (m + 2n)? a. b. c. d.
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17 patients 25 patients 20 patients 15 patients
In a basket of fruits, there are 12 bananas, 7 peaches, 18 apples and 6 oranges. What is the ratio of apples to oranges? a. b. c. d.
35.
12 10.5 1.5 9
Every patient that goes into surgery has a chance of complications. If 1 in every 25 patients has some form of complications, how many patients are expected to have complications if 425 patients go into surgery? a. b. c. d.
34.
15 students 250 students 252 students 643 students
40 48 50 56
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36.
John spends 12% of his salary on groceries each month. If his monthly salary is $3400, how much does he spend on groceries? a. b. c. d.
37.
In the Global Auction Market, an oak rocking chair valued at $4200, sold for $9400. What is the percent of increase in the value of the chair? a. b. c. d.
38.
7500 7700 7850 8500
A washing machine is marked down 32% from its original price of $450. What is the sale price of the washing machine? a. b. c. d.
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11.11% 12.21% 14.11% 21.11%
If 28% of 20% of A is 420, what is A? a. b. c. d.
40.
103.81% 111.38% 113.18% 123.81%
A student paid an auto insurance premium of $360 for six months. Then the premium dropped to $320. Find the percent of decrease in the premium. a. b. c. d.
39.
$448 $424 $412 $408
$360 $306 $300 $266
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41.
A carpet is on sale for $198. The regular price of the carpet was $264. What is the markdown on the price of the carpet? a. b. c. d.
42.
A is 29% of 2900, and B% of 290 is 29. What is A + B? a. b. c. d.
43.
$88.51 $79.51 $76.15 $67.51
Add 2.3 times 3.2 to a. b. c. d.
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$227.39 $244.43 $264.23 $268.43
John wanted to purchase 3 CD packages and 5 rolls of film. If the price of each CD package is $12.82 and the price of each roll of film is $8.21, how much does it cost to purchase these items? a. b. c. d.
45.
812 831 841 851
On the first day of the month, the original price of a sofa, which was $304, was marked down 15%. The following day, the discounted price was marked down 12%. What is the marked down price on the second day? a. b. c. d.
44.
32% 29% 27% 25%
48.33 46.33 44.03 42.03
2 3
the sum of 23 and 32.
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46.
A grocery store sells 12 cans of soda for $6.24 and 6 cans of soda for $3.92. How much less expensive per can is it if you buy 12 cans? a. b. c. d.
47.
$0.23 $0.13 $0.11 $0.10
To make 4 cake? a. b. c. d.
48.
3 5
cakes, 3
2 3
pounds of flour is needed. How much flour is needed to make one
0.08 pound 0.68 pound 0.78 pound 0.80 pound
Given A and B below, what is the sum of A and B?
1 1 1 + 3 A = 2 3 2 1 1 1 − 3 B = 2 3 2 a. b. c. d.
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1 2 1 3 12 1 7 2 1 12 2 3
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49.
In the process of film development, photographers use a chemical called “stop bath.” A 2 2 photographer used 2 bottles of stop bath for the first group of rolls of film and 4 bottles of 3 3 stop bath for the second group of rolls of film. How much stop bath did he use for all of the rolls of film?
a. b. c. d. 50.
2 3 1 9 2 1 7 3 1 6 4 9
The sum of which numerical expression has the greatest whole number part? 2 1 3 +2 4 K= 3 13 6 1 +1 4 L= 3 8 10 +2 4 M= 3 N= a. b. c. d.
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5
1 3
+3
1 2
K L M N
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51.
Given A, B, and C below, find A + 2B − 3C. 5 3 A= 7 2 1 B= 5 1 C= 3
a. b. c. d. 52.
8 6 5 5
13 35 3 35 18 35 1 21
A house built on ground sank every year according to the following list: 2 2008: 3 in. 1 2009: 7 in. 1 2010: 5 in. 1 2011: 5 in. In which of the following combination of years did the house sink the most? a. b. c. d.
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2008 and 2009 2009 and 2010 2010 and 2011 2008 and 2011
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53.
The sum of which list of numbers is greatest? A: Even whole numbers between 24 and 34 B: Odd whole numbers between 23 and 33 C: Even whole numbers from 24 to 34 D: Odd whole numbers from 23 to 33 a. b. c. d.
54.
A B C D
Michelle’s income and spending for the first four months of the year are given in the table below. In which two months was her savings the highest? Month January February March April a. b. c. d.
55.
Income $3420 $2927 $3189 $3024
Spending $2970 $2212 $3020 $2730
January and February February and March March and April January and March
Casey went to a supermarket with $65 in his wallet. He wanted to purchase some sodas and potato chips. Here are the prices after taxes were added to the sale price: A case of Soda: $6.00 A bag of potato chips: $3.00 His money would be sufficient to purchase which of the following: a. b. c. d.
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9 cases of soda, and 4 bags of potato chips 7 cases of soda, and 5 bags of potato chips 6 cases of soda, and 11 bags of potato chips 4 cases of soda, and 15 bags of potato chips
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56.
A, b, c, and d are whole numbers such that a = 2b and b = 2c. Which expression is definitely a whole number?
a. b. c. d.
57.
The ratio of a to b is a. b. c. d.
58.
a+b+c 2 a + b + 2c 8 a + b + 2c 10 a + b + 2c 12
14 3 14 5 5 3
2 3
and the ratio of c to b is
2 . What is the ratio of a to c? 15
The dimensions of the rectangle ABCD are proportional to the dimensions of the rectangle KLMN. Given the following measurements, find the length of the rectangle KLMN. AB = 12 in. and BC = 9 in. Width LM = 18 in. a. b. c. d.
59.
Which statement is true given the proportion a. b. c. d.
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32 in. 24 in. 20 in. 16 in.
a c = d b d b = a c c b = d c d c = b a
a c = ? b d
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60.
Which of the following quantities has the highest rate of change? a. b. c. d.
61.
The price of land in Jonesboro has been constantly increasing since the year 2001 at the same rate. The price of an acre in 2001 was $420 and, in 2011, it was $540. What is the rate of change per year? a. b. c. d.
62.
$18.00 $17.00 $12.00 $11.00
Given x = 3.24, y = 2.23, and z = 3.42, what is the value of xyz(x + y + z) to the nearest tenth? a. b. c. d.
63.
Increase of the height of Michelle from 98 cm at the age of 9 to 108 cm at the age of 14 Increase of the height of Sarah from 74 cm at the age of 7 to 92 cm at the age of 11 Increase of the height of Joanne from 56 cm at the age of 6 to 82 cm at the age of 10 Increase of the height of Alison from 52 cm at the age of 5 to 108 cm at the age of 14
251.3 219.7 205.5 201.2
The plastic bags are supplied with three types of thickness as follows: Light weight: 0.002 in. Regular weight: 0.0025 in. Heavy weight: 0.003 in. What is the thickness of the stack of 65 light weight, 34 regular weight, and 54 heavy weight bags rounded to the nearest thousandth inch? a. b. c. d.
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0.272 in. 0.377 in. 0.389 in. 0.477 in.
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64.
65.
m+ n Given m = 3.2, n = 2.2, and p = 2.1, what is the value of mnp to the nearest tenth? np a. 798.5 b. 789.3 c. 798.5 d. 798.3 Given A = 0.035, B = 0.0053, and C = 0.55, round the result of the product (A + 0.25)(B + 0.35)(C + 0.45) to the nearest hundredth. a. b. c. d.
66.
0.10 0.11 0.15 0.16
The sides of the triangle ABC are as follows: AB = 2.34 in. BC = 4.034 in. AC = 5.0034 in. Each side of the triangle MNP is twice the corresponding side of the triangle ABC. Round the sum of the perimeters of these triangles in inches. a. b. c. d.
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30 in. 31 in. 32 in. 34 in.
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67.
Which of the following formats of subtraction is arranged properly using the regrouping method for 9415 − 4786? 8 13 11 15
9415 a.
b.
c.
d. 68.
8 13 10 5
9415 − 4786 8 13 10 15
9415 − 4786
43,0987 − 34,0765 20,007 − 10,003 34,087 − 32,986 54,983 − 44,572
3799 ft2 3898 ft2 3978 ft2 3988 ft2
The volume of gasoline in a tanker dropped from 9468 gallons to 7569 gallons after pumping gasoline to the reservoir of a gas station. How much gasoline did the tanker pump into the reservoir? a. b. c. d.
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9415 − 4786
John owned a tract of land with an area of 33,456 ft2. He sold 29,657 ft2 of the land. How much land is left? a. b. c. d.
70.
8 12 10 15
Which subtraction can be performed using the regrouping method? a. b. c. d.
69.
− 4786
1879 gallons 1899 gallons 1989 gallons 1999 gallons
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71.
Convert 2π to a decimal number rounded to the nearest tenthousandth. a. b. c. d.
72.
π The circumference of an irregular closed curve is determined using the formula C = 3π + d , 3 where d is the longest distance between two points on its circumference. If d = 3 feet, find the circumference of this closed curve, rounded to the thousandths. a. b. c.
d.
73.
55 52 45 43
John was born in the year MCMXLIX. Convert his birth year to an Arabic Numeral. a. b. c. d.
TOP
2008 2009 2011 2012
Which numeral represents the Roman expression XXXI + XXIV? a. b. c. d.
75.
14.556 ft2 12.566 ft2 10.862 ft2 10.266 ft2
What year is the Arabic numeral MMXII? a. b. c. d.
74.
6.2832 6.3832 6.6821 6.8861
1848 1884 1944 1949
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76.
Which expression represents 70 + 80 + 90? a. b. c. d.
77.
Ronald earns $3225 per month. 12% of his salary is withheld for income tax. Find the amount of his take home per month. a. b. c. d.
78.
Salary = $3402; Total Deduction = 14% Salary = $3150; Total Deduction = 15% Salary = $3655; Total Deduction = 17% Salary = $4455; Total Deduction = 24%
Jane’s monthly income in the year 2010 was $48,200, where 14% of her salary was withheld for income tax. In the year 2011, her monthly salary was $51,800, where 16% of her income was withheld for income tax. What was her average take home pay during the years 20102011? a. b. c. d.
TOP
$3211 $3121 $3112 $3011
The following list shows the salaries of four people along with their total deductions for each month. Which one has the greatest takehome amount? a. b. c. d.
80.
$2883 $2838 $2787 $2778
Jason pays 24% of his earnings per month for his home installment. If his income is $4225, how much does he take home after paying the installment? a. b. c. d.
79.
LX + LXX + LXXX LXX + LXXX + LXXXX LCX + LXXX + LXXX LXX + LCXX + LXXX
$48,482 $46,486 $44,462 $42,482
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81.
The price of one bottle of soda in a grocery store is $0.85. But the store advertised that it will give a discount of 12% for any purchase of more than 8 bottles. What is the sales price of 12 bottles of soda? a. b. c. d.
82.
A stereo system has an original price of $328, and a laptop computer has an original price of $420. A store advertised that for purchasing both a stereo and a laptop, it will give a 12% discount on the total purchase. What is the total sale price of a stereo and a laptop? a. b. c. d.
83.
$658.24 $678.44 $687.24 $689.46
Different stores offer different prices and discounts for a chair and an ottoman as follows. Which store offers the best purchase price? a. b. c. d.
84.
$8.98 $8.68 $7.96 $6.86
Store A: Original price = $580 with 11% discount Store B: Original price = $520 with 9% discount Store C: Original price = $490 with 7% discount Store D: Original price = $450 with 5% discount
The price of office supplies in a store are as follows: Pen: 24 cents Pencil: 18 cents Notebook: $1.24 Paper pack: $3.92 Which equation can be used to calculate the total price of m pens, n pencils, p notebooks and q packages of paper? a. b. c. d.
TOP
2.4m + 1.8n + 1.24p + 3.92q 0.24m + 0.18n + 12.4p + 3.92q 0.24m + 0.18n + 1.24p + 3.92q 0.24m + 0.18n + 1.24p + 39.2q
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85.
Rosie checked her checking account online at 8:00 AM and noticed that her account balance is $4,323. At 9:00 PM, she checked her account again and noticed that the following transactions were posted to her account. Find her final balance after reconciling these transactions: Electronic withdrawal: $320 Electronic withdrawal: $22 Electronic withdrawal: $124 a. b. c. d.
86.
The balance of Aaron’s savings account at the beginning of the year was $3197. For six months he deposited $230 each month in his savings account. What is the balance after six months? a. b. c. d.
87.
$3958 $3937 $3857 $3807
$4378 $4577 $4676 $4766
Carol had $4531 in her checking account before going on a trip. At the end of her trip she noticed that the following transactions were posted to her account: Withdrawal: $437 Withdrawal: $291 Withdrawal: $29 Withdrawal: $37 Find her account balance at the end of her trip. a. b. c. d.
TOP
$3938 $3937 $3836 $3737
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88.
Jeanne had $2024 in her savings account at the beginning of April. By the end of the month she took the following amounts from her savings account: $212 $102 $210 What is her account balance at the end of the month? a. b. c. d.
89.
$1650 $1600 $1500 $1350
Russ usually writes checks on his checking account. During the month of May, he wrote checks in the following amounts: $171 $47 $321 $117 If at the beginning of the month his account balance was $3739, what is the balance at the end of the month? a. b. c. d.
90.
Which expression is equivalent to 3 + 4(9 − 3) + 11? a. b. c. d.
91.
3 + 4 × 9 − 3 + 11 3 + 4 × 9 − 4 × 3 + 11 3 + 4 × 9 + 4 × 3 + 11 3 − 4 × 9 + 4 × 3 + 11
Which expression is the translation of “three times a quantity added to 12, divided by 12?” a. b. c. d.
TOP
$3802 $3383 $3083 $3080
(3 + 12x) ÷ 12 (3x + 12) ÷ 12 3(x ÷ 12) + 12 3(x + 12 ÷ 12)
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92.
What is the value of −4[3 − 4(8 + 1) ÷ 3 − 3] + 12? a. b. c. d.
93.
To convert degrees Celsius to degrees Fahrenheit, multiply by 9, divide by 5 and add 32. Write a formula that represents these operations.
a. b. c. d. 94.
− 49 −44 48 44
Mika is planning a trip that will cover 1232 miles. Her car gets 28 miles to a gallon. If the price of gas is $3.25 per gallon, determine the cost of gas during her trip? a. b. c. d.
TOP
9 C 5 + 32. 5 C 9 + 32. 32 C 5 + 9. 32 C 9 + 5.
What is the value of 4(29 − 19) ÷ 5 − 4 × 13? a. b. c. d.
95.
69 63 60 57
$153 $148 $145 $143
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96.
Sandra purchased the following items for her Club meeting. 12 Packages of cookies each for $4.25 4 Baskets of fruits each for $12.50 42 Cans of soda each for $0.32 How much did she spend in all? a. b. c. d.
97.
Wendy wants to invite a number of friends to an anniversary party at a restaurant. She would like to invite between 1418 friends. She checked with different restaurants, and they offered the following packages. Which restaurant offered the lowest quote for each guest? a. b. c. d.
98.
$114.44 $112.42 $104.42 $102.24
Restaurant A: Restaurant B: Restaurant C: Restaurant D:
$705 for 15 guests $736 for 16 guests $1020 for 20 guests $1250 for 25 guests
Catherine is planning to make cookies for her grandchildren. She purchased the following items: 3 Pounds flour each for $1.23 2 Pounds Sugar each for $1.25 3 Packages of Butter each for $3.45 2 Gallons Milk for $3.25 How much did she spend in total? a. b. c. d.
99.
Church Hill College is planning to invite 34 guests for a conference to be held during their centennial anniversary. If the cost of daily meals of each guest is $21 and the conference is to be held for 3 days, what is the total cost of the meals? a. b. c. d.
TOP
$27.14 $25.04 $24.14 $23.04
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100. Which list shows the following numbers from the smallest to the greatest?
1 5 4 14 3 , 6 , 5 , 15
a. b. c. d.
1 3, 5 6, 4 5, 1 3,
5 6, 1 3, 1 3, 4 5,
14 4 15 , 5 4 14 5 , 15 5 14 6 , 15 5 14 6 , 15
101. Three telecommunication companies plan to lay off some of their workers as listed below: Company A: Company B: Company C: Company D:
70 workers of its 210 workers 30 workers of its 140 workers 80 workers of its 200 workers 60 workers of its 190 workers
Which company plans to lay off the highest fraction of it workers? a. b. c. d.
TOP
Company A Company B Company C Company D
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102. Which list shows the following numbers from the greatest to the smallest?
7 9 11 23 , , , 8 16 12 24
a. b. c. d.
11 12 , 7 8, 9 16 , 23 24 ,
23 7 9 24 , 8 , 16 9 11 16 , 12 23 7 11 24 , 8 , 12 11 7 9 12 , 8 , 16
103. In a Study Hall, the English teacher assigned four different novels to four different students. At the end of the first week, the following students had the following number of pages left to read: Rachael: 130 pages Raymond: 132 pages Russ: 126 pages Regina: 144 pages At the end of the month, the following pages remained unread. Rachael: 42 pages Raymond: 24 pages Russ: 38 pages Regina: 56 pages Which student left the largest fraction of the novel unread? a. b. c. d.
TOP
Rachael Raymond Russ Regina
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104. Which are the two greatest numbers in the following list?
17 7 11 1 , , , 32 12 24 6
a. b. c. d.
17 11 24 and 32 7 11 12 and 24 7 17 12 and 32 7 1 12 and 6
105. Order the following numbers from the smallest to the greatest:
12.25,
a. b. c. d.
TOP
11
3 89 5 , 9 , 12.025
89 3 11 9 , 5 , 12.025, 12.25 89 3 11 9 , 12.025, 12.25, 5 3 89 11 5 , 9 , 12.025, 12.25 89 3 11 12.25, 9 , 5 , 12.025
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106. John worked the following number of hours per month during the first six months of the year. January: 197.34 hours February: 199.04 hours March: 212.34 hours April: 194.45 hours May: 194.54 hours June: 221.43 hours List his monthly workhours from the lowest to the highest in terms of months. a. b. c. d.
June, March, April, May, January, February June, March, April, January, May, February April, June, January, February, March, May April, May, January, February, March, June
107. Find the middle number among the following data? 321.243, 321 a. b. c. d.
56 , 321.432 , 322.254, 322.245 67
321.243
321
56 67
321.432 322.254
108. What is the difference between the smallest and the largest numbers in the following list?
23, 23.01, a. b. c. d.
TOP
230 17
9.74 9.48 7.72 7.47
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109. Different schools reported the ratios of the female students to male students in different numerical formats as follows: School A: 1.9 School B: 2
7 School C : 9
School D: 1.09
Which school has the highest fraction of female students? a. b. c. d.
School A School B School C School D
110. An Excel spreadsheet is set up in a way that by entering a fraction into a cell, it automatically converts it to a number with two decimal digits. The following numbers are displayed in a spreadsheet. 2.24, 3.25, 0.26 Which list represents the equivalents of these numbers?
a. b. c. d.
TOP
52 13 13 , , 25 4 50 56 11 13 , , 25 4 50 56 13 11 , , 25 4 50 56 13 13 , , 25 4 50
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111. Which list represents the equivalents of the following decimal numbers? 4.15, 4.65, 4.25
a. b. c. d.
83 93 17 25 , 20 , 4 83 93 17 20 , 20 , 4 83 93 17 20 , 25 , 4 83 97 17 20 , 20 , 4
112. The dimensions of a rectangular tract of land are 23 used to find the area of the land?
a. b. c. d.
283 12 281 12 283 12 283 14
and and and and
7 5 ft. and 24 ft. Which fractions can be 8 12
197 8 197 8 193 8 197 8
113. Which list represents the equivalents of the following fractions?
84 35 14 35 , , , 49 49 21 63
a. b. c. d. TOP
12 5 7 , 7, 5 12 9, 7 , 11 5 7 , 7, 12 5 7 , 7,
2 3, 5 7, 2 3, 2 3,
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114. The probabilities of four different events occurring are as follows: 0.32, 0.45, 0.55, 0.75 Which list represents these probabilities in simplest fractional form?
a. b. c. d.
7 25 , 8 25 , 8 25 , 8 25 ,
9 20 , 9 20 , 9 20 , 9 20 ,
11 20 , 17 20 , 11 20 , 13 20 ,
3 4 3 4 3 4 3 4
115. In which number does the digit 9 have the highest place value? a. b. c. d.
3409008 3490806 3400908 3400790
116. A physics teacher wrote 238,857 miles on the board as the distance between the moon and the earth. How is it expressed in words? a. b. c. d.
two hundred thousand thirtyeight, eight hundred fiftyseven two hundred thirtyeight, eight hundred fiftyseven two hundred thirtyeight thousand, eight hundred fiftyseven two million thirtyeight, eight hundred fiftyseven
117. Which is the name of the number 45,600,006? a. b. c. d.
TOP
fortyfive million, six thousand, sixty fortyfive million, six hundred thousand, sixty forty million, fortysix hundred thousand, six fortyfive million, six hundred thousand, six
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118. The exact distance between two islands in the Atlantic Ocean is 440,056 ft. What is the order of magnitude of this number? a. b. c. d.
8 7 6 5
119. The weight of a notebook is 8.23 oz. and the weight of each package of pencils is 4.23 oz. The weight of a box containing 24 notebooks and 24 packages of pencils can be calculated using the expression 24 × 8.23 + 24 × 4.23. Which expression is equivalent to this expression? a. b. c. d.
24(34.81) 24(12.46) 8.23 + 101.52 197.52 + 4.23
120. Which expression is equivalent to 3(12 − 1) + 4(13 + 2)?
a.
b. c. d.
3 × 12 − 4 × 13 + 4 × 2 − 3 × 1 3 × 12 + 4 × 13 + 4 × 2 − 3 3 × 12 + 4 × 13 + 2 − 1 3 × 12 + 4 × 13 + 4 × 2 − 3 × 1
121. Which operation must be performed first when calculating (129 + 321 × 481 + 2)? a. b. c. d.
129 + 321 481 + 2 481 × 2 321 × 481
122. Which of the following equations is false? a. b. c. d.
TOP
21 + (11 + 9) = (21 + 11) + 9 21 × (11 + 9) = (11 + 9) × 21 21 ÷ (11 + 9) = (11 + 9) ÷ 21 21 × (11 − 9) = (11 − 9) × 21
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123. In a horse race, Horse A beat Horse B by 2 lengths, and Horse B finished 3 lengths ahead of Horse C. By how many lengths did Horse C lose the race to Horse A? a. b. c. d.
6 5 4 3
124. In a school auditorium, there are 24 rows in the main floor and 11 rows in the balcony. If there are 19 seats in each row, which expression can be used to find the number of the seats? a. b. c. d.
19(24) + 11 19(11) + 24 19(24 + 11) 19(24)(11)
1 4
125. Which of the following is the value of 4[12 + 3(1 + 5)] ÷ 4 ?
a. b. c. d.
4 17 1 28 17 4 27 17 7 26 17 28
126. If a truck carries a 2 pounds? a. b. c. d.
3 tons load, how many pounds is it hauling, knowing that 1 ton = 2000 4
5250 pounds 5450 pounds 5500 pounds 5600 pounds
1 1 127. Which of the following is equivalent to 6 ÷ 3 ? 4 8 a. 8 b. 7 c. 5 d. 2 TOP Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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128. The area of an irregular 4sided shape is calculated using the formula c and d are the side lengths. If, a = 3, b = 4, c = 3 calculate the area?
a. b. c. d.
1 a ( b + c + d ) , where a, b, 3
1 and d = 6, which expression can be used to 4
13 4 + + 6 4 13 3 4 + + 6 4 1 13 4 + + 6 3 4 11 4 + + 6 4
5 129. What is the proper procedure to calculate 12 3 + 4 (1  7 ) ÷ 3 ? 12
a. b. c. d.
Simplify inside brackets, multiply by 12, then divide by the mixed number. Simplify inside parentheses, multiply by 12, then divide by the mixed number. Simplify inside brackets, multiply by 12 by the mixed number, then divide by 12. Simplify inside parentheses, multiply by 3 and 12, then divide by the fraction.
130. For a Physics Project, John designed a microtool in the shape of an irregular hexagon. He must also include in his report a general formula for the perimeter of the tool. After measuring the sidelengths repeatedly he found the sidelengths as, 2 mm, 4 mm, 8 mm, 16 mm, 32 mm, and 64 mm. If a is to be the shortest side of the tool, which of the following is a general formula for the perimeter? a. b. c. d.
49a mm 51a mm 62a mm 63a mm
7 131. To calculate the division 7.73 ÷ 7 , which set of the procedures can be used? 3 a. Convert the mixed number to a decimal, divide the decimals. b. Convert the mixed number to a decimal, convert the decimal to a mixed number. c. Convert the decimal to a mixed number, then multiply. d. Divide 7.73 by 7, then add to the fraction.
TOP
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132. Find x. 12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = x a. b. c. d.
387 368 312 268
133. In the US, about
4 3 of the residents are registered to vote. In one elections, of the registered 5 4
voters actually voted. What portion of the citizens voted in this election?
a. b. c. d.
3 4 1 4 3 5 1 5
134. Perform the following calculations: 1 3 57 +4 ÷ 11 4 4
(1.1 ) 1
a. b. c. d.
TOP
22 15 23 15 19 13 17 13
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135. Calculate the following expression:
1 2 1 2 + 3 1+ 1 + 3 5 3+ 1 3 a. b. c. d.
9.3 9.1 8.9 6.3
136. Cindy measures a side and a diagonal of a squareshaped garden, and after repeating the measurements, she found the following lengths: Side length = 1200 ft. Diagonal length = 1690 ft. Her friend suggests that if the side length is accurate, then the length of the diagonal must be adjusted in her calculation. Assuming the side length is accurate, which of the following measurements will replace the length of the diagonal if more precise calculations are made? a. b. c. d.
1798 ft. 1789 ft. 1697 ft. 1679 ft.
137. The hypotenuse and the altitude of a right triangle are given as 4 ft. and 13 ft. A student measures the legs of the triangle and comes up with measurements of 12 ft. and 5 ft. To what number must the altitude be adjusted? a. b. c. d.
TOP
5.82 ft. 5.62 ft. 4.81 ft. 4.62 ft.
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138. Michelle wants to find some ordered pairs to fit in the equation y = 3x − 2. She created the following table: x 3 5 7 8 11
y 7 13 19 21 31
Which value in the table must be adjusted in order to verify that the given function represents all the given values in the table? a. b. c. d.
21 must be changed to 22 21 must be changed to 26 31 must be changed to 30 31 must be changed to 33
139. A survey of a group of 300 people shows that 41.33% of the people preferred a twin size bed. Since the fractional part in the context (.33) of individuals may not make sense for a group or audience, how can you adjust the result to make it more sensible? a. b. c. d.
41% 42% 45% 40%
140. An irregular shape is made up of four triangles with areas 143 ft2, 34 ft2, 56 ft2 and 122 ft2. What operation is needed to find the area of the shape? a. b. c. d.
Multiplication Division Subtraction Addition
141. To express the value 0.32 as a percent what operation is needed? a. b. c. d.
TOP
Multiplication Division Addition Subtraction
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142. Shannon can type 32 words per minute. To find out how many minutes it takes her to type 2341 words, what operation should be performed on these numbers? a. b. c. d.
Addition Subtraction Multiplication Division
143. Each ton is about 2000 pounds. To find out how many tons make up 4589 pounds, what operation must be performed using these numbers? a. b. c. d.
Multiplication Division Addition Subtraction
144. Which of the following is the best estimation of 2300 × 3209? a. b. c. d.
7,360,000 7,370,000 7,380.000 7,400,000
145. Mt. Whitney is 14,494 feet above sealevel and Rock Valley is 347 feet below sealevel. Which of the following is the best estimation of the difference in these elevations? a. b. c. d.
14000 14500 15000 ft. 1480 ft.
146. Which is the best estimation of a. b. c. d.
TOP
30 29.29 29 28.89
45008 ? 1505
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147. A submarine is submerging at the rate of 11 feet per second. Which is the best estimate of its distance from the surface of the ocean after 39 seconds? a. b. c. d.
440 ft. 400 ft. 385 ft. 380 ft.
148. To find a reasonable estimate of
a. b. c. d.
340000 1100 330000 1100 33000 1100 330000 110
330003 , which fraction is the best choice? 1129
149. The thickness of each bag of wheat stacked in a silo is 9 inches. If in each column of the silo 43 bags are stacked, which of the following is a reasonable estimate of the height of the bags? a. b. c. d.
300 in. 330 in. 400 in. 450 in.
150. To find a reasonable estimate of 1000.01 × 100, which expression is the best choice? a. b. c. d.
TOP
10010 × 100 1000 × 100 1001 × 100 1000 × 101
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151. Which is a reasonable estimate of the total amount of the following coins, in dollars? 40 quarters 10 dimes 20 nickels 770 pennies a. b. c. d.
$20 $19 $18 $17
152. Which ratio is proportional to
a. b. c. d.
7 24 5 28 7 28 6 28
12 ? 48
153. Which proportion is true?
a. b. c. d.
22 18 = 77 64 11 18 = 77 63 22 16 = 77 63 22 18 = 77 63
154. There are 3 teachers for every 38 students in Cherokee Middle School. If there are 798 students, how many teachers are at the Cherokee Middle School? a. b. c. d. TOP
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155. Which number must be placed inside the box a. b. c. d.
12.25 12.85 13.25 13.75
11 ? = 28 35
156. On weekends, 22% of customers of a restaurant are senior citizens. If during one weekend the number of customers of the restaurant were 1050, how many of them were senior citizens? a. b. c. d.
213 219 231 243
157. Let p and q represent the following simple statement: p is a number less than zero. q is a negative number. Which statement is true? a. b. c. d.
If p, then q. If q, then not p. If q but not p, then q. If q but not p, then q.
158. The following simple statements are given: p: Mika likes Ronald q: Ronald likes Mika. Which symbolic statement is true? a. b. c. d.
TOP
p∨q p ∧q p∨q∨p p∨q → q
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159. p and q define the following statements: p: John visited New York. q: John visited London. Which statement represents “John visited New York or London, but not both at the same time?” a. b. c. d.
q → q∨p p∨q∨p p ∧q p∨q
160. The following statements are given: Elementary schools are closed on Sunday. It is Sunday. Write a conditional statement by combining these statements. a. b. c. d.
If elementary schools are closed, then it’s Sunday. It is either Sunday or the elementary schools are closed. If it is Sunday, then the elementary schools are closed. If the elementary schools are closed, then it may not be Sunday.
161. The following statement is given: In any right triangle, the sum of two acute angles is 90º. Which triangle is a right triangle? a. b. c. d.
TOP
Triangle ABC, in which the difference of two angles is 90º. Triangle DEF, in which no angle is obtuse. Triangle GHK, in which two angles are acute. Triangle LMN, in which one angle is obtained by subtracting the other angle from 90º.
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162. The following simple statements are given: All members of a Literature club are published authors. John is a member of this club. Which statement is true? a. b. c. d.
John is a publisher. John may be both an author and a member of the club. John may be a published author. John is a published author.
163. The following statements are given: S = set of integers that are even and are divisible by 3. a is an even integer. Which statement is true? a. b. c. d.
a is not definitely a member of S. a is not a member of S. a may be a member of S. a is a member of S.
164. The following statements are given: All the students in Algebra class are attending Geometry class. All the students in Geometry class are attending History class. John is in History Class. Which statement is true? a. b. c. d.
John may attend Algebra and/or Geometry class(es). John is not attending Algebra class. John is not attending Geometry class. John is attending both Algebra and Geometry classes.
165. Which general formula can be used for all the numbers in the following series? 2, 6, 12, 20… a. b. c. d. TOP
2n(2n − 1) n(n  1) 2n(n + 1) n(n + 1) Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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166. The sum 1 + 2 + 3 = 6 is simplified as 32 – 3 = 6 which means that the sum equals the square of the last term minus the last term. Using this method, the sum 1, 2, 3, . . . , n is generalized as n2 − n. Which number disproves this generalization? a. b. c. d.
2 3 4 Both 2 and 4
167. A brick staircase is made up of 8 steps. The bottom step has 18 bricks, and each successive step has two less bricks. How many bricks are used in the staircase? a. b. c. d.
88 82 76 66
TEAS Practice Exam – Math  Section 2 Algebra 168. Solve 3x + 11 = 31 – x. a. b. c. d.
7 5 4 2
169. Sarah and her father together are 47 years old. If her father is 34 years old, what is Sarah’s age? a. b. c. d.
TOP
19 17 13 11
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170. The ratio of two numbers is 13. If the larger number is 1027, what is the smaller number? a. b. c. d.
79 83 87 89
171. Solve the equation 5x − 11 = 39. a. b. c. d.
14 13 11 10
172. The sidelengths of a triangle are described by x2 + x + 1, 3x − 2, and 3x2 + x. What is the perimeter of the triangle? a. b. c. d.
