teas v math 2014 practice exam kit

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Practice Test for the TEAS V Mathematics

__________________________________________ Published by Tests.com LLC PO Box 232 Lititz, PA 17543 www.Tests.com ISBN: 978-1-938967-41-2 Copyright © 2013-2014 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.

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Table of Contents Review of the TEAS V ..................................................................................................................... 1 Practice Exam Questions

Section 1 – Numbers and Operations .................................................................................... 8 Section 2 – Algebra ............................................................................................................... 48 Section 3 – Data Interpretation ............................................................................................ 64 Section 4 – Measurements ................................................................................................... 79

Practice Exam Answers ................................................................................................................ 87 Practice Exam Questions with Answers .................................................................................... 129 Test Preparation and Test Taking Tips ...................................................................................... 244 Bubble Sheet .............................................................................................................................. 247


1

Review of the TEAS V

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), version V. This review discusses the requirements of

the TEAS V.

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 pre-admission testing prior to the admissions deadline for the respective

program.

The TEAS is an aptitude test. It is a four-part 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. 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 test-takes performance on the

test. The following scores are given in ATI’s TEAS score report:

1. Adjusted Individual Score

2. National mean

3. Program mean


3

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 sub-test measures knowledge of grammar, sentence structure, punctuation,

contextual words and spelling. The time given to take this section is 34 minutes. It has a total of

55 testing items.


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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 sub-test covers whole numbers, metric conversions, fractions and decimals,

algebraic equations, percentages and ratio/proportions. This section of TEAS has 45 testing

items that need to be answered in 51 minutes. You will get a little more than a minute to

answer each question.

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 use of calculators is prohibited in this section since the

emphasis is on mental activity. Moreover, the questions are such that can be solved with simple

mental calculations or with some scratch work.


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Science

The science portion of the exam covers science reasoning, science knowledge, biology,

chemistry, anatomy and physiology, basic physical principles and general science. There are 30

science testing items asked and the 66 minutes are given to complete the test.

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 sub-test covers paragraph comprehension, passage

comprehension and inferences and conclusions. The reading section of TEAS contains a total of

40 testing items to answer 58 multiple-choice questions.

This section is a typical reading test where students are asked to read a passage and answer

questions that follow it. It 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. There can be direct

questions as well as indirect questions based on the passage. However, 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 pre-registering. Log on to www.atitesting.com. Click Create New Account

http://www.atitesting.com/�


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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 computer-based 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.




8

TEAS Practice Exam – Math - Section 1 Numbers and Operations

1. 1/4 + 2/8 = a. 3/12 b. 3/4 c. 5/4 d. 1/2

2. 4 x 3/7 = a. 1 b. 3/7 c. 1 5/7 d. 12/28 3. 5/6 x 3/4 = a. 5/8 b. 8/10 c. 15/10 d. None of the above. 4. 348 ÷ 6 = a. 48 b. 58 c. 68 d. 74 5. 8 – 3 x 4 + 9 = a. 5 b. - 5 c. 65 d. - 65


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6. 18 – 23 + 99 ÷ 3 = a. 28 b. 285 c. 105 d. 37.3 7. – 33 – 5 x 1 = a. 39 b. 38 c. - 38 d. 1 8. 2/3 ÷ 4/5 = a. 3/5 b. 5/6 c. 6/8 d. None of the above.