4x2 + 5x − 1 4x2 + 4x − 1 4x2 + 5x + 3 4x2 + 5x − 2
173. Subtract (3x2 + 1) from (4x3 + 2x2 + x). a. b. c. d.
4x3 − x2 + 2x − 1 4x3 − 2x2 + x − 1 4x3 − x2 + x + 1 4x3 − x2 + x − 1
174. The dimensions of a rectangle are described by (x + 2) and (x + 3). Which of the following describes the area of the rectangle? a. b. c. d.
x2 + 5x + 5 x2 + 6x + 6 x2 + 5x + 6 x2 + 6x + 5
175. Add (x2 + x) to (8x3 + 2x2 − x − 1). a. b. c. d. TOP
8x3 + 3x − 1 8x3 − 3x2 − 1 8x3 + 3x2 − 1 8x3 + 3x2 − 2x Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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176. Write an equation: “value of x is two more than three times x.” a. b. c. d.
3x = x + 2 3x = x − 2 x = 2 + 3x x = 2 − 3x
177. Which of the following is the translation of the expression “The sum of 3 times a number and 3, added to 5 times the number?” a. b. c. d.
8x + 3 5x + 3 8x + 5 5x + 8
178. The sum of the right angle and an acute angle in a right triangle is greater than 123º. Which expression represents this relationship? a. b. c. d.
x + 90 < 123 x + 90 > 123 x + 123 > 90 x + 123 < 90
179. Which is the translation of the phrase “11 more than the triple of a number?” a. b. c. d.
11x + 3 3x + 11 3(x + 11) 3x + 33
180. Which of the following is the solution to the equation x + 12 = 25? a. b. c. d.
TOP
12 or 37 17 or 33 13 or −37 −13 or 37
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181. The temperature on the surface of Mars fits the inequality C + 85 ≤ 56 , in degrees Celsius. What is the range of the temperature? a. b. c. d.
−29 ≤ C ≤ −141 29 ≤ C ≤ 141 141 ≤ C ≤ 29 −141 ≤ C ≤ −29
182. Which is the solution set to the inequality x + 5 > 16 ? a. b. c. d.
x > −11 or x < −21 x > 11 or x < −21 x < 11 or x < 21 x < 11 or x < 21
183. A physician who has practiced medicine for over 20 years realizes that more than 92% of the babies he delivered weighed p pounds such that p  7 ≤ 2 . What is the range of the weights of the babies? a. b. c. d.
9 ≥p ≥ −5 9≥p > 5 9>p ≥ 5 9≥p ≥ 5
184. Solve the equation 3x + 11 = 51 − x. a. b. c. d.
12 10 6 2
185. The length of a rectangle is 12 ft. longer than twice its width. If the total length of a width and a length is 44 ft., what is the measure of a width? a. b. c. d.
TOP
x = 22 ft. x = 19 ft. x = 18 ft. x = 16 ft.
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186. Solve the inequality 5x − 19 > 3x + 33. a. b. c. d.
x > 26 x > 28 x < 26 x < 28
187. If the radius of a circle is doubled, how will its area be changed? a. b. c. d.
Increase two times. Increased four times. Increased by two. Increased by four.
188. If x in x(22 − 19) is tripled, how much is the value of the expression changed? a. b. c. d.
Will Increase by 6x Will increase 6x times Will increase by 8x Will increase 8x times
189. If x in the expression 12(x + 3) + 9 is increased by 9, how will the value of the expression be changed? a. b. c. d.
Will be increased by 132 Will be decreased by 132 Will be increased by 126 Will be decreased by 126
190. A sidelength of a squareshape pool is 44 ft. If its length extended to 48 ft., how much will its area be increased? a. b. c. d.
466 ft2 468 ft2 386 ft2 368 ft2
191. If x in the expression 3(x + 9) − 12 is decreased by 9, how much will the value of the expression be changed? a. b. c. d. TOP
Will be decrease by 62 Will be decreased by 51 Will be decreased by 43 Will be decreased by 27 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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192. To solve equations such as 3.23x + 4.12 = 1.19 − 21.8x, which step must be followed first in order to make the solution easier? a. b. c. d.
Remove the decimal from the left side. Cancel the decimals. Multiply all the terms by 10 Multiply all the terms by 100.
193. To solve the equation a. b. c. d.
x 4 = 3 , what step must be taken first? 5 9
Divide the fractions by 45. Multiply the denominators by 45. Cross multiply the proportion. Change the mixed number to an improper fraction.
194. To solve equations such as solution easier?
1 5 1 x + = , which step must be followed first in order to make the 18 12 6
1 to the left side. 6
a.
Move
b.
Add
c. d.
Multiply all the terms by 36. Divide all the terms by 36.
1 to the left side. 6
195. What are two different methods to verify that a. b. c. d.
Division and Reducing Crossmultiplication and Reducing Multiplication and Reducing Crossmultiplication and Division
24 3 = ? 32 4
196. The equation 12 = 6(3 + x) is obtained from the equation 12 − 3(3 + x) = 3(3 + x), using algebraic operations. How is the expression (3 + x) doubled on the right side? a. b. c. d.
TOP
By multiplying all the terms by 2. By replacing x by x + 3. By adding 3(3 + x) to both sides. By subtracting 3(3 + x) from both sides.
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197. Solving the equation a. b. c. d.
1 5 11 5 = yields 14 = x . How can you complete the solution? 2 7 x
By crossmultiplication By division By subtraction By multiplication
198. We know that the perimeter of a rectangle with the dimensions a and b is equal to 2(a + b). How does doubling the sum of a and b give the perimeter? a. b. c. d.
Perimeter = 2a + a + 2b + b = 2(a + b) Perimeter = 2a + 2a + b + b = 2(a + b) Perimeter = a + a + b + b = 2(a + b) None of the above
199. The following set of numbers fit the sides of right triangles: a=3 a=6 a=9 a = 12
b=4 b=8 b= 12 b = 16
c=5 c = 10 c = 15 c = 20
Using this pattern, find a general formula for the sides of right triangles. a. b. c. d.
a = n(3), b = n(5), and c = n(6) a = n(2), b = n(4), and c = n(5) a = n(3), b = n(5), and c = n(7) a = n(3), b = n(4), and c = n(5)
200. What pattern is used for generating numbers in the series below: 4, 9, 19, 39, 79, . . . , a. b. c. d.
TOP
Add 1 to each number, then double. Double each number, then add 1. Subtract 1 from each number, then double. Double each number, then add 2.
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201. Raymond is studying hard in his Algebra class to improve his exam scores. The following numbers show his scores for the first five exams: 45, 56, 63, 75, 84 What is likely to be his score in the sixth exam? a. b. c. d.
70 85 89 94
202. Which formula is used to generate the numbers in the series below? 4, 9, 19, 34, 54, . . . , a. b. c. d.
6 added to each term, then 1 is subtracted. 5 added to each term, then added 10. Multiple of 5 added to each term beginning with 5. Multiple of 10 added to each term beginning with 10.
203. The numbers below follow a general pattern. What is the next number in the series? 100, 98, 94, 88, . . . a. b. c. d.
72 78 80 82
204. The relationship between P and n is defined by P = 4n. If n increases, how will P change? a. b. c. d.
P will increase. P will decrease. P first will increase, then will decrease. P first will decrease, then will increase.
205. The area of a rectangle is A = ab. Given A as a constant, how will b vary if a is doubled? a. b. c. d. TOP
b will be decreased by onehalf. b will be increased by onehalf. b will be decreased by onethird. b will be doubled. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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5 x
206. The relationship between R and x is defined by R = . If x increases how will R change? a. b. c. d.
R will increase. R will decrease. R first will increase, then will decrease. R first will decrease, then will increase.
207. Volume of a gas varies with its temperature and its pressure. This relationship is described by V = TP, where V is volume, T is temperature and P is pressure. If the volume of a gas is constant, then what is the relationship between T and P? a. b. c. d.
If T decreases, then P decreases If T stays constant, then P increases. If T increases, then P decreases. If T increases then P increases.
208. Which function can be described by the given graph below?
a. b. c. d.
TOP
y = mx + b
xy =
5 4
y = x2 + 3x − 7 y = 3x3 + 4x
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209. Which function represents the graph below?
a. b. c. d.
y = 2x + c y = 2x3 + 3x + c y = 2x + 3x + c y = ax2 + bx + c
Go to the next page.
TOP
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210. Which graph can represent the path of launching a projectile? a.
b.
c.
d.
211. The difference between an acute angle and the right angle in a right triangle is 32º. Which equation can be used to find the acute angle? a. b. c. d. TOP
90 − x = 32 90 + x = 32 32 − x = 90 −32 + x = 90 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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212. Which expression represents the phrase “nine times a number added to 32, subtracted from 193”? a. b. c. d.
222 + 9x 222 − 9x 160 + 9x 161 − 9x
213. The sum of two consecutive even integers is 650. Which equation can be used to find these numbers? a. b. c. d.
2x + 1 = 650 2(x + 1) = 650 2x − 1 = 650 2(x − 1) = 650
214. John scored 89 and 83 in his first two Geometry exams. He wants to score an average of 90 in the exams. Which equation can be used to predict his score in the third exam? a. b. c. d.
x + 162 = 290 x + 182 = 280 x + 172 = 270 x − 172 = 265
215. Which statement is true? a. b. c. d.
If p: (x − 1)(x + 3) = 0, then q: x = 1. If p: (x − 1)(x + 3) = 0, then q: x = −1. If p: (x − 1)(x + 3) = 0, then q: x = 3. If p: (x − 1)(x + 3) = 0, then q: x = 4.
216. The following equation is given along with solutions: p: (x + 9)(x − 5) = 0 q: x = −9 r: x = 5 Which statement is true? a. b. c. d. TOP
q∨r p∧q p ∨ q ∧p r → q ∧p
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217. If (x + 3)(x + 23) = 0, then which statement is true? a. b. c. d.
x = −3 or x = −23 x = −3 and x = −23 x = 3 or x = −23 x = 3 and x = −23
218. The following statements are given: All the members of the Hemingway Club are published authors. Ronald is not a member of a Sport club. Jason is a published author. Olivia is a member of the Hemingway Club. Which statement is true? a. b. c. d.
Olivia is a member of the Sport Club. Jason is a member of the Hemingway Club. Ronald is a member of the Hemingway Club. Olivia is a published author.
219. The sum of the numbers 1 + 2 + 3 + 4 + 5 +, . . . , + n is equal to S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15? a. b. c. d.
n (n + 1 ) . What is the sum of 2
144 140 120 112
220. Ronald concluded that 3 = 4 by dividing both sides of the equation 3(x − 1) = 4(x − 1) by the same expression (x − 1). How did he use the simplification of an equation improperly? a. b. c. d.
TOP
Subtracted zero from both sides. Multiply both sides by zero. Added zero to both sides. Divided both sides by zero.
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221. Consider the pattern among the following equations: 37 × 3 = 111 37 × 6 = 222 37 × 9 = 333 37 × 12 = 444 37 × 15 = 555 Which number must fill the blank in the equation 37 × __= 888? a. b. c. d.
19 20 23 24
222. Consider the numerical equations below: (1 × 9) + 2 = 11 (12 × 9) + 3 = 111 (123 × 9) + 4 = 1111 (1234 × 9) + 5 = 11111 (12345 × 9) + 6 = 111111 Following the same pattern, which number must fill the blank in the equation (12345678 × 9) + ___ = 111111111? a. b. c. d.
TOP
9 8 7 6
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TEAS Practice Exam – Math  Section 3 Data Interpretation 223. The numbers of hours of sunshine in Roan Mountain during one week of the summer is displayed in the graph below: 10 9 8 7 6 5 4 3 2 1 0 Sun Mon Tue Wed Thu
Fri
Sat
Which data table fits the bar graph? a. Day Sunshine
Fri 7.0
Sat 8.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 5.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 5.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 7.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 8.2 9.0 6.2 5.5
b. Day Sunshine c. Day Sunshine d. Day Sunshine
TOP
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224. Which frequency table represents the following data: 126, 129, 126, 126, 126, 128, 126, 126, 129, 129, 127, 130, 127, 127, 128, 128, 128, 129, 128, 126 a. Data Frequency 126 8 127 3 128 6 129 4 130 1 b. Data Frequency 126 7 127 3 128 5 129 3 130 1 c. Data Frequency 126 7 127 3 128 5 129 4 130 2 d. Data Frequency 126 7 127 3 128 5 129 4 130 1
TOP
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225. The percentages of different elements in a chemical substance is shown in the table below. Carbon Oxygen Hydrogen Sulfur Nitrogen
34% 26% 21% 12% 7%
Which pie chart represents the data in the table?
a.
b.
c.
d.
TOP
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226. The following table shows the number of graduates of Boone Creek High School during years 20042011. Year 2004 2005 2006 2007 2008 2009 2010 2011
Number of Graduates 453 571 356 398 433 405 447 511
Which line graph represents the data in the table? (Numbers starting from 1 represent the years 2004, 2005, and so forth.)
a.
b.
TOP
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c.
d.
227. The Venn Diagram below displays the number of students attending different classes.
What is total number of students attending Literature class? a. b. c. d.
TOP
51 49 43 37
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228. The graph below represents the amount of rain during a week of spring in New York, in millimeters. 10 9 8 7 6 5 4 3 2 1 0 Fri
Sat
Sun
Mon
Tue
Wed
Thu
Which is the best estimate of the range of the data given in the graph? a. b. c. d.
4.2 mm 5.6 mm 5.9 mm 6.2 mm
229. The following stem  and  leaf graph represents a set of data.
What is the median of the data? a. b. c. d.
TOP
46 51 55 58
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Use the following information to answer questions 230 and 231. The amounts of money a Telecommunication Company spent on ads for the years 20052010 are shown in the table below. Year 2005 2006 2007 2008 2009 2010
Amount (in dollars) 190,000 230,000 110,000 150,000 160,000 180,000
230. In which year was the advertisement cost the highest? a. b. c. d.
2005 2006 2009 2010
231. In which year was the advertisement cost the lowest? a. b. c. d.
2006 2007 2008 2010
232. The values of the variables a, b, c and d are given in the table. On which variable is P dependent, such that P = 3 + 2x? P 1 9 21 a. b. c. d.
TOP
a 2 4 2
b −1 3 9
c 6 −1 8
d −2 3 −7
Variable a Variable b Variable c Variable d
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233. The values of the variables m, n, p and q are given in the table. On which variable is T dependent, such that T = 3x2 − 1? T 11 26 2 a. b. c. d.
m 2 −4 2
n −3 7 5
p 4 −1 8
q −2 3 −1
Variable m Variable n Variable p Variable q
234. The values of the variables m, n, p and q are given in the table. On which variable is R dependent on, such that R =
3x + 2 ? 2 R −5 7 10
a. b. c. d.
m −4 4 6
n −1 3 9
p 6 −1 8
q 1 3 −7
Variable m Variable n Variable p Variable q
235. The pie chart below represents the data in the table. What is the relationship between the sum of percentages and the area of the circle? Service Army Navy Marine Corp Air Force Coastal Guard
a. b. c. d. TOP
Percent 33% 27% 12% 25% 3%
The sum of the numbers is equal to the area of the circle. The sum of the numbers is equal to the circumference of the circle. The sum of the numbers is 100% and the total shaded regions is 100% of the circle. The sum of the numbers is 100% of the diameter of the circle Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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236. The bar graph represents the data in the table. How are the areas of the States of Alabama, Maryland and Minnesota shown in the graph?
State Alabama Alaska California Colorado Maryland Minnesota
Land Area 50700 573,000 155900 103700 9770 79600
700000 600000 500000 400000 300000 200000 100000 0
a. b. c. d.
TOP
By the columns above the horizontal line 200,000. By the columns between the horizontal lines of 100,000 and 200,000. By the column above the horizontal line 100,000. By the columns below the horizontal line 100,000.
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237. The bar graph represents the data in the table. How are the areas of the States of Arizona and Montana shown in the graph? State Arkansas Arizona Connecticut Michigan Montana Minnesota
Land Area 52000 113,650 4850 56800 145550 79600
160000 140000 120000 100000 80000 60000 40000 20000 0
a. b. c. d.
TOP
By the columns above the horizontal line 100,000. By the columns below the horizontal line 100,000. By the columns between the horizontal lines 100,000 and 80,000. By the columns between the horizontal lines 80,000 and 60,000.
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Use the following information to answer questions 238 through 242. The scores of six students in Science verses their scores in History are shown in the table below. Student A
Student B
Student C
Student D
Student E
Student F
71
98
86
67
81
92
Science Score History Score
86
76
68
94
92
73
238. Which student scored lowest grade only in History? a. b. c. d.
Student A Student B Student D Student E
239. What is the difference between the ranges of the scores of the two subjects? a. b. c. d.
1 2 4 5
240. Which student scored the lowest grade only in Science? a. b. c. d.
Student A Student C Student D Student E
241. Which student scored the highest in Science and lowest in History? a. b. c. d.
TOP
Student A Student B Student D Student E
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242. What is the difference between the mean of the scores of both subjects? a. b. c. d.
4 3.5 1.5 1
Use the following information to answer questions 243 through 247. In a clinical trial, during four weeks of the trial period, each week certain number of patients in each group pulled out from the trial. The following table shows the number of pullouts for all groups. Groups Group A Group B Group C Group D
First Week 11 32 14 30
Second Week 32 44 21 39
Third Week 20 9 21 11
Fourth Week 19 33 29 12
243. In which week was the number of patients who pulled out from the trial the highest? a. b. c. d.
First week Second week Third week Fourth week
244. Which group had the highest number of pull outs? a. b. c. d.
Group A Group B Group C Group D
245. Which group had the lowest number of pull outs? a. b. c. d.
TOP
Group A Group B Group C Group D
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246. In which week was the number of patients who pulled out from the trial the lowest? a. b. c. d.
First week Second week Third week Fourth week
247. Which group had the highest pullout average? a. b. c. d.
Group A Group B Group C Group D
248. In a daycare, the ages of children are as follows: 4, 5, 3, 5, 4, 6, 6, 4, 7, 3, 5 What is the median of the ages? a. b. c. d.
3 4 5 6
249. The average of three consecutive integers is 16. What is the smallest integer? a. b. c. d.
15 16 17 18
250. The heights of a group of students are given below, in centimeters. What is the range of the heights? 145, 146, 146, 154, 158, 166, 172, 174 a. b. c. d.
TOP
29 cm 30 cm 32 cm 35 cm
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251. Olivia made the following scores in her History tests. What is the average of her scores? 86, 72, 78, 88 a. b. c. d.
81 80 78 75
252. What is the mode of the following data? 20, 11, 15, 17, 15, 17, 19, 15, 11, 11, 20, 15 a. b. c. d.
11 15 17 20
253. A 6sided die is rolled. The probability of getting an odd number is represent? a. b. c.
It means that the chance of an odd number is 3 out of 1. It means that the chance of an odd number is 1 out of 3. It means that the chance of an odd number is 1 out of 6.
d.
It means that the chance of an odd number is 1 out of
1 . What does this fraction 3
1 . 3
254. A box contains 42 red and green marbles. The probability of choosing a red marble from the box is a. b. c. d.
TOP
4 . What can be concluded from this fraction? 7 There are 36 red marbles in the box. There are 24 red marbles in the box. There are 22 red marbles in the box. There are 18 red marbles in the box.
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255. There are 32 students in Algebra class. The chance of choosing a female student is What does this fraction represent? a. b. c. d.
9 . 16
The number of male students is 14. The number of male students is 16. The number of male students is 15. The number of male students is 12.
256. Box A contains 124 cards marked with positive integers. The chance of choosing an odd integer is
12 . What does this fraction represent? 31 a. b. c. d.
There are 42 even integers in the box. There are 44 even integers in the box. There are 48 even integers in the box. There are 76 even integers in the box.
257. What chance is there of choosing a number divisible by 5 from the numbers between 53 and 75?
a. b. c. d.
7 18 4 17
5 18
4 21
258. Of a group of 50 students, 20 attend Algebra class. If a student is chosen randomly from the group of 50, what is the chance that the student is not attending Algebra class?
a. b. c. d.
TOP
3 5 4 5 1 5 2 3
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259. Describe the correlation between height and shoe size. a. b. c. d.
Positive Negative No correlation Cannot be determined.
260. Describe the correlation between time spent exercising and weight. a. b. c. d.
positive negative no correlation cannot determine
261. For years, teachers have always said the more you study, the better you do on your test. Juan wanted to conduct an experiment to see if that was indeed true. He had studied for his first science test for 5.5 hours and got a 93%, his second science test for 2 hours and got a 89% and for his last science test for half an hour and got a 78%. Which of the following sentences best describe this situation? a. b. c. d.
There is a positive correlation between studying and grades. The grade is the independent variable. The two parameters are inversely related Cannot be determined.
262. Describe the correlation between height and hair length. a. b. c. d.
TOP
positive negative no correlation cannot determine
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263. The table represents the side of a square compared to its area. Side Length 2 inches 4 inches 9 inches 12 inches
Area 4 square inches 16 square inches 81 square inches 144 square inches
Which of the following statements are true based on the previous relationship? a. b. c. d.
If these two variables were graphed, the result would be linear. If these two variables were graphed, the area would be the independent variable. If these two variables were graphed, the slope is always positive. If these two variables were graphed, there would not be any correlation.
TEAS Practice Exam – Math  Section 4 Measurements 264. 1000 mg = ___ g a. b. c. d.
1 10 100 110
265. 160 cm = ____ mm a. b. c. d.
1.6 16 160 1600
266. 109 g = ____kg a. b. c. d.
TOP
.0109 .109 1.09 10.9
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267. 4 L = ___ml a. b. c. d.
.4 40 400 4000
268. 75 ml = ___L a. b. c. d.
.0075 .075 .75 7.5
269. A man weighs 80 kilograms. How much does he weigh in pounds? a. b. c. d.
176 lbs. 185 lbs. 210 lbs. 80 lbs.
270. A kitten was weighed at 4 weeks old and the scale registered 0.8 lbs. If the kitten gains 0.05 lbs. per week, what will the kitten weigh at 8 weeks old? a. b. c. d.
4.5 lbs. 4.2 lbs. 1.0 lbs. 8.2 lbs.
271. Greg is building a rectangle dog run. He has 14 pieces of fencing, each piece measuring 5’ by 5’. Which of the following areas are plausible for the dog run? a. b. c. d.
150 ft2 250 ft2 300 ft2 All of the above
272. David walks 6 miles in 4 hours. What is the unit rate? a. b. c. d. TOP
6 mph 2 mph 1.5 mph 3 mph Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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273. During what time period is the greatest rate of change?
a. b. c. d.
0 – 1.0 2.0 – 3.0 1.0 – 2.0 4.0 – 5.0
274. 54⁰ F = _____⁰ C a. b. c. d.
1.2 10.22 12.22 102.22
275. 32⁰ C = _____⁰ F a. b. c. d.
TOP
89.6 88.9 86.9 100
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276. A woman weighs 132 pounds. What is her weight in kilograms? a. b. c. d.
13,200 1,320 132 60
277. A man is 6’4” in height. How tall is he in centimeters? a. b. c. d.
152 164 193 640
278. Which of the following is equivalent to 3 pounds and 12 ounces? a. b. c. d.
42 ounces 48 ounces 52 ounces 60 ounces
279. The weight of the object M is 9 kg and 112 g, and the weight of the object N is 1200 g. What is the total weight in grams? a. b. c. d.
10122 grams 10312 grams 11021 grams 13021 grams
280. What is the total, in inches, of 5 yards, 5 feet and 22 inches? a. b. c. d.
262 inches 254 inches 248 inches 234 inches
281. How many miles are in 24,500 kilometers? a. b. c. d. TOP
12,512.5 miles 15,312.5 miles 15,315.5 miles 15,512.5 miles Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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282. Which of the following has the unit rate of 32 miles per hour? a. b. c. d.
128 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 4 ℎ𝑟𝑟 64 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 2 ℎ𝑟𝑟 256 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 8 ℎ𝑟𝑟
All of the above
283. Tim drives a truck 6 days a week for 9 hours a day. Each week, he logs about 3,600 miles. What is his average speed while driving? a. b. c. d.
59 mph 62 mph 72 mph 67 mph
284. What is the difference between the following lengths, in meters? M: 12 m, 119 cm N: 1.2 m a. b. c. d.
1379 cm 1289 cm 1299 cm 1199 cm
285. A student mixed the following materials to make a chemical substance: Carbon = 606 grams Phosphor = 1443 grams What is the weight of the mixture in kilograms? a. b. c. d.
TOP
4 kg 3 kg 2 kg 1 kg
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286. Using “Vernier calipers”, the diameters of two steel bearings are measured as 4.34 cm and 3.39 cm. What is the sum of the diameters of the bearings in millimeters? a. b. c. d.
77.3 mm 73.7 mm 63.7 mm 60.3 mm
287. The distance between the Low and High settings in a “Volume Control” is 24 cm. If the distance is marked by 16 equally spaced lines, what is the distance between each two adjacent lines, in millimeters? a. b. c. d.
15 mm 14 mm 12 mm 10 mm
288. The scale of a map is 3 centimeters = 60 miles. The distance, on the map, from the east boundary to the west boundary of Kingston is 1.2 cm. What is the distance from the east boundary to the west boundary in miles? a. b. c. d.
29 miles 26 miles 24 miles 21 miles
289. A picture is enlarged by the scale factor of 5. If the dimensions of the picture were 4.2 in. by 8.4 in. before enlargement, what are its dimensions after enlargement? a. b. c. d.
24 by 34 21 by 32 26 by 34 21 by 42
290. If we want to draw a plan for a basketball court with the dimensions 85 feet by 50 feet using the scale factor of 5 ft. = 1 in., then what would be the new dimensions? a. b. c. d.
TOP
18 in. by 11 in. 17 in. by 10 in. 15 in. by 13 in. 15 in. by 10 in.
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291. How many inches are in one yard? a. b. c. d.
38 inches 36 inches 34 inches 32 inches
292. How many cubic centimeters are in a liter? a. b. c. d.
10 100 1000 10000
293. How many pints are in a gallon? a. b. c. d.
4 5 6 8
294. What is (2 gallons, 8 quarts) in quarts only? a. b. c. d.
10 14 16 20
295. What is (2 decameters, 34 decimeters) in centimeters? a. b. c. d.
2340 cm 2420 cm 2440 cm 2624 cm
296. What is (5 yards, 4 feet) in inches? a. b. c. d.
TOP
228 in. 218 in. 192 in. 188 in.
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297. Cindy wants to add some preservative to 0.8 kg dried fruit. What unit of measurement should she use to weigh the preservative? a. b. c. d.
Kilogram Gram Pound Liter
298. A carton contains 112 notebooks. If each notebook weighs 6 ounces, what weight unit should be used on the carton where the total weight is recorded? a. b. c. d.
Liter Ton Kilogram Pound
299. A truck is carrying 124 boxes of rootbeer. Each box contains 24 bottles and the weight of each bottle is 340 grams. What measuring unit is proper to represent the total load of the truck? a. b. c. d.
Pound Gram Ton Liter
300. A patient is to receive 2 grams of a drug. The drug comes in 500 mg/5 cc. Each vial has 10 cc. How many vials does the patient need? a. b. c. d.
1 2 3 4
301. What is the volume of a gold bar that is 4.5 cm long, 3.5 cm wide and 2 cm thick? a. b. c. d.
TOP
10 cm³ 15.75 cm³ 20.25 cm³ 31.5 cm³
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302. The dimensions of a rectangle are 2 feet and 240 inches. What is the area of the rectangle? a. b. c. d.
5760 in.2 5780 in.2 5860 in.2 5980 in.2
303. The line segment AE is made up of AB = 2 ft., BC = 25 in., CD = 3 ft. and DE = 35 in. What is the length of AE in inches? a. b. c. d.
54 ft. 60 ft. 118 in. 120 in.
304. The area of a tract of land A is 232 square meters and the area of the land B is 420,000 square decimeters. Find the total area of A and B in square meters. a. b. c. d.
608 m2 612 m2 652 m2 672 m2
305. The average temperature of New York on a sunny day is 77 degrees Fahrenheit. Which is the equivalent of this temperature in degrees Celsius? a. b. c. d.
TOP
37 31 27 25
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TEAS Practice Exam – Math  Section 5 Geometry 306. Find the area of the shaded region. 7 cm
9 cm
11 cm
9 cm a. b. c. d.
99 cm2 81 cm2 97 cm2 101 cm2
307. Find the perimeter of the following regular figure.
4 in
a. b. c. d.
TOP
64 in 40 in 48 in 60 in
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308. What is the area of the following figure? Keep your answer in terms of pi. 4 ft.
a. b. c. d.
16π ft2 12π ft2 π ft2 4π ft2
309. Find the area of the shaded area rounded to the nearest hundredth. Use 3.14 as π. 16 in
5 in
a. b. c. d.
TOP
75.38 in 2 14.625 in 2 1,760 in 2 95 in 2
22 in
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310. Find the perimeter of the figure. Use 3.14 as π.
6
8.73 6.29
14.2 a. b. c. d.
36.84 32.48 35.22 45.33
311. Find the area of the figure. Use 3.14 as π.
6
6
a. b. c. d.
TOP
12
54 432 82.26 36.84
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312. Tom is building a wooden fence for his rectangular back yard. The dimensions that he wants the fence is 18 ft. by 24 ft., with one fivefoot metal gate. Each piece of wood is 5 inches wide and 5 feet tall. Tom also wants one inch between each piece of wood. How many pieces of wood will he need to buy? a. b. c. d.
185 pieces 158 pieces 74 pieces 72 pieces
313. What is the correct equation to find the perimeter of a rectangle with a length of 4 cm and a width of 8 cm? a. b. c. d.
4 + 8 = 12 4 * 8 = 32 (4*8)/2 = 16 2(4) + 2(8) = 24
314. What is the length of the arc of a circle made by a 90° angle? The circle has a diameter of 8 ft. Leave your answer in terms of π. a. b. c. d.
TOP
4π ft. 16π ft. 8π ft. 2π ft.
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315. The illustration is of a small white circle within a large blue circle. The radius of the small circle is 4 in. The diameter of the large circle is 12 in. Find the area of the shaded region. Leave your answer in terms of π.
a. b. c. d.
16π in 2 36π in 2 20π in 2 128π in 2
316. If RS = 12 cm, what is the length of a radius of the circle A?
R
90
A
a. b. c.
d.
S
9.68 cm 9.28 cm 8.82 cm 8.48 cm
317. In the isosceles triangle ABC, the vertex angle A is 40º. What is the measurement of a sideangle? a. b. c.
d. TOP
70º 62º 60º 55º Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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318. In the rhombus ABCD, m∠A = 34º. What is m∠DBC? A
B
D
C
a. b. c. d.
83º 82º 78º 73º
319. In the isosceles right triangle ABC, BC = 14 in. What is the area of the triangle? B
C
A
a. b. c. d.
TOP
56 in.2 52.04 in.2 49 in.2 48.02 in.2
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320. The segment line AB with A(3, 5) and B(7, 8) is translated 3 units vertically up. What are the new locations of A and B? a. b. c. d.
A’(8, 3) and B’(3, 11) A’(3, 8) and B’(11, 3) A’(3, 11) and B’(3, 7) A’(3, 8) and B’(3, 11)
321. The following statements are given in the triangle ABC. p : Triangle ABC is equilateral q : Altitudes AD and BE are equal. a. b. c. d.
If p, then q. If q, then p. If q, then not p. If p, then not q.
322. Which set of angle measures can represent the interior angles of a triangle? a. b. c. d.
54º, 67 and 34º 32º, 48º and 90º 42º, 90º and 58º 33º, 80º and 67º
323. Which set of sidelengths can represent the sides of a triangle? a. b. c. d.
TOP
12, 18, 22 11, 13, 24 13, 15, 29 14, 18, 38
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TEAS VI Practice Exam – Math Answers with Explanations 1.
d  To add or subtract fractions, you need a common denominator. 2/8 reduces to 1/4 1/4 + 1/4 = 2/4 2/4 can be reduced to 1/2.
2.
c  To multiply an integer and a fraction, you do not need a common denominator. The numerator of the fraction is multiplied by the integer and the denominator is multiplied by one and stays the same. 4/1 x 3/7 = 12/7 = 1 5/7
3.
a  To multiply a fraction by another fraction, multiply numerators and denominators: 5/6 x 3/4 = 15/24 = 5/8
4.
b  The quotient of 348 divided by 6 is 58. If you multiply 6 by 58, you get 348 as the product.
5.
a  By the order of operations, you first carry out multiplication before addition or subtraction. 8 – 12 + 9 = x 4 + 9 = x X=5
6.
a  By the order of operations, you first carry out division before addition or subtraction. 18 – 23 + 33 = x x = 51 – 23 x = 28
7.
c  By the order of operations, you first carry out multiplication before addition or subtraction. A number multiplied by 1 will be itself. Therefore: 33 – 5 = x X =  38
8.
b  To divide a fraction by another fraction, invert the terms of the divisor and then multiply: 2/3 x 5/4 = 10/12 = 5/6
9.
c  An easy way to figure this problem out is to convert the decimal by multiplying by 10, such that .4 becomes 4 and 36 become 360. The division of 360 by 4 may be easier for one to understand.
10. a  By the order of operations, you first carry out multiplication before addition or subtraction. 7 x 9 equals 63 and adding .08 equals 63.08.
11.
b  To convert from a percent to a decimal, divide the percentage number by 100. 425 ÷ 100 = 4.25. D is wrong because that just drops the percent sign, but that is not the right way to convert between percents and decimals. TOP Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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12.
a  Fractions are part over whole. The part is the two bananas and the whole is the 12 pieces of fruit. The fraction would be 2/12, but the question specifically states the fraction needs to be in simplest form, so b is not correct. 2/12 can be reduced by a factor of 2 because 2 is the greatest common factor between 2 and 12. The fraction reduces to 1/6.
13.
c  To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). 3 ÷ 4 = .75. Choice a happens often because the 3 and the 4 are combined to make a decimal, while choice d occurs when 4 is divided by 3.
14.
d  To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). 1 ÷ 2 = .5. To convert a decimal to a percent, multiply the decimal by 100, and place the percent sign at the end. .5 * 100 = 50%. Choice c is also correct because if 3/6 is reduced, the simplest form is ½, so the final answer is d, all of the above.
15.
b  To convert a decimal to a fraction, look at the place value of the smallest digit. .6 is read as 6 tenths, and the 6 is in the tenths place. The 10 becomes the denominator, and the 6 is the numerator. The fraction becomes 6/10, which reduces to 3/5. Choice c would be correct if the question was .06, because the 6 is now in the hundredths place.
16.
c  We need to figure out the ending balance for each person. Anna found 3 dimes, or a total of 30 cents, and after adding that to her $1.24, her ending balance was $1.54. Timmy’s dad gave him $1.25, so adding this to his $2.42 makes his final balance 3.67. Sara spent $9.24 from the $12.40, so subtract to get $3.16. Therefore, Timmy has the most money at the end of the day.
17.
c  Percent of students that are male = 100% − 45% = 55% Now, convert 55% to a fraction. 55 11 = 55% = 100 20
18.
c  Subtract 1 1

2 5
=
2 5
52 5
=
Now, convert 3 5
19.
=
3 × 20 5 × 20
=
from
1
to obtain the fraction of the members which are not published writers:
3 5 3
5 60
100
to a percent by converting its denominator to 100: = 60%
b  Since 25% of A is 48, we can find the value of A by multiplying 48 by the reciprocal of
So,
A=
100 25
25 100
.
( 48 ) = 192
Multiply 192 by TOP
1
2 to get the answer. 3 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
98
2 (192 ) = 128 3 20.
c  Set up the numerical expression first, and then simplify: Total purchase = 3(12.54) + 2(29.98) = 37.62 + 59.96 = $97.58
21.
b  Divide each annual salary by 12 to obtain the monthly salary. Then subtract the monthly salaries.
48,560.45 48,321.55 48,560.45  48,321.55 = 12 12 12 = 19.91 So, the difference between the monthly salaries is $19.91. 22.
b  To compare different numbers, the bigger number has the biggest digit in the biggest place. Looking at choice a, 25 is bigger than 5 since 25 has a 2 in the tens digit, and 5 does not have a tens place, so that would be 0. Looking at choice b, the two numbers have the same value in both the tens and ones digit, so we have to look at the tenths place. 12.124 has a 1 in the tenths place, while 12.214 has a 2 in the tenths place. Therefore, choice b is correct.
23.
c  To order rational numbers in increasing order, list the numbers starting with the smallest moving to largest. Imagine where each of the numbers belong on the timeline to help. The furthest number on the left of the number line is the smallest number. That would be 3. Then moving right, we have .3, .3, 3. Therefore, choice c is correct. Choice d is in decreasing order.
24.
b  To order rational numbers in decreasing order, list the numbers starting with the largest moving to smallest. Imagine where each of the numbers belong on the timeline to help. The furthest number on the right of the number line is the largest number. That would be .198. Then moving left, we have .203, .23, .41. Therefore, choice b is correct. Choice a is in increasing order.
25.
b  Since ½ is bigger or greater than 1/3, we know that choice b is correct.
26.
c  Since Lily uses 8 mL each day, we need to figure out how many days will she use 120 mL. To do that, we need to divide 120 / 8. That will give us 15 days, so choice c.
27.
b  To figure out her account balance, she needs to subtract the purchases (debits) from the balance, and add the deposits (credits). She started with $129.23 and spent $12.87, so subtraction is necessary. $129.23  $12.87 = $116.36. Next we have to subtract the 2.79. $116.36 – $2.79 = 113.57. Then she deposited $25, so now we add. $113.57 + 25 = $138.57. Finally, we subtract the $28.35 for gas. $138.57 – $28.35 = $110.22. Choice a is the net balance without taking in consideration the starting balance. Choice c is if you add all of the transactions up, without taking into consideration debits and credits.
28.
b  First, subtract the tax. $107.00 is 107% of the sale price, so divide $107 by 1.07 (107% as a decimal) which is $100. That is the sale price, but we are looking for the original price. Since it was on sale for 25% off, the $100 is 75% of the original price. Translating words to symbols, that becomes 100 = .75 * x. Solve for x by dividing each side by .75.
TOP
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99
29.
100/.75 = x x = 133.33
30.
b  To solve, set up a proportion and solve for the variable. 𝑥𝑥 2 = 28 7 Take the cross products. 7x = 2 * 28 which reduces to 7x = 56. Solving for x, we divide each side by 7 to show that x is 8.
31.
d  To solve, set up a proportion and solve for the variable. 𝑥𝑥 1 = 1,500 30,000 Take the cross products. 1,500x = 1 * 30,000 which reduces to 1,500x = 30,000. Solving for x, we divide each side by 1,500 to show that x is 20.
32.
c  To solve, set up a proportion and solve for the variable. Since the newspaper said that 15% of high school students are in band, only look at the number of students in the high school. Do not account for any of the other students. 𝑥𝑥 15 = 1,680 100 Take the cross products. 100x = 15 * 1,680 which reduces to 10x = 25,200. Solving for x, we divide each side by 100 to show that x is 252. Answer D is incorrect because it is 15% of all three schools added together.
33.
b  To solve, set up a proportion and solve for the variable. Make sure to convert the 2 weeks into 14 days before solving the proportion. 𝑥𝑥 3 = 14 4 Take the cross products. 4x = 3 * 14 which reduces to 4x = 42. Solving for x, we divide each side by 4 to show that x is 10.5.
34.
a  To solve, set up a proportion and solve for the variable. 𝑥𝑥 1 = 425 25 Take the cross products. 25x = 1 * 425 which reduces to 25x = 425. Solving for x, we divide each side by 25 to show that x is 17.
35.
a  There are 18 apples and 6 oranges. The other fruits are there as distractors. Thus, the ratio is 18:6. Just like fractions, ratios can be reduced in the same way. The greatest common factor between 18 and 6 is 6 so divide both sides by 6. The resulting ratio is 3:1.
36.
c  24% is equal to
24 100
. To find (m + 2n) multiply 48 by the reciprocal of
100 (48) = 200 (m + 2n) = 24
24 100
.
Now, find 25% of 200. TOP
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100
25 200(25%) = 200 = 50 100 37.
d  Simply find 12% of 3400. 12 (12% )(3400 ) = (3400 ) = 408 100 So, he spends $408 per month.
38.
d  Find the increase in the price first. Increase in the price = $9,400 − $4,200 = $5,200 This means that for $4200, the increase was $5200. Set up the ratio of these values and then create a 100 in the denominator: 100 52 5200 52 42 123.81 = = = = 123.81% 4200 42 100 100 42 42 So, the percent of increase was 123.81%.
39.
a  Find the difference of the premiums first. $360 − $320 = $40 This means that for $360, the decrease was $40. Set up the ratio of these values and then create a 100 in the denominator: 100 40 1 9 11.11 = = = = 11.11% 360 9 100 100 9 9 So, the percent of decrease was 11.11%.
40.
a  28% is equivalent to the fraction 20 100
=
1 5
28 100
=
7 25
and 20% is equivalent to the fraction
. To find 20% of A, we must multiply 420 by the reciprocal of the fraction
20% of A =
7 25
.
25 = 1500 7
420
Now, to find A, we must multiply 1500 by the reciprocal of
1 5
.
5 1500 = 7500 1 A=
TOP
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41.
b  First find the 32% of 450 to get the discount amount: 32 ( 32% )( 450 ) = ( 450 ) = 144 100 Discount = Subtracting the discount amount from the original price gives the marked down price. Sale Price = $450 − $144 = $306
42.
d  First find the amount of the discount. $264 − $198 = $66 An unknown percent of 264 gives 66. To find the percent, we must divide 66 by 264, and then convert the result to a percent. 66 1 Discount rate = = = 0.25 264 4 We know that 0.25 is equal to 25%.
43.
d  First find 29% of 2900. 29 2900 = 841 A = 100 On the other hand, to find B, we must divide 29 by 290, and then multiply the result by 100. 29 (100 ) = 10 B = 290 Therefore, A + B = 841 + 10 = 851
44.
a  First calculate the marked down price on the first day:
15 = 45.6 100
Discount on first day = 304
Marked down price on first day = $304 − $45.6 = $258.4 12 Discount on the second day = 258.4 = 31.01 100 Marked down price on the second day = $258.4 − $31.01 = $227.39 45.
b  First set the numerical expression in terms of both purchases, and then calculate: 3(12.82) + 5(8.21) = $79.51
46.
c  First find
TOP
2 the sum of 23 and 32: 3 2 2 ( 23 + 32=) ( 55=) 36.67 3 3 Now add 36.67 to 2.3 time 3.2: 36.67 + 2.3(3.2) = 44.03
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47.
b  Find the price of each can using the different packprices: $6.24 ÷ 12 = $0.52 $3.92 ÷ 6 = $0.65 Subtract these prices. $0.65 − $0.52 =$0.13
48.
d  Simply divide the weight of the flour by the weight of the cake: 2 3 11 23 11 5 3 ÷ 4 = ÷ = × = 0.80 3 5 3 5 3 23
49.
a  First simplify A and B. 1 1 1 5 7 35 + 3 = = A = 2 3 2 6 2 12 1 1 1 1 7 7  3 = = B = 2 3 2 6 2 12 35 7 35 7 42 1 + = =3 2 Now add 12 and 12 : 12 12 12
50.
c  Add 2
51.
d  Simplify each numerical expression. 2 1 11 9 44 + 27 11 3 +2 = + = =5 4 3 4 12 12 K= 3 13 6 16 5 47 5 1 +1 = + = =7 4 3 2 6 6 L= 3
2 and 4 , and simplify the result: 3 3 2 2 8 14 22 1 2 +4 = + = =7 3 3 3 3 3 3 Bottles
8
2
+2
10
=
8
+
9
=
43
=7
1
4 3 2 6 6 M= 3 1 1 16 7 32 + 21 53 5 + = = =8 5 +3 = 2 3 2 6 6 6 N= 3
The mixed number 8 52.
TOP
5 has the greatest whole number part. 6
c  Set up the numerical expression and simplify. 26 × 5 + 14 × 7  35 193 18 5 26 14 = =5 3 1 2 35 35 35 A + 2B − 3C = 7 + 2 1 − 3 = 7 + 5 − 1 = 5 3
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53.
d  Calculate each sum given in the answer choices and then compare the results: 2 1 14 + 3 17 = = 0.81 2008 and 2009 : + = 3 7 21 21 1 1 5 + 7 12 2009 and 2010 : + = = = 0.34 7 5 35 35 1 1 1 +1 2 = = 0.40 2010 and 2011 : + = 5 5 5 5 2 1 10 + 3 13 = = 0.87 2008 and 2011 : + = 3 5 15 15 Obviously, the fraction (d) which is the highest number.
54.
c  Calculate each sum. A= 26 + 28 + 30 + 32 = 116 B = 25 + 27 + 29 + 31= 112 C = 24 + 26 + 28 + 30 + 32 + 34 = 174 D = 23 + 25 + 27 + 29 + 31 + 33 = 168
55.
a  Subtract the income and spending for each month to find the amount of saving: January: $3420 − $2970 = $450 February $2927 − $2212 = $715 March $3189 − $3020 = $169 April $3024 − $2730 = $294 Comparing the values of the savings shows that she had the highest savings in January and February.
56.
b  Find the total cost of each group of items by setting numerical expressions as follows: 9(6) + 4(3) = 54 + 12 = $66 7(6) + 5(3) = 42 + 15 = $57 6(6) + 11(3) = 36 + 33 = $69 4(6) + 15(3) = 24 + 45 = $69 Since $57 is less than $65, then the correct answer is (b).
57.
b  Combine the given relations in terms of c. a = 2b Replace b = 2c in (1). a = 2(2c) = 4c Also, we are given b = 2c Now, replace (2)(3) in the choice (b), and simplify. a + b + 2c 4c + 2c + 2c 8c = = = c 8 8 8 So, (b) results in a whole number. You can check the other choices similarly. But you will not obtain a whole number.
TOP
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58.
c  Write the ratios as given in the problem. a 2 = b 3 c 2 = b 15 Divide these proportions side by side. a 2 b= 3 2 c b 15 ab 2 × 15 = bc 2 × 3 a 15 = = 5 c 3
59.
b  First notice that if BC were not designated as a width, then we will have two different answers. So, such specification leads us to a unique answer. Set the proportional relationship among the dimensions of the rectangles. AB BC = KL LM Now, replace the given values and find the missing length. 12 9 1 = = KL 18 2 KL = 24 in.
60.
d  Crossmultiply the given proportion first. ad = bc Now cross divide by ab: ad bc = ab ab d c = b a
61.
c  Find the rate of change for each case, and then compare: 108 − 98 10 Rate of change in height of Michelle = = = 2 14 − 9 5 92 − 74 18 = = 4.5 Rate of change in height of Sarah = 11 − 7 4 82 − 56 26 = = 6.5 Rate of change in height of Joanne = 10 − 6 4 108 − 52 56 = = 6.22 Rate of change in height of Alison = 14 − 5 9 So, Joanne had the highest rate of change
TOP
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62.
c  Set the rate of change as follows: 540 − 420 120 = = 12 Rate of change = 2011 − 2001 10
63.
b  Replace the given values in the expression and simplify. xyz(x + y + z) = (3.24)(2.23)(3.42)(3.24+2.23+ 3.42) = (24.710184)(8.89) = 219.67
64.
b  Set up the numerical expression and simplify: (65)(0.002) + (34)(0.0025) + (54)(0.003)= 0.13 + 0.085 + 0.162 = 0.377 in.
65.
d  Replace the given values in mnp
m+ n . np
m+ n 3.2 + 2.2 = (3.2)(2.2)(2.1) 2.2  2.1 np 5.4 = (14.784) 0.1 mnp
= 798.336 ≈ 798.3
66.
a  Replace the given values in (A + 0.25)(B + 0.35)(C + 0.45), and simplify. (A + 0.25)(B + 0.35)(C + 0.45) = (0.035 + 0.25)(0.0053 + 0.35)(0.55 + 0.45) = (0.285)(0.3553)(1) = 0.1012605 ≈ 0.10
67.
d  Add the side lengths of ABC to twice the same lengths to find the sum of the perimeters. 2.34 + 4.034 + 5.0034 + 2(2.34) + 2(4.034) + 2(5.0034) = 11.3774 + 4.68 + 8.068 + 10.0068 = 34.1322 ≈ 34 in. 8 13 10 15
9415 − 4786 4629
68.
d
69.
c  Because the digit 9 in the subtrahend is greater than the corresponding digit in the minuend. 2 12 13 14 16
33456 − 2965 7 70. TOP
a
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8 13 15 18
9468 − 75 6 9 1899
71.
b
72.
a  Given π = 3.141592…., then 2π = 6.283184. Rounding this number to tenthousandth gives 2π = 6.2832
b  Replace the 4digit value of π and d = 3 in the formula and then round up. 3.1415 C 3 ( 3.1415 ) + = (3) 3 = 3 ( 3.1415 ) + 3.1415 73.
= 12.566 ft 2
74.
d  Here is the list of Arabic equivalents for the Roman numerals used in the problem: M = 1000 X = 10 II = 2 Then, replace their Arabic equivalents in MMXII: MMXII = 1000 + 1000 + 10 + 2 = 2012
75.
a  Replace the following equivalents in the expressions: X = 10 I=1 IV = 4 XXXI + XXIV = (10 + 10 + 10 + 1) + (10 + 10 + 4) = 31 + 24 = 55
76.
d  Replace the following equivalents in the numeral: M = 1000 CM = (1000 − 100) XL = (50 − 10) IX = (10 − 1) MCMXLIX = 1000 + (1000 − 100) + (50 − 10) + (10 − 1) = 1949
77.
b  Use the following equivalents: L = 50 X = 10 70 + 80 + 90 = (50 + 10 + 10) + (50 + 10 + 10 + 10) + (50 + 10 + 10 + 10 + 10) = (L + X + X) + (L + X + X + X) + (L + X + X + X + X) = LXX + LXXX + LXXXX
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78.
b  First find 12% of 3225. 12 (3225)(12%) = (3225) 100 = 387 Tax = Subtract the tax amount from his earning. 3225 − 387 = 2838
79.
a  First find 24% of 4225. 24 Installment = (4225)(24%) = (4225) = 1014 100 Subtract the installment amount from his earning. 4225 − 1014 = 3211
80.
d  First find take home amount of each person, and then compare. 14 Deduction = (3402)(14%) = (3402) = 476.28 100 Takehome amount = 3402 − 476.28 = $2925.72 15 (b) Deduction = (3150)(15%) = (3150) = $472.5 100 Takehome amount = 3150 − 472.5 = $2677.5 17 (c) Deduction = (3655)(17%) = (3655) = $621.35 100 Takehome amount = 3655 − 621.35 = $30333.65 24 (d) Deduction = (4455)(24%) = (4455) = 1069.20 100 Takehome amount = 4455 − 1069.20 = $3385.80
Among the outcomes, $3385.80 is the greatest. 81.
d  Find the amount of tax for 2010 and deduct from income. 14 Amount of tax for 2010 = 48200 = 6748 100 Amount of take home in 2011 = 48200 − 6748 = $41452 Find the amount of tax for 2011 and deduct from income. 16 Amount of tax for 2011 = 51800 = 8288 100 Amount of take home in 2011 = 51800 − 8288 = $43,512 Now find the average. (41452 + 43512) ÷ 2 = $42482
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82.
a  First find the original price of 12 bottles. Price of 12 bottles = 12(0.85) = $10.20 12 Amount of discount = 10.20 = 1.224 100 The prices after discount = 10.20 − 1.224 = $8.98
83.
a  The total price of items = 328 + 420 = 748 Find 12% of 748. 12 Amount of discount = 748 = 89.76 100 Price after discount = 748 − 89.76 = $658.24
84.
d  Find the sale price for each store. 11 Store A: Amount of discount = 580 = 63.80. Price after discount = 580 − 63.80 = 516.20 100 9 Store B: Amount of discount = 520 = 46.80. Price after discount = 520 − 46.80 = 473.20 100 7 Store C: Amount of discount = 490 = 34.30. Price after discount = 490 − 34.30 = 455.70 100 5 Store D: Amount of discount = 450 = 22.50. Price after discount = 450− 22.50 = 427.50 100 Store D offers the lowest price.
85.
c  Multiply the number of each item by its price, and then add them up. Don’t forget to convert cents to dollar. 0.24m + 0.18n + 1.24p + 3.92q
86.
c  Add the transactions, and then subtract the result from the balance at 8:00 AM. Account balance at 9:00 PM = 4323 − (320 + 22 + 124) = 4323 − 466 = 3857
87.
b  Add six times 230 to the original account balance. Balance after six months = 3197 + 6(230) = 4577
88.
d  Add all the transactions, and subtract the result from the account balance. Balance after withdrawals = 4531 − (437 + 291 + 29 + 37) = 3737
89.
c  Deduct the sum of the transactions from the account balance. Account balance after withdrawals = 2024 − (212 + 102 + 210) = 1500
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90.
c  Deduct the sum of the withdrawals from the account balance. Account balance at the end of the month = 3739 − (171 + 47 + 321 + 117) = 3083
91.
b  In the given expression, 4 must be distributed over the parentheses. Therefore, 3 + 4(9 − 3) + 11 = 3 + 4 × 9 − 4 × 3 + 11 The correct answer is b.
92.
b  Three times a quantity is 3x. Adding this quantity to 12 gives (3x + 12). Dividing this expression by 12 gives (3x + 12) ÷ 12.
93.
c  First simplify inside the brackets. −4[3 − 4(8 + 1) ÷ 3 − 3] + 12 = −4[3 − 36 ÷ 3 − 3] + 12 = −4(3 − 12 − 3] + 12 = −4(−12) + 12 = 48 + 12 = 60
94.
a  Denote degrees Celsius by C and degrees Fahrenheit by F. Then, multiplying C by 9 gives 9C. 9 9 Dividing 9C by 5 gives C . Adding 32 to this amount gives C + 32. 5 5 b  First simplify inside the parentheses. 4(29 − 19) ÷ 5 − 4 × 13 = 4(10) ÷ 5 − 4 × 13 = 40 ÷ 5 − 52 = 8 − 52 = −44
95.
d  First determine how many gallons of gas will she use. 1232 ÷ 28 = 44 gallons Cost of gas = 44 × 3.25 = 143
96.
a  Total spending = 12(4.25) + 4(12.50) + 42(0.32) = 51 + 50 + 13.44 = 114.44
97.
b  Divide the price of each package by the number of guests to find the price for each guest. Restaurant A: 705 ÷ 15 = $47 Restaurant B: 736 ÷ 16 = $46 Restaurant C: 1020 ÷ 20 = $51 Restaurant D: 1250 ÷ 25 = $50 The lowest price is offered by the Restaurant B.
98.
d  Find the prices of each item, and then add them up Total purchase = 3(1.23) + 2(1.25) + 3(3.45) + 2(3.25) = 3.69 + 2.50 + 10.35 + 6.50 = 23.04 TOP Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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99.
c  Multiply the number of guests (34), by the price of each meal (21), and by the number of days. Total cost of meals = 34 × 21 × 3 = 2142
100. d  First multiply the denominator and numerator of each fraction by a certain number such that all the fractions share the same denominator, and then compare their numerators: 5 4 14 1 6 5 15 3
1 ×10 3×10 10 30
5×5 6×5
4 ×6 5×6
14 × 2 15 × 2
25 30
24 30
28 30
These fractions can be listed in an ascending order as follows:
10 24 25 28 30 , 30 , 30 , 30 1 4 5 14 Their corresponding fractions are 3 , 5 , 6 , 15 . 101. c  Find the ratio of each company in decimal forms. Company A: Company B: Company C:
70 = 0.33 210 30 = 0.21 140 80 = 0.40 200 60 = 0.32 190
Company D: Therefore, Company C is the answer, since 0.40 is greater than all the other numbers. 102. d  First multiply the denominator and numerator of each fraction to make their denominators the same.
7 8 7×6 8×6 42 48
9 16 9×3 16 × 3 27 48
11 12 11 × 4 12 × 4 44 48
23 24 23 × 2 24 × 2 46 48
Arranging these fractions based on their numerators we get fractions to these fractions are TOP
23 11 7 9 . , , , 24 12 8 16
46 44 42 27 , , , . The corresponding 48 48 48 48
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103. d  Find the ratio for each novel:
42 = 0.32 Rachael: 130 24 = 0.18 Raymond: 132 38 = 0.30 Russ: 126 56 = 0.39 Regina: 144
Regina has the greatest number.
104. c  Multiply the denominator and numerator of each fraction by a certain number to make all the denominators the same: 17 7 1 11 12 32 6 24 7×8 1 × 16 17 × 3 11 × 4 32 × 3 6 × 16 12 × 8 24 × 4
51 96
56 96
The two greatest fractions are
44 96
16 96
7 17 56 51 and . Their corresponding fractions are and . 96 96 12 32
105. a  Convert the fractions to decimal numbers:
3 11 = 11 + 0.60 = 11.60 5 89 = 9.89 9
Here are the numbers from the smallest to the greatest: 9.80, 11.60, 12.025, 12.25 Replace the equivalents of the decimals 9.80 and 11.60.
89 3 11 9 , 5 , 12.025, 12.25 106. d  Here is the ascending list along with each month workhours: April: 194.45 hours, May: 194.54 hours, January: 197.34 hours, February: 199.04 hours, March: 212.34 hours, June: 221.43 hours So, eliminating the numbers we get, April, May, January, February, March, June 107. b  321
56 = 321 + 0.84 = 321.836 67
The numbers in order are 321.243, 321.432, 321.836, 322.245, 322.254. The middle number is 321.836. TOP
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The equivalent of this number is 321
56 . 67
108. b  First convert the fraction to a decimal:
230 = 13.53 . The largest number and the smallest 17
number are 23.01 and 13.53. Then 23.01 − 13.53 = 9.48 109. b  First convert the fraction to a decimal.
7 = 0.78 . Comparing the numbers shows that 2 is the 9
greatest. So, School B has the highest ratio.
110. d 
224 56 × 4 56 = = 100 25 × 4 25
2= .24
325 = 100 26 0= .26 = 100
3= .25
111. b 
25 × 13 = 25 × 4 2 × 13 = 50 × 2
13 4 13 50
415 5 × 83 83 = = 100 5 × 20 20
4= .15
465 = 100 425 4= .25 = 100 4= .65
5 × 93 = 5 × 20 17 × 25 = 25 × 4
93 20 17 4
7 12 × 23 + 7 283 = 23 = 12 12 112. a  12 5 24 × 8 + 5 197 24 = = 8 8 8
84 49 35 = 49 14 = 21 35 = 63
113. a = 
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7 × 12 12 = 7×7 7 7×5 5 = 7×7 7 2×7 2 = 3×7 3 7×5 5 = 7×9 9
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32 = 100 114. c 45 0= .45 = 100 55 0= .55 = 100 75 0= .75 = 100 0= .32
8 25 9 20 11 20 3 4
115. b  The digit 9 represents the 100,000 place value. 116. c  We can read the number in two parts and then combine them: 238857 = 238000 + 857 = two hundred thirtyeight thousand, eight hundred fiftyseven 117. d  We can partition the number in three parts, and then combine their names. 45,600,006 = 45,000,000 + 600,000 + 006 = fortyfive million, six hundred thousand, six 118. d  The distance 440,560 is rounded to 400,000 which is equal to 4.0 × 105. So, the order of magnitude is 5. 119. b  Using the Distribution Property we have 24 × 8.23 + 24 × 4.23 = 24(8.23 + 4.23) = 24(12.46) 120. b  3(12 − 1) + 4(13 + 2) = 3 × 12 − 3 × 1 + 4 × 13 + 4 × 2 (Distribution Property) = 3 × 12 + 4 × 13 + 4 × 2 − 3 × 1 (Commutative Property) = 3 × 12 + 4 × 13 + 4 × 2 − 3 121. d  The multiplication must be performed first. 122. c  21 ÷ (11 + 9) = 21 ÷ 20 = 1.05 (11 + 9) ÷ 21 = 20 ÷ 21 = 0.95 Hence, the right sides of the equations are not the same. 123. b  Horse A has 2 more lengths than the Horse B Horse B has 3 more lengths than Horse C. Therefore, the horse C lost the race by 2 + 3 = 5 lengths. 124. c  The total of the rows is (24 + 11). Multiplying the total rows by the number of seats in each row gives the total seats.
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1 4
125. a  4[12 + 3(1 + 5)] ÷ 4 = 4(12 + 3 × 6) ÷
17 = 4(30) ÷ 4 120 4 × = 1 17 480 = 17 4 28 = 17
17 4
126. c  Multiply the number of tons by the number of pounds in each ton:
3 11 2 × 2000 = × 2000 4 4 11 × 2000 4 = = 5500 pounds
1 1 25 25 3 ÷ 6 ÷ = 127. d  4 8 4 8
25 8 × = 4 25
=2
128. a  Replace the given values in the formula: 1 1 1 a (b + c += d) ( 3 ) 4 + 3 + 6 3 3 4 13 4 + + 6 4 = 129. a  First convert all the expression inside the brackets to one number, multiply by 12, and then divide by the mixed number. 130. d  If a = the shortest side, then Perimeter = a + 2a + 4a + 8a + 16a + 32a= 63a 131. a  Convert the mixed number to a decimal, divide the two decimal numbers 132. a  12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = 12[32 − 12(1) + 12] + 12 ÷ 4 = 12(32 − 12 + 12) + 3 = 12(32) + 3 = 387 TOP
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3 133. c  Find 4 of 4 3 12 × = = 5 4 20
4 5 3 5
1 3 57 11 12 19 57 +4 ÷ = + ÷ 11 4 4 10 11 4 4
(1.1 ) 1
134. b 11 × 12 19 4 = + × 10 × 11 4 57
6 1 + 5 3 23 = 15
=
1 7 2 1 6 2 + 3 1+ 1 + 3 =2 + 3 1 + + 3 5 3+ 1 5 10 3 3 135. a 11 7 = 2 + 3 + 5 10 2 33 7 = + + 1 5 10 20 + 66 + 7 = 10 93 = 10 = 9.3 136. c  Using the Pythagorean Theorem, if a side of the square is 1200, then a diagonal has the following measurement: d2 = (1200)2 + (1200)2 = 1440000 + 1440000 = 2880000 d = 1697 ft. 137. d  In a right triangle, the product of the two legs is the same as the product of the hypotenuse and the altitude. Let’s have the altitude = x. Then, 13 × x = 12 × 5. This gives
60 x = 13 = 4.62 138. a  Replace x = 8 in the function. y = 3(8) − 2 = 24 − 2 = 22. So, the value of y on the fourth row must be changed to 22. TOP
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Checking the other values in a similar way shows that they fit the function. 139. a  Round off 41.33% to 41%. 140. d  Area is found by simply adding the areas of all the segments of the shape. 141. a  To convert a decimal to a percent, simply multiply by 100. 142. d  She must find the ratio of two numbers. So, the division operation is needed. 143. b  We must find the ratio of 4589 to 2000. So, the type of the operation is division. 144. c  To estimate the result simply multiply 2300 × 3209 = 7,380,700. Round down in this case to get the best estimate. 145. c  Since one is above the sea level, and the other is below the sea level, to find their difference, we must consider the elevation of the Rocky Valley a negative number. Subtract the elevations: 14494 − (−347) = 14494 + 347
= 14841 ≈ 15000
146. a  The easiest and simplest way to estimate the result is round the fraction before the division:
45008 45000 30 ≈ = 1505 1500 147. b  Multiply 11 by 39 to find the distance after 39 seconds. 11 × 39 = 429 ft. ≈ 400 ft. 148. b  The denominator and numerator of the fraction can be rounded off as follows:
330000 ≈ 300 1100 149. c  Round 9 to 10 and 43 to 40. 9 × 43 ≈ 10 × 40 = 400 in. 150. b  Rounding 1000.01 to the nearest unit, we get 1000. So, the expression 1000 × 100 gives the best estimate. 151. a  Convert all the coins to dollars, and round off. 40(0.25) + 10(0.10) + 20(0.05) + 770(0.01) = 10 + 1 + 1 + 7.7 = 19.7 ≈ 20
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12 7 = 152. c  48 28
Cross multiply the proportion. 12 × 28 = 7 × 48 336 = 336 Both sides are the same. Repeating this procedure in a similar way with the other ratios does not yield a true equation.
153. d  Cross multiply the proportion
22 18 = . 77 63
22 × 63 = 18 × 77 1386 = 1386 So, the proportion in d is true. Checking the other proportions in a similar way does not lead to true equations. 154. a  Set up the proportion and solve for x.