9. 36 ÷ .4 = a. 9 b. 40 c. 90 d. 144 10. .08 + 7 x 9 = a. 63.08 b. 62.73 c. 63.72 d. 62.37


10

11. In Science Hill High School, 45% of students are female. What fraction of the students is male?

a. 1125

b. 1320

c. 1120

d. 9

20

12. Two fifths of the members of a Literature Club are published writers. What percent of the members are not published writers? a. 25% b. 40% c. 60% d. 65%

13. If 25% of A is equal to 48, then what is 23

of A?

a. 124 b. 128 c. 142 d. 122

14. If 35

the expression (2x + 3y) is 60, then what is 3.25 times the expression (2x + 3y)?

a. 325 b. 322 c. 314 d. 304

15. What is 25% of

33.25 +

4?

a. 5 b. 4 c. 3 d. 1


11

16. What is the product of 0.32002 × 3200.5? a. 1042.242010 b. 1204.224010 c. 1024.224010 d. 102.4224010

17. 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. $78.97 b. $87.79 c. $97.58 d. $99.85

18. 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 2010-2011, to the nearest hundredth? a. $19.19 b. $19.91 c. $91.19 d. $29.91

19. What is the quotient of the division 2004.52 ÷ 4.52 to the nearest hundredth? a. 424.37 b. 443.47 c. 483.47 d. 524.73

20. If 24% of the expression (m + 2n) is 48, then what is 25% of (m + 2n)? a. 40 b. 48 c. 50 d. 56


12

21. John spends 12% of his salary on groceries each month. If his monthly salary is $3400, how much does he spend on groceries? a. $448 b. $424 c. $412 d. $408

22. 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. 103.81% b. 111.38% c. 113.18% d. 123.81%

23. 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. 11.11% b. 12.21% c. 14.11% d. 21.11%

24. If 28% of 20% of A is 420, what is A? a. 7500 b. 7700 c. 7850 d. 8500

25. A washing machine is marked down 32% from its original price of $450. What is the sale price of the washing machine? a. $360 b. $306 c. $300 d. $266


13

26. 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. 32% b. 29% c. 27% d. 25%

27. A is 29% of 2900, and B% of 290 is 29. What is A + B? a. 812 b. 831 c. 841 d. 851

28. 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. $227.39 b. $244.43 c. $264.23 d. $268.43

29. What is the result of adding 23

the division of 32.24 by 24.32 to the product of 24 and 32?

a. 779.79 b. 777.39 c. 769.93 d. 768.88

30. 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. $88.51 b. $79.51 c. $76.15 d. $67.51


14

31. Add 2.3 times 3.2 to 23

the sum of 23 and 32.

a. 48.33 b. 46.33 c. 44.03 d. 42.03

32. 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. $0.23 b. $0.13 c. $0.11 d. $0.10

33. Given A = 5

126

and B = 7

12, what is

-A BA + B

?

a. 147161

b. 157151

c. 137161

d. 129161

34. To make 3

45

cakes, 2

33

pounds of flour is needed. How much flour is needed to make one cake?

a. 0.08 pound b. 0.68 pound c. 0.78 pound d. 0.80 pound

35. Find the ratio of M + 2N to 2M + N, if M =

1 52 - 1

4 4 and N =

1 44 - 2

4 5.

a. 6 b. 5 c. 3 d. 2


15

36. Given A = 1

26

and B = 13

, divide

12 + 3

3A by

12 -

3B .

a. 29 b. 26 c. 23 d. 22 37. Given A and B below, what is the sum of A and B?

A =

1 1 1+ 3

2 3 2

B = −

1 1 13

2 3 2

a. 132

b. 13

12

c. 172

d. 1122

38. In the process of film development, photographers use a chemical called “stop bath.” A

photographer used 2

23

bottles of stop bath for the first group of rolls of film and 2

43

bottles of 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. 293

b. 192

c. 173

d. 164


16

39. The sum of which numerical expression has the greatest whole number part?

K = 2 1

3 + 23 4

L = 13 6

1 + 13 4

M = 8 10

+ 23 4

N = 1 1

5 + 33 2

a. K b. L c. M d. N

40. Given A, B, and C below, find A + 2B − 3C.

A = 5

37

B = 2

15

C = 13

a. 13

835

b. 3

635

c. 18

535

d. 1

521


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41. A house built on ground sank every year according to the following list:

2008: 23

in.

2009: 17

in.

2010: 15

in.

2011: 15

in.