798 38 = x 3
38x = 3 × 798 38x = 2394 x = 63 155. d  Denote the unknown number inside the box by x. Then Solve the proportion. 28x = 11 × 35 28x = 385 x = 13.75
11 x = . 28 35
156. c  Find 22% of 1050. 22 ( 22% )(1050 ) = (1050 ) 100 2 × 11 × 21 × 50 = 100 = 231 157. a  Since all the negative numbers are less than zero, q is a consequence of p. Therefore, if p, then q. 158. b  Mika and Ronald like each other; that is, p and q occur at the same time. Hence p ∧ q . ∧ means “logical and”; ∨ means “logical or”; → means “logical implication”. 159. d  p ∨ q means that either p or q occurs, but both do not occur at the same time. ∧ means “logical and”; ∨ means “logical or”; → means “logical implication”. TOP
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160. c  Since on Sundays, all the schools are closed, c is a conditional statement. 161. d  Having the sum of two angles equal to 90º is a necessary condition for any right triangle. Denote the acute angles by a and b. Then a + b = 90º or a = 90º − b 162. d  Since all the members are published author, then John as one of these members must be a published author. 163. c  The set S contains even integers that are both even and divisible by 3. The item “a” is an even integer that may or may not be divisible by 3. So, c is a true statement. 164. a  We do not know whether all the History students are attending Algebra and/or Geometry classes. So, a is a true statement. 165. d  The given numbers can be described using the following expressions 2 = 1(1 + 1) 6 = 2(2 + 1) 12 = 3(3 + 1) 20 = 4(4 + 1) Comparing the patterns of these expressions to n(n + 1) shows that d is true. 166. d  Both n = 2 and n = 4 disprove the generalization. n=2 1+2=3 Replacing 2 in the formula yields 2²  2 = 2 n=4 1 + 2 + 3 + 4 = 10 Replacing 4 in the formula yields 42 − 4 = 12 167. a  The numbers of bricks starting from the bottom step up to the eighth step are as follows: 18, 16, 14, 12, 10, 8, 6, 4 = 88 This is an arithmetic progression. Use the formula S = bricks.
n ( a1 + an ) to find the total number of 2
8 (18 + 4 ) S= 2 = 88 168. b  Subtract 11 from each side and add x to each side. 3x + 11 −11 + x = 31 − x − 11 + x 4x = 20 x=5 169. c  Denote the age of Sarah by x. Then x + 34 = 47 Subtract 34 from each side, and simplify. TOP
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x + 34 − 34 = 47 − 34 x = 13
1027 13 = 1 170. a  x 13x = 1027 x = 79
171. d  Add 11 to each side, and simplify. 5x − 11 + 11 = 39 + 11 5x = 50 x = 10 172. a  Add the given polynomials. (x2 + x + 1) + (3x − 2) + (3x2 + x) = 4x2 + 5x − 1 173. d  (4x3 + 2x2 + x) − (3x2 + 1) = 4x3 + 2x2 + x − 3x2 − 1 = 4x3 − x2 + x − 1 174. c  Multiply the dimensions, and simplify. Area = (x + 2)(x + 3) = x2 + 2x + 3x + 2 × 3 = x2 + 5x + 6 175. c  (x2 + x) + (8x3 + 2x2 − x − 1) = x2 + x + 8x3 + 2x2 − x − 1 = 8x3 + 3x2 − 1 176. c  Three times x is 3x. x is 2 more than 3x. So, x = 2 + 3x 177. a  Three times a number is 3x. The sum of 3x and 3 is (3x + 3). 5 times the number is 5x. Adding these two expressions we get (3x + 3) + 5x = 8x + 3 178. b  The measurement of the right angle is 90º. The sum of an acute angle and 90º is greater than 123º. Therefore, x + 90 > 123 179. b  The triple of a number is 3x. 11 more than 3x is 3x + 11. 180. c  The given equation can be written in the following forms: (a) x + 12 = 25 or (b) x + 12 = −25 Solution to (a) x + 12 = 25 x + 12 − 12 = 25 − 12 x = 13 Solution to (b) x + 12 = −25 x + 12 − 12 = −25 − 12 TOP
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x = −37 When a number or an algebraic expression is between the two lines , then we consider them without their algebraic signs. 181. d  C + 85 ≤ 56 can be rewritten in the following forms. (a) C + 85 ≤ 56 and (b) C + 85 ≥ −56 Solution to (a) C + 85 ≤ 56 C + 85 − 85 ≤ 56 − 85 C ≤ −29 Solution to (b) C + 85 ≥ −56 C + 85 − 85 ≥ −56 − 85 C ≥ −141 Answer: −141 ≤ C ≤ −29 182. b  x + 5 > 16 can be rewritten in the following forms. (a) x + 5 > 16 and (b) x + 5 < −16 Solution to (a) x + 5 > 16 x + 5 − 5 > 16 − 5 x > 11 Solution to (b) x + 5 < −16 x + 5 − 5 < − 16 − 5 x < −21 Answer: x > 11 or x < −21 183. d  The given inequality can be written in the following forms: (a) p − 7 ≤ 2 (b) p − 7 ≥ − 2 Solution to (a) p − 7≤ 2 p − 7+ 7 ≤ 2 + 7 p≤9 Solution to (b) p − 7+ 7 ≥ − 2 + 7 p≥5
Solution set: 9 ≥ p ≥ 5 184. b  Add x to both sides and subtract 11 from each side, and simplify. 3x + 11 + x − 11 = 51 − x + x − 11 4x = 40 x = 10
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185. d  Let x = length of a width. Then the measure of a length is 2x + 12. x + (x + 12) = 44 2x + 12 = 44 2x + 12 − 12 = 44 − 12 2x = 32 x = 16 ft. 186. a  Add 19 to both sides and subtract 3x from each side, and simplify. 5x − 19 + 19 − 3x > 3x + 33 + 19 − 3x 2x > 52 x > 26 187. b  Denote the radius of the circle by r and the area of the circle before a change by A. Then A = πr2 Doubling the radius, changes its length to 2r. Denote the area of the circle after change by S. Then S = π ( 2r ) = 4 πr 2 S is as four times as A. So, the area increased four times. 2
188. a  Subtract x(22 − 19) from (3x)(22 − 19). (3x)(22 −19) − x(22 − 19) = 3x(3) − x(3) = 9x − 3x = 6x 189. c  Replace x by (x + 9) and subtract the given expression from the new expression. 12(x + 9 + 3) + 9 − [12(x + 3) + 9] = 12(x + 12) + 9 − (12x + 36 − 9) = 12x + 144 + 9 − 12x − 27 = 126 190. d  Denote the area of the pool before expansion by A and after expansion by P. Then subtract these areas. A = 442 = 1936 ft2 P = 482 = 2304 2304 − 1936 = 368 ft2 191. d  Replace x by x − 9 and subtract the result from the given expression. 3(x + 9) − 12 − [3(x − 9 + 9) − 12] = 3x + 27 − 12 − 3x + 12 = 27 192. d − Multiplying all the terms by 100, converts the decimals to whole numbers. This way, the calculations become simpler and easier. 193. d  The mixed number must be converted to an improper fraction in order to perform cross multiplication. 194. c  Multiplying all the terms by the least common denominator, 36, converts all the fractions to whole numbers. 195. b  1. Cross multiply. 2. Reduce the first ratio. TOP
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196. c  Adding 3(3 + x) to both sides, cancelled out it from the left side and doubled it on the right side. Then the sides of the equation are exchanged. 197. a  Cross multiplying the proportion yields x = 70. 198. c  The perimeter is a + a + b + b, (a + a) + (b + b), (2a + 2b), or 2(a + b). 199. d  We can revise the side lengths to relate them to the first triangle as follows: a = 1(3) b = 1(4) c = 1(5) a = 2(3) b = 2(4) c = 2(5) a = 3(3) b = 3(4) c = 3(5) a = 4(3) b = 4(4) c = 4(5) So, a = n(3), b = n(4), and c = n(5), where n is a positive integer. 200. b  Each number is doubled, then added 1 to generate the following number. 201. d  The pattern of the scores reveals that in each exam he jumped from one range to a following range. So, his next score will be in the range of 90100. 202. c  To generate the numbers in the series, a multiple of 5 is added to each term beginning with 5. 203. c  Starting from 2, the even numbers are subtracted. 204. a  This is a direct variation. Increase in n implies an increase in P. 205. a  Since A is constant, then by doubling “a” we must divide “b” by 2. 206. b  This is an inverse variation. Increase in x implies a decrease in R. 207. c  Since V, product of T and P, is a constant, then if P increases then T must be decreased, and vice versa. 208. a  The graph is a straight line and the correct answer is the straight line equation (y = mx + b). Y is the distance along the Y axis. X is the distance along the X axis. B is where the line passes the Y axis. The m is the slope or gradient, or how steep the line is. 209. d  The graph is curved and has two points of intersection with xaxis. Therefore, the quadratic function (d) represents this graph. 210. c  Path of a projectile has only one maximum point. Hence, (c) is the answer. 211. a  The measure of the right angle is 90º. Denote the unknown angle by x. The difference between 90 and x is 32. Therefore, we obtain the equation 90 − x =32. 212. d  Nine times a number is 9x. Adding 9x to 32 yields (9x + 32). Subtracting this expression from 193 gives 193 −(9x + 32) = 161 − 9x. TOP
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213. b  Denote the first number by x. Then the second number is (x + 2). Sum of these numbers is 650. Therefore, x + x + 2 = 650 2x + 2 = 650 2(x + 1) = 650 So, 2(x + 1) = 650 can be used to solve this problem. 214. c  Denote the score of the third exam by x. Then (x + 89 + 83) ÷ 3 = 90 or x + 172 = 270. This is the equation we can use to find x. 215. a  Out of the given solutions of x, only x = 1 fits the equation. So, if (x − 1)(x + 3), then x = 1. 216. a  Both x = − 9 and x = 5 are the solutions to the equations, but they do not fit the equation at the same time. Therefore, r or q is true. 217. a  X cannot be both – 3 and – 23 at the same time in this equation. It can only be one or the other to get 0. Using “and” logically means that they are valid at the same time. The term “and” in logic has different meaning from the ordinary language. 218. d  Since all the members of the Hemingway Club are published author, then Olivia as a member of this club must be a published author. 219. c  Replace n = 15 in the general formula and simplify: 15 (15 + 1 ) 15 × 16 = = 120 S= 2 2 220. d  If we carry out the equation, we find that x – 1 = 0. 3(x − 1) = 4(x − 1) 3x − 3 = 4x − 4 4x − 3x = 4 − 3 x = 1 or x − 1 = 0
We can divide both sides of an equation by a number distinctive from zero. x − 1 = 0 does not allow us to divide both sides by 0. We can only divide by any nonzero number. 221. d  If we continue the same pattern, we obtain 37 × 18 = 666 37 × 21 = 777 37 × 24 = 888. 222. a  Following the same pattern we obtain (12346 × 9) + 7 = 1111111 (1234567 × 9) + 8 = 11111111 (12345678 × 9) + 9 = 111111111 223. b  Comparing each data point to all the tables shows that the data in (b) fits the graph. TOP
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224. d  Checking data from each table one by one with the given set of data indicates that table (d) matches the data set. 225. c  Comparing the table to each pie chart indicates that chart (c) represents the data. 226. d  Comparing the data in the table to each graph indicates the line graph (d) represents the table. 227. c  Number of students attending Literature class only = 19 Number of students attending Literature and Algebra classes only = 9 Number of students attending Literature and History classes only = 11 Number of students attending Literature and the other classes = 4 Adding these numbers gives the total number of students attending Literature class. 19 + 9 + 11 + 4 = 43 228. a  The highest measure is about 9.4 and the lowest is about 5.2. Range = 9.4 −5.2 = 4.2 229. c  There are 17 data points in the graph. Therefore, the ninth data point is the median. Counting from either end we reach the number 55. 230. b  Comparing the numbers on the right column shows that 230,000 is the highest. 231. b  Comparing the numbers on the right column shows that 110,000 is the lowest. 232. b  Replacing the values of b for x gives the corresponding values of P given in the table. 233. d  Replacing the values of q for x gives the corresponding values of T given in the table. 234. a  Replacing the values of m for x in R gives the corresponding values of R given in the table. 235. c  Adding the numbers in the table we get 100%. Adding the areas of the regions in the circle we get 100% of the area of the circle. 236. d  The areas of the states Alabama, Maryland and Minnesota are shown below the horizontal line 100,000. 237. a  The tops of the columns representing these states are above the horizontal line 100,000 238. c  Among the History scores 67 is the lowest. 239. d  Range of scores of History = 98 −67 = 31 Range of scores of Science = 94 − 68 = 26 Difference of ranges = 31 − 26 = 5 240. b  Among the Science scores, 68 is the lowest. 241. c  Student D scored 94 in Science and 67 in History. TOP Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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242. d  The mean of scores of Science = (86 + 76 + 68 + 94 + 92 + 73) ÷ 6 = 81.5 The mean of scores of History = (71 + 98 + 86 + 67 + 81 + 92) ÷ 6 = 82.5 Difference = 82.5 − 81.5 = 1 243. b  Number of patients pulled out in First week = 11 + 32 + 14 + 30 = 87 Number of patients pulled out in Second week = 32 + 44 + 21 + 39 = 136 Number of patients pulled out in Third week = 20 + 9 + 21 + 11 = 61 Number of patients pulled out in Fourth week = 19 + 33 + 29 + 12 = 93 The highest number is 136. 244. b  Number of patients pulled out from Group A = 11 + 32 + 20 + 19 = 82 Number of patients pulled out from Group B = 32 + 44 + 9 + 33 = 118 Number of patients pulled out from Group C = 14 + 21 + 21 + 29 = 85 Number of patients pulled out from Group D = 30 + 39 + 11 + 12 = 92 The highest number is 118. 245. a  Number of patients pulled out from Group A = 11 + 32 + 20 + 19 = 82 Number of patients pulled out from Group B = 32 + 44 + 9 + 33 = 118 Number of patients pulled out from Group C = 14 + 21 + 21 + 29 = 85 Number of patients pulled out from Group D = 30 + 39 + 11 + 12 = 92 The lowest number is 82. 246. c  Number of patients pulled out in First week = 11 + 32 + 14 + 30 = 87 Number of patients pulled out in Second week = 32 + 44 + 21 + 39 = 136 Number of patients pulled out in Third week = 20 + 9 + 21 + 11 = 61 Number of patients pulled out in Fourth week = 19 + 33 + 29 + 12 = 93 The lowest number is 61. 247. b  Average of patients pulled out from Group A = (11 + 32 + 20 + 19) ÷ 4 = 21.5 Average of patients pulled out from Group B = (32 + 44 + 9 + 33) ÷ 4 = 29.5 Average of patients pulled out from Group C = (14 + 21 + 21 + 29) ÷ 4 = 21.25 Average of patients pulled out from Group D = (30 + 39 + 11 + 12) ÷ 4 = 23 248. c  Arrange the data in ascending order: 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7 The middle number is 5. 249. a  Denote the first integer by x. Then the following integers are (x + 1) and (x + 2). Using the definition of average, we conclude [x + (x + 1) + (x + 2)] ÷ 3 = 16. Solve this equation. 3x + 3 = 48 3x + 3 − 3 = 48 − 3 3x = 45 x = 15 250. a  The longest and the shortest heights are 174 and 145. Difference of these heights is 174 − 145 = 29. TOP
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251. a  Average score = (86 + 72 + 78 + 88) ÷ 4 = 324 ÷ 4 = 81 252. b  Arrange the numbers in the following form: 11, 11, 11 15, 15, 15, 15 17, 17 19, 20, 20 This arrangement shows that 15 is repeated more than the other numbers. 253. b  It means that the chance of choosing one of the three numbers 1, 3, 5 out of the six numbers 1, 2, 3, 4, 5, and 6 is 1 out of 3. 254. b  Multiply the denominator and the numerator of the fraction
4 × 6 24 = 7 × 6 42 .
4 by 6. 7
This means that there are 24 red marbles among the total of 42 marbles in the box. 255. a  Multiply the denominator and the numerator of the fraction by 2.
9 × 2 18 = . This means that 18 students out of 32 students are female. Then 16 × 2 32
Number of male students = 32 − 18 = 14
256. d  Multiply the denominator and the numerator of the fraction
12 by 4. 31
12 12 × 4 48 = = . This means that 48 cards out of 124 cards are marked with odd integers. 31 31 × 4 124 So, 124 − 48 = 76 cards are marked with even integers.
257. d  The numbers between 53 and 75 are 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74. The count of these numbers is 21. Among these numbers only 55, 60, 65, and 70 are divisible by 5. The count of these numbers is 4. So, the chance is
4 . 21
258. a  The number of students do not attend Algebra class is 50 − 20 = 30.
30 3 = Therefore, the chance is 50 5 . 259. a  As a person’s height increases, the shoe size also increases. That is the definition of a positive correlation. 260. b  The more a person exercises, the lower is his or her weight typically. That is the definition of a negative correlation. TOP
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261. a  The more Juan studies, the better the grade he received. That is the definition of a positive correlation. The independent variable is what can be controlled, and Juan could control the amount of time studied, not his grade. If the parameters were inversely related, that would mean as one increases, the other decreases at a fixed rate, but that did not happen in this case. 262. c  The height of people does not have anything to do with their hair length. That is completely their opinion so there is no correlation between the two. 263. c  The relationship between the two variables is that if you square the side length of the square, you obtain the area. The relationship is always positive because as the side length increases, so does the area. The relationship is not linear because the area increases at a much quicker rate than the side length. 264. a  1000 milligrams equals 1 gram. Milligrams and grams are units of weight in the metric system. 265. d  1 cm equals 10 millimeters. Therefore, 160 cm will equal 1600 mm (160 x 10). Centimeters and millimeters are units of distance in the metric system. 266. b  1 gram equals .001 kilograms. 109 x .001 = .109. Grams and kilograms are units of weight in the metric system. 267. d  I liter equals 1000 milliliters. 4 x 1000 = 4000 milliliters. Liters and milliliters are units of volume in the metric system. 268. b  1 milliliter equals 1/1000 liter. 75 ÷ 1000 = .075 liters. Liters and milliliters are units of volume in the metric system. 269. a  To convert kilograms to pounds, multiply the number of kilograms by 2.2. 80 x 2.2 = 176 lbs. A kilogram is a unit of weight in the metric system. 270. c  To determine how many pounds the kitten gains, first we need to figure out how many weeks go by between the starting date and the final date. 8 – 4 = 4 weeks. If the kitten gains 0.05 lbs. per week, we now need to multiply .05 by 4 which gives us 0.2 lbs. total. Then we need to add it to the starting weight, 0.8 lbs. 0.8 + 0.2 = 1.0 lbs. 271. d  First we need to figure out what the perimeters could possibly be. There are 14 pieces of fencing, so the fence could be 1 piece by 6 pieces (2[1] + 2[6] = 14). There could also be 2 pieces by 5 pieces, and 3 pieces by 4 pieces. To convert to feet, multiply the number of pieces by 5 since each piece is 5’. Therefore, by finding the area of each of the possible perimeters, we get (1 x 6)  5 x 30 = 150, (2 x 5)  10 x 25 = 250, and (3 x 4)  15 x 20 = 300. All of the options are correct. 272. c  To find the unit rate, first write the rate and then reduce the denominator to be a value of 1. 1.5 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 6 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 4 ℎ𝑟𝑟 TOP
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273. d  The greatest rate of change is equivalent to greatest slope. Looking at the options, choice d is the steepest slope. Therefore, choice d has the greatest rate of change. 274. c  To convert Fahrenheit to Celsius, first subtract 32 and then multiply by 5/9. 54 – 32 = 22 22 x 5/9 = 110/9 110/9 = 12.22 275. a  To convert Celsius to Fahrenheit, first multiply by 9/5 and then add 32. 32 x 9/5 = 288/5 288/5 = 57.6 57.6 + 32 = 89.6 276. d  To convert pounds to kilograms, divide the number of pounds by 2.2. 132 / 2.2 = 60 kg. A kilogram is a unit of weight in the metric system. 277. c  To answer this question, we must first convert 6’4” to inches. 6 x 12 inches = 72 inches 72 inches + 4 inches = 76 inches To find centimeters, use the following formula: inches multiplied by 2.54. 76 inches x 2.54 = 193.04 278. d  Each pound is equal to 16 ounces. Therefore, 3 pounds + 12 ounces = 3 × 16 + 12 = 48 + 12 = 60 ounces 279. b  One kilogram = 1000 grams Weight of M = 9 × 1000 + 112 = 9112 grams Weight of N = 1200 grams Weight of M and N = 9112 + 1200 = 10312 grams 280. a  One yard = 36 inches 1 foot = 12 inches 5 yards + 5 feet + 22 inches = 5 × 36 + 5 × 12 + 22 = 262 inches 281. b  The estimated relationship between mile and kilometer is 1 mile = 1.6 kilometers. Therefore, the estimated equivalent of 24,500 kilometers is calculated as follows: 24,500 ÷ 1.6 = 15,312.5 miles 282. d  To find the unit rate, first write the rate and then reduce the denominator to be a value of 1. We want our final answer to be 32 miles per 1 hour. Checking each of the choices, we see that all of them have the unit rate of 32 miles per hour. 32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 128 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 4 ℎ𝑟𝑟
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32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 64 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 2 ℎ𝑟𝑟
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32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 256 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 8 ℎ𝑟𝑟
283. d  First, multiply the number of hours Tim drives by the number of days (6 days x 9 hours per day) to find that each week, Tim drives for 54 hours. To find his average speed, find the unit rate. 3600 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 54 ℎ𝑟𝑟
= 67 mph.
284. d  We know 1 m = 100 cm. M = 12 m + 119 cm = 12 × 100 + 119 = 1319 cm N = 1.2 m = 1.2 × 100 = 120 cm Difference = 1319 − 120 = 1199 cm 285. c  1 kilogram = 1000 grams Weight of the mixture = 606 grams + 1443 grams = 2049 grams 2049 g = (2049 ÷ 1000) kg = 2.049 kg ≈ 2 kg 286. a  1 cm = 10 mm Total length of diameters = 4.34 + 3.39 = 7.73 cm Total length of diameters = 7.73 × 10 = 77.3 mm 287. a  1 cm = 10 mm Distance = 24 × 10 = 240 mm Distance between each two lines = 240 ÷ 16 = 15 mm 288. c  Denote the real distance by x. Then solve the following proportion.
3 60 = 1.2 x
3x = 60(1.2) 3x = 72 x = 24 miles 289. d  Multiply each dimension by the scale factor. 4.2 × 5 = 21 8.4 × 5 = 42 290. b  Denote the dimensions after scaling by x and y. Then solve the following proportions:
1 5 = x 85
5x = 85 x = 17 in. 1 5 = y 50 5y = 50 y = 10 in. TOP
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291. b  1 yard = 3 feet 1 foot = 12 inches 1 yard = 3 × 12 = 36 inches 292. c  One liter is equivalent to 1000 cubic centimeters. 293. d  1 gallon = 4 quarts 1 quart = 2 pints 1 gallon = 2 × 4 = 8 pints 294. c  1 gallon = 4 quarts. 2 gallons + 8 quarts = 2 × 4 + 8 = 16 quarts 295. a  1 decameter = 1000 centimeters 1 decimeter = 10 centimeters 2 dm + 34 dc = 2 × 1000 + 34 × 10 = 2000 + 340 = 2340 cm 296. a  1 yard = 36 inches 1 foot = 12 inches 5 yards + 4 feet = 5 × 36 + 4 × 12 = 180 + 48 = 228 in. 297. a  Since the preservative is a small portion of the total weight of the product, the preservative must be measured in grams. 298. d  Multiplying the weight of each notebook by the number of notebooks gives 6 × 112 = 672 ounces. Dividing this number by 16 gives the exact weight 42 pounds. 299. c  Total weight of the load = 124 × 24 × 340 = 1011840 g = 1011.840 kg = 1.002 tons 300. b  Answering this question is a twostep process. First, you must convert 2 grams to milligrams (mg). There are 1000 mg in a gram, so 2 x 1000 = 2000 mg. Then you plug 2000 mg into the following equation: 2000 mg = 500 mg x cc 5 cc 500x = 10000 x = 20 cc Since there are 10 cc in each vial, the patient will need 2 vials. 301. d  To find the volume of a rectangular solid can be calculated as follows; volume = length x width x thickness. In this case, 4.5 x 3.5 x 2 = 31.5 cm³ 302. a  Area = (2 ft.)(240 in) = (2 × 12 in.)(240 in.) = (24 in.)(240 in.) = 5760 in.2 TOP
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303. d  Replace the given measures in the equation below: AE = AB + BC + CD + DE = (2 ft.) + (25 in.) + (3 ft.) + (35 in.) = (2 × 12 in.) + (25 in.) + (3 × 12 in.) + (35 in.) = 24 in. + 25 in. + 36 in. + 35 in. = 120 in. 304. c  100 square decimeter = 1 square meter Total Area = (232 m2) + (420000 dc2) = (232 m2) + (42000 ÷ 100 m2) = 232 m2 + 420 m2 = 652 m2 305. d  Replace F = 77 with F =
9 C + 32 77 = 5 9 77 − 32 = C + 32 − 32 5 9 C 45 = 5
9 C + 32 , and solve for C. 5
C = 25
306. c  To find the area of the shaded region, find the area of the entire rectangle and the subtract the area of the triangle in the corner. The area of the rectangle is found by multiplying 9 cm and 11 cm to get 99 cm2. The area of the triangle uses the formula (b * h) / 2. The base is 2 cm since 9 cm – 7 cm = 2 cm. The height is 2 cm since 11 cm – 9 cm = 2 cm. The area is (2 * 2)/2 = 2 cm2. 99 cm2 – 2 cm2 = 97 cm2. Answer A is the area of the rectangle without subtracting the triangle. 307. a  Since the instructions say “regular” figure, we know that all of the sides are 4 inches. There are 16 sides, so either multiply 4 by 16 or use repeated addition to add 4 together 16 times. Either way, we get 64 inches. The other choices are if the number of sides are counted incorrectly. 308. b  To find the area for the partial circle, find the area of the whole circle (π*r2) and then multiply by ¾ since that is ¾ of the circle. π *42 = 16 π which is the area of the whole circle. 16 π * ¾ = 12 π. 309. a  To find the area of the composite figure, break it into a trapezoid and a circle and subtract the area of the circle from the trapezoid. The 5 represents the height of the trapezoid as well as the diameter of the circle. For the circle, find the area by using the formula π*r2. 3.14*2.52 = 19.625. For the trapezoid, use the formula ½ * h * (b 1 + b 2 ). ½ * 5 * (16 + 22) = 95. Then subtract: 95 – 19.625 = 75.375. While that is not a choice, Answer A is correct if the answer is rounded to the nearest hundredth. 310. c  To find the perimeter, add all of the sides together. Make sure to line up the decimals when adding. 6.29 + 14.2 + 8.73 + 6 = 35.22. TOP
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311. c  To find the area of the composite figure, break it into a trapezoid and a half circle. The 6 represents the height of the trapezoid as well as the diameter. For the half circle, find the area of the whole circle (π*r2) and then divide by 2. 3.14*32 = 28.26. For the trapezoid, use the formula ½ * h * (b1 + b2). ½ * 6 * (6 + 12) = 54. Then add the areas together: 28.26 + 54 = 82.26. Answer A only takes into account the trapezoid, and Answer B multiplies the 3 numbers on the figure together. 312. b  In order to figure out how many pieces of wood Tom needs to buy, find the perimeter first. 2(18) + 2(24) = 36 + 48 = 84 ft. Then subtract the 5’ gate to have 79 feet. Since each piece is 5 inches wide, with one inch in between, we need to figure out how many times does 6 inches go into 79 feet. 6 inches goes into 1 foot twice, so 6 inches goes into 79 feet 158 times. 313. d  To find the perimeter, add all of the sides together. Since it is a rectangle, there are two sides that are 4 cm and two sides that are 8 cm. The only option that matches that is D. 314. d  To find a length of the arc, multiply the circumference by the fraction of the circle that the arc covers (angle/360). Find the circumference by the following formula: C = π * d. Plugging in the value for the diameter, we get the circumference to be 8π. To find an arc, multiply the fraction of the circle represented by the circumference. Since the arc is being made by the 90° angle, the fraction of the circle is ¼ because that is 90/360. The length of the arc is ¼ * 8π = 2π. 315. c In order to find the area of the shaded region, first we find the area of the large circle and then subtract the area of the small circle. To find the area of a circle, use the formula Area = π * r 2. For the big circle, the diameter is given, so it needs to be divided in half to get the radius. π * 62 = 36π, but that is the entire circle. The area of the small circle is π * 42 = 16π. Subtracting 16 π from 36π, our final answer is 20π in 2. 316. d  Triangle ARS is a right isosceles triangle. Therefore, AS = AR. Apply the Pythagorean Theorem. (RS)2 = (RA)2 + (AS)2 (12)2 = (RA)2 + (RA)2 144 = 2(RA)2 72 = (RA)2 RA = 8.48 cm 317. a  Since ∠A is the vertex angle, then ∠B and ∠C are sideangles and are equal. ∠B = ∠C and m∠A = 40º Replace these equations in m∠A + m∠B + m∠C =180º. 40º + m∠C + m∠C = 180º 2(m∠C) = 140º m∠C = 70º 318. d  m∠A = 34 m∠A + m∠B =180 34 + m∠B = 180 m∠B = 180 − 34 = 146 BD is the angle bisector of the angle B. So, it divides 146º into two equal parts. TOP
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m∠DBC = 146 ÷ 2 = 73º 319. c  Apply BC = 14, AB = AC, and the Pythagorean Theorem. (BC)2 = (AB)2 + (AC)2 142 = (AB)2 + (AB)2 196 = 2(AB)2 98 = (AB)2 Area = (AB)(AC) ÷ 2 = (AB)(AB) ÷ 2 = (AB)2 ÷ 2 = 98 ÷ 2 = 49 in.2 320. d − Since the points are translated vertically only; therefore, their ycoordinates will be changed only. A(3, 5) will be changed to A’(3, 5 +3) = A’(3, 8) and B(7, 8) will be changed to B’(3, 8 + 3) = B’(3, 11) 321. a − In any equilateral triangle, all the altitudes are equal. 322. d  The sum of the angles must equal 180º. 33 + 80 + 67 = 180 323. a  Only in (a), the sum of two sides is greater than the third side. For example: 12 + 18 > 22
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Questions with Answers An additional practice exam format to make it easier for you to reference answers. TEAS Practice Exam – Math  Section 1 Numbers and Operations 1.
1/4 + 2/8 = a. b. c. d.
3/12 3/4 5/4 1/2 d  To add or subtract fractions, you need a common denominator. 2/8 reduces to 1/4 1/4 + 1/4 = 2/4 2/4 can be reduced to 1/2.
2.
4 x 3/7 = a. b. c. d.
1 3/7 1 5/7 12/28 c  To multiply an integer and a fraction, you do not need a common denominator. The numerator of the fraction is multiplied by the integer and the denominator is multiplied by one and stays the same. 4/1 x 3/7 = 12/7 = 1 5/7
3.
5/6 x 3/4 = a. b. c. d.
5/8 8/10 15/10 None of the above. a  To multiply a fraction by another fraction, multiply numerators and denominators: 5/6 x 3/4 = 15/24 = 5/8
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4.
348 ÷ 6 = a. b. c. d.
48 58 68 74 b  The quotient of 348 divided by 6 is 58. If you multiply 6 by 58, you get 348 as the product.
5.
8–3x4+9= a. b. c. d.
5 5 65  65 a  By the order of operations, you first carry out multiplication before addition or subtraction. 8 – 12 + 9 = x 4 + 9 = x X=5
6.
18 – 23 + 99 ÷ 3 = a. b. c. d.
28 285 105 37.3 a  By the order of operations, you first carry out division before addition or subtraction. 18 – 23 + 33 = x x = 51 – 23 x = 28
7.
– 33 – 5 x 1 = a. b. c. d.
39 38  38 1 c  By the order of operations, you first carry out multiplication before addition or subtraction. A number multiplied by 1 will be itself. Therefore:
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33 – 5 = x X =  38 8. 2/3 ÷ 4/5 = a. b. c. d.
3/5 5/6 6/8 None of the above. b  To divide a fraction by another fraction, invert the terms of the divisor and then multiply: 2/3 x 5/4 = 10/12 = 5/6
9.
36 ÷ .4 = a. b. c. d.
9 40 90 144 c  An easy way to figure this problem out is to convert the decimal by multiplying by 10, such that .4 becomes 4 and 36 become 360. The division of 360 by 4 may be easier for one to understand.
10. .08 + 7 x 9 = a. b. c. d.
63.08 62.73 63.72 62.37
a  By the order of operations, you first carry out multiplication before addition or subtraction. 7 x 9 equals 63 and adding .08 equals 63.08. 11.
Which of the following is equivalent to 425%? a. b. c. d.
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.425 4.25 42.5 425 b  To convert from a percent to a decimal, divide the percentage number by 100. 425 ÷ 100 = 4.25. D is wrong because that just drops the percent sign, but that is not the right way to convert between percents and decimals. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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12.
Terry has a basket full of various fruits. There are 12 pieces of fruit, and of those, two are bananas. What fraction of fruits is bananas? Express in simplest form. a. b. c. d.
1/6 2/12 1/4 1/3 a  Fractions are part over whole. The part is the two bananas and the whole is the 12 pieces of fruit. The fraction would be 2/12, but the question specifically states the fraction needs to be in simplest form, so b is not correct. 2/12 can be reduced by a factor of 2 because 2 is the greatest common factor between 2 and 12. The fraction reduces to 1/6.
13.
What decimal is equivalent to ¾? a. b. c. d.
.34 3.4 .75 1.25 c  To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). 3 ÷ 4 = .75. Choice a happens often because the 3 and the 4 are combined to make a decimal, while choice d occurs when 4 is divided by 3.
14.
Which of the following is equivalent to ½? a. b. c. d.
50% .5 3/6 All of the above d  To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). 1 ÷ 2 = .5. To convert a decimal to a percent, multiply the decimal by 100, and place the percent sign at the end. .5 * 100 = 50%. Choice c is also correct because if 3/6 is reduced, the simplest form is ½, so the final answer is d, all of the above.
15.
Which of the following is equivalent to .6? a. b. c. d.
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b  To convert a decimal to a fraction, look at the place value of the smallest digit. .6 is read as 6 tenths, and the 6 is in the tenths place. The 10 becomes the denominator, and the 6 is the numerator. The fraction becomes 6/10, which reduces to 3/5. Choice c would be correct if the question was .06, because the 6 is now in the hundredths place. 16.
Three friends have some money in their pockets. Anna has $1.24, Sara has $12.40, and Timmy has $2.42. Later in the day, Anna found 3 dimes on the ground and Timmy’s dad gave him a dollar bill and a quarter. Sara paid for ice cream for the 3 of them and spent $9.24. Who has the most money at the end of the day? a. b. c. d.
Anna Sara Timmy Cannot be determined c  We need to figure out the ending balance for each person. Anna found 3 dimes, or a total of 30 cents, and after adding that to her $1.24, her ending balance was $1.54. Timmy’s dad gave him $1.25, so adding this to his $2.42 makes his final balance 3.67. Sara spent $9.24 from the $12.40, so subtract to get $3.16. Therefore, Timmy has the most money at the end of the day.
17.
In Science Hill High School, 45% of students are female. What fraction of the students is male?
a. b. c. d.
11 25 13 20 11 20 9 20 c  Percent of students that are male = 100% − 45% = 55% Now, convert 55% to a fraction. 55 11 = 100 20 55% =
18.
Two fifths of the members of a Literature Club are published writers. What percent of the members are not published writers? a. b. c. d.
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c  Subtract
2 5
from
1 1
to obtain the fraction of the members which are not published
writers: 1 2 52 3  = = 1 5 5 5 3 Now, convert to a percent by converting its denominator to 100: 5 3 3 × 20 60 = = = 60% 5 5 × 20 100
19.
If 25% of A is equal to 48, then what is a. b. c. d.
124 128 142 122
2 3
of A?
b  Since 25% of A is 48, we can find the value of A by multiplying 48 by the reciprocal of 25 . 100 100 A= ( 48 ) = 192 25 So, 2 Multiply 192 by to get the answer. 3 2 (192 ) = 128 3 20.
Barbara purchased three shirts each for $12.54, and two pairs of shoes each for $29.98. How much did she pay in total for these items? a. b. c. d.
$78.97 $87.79 $97.58 $99.85 c  Set up the numerical expression first, and then simplify: Total purchase = 3(12.54) + 2(29.98) = 37.62 + 59.96 = $97.58
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21.
John’s annual salary in the year 2010 was $48,560.45 and in the year 2011 was $48,321.55. What is the difference between his monthly salary in years 20102011, to the nearest hundredth? a. b. c. d.
$19.19 $19.91 $91.19 $29.91 b  Divide each annual salary by 12 to obtain the monthly salary. Then subtract the monthly salaries.
48,560.45 48,321.55 48,560.45  48,321.55 = 12 12 12 = 19.91 So, the difference between the monthly salaries is $19.91. 22.
Which of the following is a correct statement? a. b. c. d.
5.26 > 25.6 12.124 < 12.214
b  To compare different numbers, the bigger number has the biggest digit in the biggest place. Looking at choice a, 25 is bigger than 5 since 25 has a 2 in the tens digit, and 5 does not have a tens place, so that would be 0. Looking at choice b, the two numbers have the same value in both the tens and ones digit, so we have to look at the tenths place. 12.124 has a 1 in the tenths place, while 12.214 has a 2 in the tenths place. Therefore, choice b is correct. 23.
Select the correct ordering of the numbers in increasing order. a. b. c. d.
3, 3, .3, .3 .3, 3, 3, .3 3, .3, .3, 3 3, .3, .3, 3 c  To order rational numbers in increasing order, list the numbers starting with the smallest moving to largest. Imagine where each of the numbers belong on the timeline to help. The furthest number on the left of the number line is the smallest number. That would be 3. Then moving right, we have .3, .3, 3. Therefore, choice c is correct. Choice d is in decreasing order.
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24.
Select the correct ordering of the numbers in decreasing order. a. b. c. d.
.41, .23, .203, .198 .198, .203, .23, .41 .198, .203, .41, .23 .203, .198, .23, .41 b  To order rational numbers in decreasing order, list the numbers starting with the largest moving to smallest. Imagine where each of the numbers belong on the timeline to help. The furthest number on the right of the number line is the largest number. That would be .198. Then moving left, we have .203, .23, .41. Therefore, choice b is correct. Choice a is in increasing order.
25.
Tommy and Dillon each ordered a pizza. Tommy ate onehalf of his pizza, and Dillon ate onethird of his pizza.
Tommy
Dillon
Which inequality represents who ate more pizza?
a. b. c. d. b  Since ½ is bigger or greater than 1/3, we know that choice b is correct.
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26.
Lily has to give her daughter 8 mL of cough syrup at 9:30 a.m. each morning. The doctor prescribed her a bottle of 120 mL. How many days will Lily be able to give her the cough syrup before needing a refill? a. b. c. d.
13 days 14 days 15 days 16 days c  Since Lily uses 8 mL each day, we need to figure out how many days will she use 120 mL. To do that, we need to divide 120 / 8. That will give us 15 days, so choice c.
27.
Tammy is trying to figure out her bank account balance by filling in her check register. On Monday, she spent $12.87 going out to lunch, and then another $2.79 for ice cream. On Wednesday, she deposited a check for $25 dollars. Finally, this morning, she filled up her gas tank for $28.35. If her bank account had $129.23 Sunday night, what is her account balance now? a. b. c. d.
$19.01 $110.22 $69.01 $19.01 b  To figure out her account balance, she needs to subtract the purchases (debits) from the balance, and add the deposits (credits). She started with $129.23 and spent $12.87, so subtraction is necessary. $129.23  $12.87 = $116.36. Next we have to subtract the 2.79. $116.36 – $2.79 = 113.57. Then she deposited $25, so now we add. $113.57 + 25 = $138.57. Finally, we subtract the $28.35 for gas. $138.57 – $28.35 = $110.22. Choice a is the net balance without taking in consideration the starting balance. Choice c is if you add all of the transactions up, without taking into consideration debits and credits.
28.
There is a big sale at the computer store. The computer that Tom has been wanting is on sale for 25% off. If he paid $107.00 after tax, what was the original price? Tax is 7%. a. b. c. d.
$142.67 $133.33 $100.00 $400.00 b  First, subtract the tax. $107.00 is 107% of the sale price, so divide $107 by 1.07 (107% as a decimal) which is $100. That is the sale price, but we are looking for the original price. Since it was on sale for 25% off, the $100 is 75% of the original price. Translating words to symbols, that becomes 100 = .75 * x. Solve for x by dividing each side by .75. 100/.75 = x x = 133.33
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29.
A softball player hits 2 out of every 7 times at bat. At this rate, how many times will she get a hit if she went up to bat 28 times? a. b. c. d.
2 8 .5714 28 b  To solve, set up a proportion and solve for the variable. 𝑥𝑥 2 = 28 7
Take the cross products. 7x = 2 * 28 which reduces to 7x = 56. Solving for x, we divide each side by 7 to show that x is 8. 30.
A light bulb factory produces 1 defective light bulb for every 1,500 light bulbs. In one week, the factory produces 30,000 light bulbs. How many are expected to be defective? a. b. c. d.
0 2 10 20 d  To solve, set up a proportion and solve for the variable. 𝑥𝑥 1 = 30,000 1,500
Take the cross products. 1,500x = 1 * 30,000 which reduces to 1,500x = 30,000. Solving for x, we divide each side by 1,500 to show that x is 20.
31.
A newspaper reported that 15% of high school students are in band. A local school district has 1,825 students in the elementary, 1,230 in the middle school and1,680 students in the high school. How many students are expected to be in the band? a. b. c. d.
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15 students 250 students 252 students 643 students c  To solve, set up a proportion and solve for the variable. Since the newspaper said that 15% of high school students are in band, only look at the number of students in the high school. Do not account for any of the other students. 15 𝑥𝑥 = 100 1,680
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Take the cross products. 100x = 15 * 1,680 which reduces to 10x = 25,200. Solving for x, we divide each side by 100 to show that x is 252. Answer D is incorrect because it is 15% of all three schools added together. 32.
Micah runs 3 hours every 4 days. At that rate, how many hours will Micah run in 2 weeks? a. b. c. d.
12 10.5 1.5 9 b  To solve, set up a proportion and solve for the variable. Make sure to convert the 2 weeks into 14 days before solving the proportion. 3 𝑥𝑥 = 4 14 Take the cross products. 4x = 3 * 14 which reduces to 4x = 42. Solving for x, we divide each side by 4 to show that x is 10.5.
33.
Every patient that goes into surgery has a chance of complications. If 1 in every 25 patients has some form of complications, how many patients are expected to have complications if 425 patients go into surgery? a. b. c. d.
17 patients 25 patients 20 patients 15 patients a  To solve, set up a proportion and solve for the variable. 𝑥𝑥 1 = 425 25
Take the cross products. 25x = 1 * 425 which reduces to 25x = 425. Solving for x, we divide each side by 25 to show that x is 17. 34.
In a basket of fruits, there are 12 bananas, 7 peaches, 18 apples and 6 oranges. What is the ratio of apples to oranges? a. b. c. d.
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3:1 12:7 1:3 2:3
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a  There are 18 apples and 6 oranges. The other fruits are there as distractors. Thus, the ratio is 18:6. Just like fractions, ratios can be reduced in the same way. The greatest common factor between 18 and 6 is 6 so divide both sides by 6. The resulting ratio is 3:1. 35.
If 24% of the expression (m + 2n) is 48, then what is 25% of (m + 2n)? a. b. c. d.
40 48 50 56 c  24% is equal to
24 100
. To find (m + 2n) multiply 48 by the reciprocal of
100 (48) = 200 (m + 2n) = 24
24 100
.
Now, find 25% of 200. 25 200(25%) = 200 = 50 100 36.
John spends 12% of his salary on groceries each month. If his monthly salary is $3400, how much does he spend on groceries? a. b. c. d.
$448 $424 $412 $408 d  Simply find 12% of 3400. 12 (12% )(3400 ) = (3400 ) = 408 100 So, he spends $408 per month.
37.
In the Global Auction Market, an oak rocking chair valued at $4200, sold for $9400. What is the percent of increase in the value of the chair? a. b. c. d.
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103.81% 111.38% 113.18% 123.81% d  Find the increase in the price first. Increase in the price = $9,400 − $4,200 = $5,200 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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This means that for $4200, the increase was $5200. Set up the ratio of these values and then create a 100 in the denominator: 100 52 5200 52 42 123.81 = = = = 123.81% 4200 42 100 100 42 42 So, the percent of increase was 123.81%. 38.
A student paid an auto insurance premium of $360 for six months. Then the premium dropped to $320. Find the percent of decrease in the premium. a. b. c. d.
11.11% 12.21% 14.11% 21.11% a  Find the difference of the premiums first. $360 − $320 = $40 This means that for $360, the decrease was $40. Set up the ratio of these values and then create a 100 in the denominator: 100 40 1 9 11.11 = = = = 11.11% 360 9 100 100 9 9 So, the percent of decrease was 11.11%.
39.
If 28% of 20% of A is 420, what is A? a. b. c. d.
7500 7700 7850 8500 a  28% is equivalent to the fraction 20 100
=
1 5
28 100
=
7 25
and 20% is equivalent to the fraction
. To find 20% of A, we must multiply 420 by the reciprocal of the fraction
20% of A =
25
.
25 = 1500 7
420
Now, to find A, we must multiply 1500 by the reciprocal of
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7
1 5
.
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5 1500 = 7500 1 A= 40.
A washing machine is marked down 32% from its original price of $450. What is the sale price of the washing machine? a. b. c. d.
$360 $306 $300 $266 b  First find the 32% of 450 to get the discount amount: 32 ( 32% )( 450 ) = ( 450 ) = 144 100 Discount = Subtracting the discount amount from the original price gives the marked down price. Sale Price = $450 − $144 = $306
41.
A carpet is on sale for $198. The regular price of the carpet was $264. What is the markdown on the price of the carpet? a. b. c. d.
32% 29% 27% 25% d  First find the amount of the discount. $264 − $198 = $66 An unknown percent of 264 gives 66. To find the percent, we must divide 66 by 264, and then convert the result to a percent. 66 1 Discount rate = = = 0.25 264 4 We know that 0.25 is equal to 25%.
42.
A is 29% of 2900, and B% of 290 is 29. What is A + B? a. b. c. d.
812 831 841 851 d  First find 29% of 2900.
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29 2900 = 841 A = 100
On the other hand, to find B, we must divide 29 by 290, and then multiply the result by 100. 29 (100 ) = 10 B = 290 Therefore, A + B = 841 + 10 = 851
43.
On the first day of the month, the original price of a sofa, which was $304, was marked down 15%. The following day, the discounted price was marked down 12%. What is the marked down price on the second day? a. b. c. d.
$227.39 $244.43 $264.23 $268.43 a  First calculate the marked down price on the first day:
15 = 45.6 100
Discount on first day = 304
Marked down price on first day = $304 − $45.6 = $258.4 12 Discount on the second day = 258.4 = 31.01 100 Marked down price on the second day = $258.4 − $31.01 = $227.39 44.
John wanted to purchase 3 CD packages and 5 rolls of film. If the price of each CD package is $12.82 and the price of each roll of film is $8.21, how much does it cost to purchase these items? a. b. c. d.
$88.51 $79.51 $76.15 $67.51 b  First set the numerical expression in terms of both purchases, and then calculate: 3(12.82) + 5(8.21) = $79.51
45.
Add 2.3 times 3.2 to a. b. c. d.
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48.33 46.33 44.03 42.03
2 3
the sum of 23 and 32.
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2 the sum of 23 and 32: 3 2 2 ( 23 + 32=) ( 55=) 36.67 3 3 Now add 36.67 to 2.3 time 3.2: 36.67 + 2.3(3.2) = 44.03
c  First find
46.
A grocery store sells 12 cans of soda for $6.24 and 6 cans of soda for $3.92. How much less expensive per can is it if you buy 12 cans? a. b. c. d.
$0.23 $0.13 $0.11 $0.10 b  Find the price of each can using the different packprices: $6.24 ÷ 12 = $0.52 $3.92 ÷ 6 = $0.65 Subtract these prices. $0.65 − $0.52 =$0.13
47.
To make 4 cake? a. b. c. d.
3 5
cakes, 3
2 3
pounds of flour is needed. How much flour is needed to make one
0.08 pound 0.68 pound 0.78 pound 0.80 pound d  Simply divide the weight of the flour by the weight of the cake: 2 3 11 23 11 5 3 ÷ 4 = ÷ = × = 0.80 3 5 3 5 3 23
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48.
Given A and B below, what is the sum of A and B?
1 1 1 + 3 A = 2 3 2 1 1 1 − 3 B = 2 3 2 a. b. c. d.
1 2 1 3 12 1 7 2 1 12 2 3
a  First simplify A and B. 1 1 1 5 7 35 + 3 = = A = 2 3 2 6 2 12 1 1 1 1 7 7  3 = = B = 2 3 2 6 2 12 35 7 35 7 42 1 + = =3 12 12 12 12 12 2 and : Now add 49.
In the process of film development, photographers use a chemical called “stop bath.” A 2 2 photographer used 2 bottles of stop bath for the first group of rolls of film and 4 bottles of 3 3 stop bath for the second group of rolls of film. How much stop bath did he use for all of the rolls of film?
a. b. c. d.
2 3 1 9 2 1 7 3 1 6 4 9
c  Add 2 TOP
2
2 and 4 , and simplify the result: 3 3
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2 2 8 14 22 1 2 +4 = + = =7 3 3 3 3 3 3 Bottles
50.
The sum of which numerical expression has the greatest whole number part? 2 1 3 +2 4 K= 3 13 6 1 +1 4 L= 3 8 10 +2 4 M= 3 N= a. b. c. d.
5
1 3
+3
1 2
K L M N d  Simplify each numerical expression. 2 1 11 9 44 + 27 11 3 +2 = + = =5 4 3 4 12 12 K= 3 13 6 16 5 47 5 1 +1 = + = =7 4 3 2 6 6 L= 3 8
+2
10
=
8
+
9
=
43
=7
1
4 3 2 6 6 M= 3 1 1 16 7 32 + 21 53 5 + = = =8 5 +3 = 2 3 2 6 6 6 N= 3 5 The mixed number 8 has the greatest whole number part. 6
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51.
Given A, B, and C below, find A + 2B − 3C. 5 3 A= 7 2 1 B= 5 1 C= 3
a. b. c. d.
8 6 5 5
13 35 3 35 18 35 1 21
c  Set up the numerical expression and simplify. 26 14 5 26 × 5 + 14 × 7  35 193 18 3 = =5 2 1 35 35 35 A + 2B − 3C = 7 + 2 1 − 3 = 7 + 5 − 1 = 5 3 52.
A house built on ground sank every year according to the following list: 2 2008: 3 in. 1 2009: 7 in. 1 2010: 5 in. 1 2011: 5 in. In which of the following combination of years did the house sink the most? a. b. c. d.
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2008 and 2009 2009 and 2010 2010 and 2011 2008 and 2011
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d  Calculate each sum given in the answer choices and then compare the results: 2 1 14 + 3 17 = = 0.81 2008 and 2009 : + = 3 7 21 21 1 1 5 + 7 12 2009 and 2010 : + = = = 0.34 7 5 35 35 1 1 1 +1 2 = = 0.40 2010 and 2011 : + = 5 5 5 5 2 1 10 + 3 13 = = 0.87 2008 and 2011 : + = 3 5 15 15 Obviously, the fraction (d) which is the highest number. 53.
The sum of which list of numbers is greatest? A: Even whole numbers between 24 and 34 B: Odd whole numbers between 23 and 33 C: Even whole numbers from 24 to 34 D: Odd whole numbers from 23 to 33 a. b. c. d.
A B C D c  Calculate each sum. A= 26 + 28 + 30 + 32 = 116 B = 25 + 27 + 29 + 31= 112 C = 24 + 26 + 28 + 30 + 32 + 34 = 174 D = 23 + 25 + 27 + 29 + 31 + 33 = 168
54.
Michelle’s income and spending for the first four months of the year are given in the table below. In which two months was her savings the highest? Month January February March April a. b. c. d.
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Income $3420 $2927 $3189 $3024
Spending $2970 $2212 $3020 $2730
January and February February and March March and April January and March Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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a  Subtract the income and spending for each month to find the amount of saving: January: $3420 − $2970 = $450 February $2927 − $2212 = $715 March $3189 − $3020 = $169 April $3024 − $2730 = $294 Comparing the values of the savings shows that she had the highest savings in January and February. 55.
Casey went to a supermarket with $65 in his wallet. He wanted to purchase some sodas and potato chips. Here are the prices after taxes were added to the sale price: A case of Soda: $6.00 A bag of potato chips: $3.00 His money would be sufficient to purchase which of the following: a. b. c. d.
9 cases of soda, and 4 bags of potato chips 7 cases of soda, and 5 bags of potato chips 6 cases of soda, and 11 bags of potato chips 4 cases of soda, and 15 bags of potato chips b  Find the total cost of each group of items by setting numerical expressions as follows: 9(6) + 4(3) = 54 + 12 = $66 7(6) + 5(3) = 42 + 15 = $57 6(6) + 11(3) = 36 + 33 = $69 4(6) + 15(3) = 24 + 45 = $69 Since $57 is less than $65, then the correct answer is (b).
56.
A, b, c, and d are whole numbers such that a = 2b and b = 2c. Which expression is definitely a whole number?
a. b. c. d.
a+b+c 2 a + b + 2c 8 a + b + 2c 10 a + b + 2c 12 b  Combine the given relations in terms of c. a = 2b Replace b = 2c in (1). a = 2(2c) = 4c Also, we are given
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b = 2c Now, replace (2)(3) in the choice (b), and simplify. a + b + 2c 4c + 2c + 2c 8c = = = c 8 8 8 So, (b) results in a whole number. You can check the other choices similarly. But you will not obtain a whole number.
57.
The ratio of a to b is a. b. c. d.
14 3 14 5 5 3
2 3
and the ratio of c to b is
2 . What is the ratio of a to c? 15
c  Write the ratios as given in the problem. a 2 = b 3 c 2 = b 15 Divide these proportions side by side. a 2 b= 3 c 2 b 15 ab 2 × 15 = bc 2 × 3 a 15 = = 5 c 3 58.
The dimensions of the rectangle ABCD are proportional to the dimensions of the rectangle KLMN. Given the following measurements, find the length of the rectangle KLMN. AB = 12 in. and BC = 9 in. Width LM = 18 in. a. b. c. d.
32 in. 24 in. 20 in. 16 in. b  First notice that if BC were not designated as a width, then we will have two different answers. So, such specification leads us to a unique answer.
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Set the proportional relationship among the dimensions of the rectangles. AB BC = KL LM Now, replace the given values and find the missing length. 12 9 1 = = KL 18 2 KL = 24 in.
59.
Which statement is true given the proportion a. b. c. d.
a c = d b d b = a c c b = d c d c = b a
a c = ? b d
d  Crossmultiply the given proportion first. ad = bc Now cross divide by ab: ad bc = ab ab d c = b a 60.
Which of the following quantities has the highest rate of change? a. b. c. d.
Increase of the height of Michelle from 98 cm at the age of 9 to 108 cm at the age of 14 Increase of the height of Sarah from 74 cm at the age of 7 to 92 cm at the age of 11 Increase of the height of Joanne from 56 cm at the age of 6 to 82 cm at the age of 10 Increase of the height of Alison from 52 cm at the age of 5 to 108 cm at the age of 14 c  Find the rate of change for each case, and then compare: 108 − 98 10 Rate of change in height of Michelle = = = 2 14 − 9 5 92 − 74 18 = = 4.5 Rate of change in height of Sarah = 11 − 7 4 82 − 56 26 Rate of change in height of Joanne = = = 6.5 10 − 6 4 108 − 52 56 = = 6.22 Rate of change in height of Alison = 14 − 5 9 So, Joanne had the highest rate of change
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61.
The price of land in Jonesboro has been constantly increasing since the year 2001 at the same rate. The price of an acre in 2001 was $420 and, in 2011, it was $540. What is the rate of change per year? a. b. c. d.
$18.00 $17.00 $12.00 $11.00 c  Set the rate of change as follows: 540 − 420 120 Rate of change = = = 12 2011 − 2001 10
62.
Given x = 3.24, y = 2.23, and z = 3.42, what is the value of xyz(x + y + z) to the nearest tenth? a. b. c. d.
251.3 219.7 205.5 201.2 b  Replace the given values in the expression and simplify. xyz(x + y + z) = (3.24)(2.23)(3.42)(3.24+2.23+ 3.42) = (24.710184)(8.89) = 219.67
63.
The plastic bags are supplied with three types of thickness as follows: Light weight: 0.002 in. Regular weight: 0.0025 in. Heavy weight: 0.003 in. What is the thickness of the stack of 65 light weight, 34 regular weight, and 54 heavy weight bags rounded to the nearest thousandth inch? a. b. c. d.
0.272 in. 0.377 in. 0.389 in. 0.477 in. b  Set up the numerical expression and simplify: (65)(0.002) + (34)(0.0025) + (54)(0.003)= 0.13 + 0.085 + 0.162 = 0.377 in.
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64.
m+ n Given m = 3.2, n = 2.2, and p = 2.1, what is the value of mnp to the nearest tenth? np a. 798.5 b. 789.3 c. 798.5 d. 798.3 m+ n d  Replace the given values in mnp . np m+ n 3.2 + 2.2 = (3.2)(2.2)(2.1) 2.2  2.1 np 5.4 = (14.784) 0.1 = 798.336 mnp
≈ 798.3 65.
Given A = 0.035, B = 0.0053, and C = 0.55, round the result of the product (A + 0.25)(B + 0.35)(C + 0.45) to the nearest hundredth. a. b. c. d.
0.10 0.11 0.15 0.16 a  Replace the given values in (A + 0.25)(B + 0.35)(C + 0.45), and simplify. (A + 0.25)(B + 0.35)(C + 0.45) = (0.035 + 0.25)(0.0053 + 0.35)(0.55 + 0.45) = (0.285)(0.3553)(1) = 0.1012605 ≈ 0.10
66.
The sides of the triangle ABC are as follows: AB = 2.34 in. BC = 4.034 in. AC = 5.0034 in. Each side of the triangle MNP is twice the corresponding side of the triangle ABC. Round the sum of the perimeters of these triangles in inches. a. b. c. d.
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30 in. 31 in. 32 in. 34 in. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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d  Add the side lengths of ABC to twice the same lengths to find the sum of the perimeters. 2.34 + 4.034 + 5.0034 + 2(2.34) + 2(4.034) + 2(5.0034) = 11.3774 + 4.68 + 8.068 + 10.0068 = 34.1322 ≈ 34 in. 67.
Which of the following formats of subtraction is arranged properly using the regrouping method for 9415 − 4786? 8 13 11 15
a.
b.
c.
d.
9415 − 4786 8 12 10 15
9415 − 4786 8 13 10 5
9415 − 4786 8 13 10 15
9415 − 4786 8 13 10 15
9415 − 4786 d68.
4629
Which subtraction can be performed using the regrouping method? a. b. c. d.
43,0987 − 34,0765 20,007 − 10,003 34,087 − 32,986 54,983 − 44,572 c  Because the digit 9 in the subtrahend is greater than the corresponding digit in the minuend.
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69.
John owned a tract of land with an area of 33,456 ft2. He sold 29,657 ft2 of the land. How much land is left? a. b. c. d.
3799 ft2 3898 ft2 3978 ft2 3988 ft2 2 12 13 14 16
33456 − 2965 7 3799
a70.
The volume of gasoline in a tanker dropped from 9468 gallons to 7569 gallons after pumping gasoline to the reservoir of a gas station. How much gasoline did the tanker pump into the reservoir? a. b. c. d.
1879 gallons 1899 gallons 1989 gallons 1999 gallons 8 13 15 18
9468 − 75 6 9 b71.
1899
Convert 2π to a decimal number rounded to the nearest tenthousandth. a. b. c. d.
6.2832 6.3832 6.6821 6.8861 a  Given π = 3.141592…., then 2π = 6.283184. Rounding this number to tenthousandth gives 2π = 6.2832
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π The circumference of an irregular closed curve is determined using the formula C = 3π + d , 3 where d is the longest distance between two points on its circumference. If d = 3 feet, find the circumference of this closed curve, rounded to the thousandths.
72.
a. b. c.
d.
14.556 ft2 12.566 ft2 10.862 ft2 10.266 ft2
b  Replace the 4digit value of π and d = 3 in the formula and then round up. 3.1415 = C 3 ( 3.1415 ) + (3) 3 = 3 ( 3.1415 ) + 3.1415 = 12.566 ft 2
73.
What year is the Arabic numeral MMXII? a. b. c. d.
2008 2009 2011 2012 d  Here is the list of Arabic equivalents for the Roman numerals used in the problem: M = 1000 X = 10 II = 2 Then, replace their Arabic equivalents in MMXII: MMXII = 1000 + 1000 + 10 + 2 = 2012
74.
Which numeral represents the Roman expression XXXI + XXIV? a. b. c. d.
55 52 45 43 a  Replace the following equivalents in the expressions: X = 10 I=1 IV = 4 XXXI + XXIV = (10 + 10 + 10 + 1) + (10 + 10 + 4) = 31 + 24 = 55
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75.
John was born in the year MCMXLIX. Convert his birth year to an Arabic Numeral. a. b. c. d.
1848 1884 1944 1949 d  Replace the following equivalents in the numeral: M = 1000 CM = (1000 − 100) XL = (50 − 10) IX = (10 − 1) MCMXLIX = 1000 + (1000 − 100) + (50 − 10) + (10 − 1) = 1949
76.
Which expression represents 70 + 80 + 90? a. b. c. d.
LX + LXX + LXXX LXX + LXXX + LXXXX LCX + LXXX + LXXX LXX + LCXX + LXXX b  Use the following equivalents: L = 50 X = 10 70 + 80 + 90 = (50 + 10 + 10) + (50 + 10 + 10 + 10) + (50 + 10 + 10 + 10 + 10) = (L + X + X) + (L + X + X + X) + (L + X + X + X + X) = LXX + LXXX + LXXXX
77.
Ronald earns $3225 per month. 12% of his salary is withheld for income tax. Find the amount of his take home per month. a. b. c. d.
$2883 $2838 $2787 $2778 b  First find 12% of 3225. 12 (3225)(12%) = (3225) 100 = 387 Tax = Subtract the tax amount from his earning. 3225 − 387 = 2838
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78.
Jason pays 24% of his earnings per month for his home installment. If his income is $4225, how much does he take home after paying the installment? a. b. c. d.
$3211 $3121 $3112 $3011 a  First find 24% of 4225. 24 Installment = (4225)(24%) = (4225) = 1014 100 Subtract the installment amount from his earning. 4225 − 1014 = 3211
79.
The following list shows the salaries of four people along with their total deductions for each month. Which one has the greatest takehome amount? a. b. c. d.
Salary = $3402; Total Deduction = 14% Salary = $3150; Total Deduction = 15% Salary = $3655; Total Deduction = 17% Salary = $4455; Total Deduction = 24% d  First find take home amount of each person, and then compare. 14 Deduction = (3402)(14%) = (3402) = 476.28 100 Takehome amount = 3402 − 476.28 = $2925.72 15 (b) Deduction = (3150)(15%) = (3150) = $472.5 100 Takehome amount = 3150 − 472.5 = $2677.5
17 (c) Deduction = (3655)(17%) = (3655) = $621.35 100 Takehome amount = 3655 − 621.35 = $30333.65 24 (d) Deduction = (4455)(24%) = (4455) = 1069.20 100 Takehome amount = 4455 − 1069.20 = $3385.80
Among the outcomes, $3385.80 is the greatest.
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80.
Jane’s monthly income in the year 2010 was $48,200, where 14% of her salary was withheld for income tax. In the year 2011, her monthly salary was $51,800, where 16% of her income was withheld for income tax. What was her average take home pay during the years 20102011? a. b. c. d.
$48,482 $46,486 $44,462 $42,482 d  Find the amount of tax for 2010 and deduct from income. 14 Amount of tax for 2010 = 48200 = 6748 100 Amount of take home in 2011 = 48200 − 6748 = $41452 Find the amount of tax for 2011 and deduct from income. 16 Amount of tax for 2011 = 51800 = 8288 100 Amount of take home in 2011 = 51800 − 8288 = $43,512 Now find the average. (41452 + 43512) ÷ 2 = $42482
81.
The price of one bottle of soda in a grocery store is $0.85. But the store advertised that it will give a discount of 12% for any purchase of more than 8 bottles. What is the sales price of 12 bottles of soda? a. b. c. d.
$8.98 $8.68 $7.96 $6.86 a  First find the original price of 12 bottles. Price of 12 bottles = 12(0.85) = $10.20 12 Amount of discount = 10.20 = 1.224 100 The prices after discount = 10.20 − 1.224 = $8.98
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82.
A stereo system has an original price of $328, and a laptop computer has an original price of $420. A store advertised that for purchasing both a stereo and a laptop, it will give a 12% discount on the total purchase. What is the total sale price of a stereo and a laptop? a. b. c. d.
$658.24 $678.44 $687.24 $689.46 a  The total price of items = 328 + 420 = 748 Find 12% of 748. 12 Amount of discount = 748 = 89.76 100 Price after discount = 748 − 89.76 = $658.24
83.
Different stores offer different prices and discounts for a chair and an ottoman as follows. Which store offers the best purchase price? a. b. c. d.
Store A: Original price = $580 with 11% discount Store B: Original price = $520 with 9% discount Store C: Original price = $490 with 7% discount Store D: Original price = $450 with 5% discount d  Find the sale price for each store. 11 Store A: Amount of discount = 580 = 63.80. Price after discount = 580 − 63.80 = 516.20 100 9 Store B: Amount of discount = 520 = 46.80. Price after discount = 520 − 46.80 = 473.20 100 7 Store C: Amount of discount = 490 = 34.30. Price after discount = 490 − 34.30 = 455.70 100 5 Store D: Amount of discount = 450 = 22.50. Price after discount = 450− 22.50 = 427.50 100 Store D offers the lowest price.
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84.
The price of office supplies in a store are as follows: Pen: 24 cents Pencil: 18 cents Notebook: $1.24 Paper pack: $3.92 Which equation can be used to calculate the total price of m pens, n pencils, p notebooks and q packages of paper? a. b. c. d.
2.4m + 1.8n + 1.24p + 3.92q 0.24m + 0.18n + 12.4p + 3.92q 0.24m + 0.18n + 1.24p + 3.92q 0.24m + 0.18n + 1.24p + 39.2q c  Multiply the number of each item by its price, and then add them up. Don’t forget to convert cents to dollar. 0.24m + 0.18n + 1.24p + 3.92q
85.
Rosie checked her checking account online at 8:00 AM and noticed that her account balance is $4,323. At 9:00 PM, she checked her account again and noticed that the following transactions were posted to her account. Find her final balance after reconciling these transactions: Electronic withdrawal: $320 Electronic withdrawal: $22 Electronic withdrawal: $124 a. b. c. d.
$3958 $3937 $3857 $3807 c  Add the transactions, and then subtract the result from the balance at 8:00 AM. Account balance at 9:00 PM = 4323 − (320 + 22 + 124) = 4323 − 466 = 3857
86.
The balance of Aaron’s savings account at the beginning of the year was $3197. For six months he deposited $230 each month in his savings account. What is the balance after six months? a. b. c. d.
$4378 $4577 $4676 $4766 b  Add six times 230 to the original account balance.
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Balance after six months = 3197 + 6(230) = 4577 87.
Carol had $4531 in her checking account before going on a trip. At the end of her trip she noticed that the following transactions were posted to her account: Withdrawal: $437 Withdrawal: $291 Withdrawal: $29 Withdrawal: $37 Find her account balance at the end of her trip. a. b. c. d.
$3938 $3937 $3836 $3737 d  Add all the transactions, and subtract the result from the account balance. Balance after withdrawals = 4531 − (437 + 291 + 29 + 37) = 3737
88.
Jeanne had $2024 in her savings account at the beginning of April. By the end of the month she took the following amounts from her savings account: $212 $102 $210 What is her account balance at the end of the month? a. b. c. d.
$1650 $1600 $1500 $1350 c  Deduct the sum of the transactions from the account balance. Account balance after withdrawals = 2024 − (212 + 102 + 210) = 1500
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89.
Russ usually writes checks on his checking account. During the month of May, he wrote checks in the following amounts: $171 $47 $321 $117 If at the beginning of the month his account balance was $3739, what is the balance at the end of the month? a. b. c. d.
$3802 $3383 $3083 $3080 c  Deduct the sum of the withdrawals from the account balance. Account balance at the end of the month = 3739 − (171 + 47 + 321 + 117) = 3083
90.
Which expression is equivalent to 3 + 4(9 − 3) + 11? a. b. c. d.
3 + 4 × 9 − 3 + 11 3 + 4 × 9 − 4 × 3 + 11 3 + 4 × 9 + 4 × 3 + 11 3 − 4 × 9 + 4 × 3 + 11 b  In the given expression, 4 must be distributed over the parentheses. Therefore, 3 + 4(9 − 3) + 11 = 3 + 4 × 9 − 4 × 3 + 11 The correct answer is b.
91.
Which expression is the translation of “three times a quantity added to 12, divided by 12?” a. b. c. d.
(3 + 12x) ÷ 12 (3x + 12) ÷ 12 3(x ÷ 12) + 12 3(x + 12 ÷ 12) b  Three times a quantity is 3x. Adding this quantity to 12 gives (3x + 12). Dividing this expression by 12 gives (3x + 12) ÷ 12.
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92.
What is the value of −4[3 − 4(8 + 1) ÷ 3 − 3] + 12? a. b. c. d.
69 63 60 57 c  First simplify inside the brackets. −4[3 − 4(8 + 1) ÷ 3 − 3] + 12 = −4[3 − 36 ÷ 3 − 3] + 12 = −4(3 − 12 − 3] + 12 = −4(−12) + 12 = 48 + 12 = 60
93.
To convert degrees Celsius to degrees Fahrenheit, multiply by 9, divide by 5 and add 32. Write a formula that represents these operations.
a. b. c. d.
9 C 5 + 32. 5 C 9 + 32. 32 C 5 + 9. 32 C 9 + 5. a  Denote degrees Celsius by C and degrees Fahrenheit by F. Then, multiplying C by 9 gives 9 9 9C. Dividing 9C by 5 gives C . Adding 32 to this amount gives C + 32. 5 5
94.
What is the value of 4(29 − 19) ÷ 5 − 4 × 13? a. b. c. d.
− 49 −44 48 44 b  First simplify inside the parentheses. 4(29 − 19) ÷ 5 − 4 × 13 = 4(10) ÷ 5 − 4 × 13 = 40 ÷ 5 − 52 = 8 − 52 = −44
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95.
Mika is planning a trip that will cover 1232 miles. Her car gets 28 miles to a gallon. If the price of gas is $3.25 per gallon, determine the cost of gas during her trip? a. b. c. d.
$153 $148 $145 $143 d  First determine how many gallons of gas will she use. 1232 ÷ 28 = 44 gallons Cost of gas = 44 × 3.25 = 143
96.
Sandra purchased the following items for her Club meeting. 12 Packages of cookies each for $4.25 4 Baskets of fruits each for $12.50 42 Cans of soda each for $0.32 How much did she spend in all? a. b. c. d.
$114.44 $112.42 $104.42 $102.24 a  Total spending = 12(4.25) + 4(12.50) + 42(0.32) = 51 + 50 + 13.44 = 114.44
97.
Wendy wants to invite a number of friends to an anniversary party at a restaurant. She would like to invite between 1418 friends. She checked with different restaurants, and they offered the following packages. Which restaurant offered the lowest quote for each guest? a. b. c. d.
Restaurant A: Restaurant B: Restaurant C: Restaurant D:
$705 for 15 guests $736 for 16 guests $1020 for 20 guests $1250 for 25 guests
b  Divide the price of each package by the number of guests to find the price for each guest. Restaurant A: 705 ÷ 15 = $47 Restaurant B: 736 ÷ 16 = $46 Restaurant C: 1020 ÷ 20 = $51 Restaurant D: 1250 ÷ 25 = $50 The lowest price is offered by the Restaurant B. TOP
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98.
Catherine is planning to make cookies for her grandchildren. She purchased the following items: 3 Pounds flour each for $1.23 2 Pounds Sugar each for $1.25 3 Packages of Butter each for $3.45 2 Gallons Milk for $3.25 How much did she spend in total? a. b. c. d.
$27.14 $25.04 $24.14 $23.04 d  Find the prices of each item, and then add them up Total purchase = 3(1.23) + 2(1.25) + 3(3.45) + 2(3.25) = 3.69 + 2.50 + 10.35 + 6.50 = 23.04
99.
Church Hill College is planning to invite 34 guests for a conference to be held during their centennial anniversary. If the cost of daily meals of each guest is $21 and the conference is to be held for 3 days, what is the total cost of the meals? a. b. c. d.
$2414 $2214 $2142 $2042 c  Multiply the number of guests (34), by the price of each meal (21), and by the number of days. Total cost of meals = 34 × 21 × 3 = 2142
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100. Which list shows the following numbers from the smallest to the greatest?
1 5 4 14 3 , 6 , 5 , 15
a. b. c. d.
1 3, 5 6, 4 5, 1 3,
5 6, 1 3, 1 3, 4 5,
14 4 15 , 5 4 14 5 , 15 5 14 6 , 15 5 14 6 , 15
d  First multiply the denominator and numerator of each fraction by a certain number such that all the fractions share the same denominator, and then compare their numerators: 4 5 14 1 5 15 6 3
1 ×10 3×10
10 30
5×5 6×5
4 ×6 5×6
14 × 2 15 × 2
25 30
24 30
28 30
These fractions can be listed in an ascending order as follows:
10 24 25 28 30 , 30 , 30 , 30
1 4 5 14 Their corresponding fractions are 3 , 5 , 6 , 15 . 101. Three telecommunication companies plan to lay off some of their workers as listed below: Company A: Company B: Company C: Company D:
70 workers of its 210 workers 30 workers of its 140 workers 80 workers of its 200 workers 60 workers of its 190 workers
Which company plans to lay off the highest fraction of it workers? a. b. c. d. TOP
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c  Find the ratio of each company in decimal forms. Company A: Company B: Company C:
70 = 0.33 210 30 = 0.21 140 80 = 0.40 200 60 = 0.32 190
Company D: Therefore, Company C is the answer, since 0.40 is greater than all the other numbers. 102. Which list shows the following numbers from the greatest to the smallest?
7 9 11 23 , , , 8 16 12 24
a. b. c. d.
11 12 , 7 8, 9 16 , 23 24 ,
23 7 9 24 , 8 , 16 9 11 16 , 12 23 7 11 24 , 8 , 12 11 7 9 12 , 8 , 16
d  First multiply the denominator and numerator of each fraction to make their denominators the same.
7 8 7×6 8×6 42 48
9 16 9×3 16 × 3 27 48
11 12 11 × 4 12 × 4 44 48
23 24 23 × 2 24 × 2 46 48
46 44 42 27 , , , . The 48 48 48 48 23 11 7 9 . , , , corresponding fractions to these fractions are 24 12 8 16
Arranging these fractions based on their numerators we get
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103. In a Study Hall, the English teacher assigned four different novels to four different students. At the end of the first week, the following students had the following number of pages left to read: Rachael: 130 pages Raymond: 132 pages Russ: 126 pages Regina: 144 pages At the end of the month, the following pages remained unread. Rachael: 42 pages Raymond: 24 pages Russ: 38 pages Regina: 56 pages Which student left the largest fraction of the novel unread? a. b. c. d.
Rachael Raymond Russ Regina d  Find the ratio for each novel:
42 = 0.32 Rachael: 130 24 = 0.18 Raymond: 132 38 = 0.30 Russ: 126 56 = 0.39 Regina: 144
Regina has the greatest number.
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104. Which are the two greatest numbers in the following list?
17 7 11 1 , , , 32 12 24 6
a. b. c. d.
17 11 24 and 32 7 11 12 and 24 7 17 12 and 32 7 1 12 and 6 c  Multiply the denominator and numerator of each fraction by a certain number to make all the denominators the same: 17 7 1 11 32 12 6 24 17 × 3 7×8 1 × 16 11 × 4 32 × 3 12 × 8 6 × 16 24 × 4
51 96
56 96
The two greatest fractions are
44 96
16 96
56 51 7 17 and . Their corresponding fractions are and . 12 96 96 32
105. Order the following numbers from the smallest to the greatest:
12.25,
a. b. c. d.
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11
3 89 5 , 9 , 12.025
3 89 11 9 , 5 , 12.025, 12.25 3 89 11 9 , 12.025, 12.25, 5 3 89 11 5 , 9 , 12.025, 12.25 3 89 11 12.25, 9 , 5 , 12.025
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a  Convert the fractions to decimal numbers:
3 11 = 11 + 0.60 = 11.60 5 89 = 9.89 9
Here are the numbers from the smallest to the greatest: 9.80, 11.60, 12.025, 12.25 Replace the equivalents of the decimals 9.80 and 11.60.
89 3 11 9 , 5 , 12.025, 12.25 106. John worked the following number of hours per month during the first six months of the year. January: 197.34 hours February: 199.04 hours March: 212.34 hours April: 194.45 hours May: 194.54 hours June: 221.43 hours List his monthly workhours from the lowest to the highest in terms of months. a. b. c. d.
June, March, April, May, January, February June, March, April, January, May, February April, June, January, February, March, May April, May, January, February, March, June d  Here is the ascending list along with each month workhours: April: 194.45 hours, May: 194.54 hours, January: 197.34 hours, February: 199.04 hours, March: 212.34 hours, June: 221.43 hours So, eliminating the numbers we get, April, May, January, February, March, June
107. Find the middle number among the following data? 321.243, 321 a. b. c. d.
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56 , 321.432 , 322.254, 322.245 67
321.243
321
56 67
321.432 322.254
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b  321
56 = 321 + 0.84 = 321.836 67
The numbers in order are 321.243, 321.432, 321.836, 322.245, 322.254. The middle number is 321.836. The equivalent of this number is 321
56 . 67
108. What is the difference between the smallest and the largest numbers in the following list?
23, 23.01, a. b. c. d.
230 17
9.74 9.48 7.72 7.47 b  First convert the fraction to a decimal:
230 = 13.53 . The largest number and the smallest 17
number are 23.01 and 13.53. Then 23.01 − 13.53 = 9.48
109. Different schools reported the ratios of the female students to male students in different numerical formats as follows: School A: 1.9 School B: 2
7 School C : 9
School D: 1.09
Which school has the highest fraction of female students? a. b. c. d.
School A School B School C School D b  First convert the fraction to a decimal.
7 = 0.78 . Comparing the numbers shows that 2 is 9
the greatest. So, School B has the highest ratio.
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110. An Excel spreadsheet is set up in a way that by entering a fraction into a cell, it automatically converts it to a number with two decimal digits. The following numbers are displayed in a spreadsheet. 2.24, 3.25, 0.26 Which list represents the equivalents of these numbers?
a. b. c. d.
52 13 13 , , 25 4 50 56 11 13 , , 25 4 50 56 13 11 , , 25 4 50 56 13 13 , , 25 4 50
224 = 100 d325 3= .25 = 100 26 0= .26 = 100 .24 2=
56 × 4 = 25 × 4 25 × 13 = 25 × 4 2 × 13 = 50 × 2
56 25 13 4 13 50
111. Which list represents the equivalents of the following decimal numbers? 4.15, 4.65, 4.25
a. b. c. d.
83 93 17 25 , 20 , 4 83 93 17 20 , 20 , 4 83 93 17 20 , 25 , 4 83 97 17 20 , 20 , 4
b
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4= .15
415 5 × 83 83 = = 100 5 × 20 20
4= .65
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425 17 × 25 17 = = 100 25 × 4 4
4= .25
112. The dimensions of a rectangular tract of land are 23 used to find the area of the land?
a. b. c. d.
283 12 281 12 283 12 283 14
and and and and
7 5 ft. and 24 ft. Which fractions can be 12 8
197 8 197 8 193 8 197 8
7 12 × 23 + 7 283 = 23 = 12 12 a  12 5 24 × 8 + 5 197 24 = = 8 8 8
113. Which list represents the equivalents of the following fractions?
84 35 14 35 , , , 49 49 21 63
a. b. c. d.
12 5 7 , 7, 5 12 9, 7 , 11 5 7 , 7, 12 5 7 , 7,
2 3, 5 7, 2 3, 2 3,
5 9 2 3 5 9 7 9
84 7 × 12 12 = 49 7 × 7 7 35 7 × 5 5 = = 49 7 × 7 7
a= 
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14 = 21 35 = 63
2×7 = 3×7 7×5 = 7×9
2 3 5 9
114. The probabilities of four different events occurring are as follows: 0.32, 0.45, 0.55, 0.75 Which list represents these probabilities in simplest fractional form?
a. b. c. d.
7 25 , 8 25 , 8 25 , 8 25 ,
9 20 , 9 20 , 9 20 , 9 20 ,
11 20 , 17 20 , 11 20 , 13 20 ,
32 = 100 c45 0= .45 = 100 55 0= .55 = 100 75 0= .75 = 100 0= .32
3 4 3 4 3 4 3 4 8 25 9 20 11 20 3 4
115. In which number does the digit 9 have the highest place value? a. b. c. d.
3409008 3490806 3400908 3400790 b  The digit 9 represents the 100,000 place value.
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116. A physics teacher wrote 238,857 miles on the board as the distance between the moon and the earth. How is it expressed in words? a. b. c. d.
two hundred thousand thirtyeight, eight hundred fiftyseven two hundred thirtyeight, eight hundred fiftyseven two hundred thirtyeight thousand, eight hundred fiftyseven two million thirtyeight, eight hundred fiftyseven c  We can read the number in two parts and then combine them: 238857 = 238000 + 857 = two hundred thirtyeight thousand, eight hundred fiftyseven
117. Which is the name of the number 45,600,006? a. b. c. d.
fortyfive million, six thousand, sixty fortyfive million, six hundred thousand, sixty forty million, fortysix hundred thousand, six fortyfive million, six hundred thousand, six d  We can partition the number in three parts, and then combine their names. 45,600,006 = 45,000,000 + 600,000 + 006 = forty five million, six hundred thousand, six
118. The exact distance between two islands in the Atlantic Ocean is 440,056 ft. What is the order of magnitude of this number? a. b. c. d.
8 7 6 5 d  The distance 440,560 is rounded to 400,000 which is equal to 4.0 × 105. So, the order of magnitude is 5.
119. The weight of a notebook is 8.23 oz. and the weight of each package of pencils is 4.23 oz. The weight of a box containing 24 notebooks and 24 packages of pencils can be calculated using the expression 24 × 8.23 + 24 × 4.23. Which expression is equivalent to this expression? a. b. c. d.
24(34.81) 24(12.46) 8.23 + 101.52 197.52 + 4.23 b  Using the Distribution Property we have 24 × 8.23 + 24 × 4.23 = 24(8.23 + 4.23) = 24(12.46)
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120. Which expression is equivalent to 3(12 − 1) + 4(13 + 2)?
a.
b. c. d.
3 × 12 − 4 × 13 + 4 × 2 − 3 × 1 3 × 12 + 4 × 13 + 4 × 2 − 3 3 × 12 + 4 × 13 + 2 − 1 3 × 12 + 4 × 13 + 4 × 2 − 3 × 1 b  3(12 − 1) + 4(13 + 2) = 3 × 12 − 3 × 1 + 4 × 13 + 4 × 2 (Distribution Property) = 3 × 12 + 4 × 13 + 4 × 2 − 3 × 1 (Commutative Property) = 3 × 12 + 4 × 13 + 4 × 2 − 3
121. Which operation must be performed first when calculating (129 + 321 × 481 + 2)? a. b. c. d.
129 + 321 481 + 2 481 × 2 321 × 481 d  The multiplication must be performed first.
122. Which of the following equations is false? a. b. c. d.
21 + (11 + 9) = (21 + 11) + 9 21 × (11 + 9) = (11 + 9) × 21 21 ÷ (11 + 9) = (11 + 9) ÷ 21 21 × (11 − 9) = (11 − 9) × 21
c  21 ÷ (11 + 9) = 21 ÷ 20 = 1.05 (11 + 9) ÷ 21 = 20 ÷ 21 = 0.95 Hence, the right sides of the equations are not the same. 123. In a horse race, Horse A beat Horse B by 2 lengths, and Horse B finished 3 lengths ahead of Horse C. By how many lengths did Horse C lose the race to Horse A? a. b. c. d.
6 5 4 3 b  Horse A has 2 more lengths than the Horse B Horse B has 3 more lengths than Horse C. Therefore, the horse C lost the race by 2 + 3 = 5 lengths.
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124. In a school auditorium, there are 24 rows in the main floor and 11 rows in the balcony. If there are 19 seats in each row, which expression can be used to find the number of the seats? a. b. c. d.
19(24) + 11 19(11) + 24 19(24 + 11) 19(24)(11) c  The total of the rows is (24 + 11). Multiplying the total rows by the number of seats in each row gives the total seats.
1 4
125. Which of the following is the value of 4[12 + 3(1 + 5)] ÷ 4 ?
a. b. c. d.
4 17 1 28 17 4 27 17 7 26 17 28
1 4
a  4[12 + 3(1 + 5)] ÷ 4 = 4(12 + 3 × 6) ÷
17 = 4(30) ÷ 4 120 4 × = 1 17 480 = 17 4 28 = 17
126. If a truck carries a 2 pounds? a. b. c. d. TOP
17 4
3 tons load, how many pounds is it hauling, knowing that 1 ton = 2000 4
5250 pounds 5450 pounds 5500 pounds 5600 pounds Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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c  Multiply the number of tons by the number of pounds in each ton:
3 11 2 × 2000 = × 2000 4 4 11 × 2000 4 = = 5500 pounds
1 1 127. Which of the following is equivalent to 6 ÷ 3 ? 4 8 a. 8 b. 7 c. 5 d. 2 1 1 25 25 3 ÷ 6 ÷ = d  4 8 4 8
25 8 × = 4 25 =2
128. The area of an irregular 4sided shape is calculated using the formula c and d are the side lengths. If, a = 3, b = 4, c = 3 calculate the area?
a. b. c. d.
1 a ( b + c + d ) , where a, b, 3
1 and d = 6, which expression can be used to 4
13 4 + + 6 4 13 3 4 + + 6 4 1 13 4 + + 6 3 4 11 4 + + 6 4
a  Replace the given values in the formula: 1 1 1 a (b + c += d) ( 3 ) 4 + 3 + 6 3 3 4 13 4 + + 6 4 = TOP
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5 129. What is the proper procedure to calculate 12 3 + 4 (1  7 ) ÷ 3 ? 12
a. b. c. d.
Simplify inside brackets, multiply by 12, then divide by the mixed number. Simplify inside parentheses, multiply by 12, then divide by the mixed number. Simplify inside brackets, multiply by 12 by the mixed number, then divide by 12. Simplify inside parentheses, multiply by 3 and 12, then divide by the fraction. a  First convert all the expression inside the brackets to one number, multiply by 12, and then divide by the mixed number.
130. For a Physics Project, John designed a microtool in the shape of an irregular hexagon. He must also include in his report a general formula for the perimeter of the tool. After measuring the sidelengths repeatedly he found the sidelengths as, 2 mm, 4 mm, 8 mm, 16 mm, 32 mm, and 64 mm. If a is to be the shortest side of the tool, which of the following is a general formula for the perimeter? a. b. c. d.
49a mm 51a mm 62a mm 63a mm d  If a = the shortest side, then Perimeter = a + 2a + 4a + 8a + 16a + 32a= 63a
7 131. To calculate the division 7.73 ÷ 7 , which set of the procedures can be used? 3 a. Convert the mixed number to a decimal, divide the decimals. b. Convert the mixed number to a decimal, convert the decimal to a mixed number. c. Convert the decimal to a mixed number, then multiply. d. Divide 7.73 by 7, then add to the fraction.
a  Convert the mixed number to a decimal, divide the two decimal numbers 132. Find x. 12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = x a. b. c. d. TOP
387 368 312 268 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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a  12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = 12[32 − 12(1) + 12] + 12 ÷ 4 = 12(32 − 12 + 12) + 3 = 12(32) + 3 = 387
133. In the US, about
4 3 of the residents are registered to vote. In one elections, of the registered 5 4
voters actually voted. What portion of the citizens voted in this election?
a. b. c. d.
3 4 1 4 3 5 1 5 3 4 c  Find 4 of 5 4 3 12 3 × = = 5 4 20 5
134. Perform the following calculations: 1 3 57 +4 ÷ 11 4 4
(1.1 ) 1
a. b. c. d.
22 15 23 15 19 13 17 13
bTOP
1 3 57 11 12 19 57 +4 ÷ = + ÷ 11 4 4 10 11 4 4
(1.1 ) 1
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11 × 12 19 4 = + × 10 × 11 4 57
6 1 + 5 3 23 = 15
=
135. Calculate the following expression:
1 2 1 2 + 3 1+ 1 + 3 5 3+ 1 3 a. b. c. d.
9.3 9.1 8.9 6.3
1 7 2 1 6 2 + 3 1+ 1 + 3 =2 + 3 1 + + 3 1 5 5 3+ 10 3 3 a 11 7 = 2 + 3 + 5 10 2 33 7 = + + 1 5 10 20 + 66 + 7 = 10 93 = 10 = 9.3
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136. Cindy measures a side and a diagonal of a squareshaped garden, and after repeating the measurements, she found the following lengths: Side length = 1200 ft. Diagonal length = 1690 ft. Her friend suggests that if the side length is accurate, then the length of the diagonal must be adjusted in her calculation. Assuming the side length is accurate, which of the following measurements will replace the length of the diagonal if more precise calculations are made? a. b. c. d.
1798 ft. 1789 ft. 1697 ft. 1679 ft. c  Using the Pythagorean Theorem, if a side of the square is 1200, then a diagonal has the following measurement: d2 = (1200)2 + (1200)2 = 1440000 + 1440000 = 2880000 d = 1697 ft.
137. The hypotenuse and the altitude of a right triangle are given as 4 ft. and 13 ft. A student measures the legs of the triangle and comes up with measurements of 12 ft. and 5 ft. To what number must the altitude be adjusted? a. b. c. d.
5.82 ft. 5.62 ft. 4.81 ft. 4.62 ft. d  In a right triangle, the product of the two legs is the same as the product of the hypotenuse and the altitude. Let’s have the altitude = x. Then, 13 × x = 12 × 5. This gives
60 x = 13 = 4.62
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138. Michelle wants to find some ordered pairs to fit in the equation y = 3x − 2. She created the following table: x 3 5 7 8 11
y 7 13 19 21 31
Which value in the table must be adjusted in order to verify that the given function represents all the given values in the table? a. b. c. d.
21 must be changed to 22 21 must be changed to 26 31 must be changed to 30 31 must be changed to 33 a  Replace x = 8 in the function. y = 3(8) − 2 = 24 − 2 = 22. So, the value of y on the fourth row must be changed to 22. Checking the other values in a similar way shows that they fit the function.
139. A survey of a group of 300 people shows that 41.33% of the people preferred a twin size bed. Since the fractional part in the context (.33) of individuals may not make sense for a group or audience, how can you adjust the result to make it more sensible? a. b. c. d.
41% 42% 45% 40% a  Round off 41.33% to 41%.
140. An irregular shape is made up of four triangles with areas 143 ft2, 34 ft2, 56 ft2 and 122 ft2. What operation is needed to find the area of the shape? a. b. c. d.
Multiplication Division Subtraction Addition d  Area is found by simply adding the areas of all the segments of the shape.
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141. To express the value 0.32 as a percent what operation is needed? a. b. c. d.
Multiplication Division Addition Subtraction a  To convert a decimal to a percent, simply multiply by 100.
142. Shannon can type 32 words per minute. To find out how many minutes it takes her to type 2341 words, what operation should be performed on these numbers? a. b. c. d.
Addition Subtraction Multiplication Division d  She must find the ratio of two numbers. So, the division operation is needed.
143. Each ton is about 2000 pounds. To find out how many tons make up 4589 pounds, what operation must be performed using these numbers? a. b. c. d.
Multiplication Division Addition Subtraction b  We must find the ratio of 4589 to 2000. So, the type of the operation is division.
144. Which of the following is the best estimation of 2300 × 3209? a. b. c. d.
7,360,000 7,370,000 7,380.000 7,400,000 c  To estimate the result simply multiply 2300 × 3209 = 7,380,700. Round down in this case to get the best estimate.
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145. Mt. Whitney is 14,494 feet above sealevel and Rock Valley is 347 feet below sealevel. Which of the following is the best estimation of the difference in these elevations? a. b. c. d.
14000 14500 15000 ft. 1480 ft. c  Since one is above the sea level, and the other is below the sea level, to find their difference, we must consider the elevation of the Rocky Valley a negative number. Subtract the elevations: 14494 − (−347) = 14494 + 347
= 14841 ≈ 15000
146. Which is the best estimation of a. b. c. d.
30 29.29 29 28.89
45008 ? 1505
a  The easiest and simplest way to estimate the result is round the fraction before the division:
45008 45000 ≈ = 30 1505 1500 147. A submarine is submerging at the rate of 11 feet per second. Which is the best estimate of its distance from the surface of the ocean after 39 seconds? a. b. c. d.
440 ft. 400 ft. 385 ft. 380 ft. b  Multiply 11 by 39 to find the distance after 39 seconds. 11 × 39 = 429 ft. ≈ 400 ft.
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148. To find a reasonable estimate of
a. b. c. d.
340000 1100 330000 1100 33000 1100 330000 110
330003 , which fraction is the best choice? 1129
b  The denominator and numerator of the fraction can be rounded off as follows:
330000 ≈ 300 1100 149. The thickness of each bag of wheat stacked in a silo is 9 inches. If in each column of the silo 43 bags are stacked, which of the following is a reasonable estimate of the height of the bags? a. b. c. d.
300 in. 330 in. 400 in. 450 in. c  Round 9 to 10 and 43 to 40. 9 × 43 ≈ 10 × 40 = 400 in.
150. To find a reasonable estimate of 1000.01 × 100, which expression is the best choice? a. b. c. d.
10010 × 100 1000 × 100 1001 × 100 1000 × 101 b  Rounding 1000.01 to the nearest unit, we get 1000. So, the expression 1000 × 100 gives the best estimate.
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151. Which is a reasonable estimate of the total amount of the following coins, in dollars? 40 quarters 10 dimes 20 nickels 770 pennies a. b. c. d.
$20 $19 $18 $17 a  Convert all the coins to dollars, and round off. 40(0.25) + 10(0.10) + 20(0.05) + 770(0.01) = 10 + 1 + 1 + 7.7 = 19.7 ≈ 20
152. Which ratio is proportional to
a. b. c. d.
7 24 5 28 7 28 6 28
12 ? 48
12 7 = c  48 28
Cross multiply the proportion. 12 × 28 = 7 × 48 336 = 336 Both sides are the same. Repeating this procedure in a similar way with the other ratios does not yield a true equation.
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153. Which proportion is true?
a. b. c. d.
22 18 = 77 64 11 18 = 77 63 22 16 = 77 63 22 18 = 77 63 d  Cross multiply the proportion
22 18 = . 77 63
22 × 63 = 18 × 77 1386 = 1386 So, the proportion in d is true. Checking the other proportions in a similar way does not lead to true equations. 154. There are 3 teachers for every 38 students in Cherokee Middle School. If there are 798 students, how many teachers are at the Cherokee Middle School? a. b. c. d.
63 65 76 79 a  Set up the proportion and solve for x.
798 38 = x 3
38x = 3 × 798 38x = 2394 x = 63
155. Which number must be placed inside the box a. b. c. d.
12.25 12.85 13.25 13.75
11 ? = 28 35
d  Denote the unknown number inside the box by x. Then Solve the proportion. TOP
11 x = . 28 35
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28x = 11 × 35 28x = 385 x = 13.75 156. On weekends, 22% of customers of a restaurant are senior citizens. If during one weekend the number of customers of the restaurant were 1050, how many of them were senior citizens? a. b. c. d.
213 219 231 243 c  Find 22% of 1050. 22 ( 22% )(1050 ) = (1050 ) 100 2 × 11 × 21 × 50 = 100 = 231
157. Let p and q represent the following simple statement: p is a number less than zero. q is a negative number. Which statement is true? a. b. c. d.
If p, then q. If q, then not p. If q but not p, then q. If q but not p, then q. a  Since all the negative numbers are less than zero, q is a consequence of p. Therefore, if p, then q.
158. The following simple statements are given: p: Mika likes Ronald q: Ronald likes Mika. Which symbolic statement is true?
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a. b. c. d.
p∨q p ∧q p∨q∨p p∨q → q
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b  Mika and Ronald like each other; that is, p and q occur at the same time. Hence p ∧ q . ∧ means “logical and”; ∨ means “logical or”; → means “logical implication”. 159. p and q define the following statements: p: John visited New York. q: John visited London. Which statement represents “John visited New York or London, but not both at the same time?” a. b. c. d.
q → q∨p p∨q∨p p ∧q p∨q
d  p ∨ q means that either p or q occurs, but both do not occur at the same time. ∧ means “logical and”; ∨ means “logical or”; → means “logical implication”. 160. The following statements are given: Elementary schools are closed on Sunday. It is Sunday. Write a conditional statement by combining these statements. a. b. c. d.
If elementary schools are closed, then it’s Sunday. It is either Sunday or the elementary schools are closed. If it is Sunday, then the elementary schools are closed. If the elementary schools are closed, then it may not be Sunday. c  Since on Sundays, all the schools are closed, c is a conditional statement.
161. The following statement is given: In any right triangle, the sum of two acute angles is 90º. Which triangle is a right triangle? a. b. c. d. TOP
Triangle ABC, in which the difference of two angles is 90º. Triangle DEF, in which no angle is obtuse. Triangle GHK, in which two angles are acute. Triangle LMN, in which one angle is obtained by subtracting the other angle from 90º. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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d  Having the sum of two angles equal to 90º is a necessary condition for any right triangle. Denote the acute angles by a and b. Then a + b = 90º or a = 90º − b 162. The following simple statements are given: All members of a Literature club are published authors. John is a member of this club. Which statement is true? a. b. c. d.
John is a publisher. John may be both an author and a member of the club. John may be a published author. John is a published author. d  Since all the members are published author, then John as one of these members must be a published author.
163. The following statements are given: S = set of integers that are even and are divisible by 3. a is an even integer. Which statement is true? a. b. c. d.
a is not definitely a member of S. a is not a member of S. a may be a member of S. a is a member of S. c  The set S contains even integers that are both even and divisible by 3. The item “a” is an even integer that may or may not be divisible by 3. So, c is a true statement.
164. The following statements are given: All the students in Algebra class are attending Geometry class. All the students in Geometry class are attending History class. John is in History Class. Which statement is true? a. b. c. d. TOP
John may attend Algebra and/or Geometry class(es). John is not attending Algebra class. John is not attending Geometry class. John is attending both Algebra and Geometry classes. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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a  We do not know whether all the History students are attending Algebra and/or Geometry classes. So, a is a true statement. 165. Which general formula can be used for all the numbers in the following series? 2, 6, 12, 20… a. b. c. d.
2n(2n − 1) n(n  1) 2n(n + 1) n(n + 1) d  The given numbers can be described using the following expressions 2 = 1(1 + 1) 6 = 2(2 + 1) 12 = 3(3 + 1) 20 = 4(4 + 1) Comparing the patterns of these expressions to n(n + 1) shows that d is true.
166. The sum 1 + 2 + 3 = 6 is simplified as 32 – 3 = 6 which means that the sum equals the square of the last term minus the last term. Using this method, the sum 1, 2, 3, . . . , n is generalized as n2 − n. Which number disproves this generalization? a. b. c. d.
2 3 4 Both 2 and 4 d  Both n = 2 and n = 4 disprove the generalization. n=2 1+2=3 Replacing 2 in the formula yields 2²  2 = 2 n=4 1 + 2 + 3 + 4 = 10 Replacing 4 in the formula yields 42 − 4 = 12
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167. A brick staircase is made up of 8 steps. The bottom step has 18 bricks, and each successive step has two less bricks. How many bricks are used in the staircase? a. b. c. d.
88 82 76 66 a  The numbers of bricks starting from the bottom step up to the eighth step are as follows: 18, 16, 14, 12, 10, 8, 6, 4 = 88 This is an arithmetic progression. Use the formula S = bricks.
n ( a1 + an ) to find the total number of 2
8 (18 + 4 ) S= 2 = 88
TEAS Practice Exam – Math  Section 2 Algebra 168. Solve 3x + 11 = 31 – x. a. b. c. d.
7 5 4 2 b  Subtract 11 from each side and add x to each side. 3x + 11 −11 + x = 31 − x − 11 + x 4x = 20 x=5
169. Sarah and her father together are 47 years old. If her father is 34 years old, what is Sarah’s age? a. b. c. d.
19 17 13 11 c  Denote the age of Sarah by x. Then x + 34 = 47 Subtract 34 from each side, and simplify. x + 34 − 34 = 47 − 34 x = 13
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170. The ratio of two numbers is 13. If the larger number is 1027, what is the smaller number? a. b. c. d.
79 83 87 89
1027 13 = 1 a x
13x = 1027 x = 79
171. Solve the equation 5x − 11 = 39. a. b. c. d.
14 13 11 10 d  Add 11 to each side, and simplify. 5x − 11 + 11 = 39 + 11 5x = 50 x = 10
172. The sidelengths of a triangle are described by x2 + x + 1, 3x − 2, and 3x2 + x. What is the perimeter of the triangle? a. b. c. d.
4x2 + 5x − 1 4x2 + 4x − 1 4x2 + 5x + 3 4x2 + 5x − 2 a  Add the given polynomials. (x2 + x + 1) + (3x − 2) + (3x2 + x) = 4x2 + 5x − 1
173. Subtract (3x2 + 1) from (4x3 + 2x2 + x). a. b. c. d. TOP
4x3 − x2 + 2x − 1 4x3 − 2x2 + x − 1 4x3 − x2 + x + 1 4x3 − x2 + x − 1 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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d  (4x3 + 2x2 + x) − (3x2 + 1) = 4x3 + 2x2 + x − 3x2 − 1 = 4x3 − x2 + x − 1 174. The dimensions of a rectangle are described by (x + 2) and (x + 3). Which of the following describes the area of the rectangle? a. b. c. d.
x2 + 5x + 5 x2 + 6x + 6 x2 + 5x + 6 x2 + 6x + 5 c  Multiply the dimensions, and simplify. Area = (x + 2)(x + 3) = x2 + 2x + 3x + 2 × 3 = x2 + 5x + 6
175. Add (x2 + x) to (8x3 + 2x2 − x − 1). a. b. c. d.
8x3 + 3x − 1 8x3 − 3x2 − 1 8x3 + 3x2 − 1 8x3 + 3x2 − 2x c  (x2 + x) + (8x3 + 2x2 − x − 1) = x2 + x + 8x3 + 2x2 − x − 1 = 8x3 + 3x2 − 1
176. Write an equation: “value of x is two more than three times x.” a. b. c. d.
3x = x + 2 3x = x − 2 x = 2 + 3x x = 2 − 3x c  Three times x is 3x. x is 2 more than 3x. So, x = 2 + 3x
177. Which of the following is the translation of the expression “The sum of 3 times a number and 3, added to 5 times the number?” a. b. c. d.
8x + 3 5x + 3 8x + 5 5x + 8 a  Three times a number is 3x. The sum of 3x and 3 is (3x + 3). 5 times the number is 5x.
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Adding these two expressions we get (3x + 3) + 5x = 8x + 3 178. The sum of the right angle and an acute angle in a right triangle is greater than 123º. Which expression represents this relationship? a. b. c. d.
x + 90 < 123 x + 90 > 123 x + 123 > 90 x + 123 < 90 b  The measurement of the right angle is 90º. The sum of an acute angle and 90º is greater than 123º. Therefore, x + 90 > 123
179. Which is the translation of the phrase “11 more than the triple of a number?” a. b. c. d.
11x + 3 3x + 11 3(x + 11) 3x + 33 b  The triple of a number is 3x. 11 more than 3x is 3x + 11.
180. Which of the following is the solution to the equation x + 12 = 25? a. b. c. d.
12 or 37 17 or 33 13 or −37 −13 or 37 c  The given equation can be written in the following forms: (a) x + 12 = 25 or (b) x + 12 = −25 Solution to (a) x + 12 = 25 x + 12 − 12 = 25 − 12 x = 13 Solution to (b) x + 12 = −25 x + 12 − 12 = −25 − 12 x = −37 When a number or an algebraic expression is between the two lines , then we consider them without their algebraic signs.
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181. The temperature on the surface of Mars fits the inequality C + 85 ≤ 56 , in degrees Celsius. What is the range of the temperature? a. b. c. d.
−29 ≤ C ≤ −141 29 ≤ C ≤ 141 141 ≤ C ≤ 29 −141 ≤ C ≤ −29 d  C + 85 ≤ 56 can be rewritten in the following forms. (a) C + 85 ≤ 56 and (b) C + 85 ≥ −56 Solution to (a) C + 85 ≤ 56 C + 85 − 85 ≤ 56 − 85 C ≤ −29 Solution to (b) C + 85 ≥ −56 C + 85 − 85 ≥ −56 − 85 C ≥ −141 Answer: −141 ≤ C ≤ −29
182. Which is the solution set to the inequality x + 5 > 16 ? a. b. c. d.
x > −11 or x < −21 x > 11 or x < −21 x < 11 or x < 21 x < 11 or x < 21 b  x + 5 > 16 can be rewritten in the following forms. (a) x + 5 > 16 and (b) x + 5 < −16 Solution to (a) x + 5 > 16 x + 5 − 5 > 16 − 5 x > 11 Solution to (b) x + 5 < −16 x + 5 − 5 < − 16 − 5 x < −21 Answer: x > 11 or x < −21
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183. A physician who has practiced medicine for over 20 years realizes that more than 92% of the babies he delivered weighed p pounds such that p  7 ≤ 2 . What is the range of the weights of the babies? a. b. c. d.
9 ≥p ≥ −5 9≥p > 5 9>p ≥ 5 9≥p ≥ 5
d  The given inequality can be written in the following forms: (b) p − 7 ≥ − 2 (a) p − 7 ≤ 2
Solution to (a) p − 7≤ 2 p − 7+ 7 ≤ 2 + 7 p≤9 Solution to (b) p − 7+ 7 ≥ − 2 + 7 p≥5
Solution set: 9 ≥ p ≥ 5 184. Solve the equation 3x + 11 = 51 − x. a. b. c. d.
12 10 6 2 b  Add x to both sides and subtract 11 from each side, and simplify. 3x + 11 + x − 11 = 51 − x + x − 11 4x = 40 x = 10
185. The length of a rectangle is 12 ft. longer than twice its width. If the total length of a width and a length is 44 ft., what is the measure of a width? a. b. c. d.
TOP
x = 22 ft. x = 19 ft. x = 18 ft. x = 16 ft. d  Let x = length of a width. Then the measure of a length is 2x + 12. x + (x + 12) = 44 2x + 12 = 44 2x + 12 − 12 = 44 − 12 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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2x = 32 x = 16 ft.
186. Solve the inequality 5x − 19 > 3x + 33. a. b. c. d.
x > 26 x > 28 x < 26 x < 28 a  Add 19 to both sides and subtract 3x from each side, and simplify. 5x − 19 + 19 − 3x > 3x + 33 + 19 − 3x 2x > 52 x > 26
187. If the radius of a circle is doubled, how will its area be changed? a. b. c. d.
Increase two times. Increased four times. Increased by two. Increased by four. b  Denote the radius of the circle by r and the area of the circle before a change by A. Then A = πr2 Doubling the radius, changes its length to 2r. Denote the area of the circle after change 2 by S. Then S = π ( 2r ) = 4 πr 2 S is as four times as A. So, the area increased four times.
188. If x in x(22 − 19) is tripled, how much is the value of the expression changed? a. b. c. d.
Will Increase by 6x Will increase 6x times Will increase by 8x Will increase 8x times a  Subtract x(22 − 19) from (3x)(22 − 19). (3x)(22 −19) − x(22 − 19) = 3x(3) − x(3) = 9x − 3x = 6x
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189. If x in the expression 12(x + 3) + 9 is increased by 9, how will the value of the expression be changed? a. b. c. d.
Will be increased by 132 Will be decreased by 132 Will be increased by 126 Will be decreased by 126 c  Replace x by (x + 9) and subtract the given expression from the new expression. 12(x + 9 + 3) + 9 − [12(x + 3) + 9] = 12(x + 12) + 9 − (12x + 36 − 9) = 12x + 144 + 9 − 12x − 27 = 126
190. A sidelength of a squareshape pool is 44 ft. If its length extended to 48 ft., how much will its area be increased? a. b. c. d.
466 ft2 468 ft2 386 ft2 368 ft2 d  Denote the area of the pool before expansion by A and after expansion by P. Then subtract these areas. A = 442 = 1936 ft2 P = 482 = 2304 2304 − 1936 = 368 ft2
191. If x in the expression 3(x + 9) − 12 is decreased by 9, how much will the value of the expression be changed? a. b. c. d.
Will be decrease by 62 Will be decreased by 51 Will be decreased by 43 Will be decreased by 27 d  Replace x by x − 9 and subtract the result from the given expression. 3(x + 9) − 12 − [3(x − 9 + 9) − 12] = 3x + 27 − 12 − 3x + 12 = 27
192. To solve equations such as 3.23x + 4.12 = 1.19 − 21.8x, which step must be followed first in order to make the solution easier? a. b. c. d. TOP
Remove the decimal from the left side. Cancel the decimals. Multiply all the terms by 10 Multiply all the terms by 100. Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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d − Multiplying all the terms by 100, converts the decimals to whole numbers. This way, the calculations become simpler and easier.
193. To solve the equation a. b. c. d.
x 4 = 3 , what step must be taken first? 5 9
Divide the fractions by 45. Multiply the denominators by 45. Cross multiply the proportion. Change the mixed number to an improper fraction. d  The mixed number must be converted to an improper fraction in order to perform cross multiplication.
194. To solve equations such as solution easier?
1 5 1 x + = , which step must be followed first in order to make the 18 12 6
1 to the left side. 6
a.
Move
b.
Add
c. d.
Multiply all the terms by 36. Divide all the terms by 36.
1 to the left side. 6
c  Multiplying all the terms by the least common denominator, 36, converts all the fractions to whole numbers.
195. What are two different methods to verify that a. b. c. d.
Division and Reducing Crossmultiplication and Reducing Multiplication and Reducing Crossmultiplication and Division
24 3 = ? 32 4
b  1. Cross multiply. 2. Reduce the first ratio.
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196. The equation 12 = 6(3 + x) is obtained from the equation 12 − 3(3 + x) = 3(3 + x), using algebraic operations. How is the expression (3 + x) doubled on the right side? a. b. c. d.
By multiplying all the terms by 2. By replacing x by x + 3. By adding 3(3 + x) to both sides. By subtracting 3(3 + x) from both sides. c  Adding 3(3 + x) to both sides, cancelled out it from the left side and doubled it on the right side. Then the sides of the equation are exchanged.
197. Solving the equation a. b. c. d.
1 5 11 5 = . How can you complete the solution? = yields 14 x 2 7 x
By crossmultiplication By division By subtraction By multiplication a  Cross multiplying the proportion yields x = 70.
198. We know that the perimeter of a rectangle with the dimensions a and b is equal to 2(a + b). How does doubling the sum of a and b give the perimeter? a. b. c. d.
Perimeter = 2a + a + 2b + b = 2(a + b) Perimeter = 2a + 2a + b + b = 2(a + b) Perimeter = a + a + b + b = 2(a + b) None of the above c  The perimeter is a + a + b + b, (a + a) + (b + b), (2a + 2b), or 2(a + b).
199. The following set of numbers fit the sides of right triangles: a=3 a=6 a=9 a = 12
b=4 b=8 b= 12 b = 16
c=5 c = 10 c = 15 c = 20
Using this pattern, find a general formula for the sides of right triangles. a. b. c. d. TOP
a = n(3), b = n(5), and c = n(6) a = n(2), b = n(4), and c = n(5) a = n(3), b = n(5), and c = n(7) a = n(3), b = n(4), and c = n(5) Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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d  We can revise the side lengths to relate them to the first triangle as follows: a = 1(3) b = 1(4) c = 1(5) a = 2(3) b = 2(4) c = 2(5) a = 3(3) b = 3(4) c = 3(5) a = 4(3) b = 4(4) c = 4(5) So, a = n(3), b = n(4), and c = n(5), where n is a positive integer. 200. What pattern is used for generating numbers in the series below: 4, 9, 19, 39, 79, . . . , a. b. c. d.
Add 1 to each number, then double. Double each number, then add 1. Subtract 1 from each number, then double. Double each number, then add 2. b  Each number is doubled, then added 1 to generate the following number.
201. Raymond is studying hard in his Algebra class to improve his exam scores. The following numbers show his scores for the first five exams: 45, 56, 63, 75, 84 What is likely to be his score in the sixth exam? a. b. c. d.
70 85 89 94 d  The pattern of the scores reveals that in each exam he jumped from one range to a following range. So, his next score will be in the range of 90100.
202. Which formula is used to generate the numbers in the series below? 4, 9, 19, 34, 54, . . . , a. b. c. d.
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6 added to each term, then 1 is subtracted. 5 added to each term, then added 10. Multiple of 5 added to each term beginning with 5. Multiple of 10 added to each term beginning with 10.
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c  To generate the numbers in the series, a multiple of 5 is added to each term beginning with 5. 203. The numbers below follow a general pattern. What is the next number in the series? 100, 98, 94, 88, . . . a. b. c. d.
72 78 80 82 c  Starting from 2, the even numbers are subtracted.
204. The relationship between P and n is defined by P = 4n. If n increases, how will P change? a. b. c. d.
P will increase. P will decrease. P first will increase, then will decrease. P first will decrease, then will increase. a  This is a direct variation. Increase in n implies an increase in P.
205. The area of a rectangle is A = ab. Given A as a constant, how will b vary if a is doubled? a. b. c. d.
b will be decreased by onehalf. b will be increased by onehalf. b will be decreased by onethird. b will be doubled. a  Since A is constant, then by doubling “a” we must divide “b” by 2.
5 x
206. The relationship between R and x is defined by R = . If x increases how will R change? a. b. c. d.
R will increase. R will decrease. R first will increase, then will decrease. R first will decrease, then will increase. b  This is an inverse variation. Increase in x implies a decrease in R.
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207. Volume of a gas varies with its temperature and its pressure. This relationship is described by V = TP, where V is volume, T is temperature and P is pressure. If the volume of a gas is constant, then what is the relationship between T and P? a. b. c. d.
If T decreases, then P decreases If T stays constant, then P increases. If T increases, then P decreases. If T increases then P increases. c  Since V, product of T and P, is a constant, then if P increases then T must be decreased, and vice versa.
208. Which function can be described by the given graph below?
a. b. c. d.
y = mx + b
xy =
5 4
y = x2 + 3x − 7 y = 3x3 + 4x a  The graph is a straight line and the correct answer is the straight line equation (y = mx + b). Y is the distance along the Y axis. X is the distance along the X axis. B is where the line passes the Y axis. The m is the slope or gradient, or how steep the line is.
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209. Which function represents the graph below?
a. b. c. d.
y = 2x + c y = 2x3 + 3x + c y = 2x + 3x + c y = ax2 + bx + c d  The graph is curved and has two points of intersection with xaxis. Therefore, the quadratic function (d) represents this graph.
Go to the next page.
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210. Which graph can represent the path of launching a projectile? a.
b.
c.
d.
c  Path of a projectile has only one maximum point. Hence, (c) is the answer. 211. The difference between an acute angle and the right angle in a right triangle is 32º. Which equation can be used to find the acute angle? a. b. c. d. TOP
90 − x = 32 90 + x = 32 32 − x = 90 −32 + x = 90 Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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a  The measure of the right angle is 90º. Denote the unknown angle by x. The difference between 90 and x is 32. Therefore, we obtain the equation 90 − x =32. 212. Which expression represents the phrase “nine times a number added to 32, subtracted from 193”? a. b. c. d.
222 + 9x 222 − 9x 160 + 9x 161 − 9x d  Nine times a number is 9x. Adding 9x to 32 yields (9x + 32). Subtracting this expression from 193 gives 193 −(9x + 32) = 161 − 9x.
213. The sum of two consecutive even integers is 650. Which equation can be used to find these numbers? a. b. c. d.
2x + 1 = 650 2(x + 1) = 650 2x − 1 = 650 2(x − 1) = 650 b  Denote the first number by x. Then the second number is (x + 2). Sum of these numbers is 650. Therefore, x + x + 2 = 650 2x + 2 = 650 2(x + 1) = 650 So, 2(x + 1) = 650 can be used to solve this problem.
214. John scored 89 and 83 in his first two Geometry exams. He wants to score an average of 90 in the exams. Which equation can be used to predict his score in the third exam? a. b. c. d.
x + 162 = 290 x + 182 = 280 x + 172 = 270 x − 172 = 265 c  Denote the score of the third exam by x. Then (x + 89 + 83) ÷ 3 = 90 or x + 172 = 270. This is the equation we can use to find x.
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215. Which statement is true? a. b. c. d.
If p: (x − 1)(x + 3) = 0, then q: x = 1. If p: (x − 1)(x + 3) = 0, then q: x = −1. If p: (x − 1)(x + 3) = 0, then q: x = 3. If p: (x − 1)(x + 3) = 0, then q: x = 4. a  Out of the given solutions of x, only x = 1 fits the equation. So, if (x − 1)(x + 3), then x = 1.
216. The following equation is given along with solutions: p: (x + 9)(x − 5) = 0 q: x = −9 r: x = 5 Which statement is true? a. b. c. d.
q∨r p∧q p ∨ q ∧p r → q ∧p
a  Both x = − 9 and x = 5 are the solutions to the equations, but they do not fit the equation at the same time. Therefore, r or q is true. 217. If (x + 3)(x + 23) = 0, then which statement is true? a. b. c. d.
x = −3 or x = −23 x = −3 and x = −23 x = 3 or x = −23 x = 3 and x = −23 a  X cannot be both – 3 and – 23 at the same time in this equation. It can only be one or the other to get 0. Using “and” logically means that they are valid at the same time. The term “and” in logic has different meaning from the ordinary language.
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218. The following statements are given: All the members of the Hemingway Club are published authors. Ronald is not a member of a Sport club. Jason is a published author. Olivia is a member of the Hemingway Club. Which statement is true? a. b. c. d.
Olivia is a member of the Sport Club. Jason is a member of the Hemingway Club. Ronald is a member of the Hemingway Club. Olivia is a published author. d  Since all the members of the Hemingway Club are published author, then Olivia as a member of this club must be a published author.
219. The sum of the numbers 1 + 2 + 3 + 4 + 5 +, . . . , + n is equal to S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15? a. b. c. d.
n (n + 1 ) . What is the sum of 2
144 140 120 112 c  Replace n = 15 in the general formula and simplify: 15 (15 + 1 ) 15 × 16 S= = = 120 2 2
220. Ronald concluded that 3 = 4 by dividing both sides of the equation 3(x − 1) = 4(x − 1) by the same expression (x − 1). How did he use the simplification of an equation improperly? a. b. c. d.
Subtracted zero from both sides. Multiply both sides by zero. Added zero to both sides. Divided both sides by zero. d  If we carry out the equation, we find that x – 1 = 0. 3(x − 1) = 4(x − 1) 3x − 3 = 4x − 4 4x − 3x = 4 − 3 x = 1 or x − 1 = 0
We can divide both sides of an equation by a number distinctive from zero. TOP
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x − 1 = 0 does not allow us to divide both sides by 0. We can only divide by any nonzero number. 221. Consider the pattern among the following equations: 37 × 3 = 111 37 × 6 = 222 37 × 9 = 333 37 × 12 = 444 37 × 15 = 555 Which number must fill the blank in the equation 37 × __= 888? a. b. c. d.
19 20 23 24 d  If we continue the same pattern, we obtain 37 × 18 = 666 37 × 21 = 777 37 × 24 = 888.
222. Consider the numerical equations below: (1 × 9) + 2 = 11 (12 × 9) + 3 = 111 (123 × 9) + 4 = 1111 (1234 × 9) + 5 = 11111 (12345 × 9) + 6 = 111111 Following the same pattern, which number must fill the blank in the equation (12345678 × 9) + ___ = 111111111? a. b. c. d.
9 8 7 6 a  Following the same pattern we obtain (12346 × 9) + 7 = 1111111 (1234567 × 9) + 8 = 11111111 (12345678 × 9) + 9 = 111111111
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TEAS Practice Exam – Math  Section 3 Data Interpretation 223. The numbers of hours of sunshine in Roan Mountain during one week of the summer is displayed in the graph below: 10 9 8 7 6 5 4 3 2 1 0 Sun Mon Tue Wed Thu
Fri
Sat
Which data table fits the bar graph? a. Day Sunshine
Fri 7.0
Sat 8.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 5.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 5.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 5.2 9.0 6.2 7.5
Fri 7.0
Sat 4.5
Sun Mon Tue Wed Thu 8.5 8.2 9.0 6.2 5.5
b. Day Sunshine c. Day Sunshine d. Day Sunshine
b  Comparing each data point to all the tables shows that the data in (b) fits the graph.
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224. Which frequency table represents the following data: 126, 129, 126, 126, 126, 128, 126, 126, 129, 129, 127, 130, 127, 127, 128, 128, 128, 129, 128, 126 a. Data Frequency 126 8 127 3 128 6 129 4 130 1 b. Data Frequency 126 7 127 3 128 5 129 3 130 1 c. Data Frequency 126 7 127 3 128 5 129 4 130 2 d. Data Frequency 126 7 127 3 128 5 129 4 130 1 d  Checking data from each table one by one with the given set of data indicates that table (d) matches the data set.
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225. The percentages of different elements in a chemical substance is shown in the table below. Carbon Oxygen Hydrogen Sulfur Nitrogen
34% 26% 21% 12% 7%
Which pie chart represents the data in the table?
a.
b.
c.
d. c  Comparing the table to each pie chart indicates that chart (c) represents the data. TOP
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226. The following table shows the number of graduates of Boone Creek High School during years 20042011. Year 2004 2005 2006 2007 2008 2009 2010 2011
Number of Graduates 453 571 356 398 433 405 447 511
Which line graph represents the data in the table? (Numbers starting from 1 represent the years 2004, 2005, and so forth.)
a.
b.
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c.
d. d  Comparing the data in the table to each graph indicates the line graph (d) represents the table. 227. The Venn Diagram below displays the number of students attending different classes.
What is total number of students attending Literature class? a. b. c. d. TOP
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c  Number of students attending Literature class only = 19 Number of students attending Literature and Algebra classes only = 9 Number of students attending Literature and History classes only = 11 Number of students attending Literature and the other classes = 4 Adding these numbers gives the total number of students attending Literature class. 19 + 9 + 11 + 4 = 43 228. The graph below represents the amount of rain during a week of spring in New York, in millimeters. 10 9 8 7 6 5 4 3 2 1 0 Fri
Sat
Sun
Mon
Tue
Wed
Thu
Which is the best estimate of the range of the data given in the graph? a. b. c. d.
4.2 mm 5.6 mm 5.9 mm 6.2 mm a  The highest measure is about 9.4 and the lowest is about 5.2. Range = 9.4 −5.2 = 4.2
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229. The following stem  and  leaf graph represents a set of data.
What is the median of the data? a. b. c. d.
46 51 55 58 c  There are 17 data points in the graph. Therefore, the ninth data point is the median. Counting from either end we reach the number 55.
Use the following information to answer questions 230 and 231. The amounts of money a Telecommunication Company spent on ads for the years 20052010 are shown in the table below. Year 2005 2006 2007 2008 2009 2010
Amount (in dollars) 190,000 230,000 110,000 150,000 160,000 180,000
230. In which year was the advertisement cost the highest? a. b. c. d.
2005 2006 2009 2010 b  Comparing the numbers on the right column shows that 230,000 is the highest.
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231. In which year was the advertisement cost the lowest? a. b. c. d.
2006 2007 2008 2010 b  Comparing the numbers on the right column shows that 110,000 is the lowest.
232. The values of the variables a, b, c and d are given in the table. On which variable is P dependent, such that P = 3 + 2x? P 1 9 21 a. b. c. d.
a 2 4 2
b −1 3 9
c 6 −1 8
d −2 3 −7
Variable a Variable b Variable c Variable d b  Replacing the values of b for x gives the corresponding values of P given in the table.
233. The values of the variables m, n, p and q are given in the table. On which variable is T dependent, such that T = 3x2 − 1? T 11 26 2 a. b. c. d.
m 2 −4 2
n −3 7 5
p 4 −1 8
Q −2 3 −1
Variable m Variable n Variable p Variable q d  Replacing the values of q for x gives the corresponding values of T given in the table.
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234. The values of the variables m, n, p and q are given in the table. On which variable is R dependent on, such that R =
3x + 2 ? 2 R −5 7 10
a. b. c. d.
m −4 4 6
n −1 3 9
p 6 −1 8
Q 1 3 −7
Variable m Variable n Variable p Variable q a  Replacing the values of m for x in R gives the corresponding values of R given in the table.
235. The pie chart below represents the data in the table. What is the relationship between the sum of percentages and the area of the circle? Service Army Navy Marine Corp Air Force Coastal Guard
a. b. c. d.
Percent 33% 27% 12% 25% 3%
The sum of the numbers is equal to the area of the circle. The sum of the numbers is equal to the circumference of the circle. The sum of the numbers is 100% and the total shaded regions is 100% of the circle. The sum of the numbers is 100% of the diameter of the circle c  Adding the numbers in the table we get 100%. Adding the areas of the regions in the circle we get 100% of the area of the circle.
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236. The bar graph represents the data in the table. How are the areas of the States of Alabama, Maryland and Minnesota shown in the graph?
State Alabama Alaska California Colorado Maryland Minnesota
Land Area 50700 573,000 155900 103700 9770 79600
700000 600000 500000 400000 300000 200000 100000 0
a. b. c. d.
By the columns above the horizontal line 200,000. By the columns between the horizontal lines of 100,000 and 200,000. By the column above the horizontal line 100,000. By the columns below the horizontal line 100,000. d  The areas of the states Alabama, Maryland and Minnesota are shown below the horizontal line 100,000.
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237. The bar graph represents the data in the table. How are the areas of the States of Arizona and Montana shown in the graph? State Arkansas Arizona Connecticut Michigan Montana Minnesota
Land Area 52000 113,650 4850 56800 145550 79600
160000 140000 120000 100000 80000 60000 40000 20000 0
a. b. c. d.
By the columns above the horizontal line 100,000. By the columns below the horizontal line 100,000. By the columns between the horizontal lines 100,000 and 80,000. By the columns between the horizontal lines 80,000 and 60,000. a  The tops of the columns representing these states are above the horizontal line 100,000
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Use the following information to answer questions 238 through 242. The scores of six students in Science verses their scores in History are shown in the table below. Student A
Student B
Student C
Student D
Student E
Student F
71
98
86
67
81
92
Science Score History Score
86
76
68
94
92
73
238. Which student scored lowest grade only in History? a. b. c. d.
Student A Student B Student D Student E c  Among the History scores 67 is the lowest.
239. What is the difference between the ranges of the scores of the two subjects? a. b. c. d.
1 2 4 5 d  Range of scores of History = 98 −67 = 31 Range of scores of Science = 94 − 68 = 26 Difference of ranges = 31 − 26 = 5
240. Which student scored the lowest grade only in Science? a. b. c. d.
Student A Student C Student D Student E b  Among the Science scores, 68 is the lowest.
241. Which student scored the highest in Science and lowest in History? a. b. c. d. TOP
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c  Student D scored 94 in Science and 67 in History. 242. What is the difference between the mean of the scores of both subjects? a. b. c. d.
4 3.5 1.5 1 d  The mean of scores of Science = (86 + 76 + 68 + 94 + 92 + 73) ÷ 6 = 81.5 The mean of scores of History = (71 + 98 + 86 + 67 + 81 + 92) ÷ 6 = 82.5 Difference = 82.5 − 81.5 = 1
Use the following information to answer questions 243 through 247. In a clinical trial, during four weeks of the trial period, each week certain number of patients in each group pulled out from the trial. The following table shows the number of pullouts for all groups. Groups Group A Group B Group C Group D
First Week 11 32 14 30
Second Week 32 44 21 39
Third Week 20 9 21 11
Fourth Week 19 33 29 12
243. In which week was the number of patients who pulled out from the trial the highest? a. b. c. d.
First week Second week Third week Fourth week b  Number of patients pulled out in First week = 11 + 32 + 14 + 30 = 87 Number of patients pulled out in Second week = 32 + 44 + 21 + 39 = 136 Number of patients pulled out in Third week = 20 + 9 + 21 + 11 = 61 Number of patients pulled out in Fourth week = 19 + 33 + 29 + 12 = 93 The highest number is 136.
244. Which group had the highest number of pull outs? a. b. c. d. TOP
Group A Group B Group C Group D Digitally Monitored for Compliance to License Terms © 20132017 Tests.com
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b  Number of patients pulled out from Group A = 11 + 32 + 20 + 19 = 82 Number of patients pulled out from Group B = 32 + 44 + 9 + 33 = 118 Number of patients pulled out from Group C = 14 + 21 + 21 + 29 = 85 Number of patients pulled out from Group D = 30 + 39 + 11 + 12 = 92 The highest number is 118. 245. Which group had the lowest number of pull outs? a. b. c. d.
Group A Group B Group C Group D a  Number of patients pulled out from Group A = 11 + 32 + 20 + 19 = 82 Number of patients pulled out from Group B = 32 + 44 + 9 + 33 = 118 Number of patients pulled out from Group C = 14 + 21 + 21 + 29 = 85 Number of patients pulled out from Group D = 30 + 39 + 11 + 12 = 92 The lowest number is 82.
246. In which week was the number of patients who pulled out from the trial the lowest? a. b. c. d.
First week Second week Third week Fourth week c  Number of patients pulled out in First week = 11 + 32 + 14 + 30 = 87 Number of patients pulled out in Second week = 32 + 44 + 21 + 39 = 136 Number of patients pulled out in Third week = 20 + 9 + 21 + 11 = 61 Number of patients pulled out in Fourth week = 19 + 33 + 29 + 12 = 93 The lowest number is 61.
247. Which group had the highest pullout average? a. b. c. d.
Group A Group B Group C Group D b  Average of patients pulled out from Group A = (11 + 32 + 20 + 19) ÷ 4 = 21.5 Average of patients pulled out from Group B = (32 + 44 + 9 + 33) ÷ 4 = 29.5 Average of patients pulled out from Group C = (14 + 21 + 21 + 29) ÷ 4 = 21.25 Average of patients pulled out from Group D = (30 + 39 + 11 + 12) ÷ 4 = 23
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248. In a daycare, the ages of children are as follows: 4, 5, 3, 5, 4, 6, 6, 4, 7, 3, 5 What is the median of the ages? a. b. c. d.
3 4 5 6 c  Arrange the data in ascending order: 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7 The middle number is 5.
249. The average of three consecutive integers is 16. What is the smallest integer? a. b. c. d.
15 16 17 18 a  Denote the first integer by x. Then the following integers are (x + 1) and (x + 2). Using the definition of average, we conclude [x + (x + 1) + (x + 2)] ÷ 3 = 16. Solve this equation. 3x + 3 = 48 3x + 3 − 3 = 48 − 3 3x = 45 x = 15
250. The heights of a group of students are given below, in centimeters. What is the range of the heights? 145, 146, 146, 154, 158, 166, 172, 174 a. b. c. d.
29 cm 30 cm 32 cm 35 cm a  The longest and the shortest heights are 174 and 145. Difference of these heights is 174 − 145 = 29.
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251. Olivia made the following scores in her History tests. What is the average of her scores? 86, 72, 78, 88 a. b. c. d.
81 80 78 75 a  Average score = (86 + 72 + 78 + 88) ÷ 4 = 324 ÷ 4 = 81
252. What is the mode of the following data? 20, 11, 15, 17, 15, 17, 19, 15, 11, 11, 20, 15 a. b. c. d.
11 15 17 20 b  Arrange the numbers in the following form: 11, 11, 11 15, 15, 15, 15 17, 17 19, 20, 20 This arrangement shows that 15 is repeated more than the other numbers.
253. A 6sided die is rolled. The probability of getting an odd number is represent? a. b. c.
It means that the chance of an odd number is 3 out of 1. It means that the chance of an odd number is 1 out of 3. It means that the chance of an odd number is 1 out of 6.
d.
It means that the chance of an odd number is 1 out of
1 . What does this fraction 3
1 . 3
b  It means that the chance of choosing one of the three numbers 1, 3, 5 out of the six numbers 1, 2, 3, 4, 5, and 6 is 1 out of 3.
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254. A box contains 42 red and green marbles. The probability of choosing a red marble from the box is a. b. c. d.
4 . What can be concluded from this fraction? 7 There are 36 red marbles in the box. There are 24 red marbles in the box. There are 22 red marbles in the box. There are 18 red marbles in the box. b  Multiply the denominator and the numerator of the fraction
4 × 6 24 = . 7 × 6 42
4 by 6. 7
This means that there are 24 red marbles among the total of 42 marbles in the box.
255. There are 32 students in Algebra class. The chance of choosing a female student is What does this fraction represent? a. b. c. d.
9 . 16
The number of male students is 14. The number of male students is 16. The number of male students is 15. The number of male students is 12. a  Multiply the denominator and the numerator of the fraction by 2.
9 × 2 18 = . This means that 18 students out of 32 students are female. Then 16 × 2 32
Number of male students = 32 − 18 = 14
256. Box A contains 124 cards marked with positive integers. The chance of choosing an odd integer is
12 . What does this fraction represent? 31 a. b. c. d.
There are 42 even integers in the box. There are 44 even integers in the box. There are 48 even integers in the box. There are 76 even integers in the box. d  Multiply the denominator and the numerator of the fraction
12 by 4. 31
12 12 × 4 48 = = . This means that 48 cards out of 124 cards are marked with odd 31 31 × 4 124 integers. So, 124 − 48 = 76 cards are marked with even integers.
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257. What chance is there of choosing a number divisible by 5 from the numbers between 53 and 75?
a. b. c. d.
7 18 4 17 5 18
4 21
d  The numbers between 53 and 75 are 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74. The count of these numbers is 21. Among these numbers only 55, 60, 65, and 70 are divisible by 5. The count of these numbers is 4. So, the chance is
4 . 21
258. Of a group of 50 students, 20 attend Algebra class. If a student is chosen randomly from the group of 50, what is the chance that the student is not attending Algebra class?
a. b. c. d.
3 5 4 5 1 5 2 3 a  The number of students do not attend Algebra class is 50 − 20 = 30.
30 3 = Therefore, the chance is 50 5 . 259. Describe the correlation between height and shoe size. a. b. c. d.
Positive Negative No correlation Cannot be determined. a  As a person’s height increases, the shoe size also increases. That is the definition of a positive correlation.
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260. Describe the correlation between time spent exercising and weight. a. b. c. d.
positive negative no correlation cannot determine b  The more a person exercises, the lower is his or her weight typically. That is the definition of a negative correlation.
261. For years, teachers have always said the more you study, the better you do on your test. Juan wanted to conduct an experiment to see if that was indeed true. He had studied for his first science test for 5.5 hours and got a 93%, his second science test for 2 hours and got a 89% and for his last science test for half an hour and got a 78%. Which of the following sentences best describe this situation? a. b. c. d.
There is a positive correlation between studying and grades. The grade is the independent variable. The two parameters are inversely related Cannot be determined. a  The more Juan studies, the better the grade he received. That is the definition of a positive correlation. The independent variable is what can be controlled, and Juan could control the amount of time studied, not his grade. If the parameters were inversely related, that would mean as one increases, the other decreases at a fixed rate, but that did not happen in this case.
262. Describe the correlation between height and hair length. a. b. c. d.
positive negative no correlation cannot determine c  The height of people does not have anything to do with their hair length. That is completely their opinion so there is no correlation between the two.
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263. The table represents the side of a square compared to its area. Side Length 2 inches 4 inches 9 inches 12 inches
Area 4 square inches 16 square inches 81 square inches 144 square inches
Which of the following statements are true based on the previous relationship? a. b. c. d.
If these two variables were graphed, the result would be linear. If these two variables were graphed, the area would be the independent variable. If these two variables were graphed, the slope is always positive. If these two variables were graphed, there would not be any correlation. c  The relationship between the two variables is that if you square the side length of the square, you obtain the area. The relationship is always positive because as the side length increases, so does the area. The relationship is not linear because the area increases at a much quicker rate than the side length.
TEAS Practice Exam – Math  Section 4 Measurements 264. 1000 mg = ___ g a. b. c. d.
1 10 100 110 a  1000 milligrams equals 1 gram. Milligrams and grams are units of weight in the metric system.
265. 160 cm = ____ mm a. b. c. d.
1.6 16 160 1600 d  1 cm equals 10 millimeters. Therefore, 160 cm will equal 1600 mm (160 x 10). Centimeters and millimeters are units of distance in the metric system.
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266. 109 g = ____kg a. b. c. d.
.0109 .109 1.09 10.9 b  1 gram equals .001 kilograms. 109 x .001 = .109. Grams and kilograms are units of weight in the metric system.
267. 4 L = ___ml a. b. c. d.
.4 40 400 4000 d  I liter equals 1000 milliliters. 4 x 1000 = 4000 milliliters. Liters and milliliters are units of volume in the metric system.
268. 75 ml = ___L a. b. c. d.
.0075 .075 .75 7.5 b  1 milliliter equals 1/1000 liter. 75 ÷ 1000 = .075 liters. Liters and milliliters are units of volume in the metric system.
269. A man weighs 80 kilograms. How much does he weigh in pounds? a. b. c. d.
176 lbs. 185 lbs. 210 lbs. 80 lbs. a  To convert kilograms to pounds, multiply the number of kilograms by 2.2. 80 x 2.2 = 176 lbs. A kilogram is a unit of weight in the metric system.
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270. A kitten was weighed at 4 weeks old and the scale registered 0.8 lbs. If the kitten gains 0.05 lbs. per week, what will the kitten weigh at 8 weeks old? a. b. c. d.
4.5 lbs. 4.2 lbs. 1.0 lbs. 8.2 lbs. c  To determine how many pounds the kitten gains, first we need to figure out how many weeks go by between the starting date and the final date. 8 – 4 = 4 weeks. If the kitten gains 0.05 lbs. per week, we now need to multiply .05 by 4 which gives us 0.2 lbs. total. Then we need to add it to the starting weight, 0.8 lbs. 0.8 + 0.2 = 1.0 lbs.
271. Greg is building a rectangle dog run. He has 14 pieces of fencing, each piece measuring 5’ by 5’. Which of the following areas are plausible for the dog run? a. b. c. d.
150 ft2 250 ft2 300 ft2 All of the above d  First we need to figure out what the perimeters could possibly be. There are 14 pieces of fencing, so the fence could be 1 piece by 6 pieces (2[1] + 2[6] = 14). There could also be 2 pieces by 5 pieces, and 3 pieces by 4 pieces. To convert to feet, multiply the number of pieces by 5 since each piece is 5’. Therefore, by finding the area of each of the possible perimeters, we get (1 x 6)  5 x 30 = 150, (2 x 5)  10 x 25 = 250, and (3 x 4)  15 x 20 = 300. All of the options are correct.
272. David walks 6 miles in 4 hours. What is the unit rate? a. b. c. d.
6 mph 2 mph 1.5 mph 3 mph c  To find the unit rate, first write the rate and then reduce the denominator to be a value of 1. 1.5 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 6 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 4 ℎ𝑟𝑟
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273. During what time period is the greatest rate of change?
a. b. c. d.
0 – 1.0 2.0 – 3.0 1.0 – 2.0 4.0 – 5.0 d  The greatest rate of change is equivalent to greatest slope. Looking at the options, choice d is the steepest slope. Therefore, choice d has the greatest rate of change.
274. 54⁰ F = _____⁰ C a. b. c. d.
1.2 10.22 12.22 102.22 c  To convert Fahrenheit to Celsius, first subtract 32 and then multiply by 5/9. 54 – 32 = 22 22 x 5/9 = 110/9 110/9 = 12.22
275. 32⁰ C = _____⁰ F a. b. c. d. TOP
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a  To convert Celsius to Fahrenheit, first multiply by 9/5 and then add 32. 32 x 9/5 = 288/5 288/5 = 57.6 57.6 + 32 = 89.6 276. A woman weighs 132 pounds. What is her weight in kilograms? a. b. c. d.
13,200 1,320 132 60 d  To convert pounds to kilograms, divide the number of pounds by 2.2. 132 / 2.2 = 60 kg. A kilogram is a unit of weight in the metric system.
277. A man is 6’4” in height. How tall is he in centimeters? a. b. c. d.
152 164 193 640 c  To answer this question, we must first convert 6’4” to inches. 6 x 12 inches = 72 inches 72 inches + 4 inches = 76 inches To find centimeters, use the following formula: inches multiplied by 2.54. 76 inches x 2.54 = 193.04
278. Which of the following is equivalent to 3 pounds and 12 ounces? a. b. c. d.
42 ounces 48 ounces 52 ounces 60 ounces d  Each pound is equal to 16 ounces. Therefore, 3 pounds + 12 ounces = 3 × 16 + 12 = 48 + 12 = 60 ounces
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279. The weight of the object M is 9 kg and 112 g, and the weight of the object N is 1200 g. What is the total weight in grams? a. b. c. d.
10122 grams 10312 grams 11021 grams 13021 grams b  One kilogram = 1000 grams Weight of M = 9 × 1000 + 112 = 9112 grams Weight of N = 1200 grams Weight of M and N = 9112 + 1200 = 10312 grams
280. What is the total, in inches, of 5 yards, 5 feet and 22 inches? a. b. c. d.
262 inches 254 inches 248 inches 234 inches a  One yard = 36 inches 1 foot = 12 inches 5 yards + 5 feet + 22 inches = 5 × 36 + 5 × 12 + 22 = 262 inches
281. How many miles are in 24,500 kilometers? a. b. c. d.
12,512.5 miles 15,312.5 miles 15,315.5 miles 15,512.5 miles b  The estimated relationship between mile and kilometer is 1 mile = 1.6 kilometers. Therefore, the estimated equivalent of 24,500 kilometers is calculated as follows: 24,500 ÷ 1.6 = 15,312.5 miles
282. Which of the following has the unit rate of 32 miles per hour? a. b. c. d.
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128 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 4 ℎ𝑟𝑟 64 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 2 ℎ𝑟𝑟 256 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 8 ℎ𝑟𝑟
All of the above
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d  To find the unit rate, first write the rate and then reduce the denominator to be a value of 1. We want our final answer to be 32 miles per 1 hour. Checking each of the choices, we see that all of them have the unit rate of 32 miles per hour. 32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 128 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 4 ℎ𝑟𝑟 32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 64 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 2 ℎ𝑟𝑟
32 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 256 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 1 ℎ𝑟𝑟 8 ℎ𝑟𝑟
283. Tim drives a truck 6 days a week for 9 hours a day. Each week, he logs about 3,600 miles. What is his average speed while driving? a. b. c. d.
59 mph 62 mph 72 mph 67 mph d  First, multiply the number of hours Tim drives by the number of days (6 days x 9 hours per day) to find that each week, Tim drives for 54 hours. To find his average speed, find the unit rate. 3600 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 54 ℎ𝑟𝑟
= 67 mph.
284. What is the difference between the following lengths, in meters? M: 12 m, 119 cm N: 1.2 m a. b. c. d.
1379 cm 1289 cm 1299 cm 1199 cm d  We know 1 m = 100 cm. M = 12 m + 119 cm = 12 × 100 + 119 = 1319 cm N = 1.2 m = 1.2 × 100 = 120 cm Difference = 1319 − 120 = 1199 cm
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285. A student mixed the following materials to make a chemical substance: Carbon = 606 grams Phosphor = 1443 grams What is the weight of the mixture in kilograms? a. b. c. d.
4 kg 3 kg 2 kg 1 kg c  1 kilogram = 1000 grams Weight of the mixture = 606 grams + 1443 grams = 2049 grams 2049 g = (2049 ÷ 1000) kg = 2.049 kg ≈ 2 kg
286. Using “Vernier calipers”, the diameters of two steel bearings are measured as 4.34 cm and 3.39 cm. What is the sum of the diameters of the bearings in millimeters? a. b. c. d.
77.3 mm 73.7 mm 63.7 mm 60.3 mm a  1 cm = 10 mm Total length of diameters = 4.34 + 3.39 = 7.73 cm Total length of diameters = 7.73 × 10 = 77.3 mm
287. The distance between the Low and High settings in a “Volume Control” is 24 cm. If the distance is marked by 16 equally spaced lines, what is the distance between each two adjacent lines, in millimeters? a. b. c. d.
15 mm 14 mm 12 mm 10 mm a  1 cm = 10 mm Distance = 24 × 10 = 240 mm Distance between each two lines = 240 ÷ 16 = 15 mm
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288. The scale of a map is 3 centimeters = 60 miles. The distance, on the map, from the east boundary to the west boundary of Kingston is 1.2 cm. What is the distance from the east boundary to the west boundary in miles? a. b. c. d.
29 miles 26 miles 24 miles 21 miles c  Denote the real distance by x. Then solve the following proportion.
3 60 = 1.2 x
3x = 60(1.2) 3x = 72 x = 24 miles 289. A picture is enlarged by the scale factor of 5. If the dimensions of the picture were 4.2 in. by 8.4 in. before enlargement, what are its dimensions after enlargement? a. b. c. d.
24 by 34 21 by 32 26 by 34 21 by 42 d  Multiply each dimension by the scale factor. 4.2 × 5 = 21 8.4 × 5 = 42
290. If we want to draw a plan for a basketball court with the dimensions 85 feet by 50 feet using the scale factor of 5 ft. = 1 in., then what would be the new dimensions? a. b. c. d.
18 in. by 11 in. 17 in. by 10 in. 15 in. by 13 in. 15 in. by 10 in. b  Denote the dimensions after scaling by x and y. Then solve the following proportions:
1 5 = x 85
5x = 85 x = 17 in. 1 5 = y 50 5y = 50 y = 10 in. TOP
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291. How many inches are in one yard? a. b. c. d.
38 inches 36 inches 34 inches 32 inches b  1 yard = 3 feet 1 foot = 12 inches 1 yard = 3 × 12 = 36 inches
292. How many cubic centimeters are in a liter? a. b. c. d.
10 100 1000 10000 c  One liter is equivalent to 1000 cubic centimeters.
293. How many pints are in a gallon? a. b. c. d.
4 5 6 8 d  1 gallon = 4 quarts 1 quart = 2 pints 1 gallon = 2 × 4 = 8 pints
294. What is (2 gallons, 8 quarts) in quarts only? a. b. c. d.
10 14 16 20 c  1 gallon = 4 quarts. 2 gallons + 8 quarts = 2 × 4 + 8 = 16 quarts
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295. What is (2 decameters, 34 decimeters) in centimeters? a. b. c. d.
2340 cm 2420 cm 2440 cm 2624 cm a  1 decameter = 1000 centimeters 1 decimeter = 10 centimeters 2 dm + 34 dc = 2 × 1000 + 34 × 10 = 2000 + 340 = 2340 cm
296. What is (5 yards, 4 feet) in inches? a. b. c. d.
228 in. 218 in. 192 in. 188 in. a  1 yard = 36 inches 1 foot = 12 inches 5 yards + 4 feet = 5 × 36 + 4 × 12 = 180 + 48 = 228 in.
297. Cindy wants to add some preservative to 0.8 kg dried fruit. What unit of measurement should she use to weigh the preservative? a. b. c. d.
Kilogram Gram Pound Liter a  Since the preservative is a small portion of the total weight of the product, the preservative must be measured in grams.
298. A carton contains 112 notebooks. If each notebook weighs 6 ounces, what weight unit should be used on the carton where the total weight is recorded? a. b. c. d.
Liter Ton Kilogram Pound d  Multiplying the weight of each notebook by the number of notebooks gives 6 × 112 = 672 ounces. Dividing this number by 16 gives the exact weight 42 pounds.
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299. A truck is carrying 124 boxes of rootbeer. Each box contains 24 bottles and the weight of each bottle is 340 grams. What measuring unit is proper to represent the total load of the truck? a. b. c. d.
Pound Gram Ton Liter c  Total weight of the load = 124 × 24 × 340 = 1011840 g = 1011.840 kg = 1.002 tons
300. A patient is to receive 2 grams of a drug. The drug comes in 500 mg/5 cc. Each vial has 10 cc. How many vials does the patient need? a. b. c. d.
1 2 3 4 b  Answering this question is a twostep process. First, you must convert 2 grams to milligrams (mg). There are 1000 mg in a gram, so 2 x 1000 = 2000 mg. Then you plug 2000 mg into the following equation: 2000 mg = 500 mg x cc 5 cc 500x = 10000 x = 20 cc Since there are 10 cc in each vial, the patient will need 2 vials.
301. What is the volume of a gold bar that is 4.5 cm long, 3.5 cm wide and 2 cm thick? a. b. c. d.
10 cm³ 15.75 cm³ 20.25 cm³ 31.5 cm³ d  To find the volume of a rectangular solid can be calculated as follows; volume = length x width x thickness In this case, 4.5 x 3.5 x 2 = 31.5 cm³
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302. The dimensions of a rectangle are 2 feet and 240 inches. What is the area of the rectangle? a. b. c. d.
5760 in.2 5780 in.2 5860 in.2 5980 in.2 a  Area = (2 ft.)(240 in) = (2 × 12 in.)(240 in.) = (24 in.)(240 in.) = 5760 in.2
303. The line segment AE is made up of AB = 2 ft., BC = 25 in., CD = 3 ft. and DE = 35 in. What is the length of AE in inches? a. b. c. d.
54 ft. 60 ft. 118 in. 120 in. d  Replace the given measures in the equation below: AE = AB + BC + CD + DE = (2 ft.) + (25 in.) + (3 ft.) + (35 in.) = (2 × 12 in.) + (25 in.) + (3 × 12 in.) + (35 in.) = 24 in. + 25 in. + 36 in. + 35 in. = 120 in.
304. The area of a tract of land A is 232 square meters and the area of the land B is 420,000 square decimeters. Find the total area of A and B in square meters. a. b. c. d.
608 m2 612 m2 652 m2 672 m2 c  100 square decimeter = 1 square meter Total Area = (232 m2) + (420000 dc2) = (232 m2) + (42000 ÷ 100 m2) = 232 m2 + 420 m2 = 652 m2
305. The average temperature of New York on a sunny day is 77 degrees Fahrenheit. Which is the equivalent of this temperature in degrees Celsius? a. b. c. d. TOP
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d  Replace F = 77 with F =
9 C + 32 77 = 5 9 77 − 32 = C + 32 − 32 5 9 C 45 = 5
9 C + 32 , and solve for C. 5
C = 25
TEAS Practice Exam – Math  Section 5 Geometry 306. Find the area of the shaded region. 7 cm
9 cm
11 cm
9 cm a. b. c. d.
99 cm2 81 cm2 97 cm2 101 cm2 c  To find the area of the shaded region, find the area of the entire rectangle and the subtract the area of the triangle in the corner. The area of the rectangle is found by multiplying 9 cm and 11 cm to get 99 cm2. The area of the triangle uses the formula (b * h) / 2. The base is 2 cm since 9 cm – 7 cm = 2 cm. The height is 2 cm since 11 cm – 9 cm = 2 cm. The area is (2 * 2)/2 = 2 cm2. 99 cm2 – 2 cm2 = 97 cm2. Answer A is the area of the rectangle without subtracting the triangle.
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307. Find the perimeter of the following regular figure.
4 in
a. b. c. d.
64 in 40 in 48 in 60 in a  Since the instructions say “regular” figure, we know that all of the sides are 4 inches. There are 16 sides, so either multiply 4 by 16 or use repeated addition to add 4 together 16 times. Either way, we get 64 inches. The other choices are if the number of sides are counted incorrectly.
308. What is the area of the following figure? Keep your answer in terms of pi. 4 ft.
a. b. c. d.
16π ft2 12π ft2 π ft2 4π ft2 b  To find the area for the partial circle, find the area of the whole circle (π*r2) and then multiply by ¾ since that is ¾ of the circle. π *42 = 16 π which is the area of the whole circle. 16 π * ¾ = 12 π.
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309. Find the area of the shaded area rounded to the nearest hundredth. Use 3.14 as π. 16 in
5 in
a. b. c. d.
22 in
75.38 in 14.625 in 2 1,760 in 2 95 in 2 2
a  To find the area of the composite figure, break it into a trapezoid and a circle and subtract the area of the circle from the trapezoid. The 5 represents the height of the trapezoid as well as the diameter of the circle. For the circle, find the area by using the formula π*r2. 3.14*2.52 = 19.625. For the trapezoid, use the formula ½ * h * (b 1 + b 2 ). ½ * 5 * (16 + 22) = 95. Then subtract: 95 – 19.625 = 75.375. While that is not a choice, Answer A is correct if the answer is rounded to the nearest hundredth. 310. Find the perimeter of the figure. Use 3.14 as π.
6
8.73 6.29
14.2 a. b. c. d.
36.84 32.48 35.22 45.33 c  To find the perimeter, add all of the sides together. Make sure to line up the decimals when adding. 6.29 + 14.2 + 8.73 + 6 = 35.22.
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311. Find the area of the figure. Use 3.14 as π.
6
6
a. b. c. d.
54 432 82.26 36.84
12
c  To find the area of the composite figure, break it into a trapezoid and a half circle. The 6 represents the height of the trapezoid as well as the diameter. For the half circle, find the area of the whole circle (π*r2) and then divide by 2. 3.14*32 = 28.26. For the trapezoid, use the formula ½ * h * (b1 + b2). ½ * 6 * (6 + 12) = 54. Then add the areas together: 28.26 + 54 = 82.26. Answer A only takes into account the trapezoid, and Answer B multiplies the 3 numbers on the figure together. 312. Tom is building a wooden fence for his rectangular back yard. The dimensions that he wants the fence is 18 ft. by 24 ft., with one fivefoot metal gate. Each piece of wood is 5 inches wide and 5 feet tall. Tom also wants one inch between each piece of wood. How many pieces of wood will he need to buy? a. b. c. d.
185 pieces 158 pieces 74 pieces 72 pieces b  In order to figure out how many pieces of wood Tom needs to buy, find the perimeter first. 2(18) + 2(24) = 36 + 48 = 84 ft. Then subtract the 5’ gate to have 79 feet. Since each piece is 5 inches wide, with one inch in between, we need to figure out how many times does 6 inches go into 79 feet. 6 inches goes into 1 foot twice, so 6 inches goes into 79 feet 158 times.
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313. What is the correct equation to find the perimeter of a rectangle with a length of 4 cm and a width of 8 cm? a. b. c. d.
4 + 8 = 12 4 * 8 = 32 (4*8)/2 = 16 2(4) + 2(8) = 24 d  To find the perimeter, add all of the sides together. Since it is a rectangle, there are two sides that are 4 cm and two sides that are 8 cm. The only option that matches that is D.
314. What is the length of the arc of a circle made by a 90° angle? The circle has a diameter of 8 ft. Leave your answer in terms of π. a. b. c. d.
4π ft. 16π ft. 8π ft. 2π ft. d  To find a length of the arc, multiply the circumference by the fraction of the circle that the arc covers (angle/360). Find the circumference by the following formula: C = π * d. Plugging in the value for the diameter, we get the circumference to be 8π. To find an arc, multiply the fraction of the circle represented by the circumference. Since the arc is being made by the 90° angle, the fraction of the circle is ¼ because that is 90/360. The length of the arc is ¼ * 8π = 2π.
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315. The illustration is of a small white circle within a large blue circle. The radius of the small circle is 4 in. The diameter of the large circle is 12 in. Find the area of the shaded region. Leave your answer in terms of π.
a. b. c. d.
16π in 2 36π in 2 20π in 2 128π in 2 c In order to find the area of the shaded region, first we find the area of the large circle and then subtract the area of the small circle. To find the area of a circle, use the formula Area = π * r 2. For the big circle, the diameter is given, so it needs to be divided in half to get the radius. π * 62 = 36π, but that is the entire circle. The area of the small circle is π * 42 = 16π. Subtracting 16 π from 36π, our final answer is 20π in 2.
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316. If RS = 12 cm, what is the length of a radius of the circle A?
R
90
A
a. b. c.
d.
S
9.68 cm 9.28 cm 8.82 cm 8.48 cm d  Triangle ARS is a right isosceles triangle. Therefore, AS = AR. Apply the Pythagorean Theorem. (RS)2 = (RA)2 + (AS)2 (12)2 = (RA)2 + (RA)2 144 = 2(RA)2 72 = (RA)2 RA = 8.48 cm
317. In the isosceles triangle ABC, the vertex angle A is 40º. What is the measurement of a sideangle? a. b. c.
d.
70º 62º 60º 55º a  Since ∠A is the vertex angle, then ∠B and ∠C are sideangles and are equal. ∠B = ∠C and m∠A = 40º Replace these equations in m∠A + m∠B + m∠C =180º. 40º + m∠C + m∠C = 180º 2(m∠C) = 140º m∠C = 70º
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318. In the rhombus ABCD, m∠A = 34º. What is m∠DBC? A
B
D
C
a. b. c. d.
83º 82º 78º 73º d − m∠A = 34 m∠A + m∠B =180 34 + m∠B = 180 m∠B = 180 − 34 = 146 BD is the angle bisector of the angle B. So, it divides 146º into two equal parts. m∠DBC = 146 ÷ 2 = 73º
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319. In the isosceles right triangle ABC, BC = 14 in. What is the area of the triangle? B
C
A
a. b. c. d.
56 in.2 52.04 in.2 49 in.2 48.02 in.2 c − Apply BC = 14, AB = AC, and the Pythagorean Theorem. (BC)2 = (AB)2 + (AC)2 142 = (AB)2 + (AB)2 196 = 2(AB)2 98 = (AB)2 Area = (AB)(AC) ÷ 2 = (AB)(AB) ÷ 2 = (AB)2 ÷ 2 = 98 ÷ 2 = 49 in.2
₂ 320. The segment line AB with A(3, 5) and B(7, 8) is translated 3 units vertically up. What are the new locations of A and B? a. b. c. d.
A’(8, 3) and B’(3, 11) A’(3, 8) and B’(11, 3) A’(3, 11) and B’(3, 7) A’(3, 8) and B’(3, 11) d − Since the points are translated vertically only; therefore, their ycoordinates will be changed only. A(3, 5) will be changed to A’(3, 5 +3) = A’(3, 8) and B(7, 8) will be changed to B’(3, 8 + 3) = B’(3, 11)
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321. The following statements are given in the triangle ABC. p : Triangle ABC is equilateral q : Altitudes AD and BE are equal. a. b. c. d.
If p, then q. If q, then p. If q, then not p. If p, then not q. a − In any equilateral triangle, all the altitudes are equal.
322. Which set of angle measures can represent the interior angles of a triangle? a. b. c. d.
54º, 67 and 34º 32º, 48º and 90º 42º, 90º and 58º 33º, 80º and 67º d  The sum of the angles must equal 180º. 33 + 80 + 67 = 180
323. Which set of sidelengths can represent the sides of a triangle? a. b. c. d.
12, 18, 22 11, 13, 24 13, 15, 29 14, 18, 38 a  Only in (a), the sum of two sides is greater than the third side. For example: 12 + 18 > 22
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10 Test Preparation Tips 1. Start Studying 3 Months Before The Test  You have a lot of information to review to get prepared. Give yourself enough time to study all of it in a relaxed state of mind. Trying to cram your study in a month or a few weeks before the test will just create anxiety and even panic which is not conducive to learning. 2. Outline a Study Schedule and Stick to It– You first need to find out what subjects the test covers, then break them down into a study outline. An outline of the material will give you a birdseyeview of what you have to cover and allow you to plan to actually study it. Include review days throughout the schedule where you review material you studied the month or two before. Include practice test sessions in your schedule as well. Once you have a study schedule established, commit to it and be disciplined. It will only help you, and give you the benefit of comprehensive study, if you actually follow it. 3. Study Every Day for at Least One Hour – Getting prepared for an entrance exam takes commitment. To maintain this commitment, it is best to make it part of your regular schedule. Plan an hour a day to study the material you have scheduled for the day. 4. Obtain a Good Study Guide – A good study guide is very important. It will give you the substance you need to know for the test. 5. Use Flashcards – Flashcards are easy to use and can interject some fun into the study process. Flashcards that give you a question on one side and an answer on the other are the most effective. Use them regularly throughout your study schedule. 6. Take Untimed Practice Tests Periodically to Assess Your Knowledge of the Material – Use the Tests.com Practice Test to find out how well you know the material. For the first couple times, do not time yourself, but use the test simply to determine your strengths and weaknesses. Focus your study on the areas of the exam where you had the most trouble. 7. Take a Timed Practice Test Periodically to Practice Test Taking Skills – Take the Tests.com Practice Test using a timer setting. Determine how many questions are on your state exam and complete that amount of questions in the allotted time. This exercise will allow you to get a sense of how fast you need to work under time pressure. 8. Tab and Highlight your Reference Books – Depending on the test, some organizations have open book tests, allowing you to use a reference book while you take the test. Most testing rules do not allow notes in the reference book you use, but many allow highlighting and tabbing. When you use a reference book during a test, it is important to use it in such a way that allows you to work efficiently and not slow you down. Place colored tabs on the pages of the book referencing the sections, so you can turn to them quickly and not have look up page numbers in the Table of TOP
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Contents. Highlight those sections which you believe to be important and that will be subject to testing. 9. Meet with Friends who are Studying for the Test and have a Group Discussion  Your friends and colleagues who are studying for the test will have different strength and weaknesses than you. You can benefit each other by sharing information, discussing issues and asking each other questions about the information subject to testing. 10. Don’t Study the Day or Night Before the Test – You have prepared for months. Even though you may feel a bit anxious the day before the test, it is important that you give your brain a rest. During the test, you must be clear of mind and able to nimbly move from question to question. If your brain is tired and your eyes are having trouble focusing, you will put yourself at a great disadvantage. Do not study late into the night. You know the material more than you realize. Take the day off, go for a walk, a bike ride or see a movie.
10 Test Taking Tips 1. Get Good Rest the Night before the Test – All the study in the world will not save you if you can’t focus your eyes and your mind is cloudy due to staying up late at night to study before the test. Test taking is an art and you must have a clear, well rested mind to do well. An important tip, and the first in this list for a reason, is to get a good night’s rest the day before the test. 2. Eat a Good Meal before Leaving for the Test – Tests usually last a couple of hours. They take much concentration and mental energy. You don’t want to have your blood sugar level affect your ability to concentrate. Eat a good meal before leaving to take the test. Stay away from foods that would make you tired. 3. Get to the Testing Location on Time and Mentally Prepare Yourself – You do not want to get lost on your way to the testing location or leave too late such that you miss the beginning of the exam or even have to rush to get to your seat. You want to arrive in enough time to sit for 10 or 15 minutes prior to the test to collect your thoughts and clear your mind. Make sure you have the address to the testing location the day before the test, ensure you have the right directions or use a GPS system and find out beforehand how much time it will take to get there so you know when to leave. 4. Read the Question and Understand What it is Asking – A cardinal rule of test taking is “Do not read into the question and Answer only What is Asked.” Before you read the answers, make sure you understand what the question is asking. Do not let yourself insert qualifications into the questions or assume additional fact patterns. 5. Form an Answer in Your Mind before Reading the Answer Options – If an answer comes to you before you read the answer options, and the answer that came to you matches an answer option, TOP
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odds are that the answer option corresponding to the answer that popped into your head is the correct answer. You know more than you realize. This is how preparation benefits you. 6. Read all of the Answers  Even though the first answer option looks right, read all of the answer options all of the time. One of the answers is the correct choice. All the information to answer the question is there. Read all the answer options to understand what options are available. You will find, while one of the first top selections seems right some of the time, a bottom option will occasionally be the right selection because it qualifies the answer in the correct way. If you just take the first answer that seems right without reading the other answer options, you will not get the benefit of all the information in the answer options. 7. Eliminate Obviously Wrong Answers – Some of the answer options will obviously be wrong. You can increase the odds you will select the right answer and work more efficiently by first eliminating obviously wrong answers. 8. Don’t get Stuck on Difficult Questions – Some questions will have difficult or complex fact patterns that require some thought or calculation. If you find yourself getting lost in the facts or numbers, or stuck on the answer options, such that you start feeling anxious that you are wasting time, take the following steps: guess and register an answer, mark the question with some notation that will tell you it was a guess, and come back to it at the end of the test, after you finished all other questions. 9. Pace Yourself  Don’t Work too Fast; Don’t Work too Slow – Time is a very important element of test taking. Aside from the subject matter, it is the factor that most causes pressure and stress. To obtain a good score, it is important that you have the time to read and answer all of the questions. Tests only allow a certain amount of time per questions. Determine what that time per question is by dividing the time by the number of questions. Pace yourself when taking the test so that you allow yourself enough time to read and answer all questions. You don’t want to work too fast or too slow. 10. Maintain a Good Attitude during the Test – It is important to keep your composure during the test. Having a good attitude will allow you to get through the challenging parts of an exam and avoid becoming down or defeatist, which could slow you down or stop you altogether from finishing the exam. Hang in there and have confidence. If you prepare for the exam following the preparation and test taking tips discussed here, you can have confidence that you will succeed.
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Tests.com Format Comparison Chart Features & Benefits
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