In which of the following combination of years did the house sink the most? a. 2008 and 2009 b. 2009 and 2010 c. 2010 and 2011 d. 2008 and 2011

42. 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. A b. B c. C d. D

43. 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 Income Spending January $3420 $2970 February $2927 $2212 March $3189 $3020 April $3024 $2730

a. January and February b. February and March c. March and April d. January and March


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44. 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. 9 cases of soda, and 4 bags of potato chips b. 7 cases of soda, and 5 bags of potato chips c. 6 cases of soda, and 11 bags of potato chips d. 4 cases of soda, and 15 bags of potato chips

45. A, b, c, and d are whole numbers such that a = 2b and b = 2c. Which expression is definitely a whole number?

a. 2

a b c+ +

b. 2

8a b c+ +

c. 210

a b c+ +

d. 212

a b c+ +

46. The ratio of a to b is 23

and the ratio of c to b is 215

. What is the ratio of a to c?

a. 143

b. 145

c. 5 d. 3


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47. 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. 32 in. b. 24 in. c. 20 in. d. 16 in.

48. Which statement is true given the proportion a c=b d

?

a. a c=d b

b. d b=a c

c. c b=d c

d. d c=b a

49. Which of the following quantities has the highest rate of change? a. Increase of the height of Michelle from 98 cm at the age of 9 to 108 cm at the age of 14 b. Increase of the height of Sarah from 74 cm at the age of 7 to 92 cm at the age of 11 c. Increase of the height of Joanne from 56 cm at the age of 6 to 82 cm at the age of 10 d. Increase of the height of Alison from 52 cm at the age of 5 to 108 cm at the age of 14

50. 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. $18.00 b. $17.00 c. $12.00 d. $11.00


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51. 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. 251.3 b. 219.7 c. 205.5 d. 201.2

52. 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. 0.272 in. b. 0.377 in. c. 0.389 in. d. 0.477 in.

53. Given m = 3.2, n = 2.2, and p = 2.1, what is the value of

+-

m nmnp

n p to the nearest tenth?

a. 798.5 b. 789.3 c. 798.5 d. 798.3

54. 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. 0.10 b. 0.11 c. 0.15 d. 0.16


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55. 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. 30 in. b. 31 in. c. 32 in. d. 34 in.

56. Which of the following formats of subtraction is arranged properly using the regrouping method for 9415 − 4786?

a.

8 13 11 15

9 4 1 54 7 8 6−

b.

8 12 10 15

9 4 1 54 7 8 6−

c.

8 13 10 5

9 4 1 54 7 8 6−

d.

8 13 10 15

9 4 1 54 7 8 6−

57. Which subtraction can be performed using the regrouping method? a. 43,0987 − 34,0765 b. 20,007 − 10,003 c. 34,087 − 32,986 d. 54,983 − 44,572


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58. 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. 3799 ft2 b. 3898 ft2 c. 3978 ft2 d. 3988 ft2

59. 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. 1879 gallons b. 1899 gallons c. 1989 gallons d. 1999 gallons

60. Convert 2π to a decimal number rounded to the nearest ten-thousandth. a. 6.2832 b. 6.3832 c. 6.6821 d. 6.8861

61. An irrational number is rounded to 9.94987. This number is between 6 and 10. Find the irrational number. a. 28 b. 39 c. 98 d. 99

62. The circumference of an irregular closed curve is determined using the formula π= 3π +3

C d ,

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. 14.556 ft2 b. 12.566 ft2 c. 10.862 ft2 d. 10.266 ft2


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63. Which fraction is approximately equal to π ?

a. 327

b. 317

c. 297

d. 227

64. What year is the Arabic numeral MMXII? a. 2008 b. 2009 c. 2011 d. 2012

65. Which numeral represents the Roman expression XXXI + XXIV? a. 55 b. 52 c. 45 d. 43

66. John was born in the year MCMXLIX. Convert his birth year to an Arabic Numeral. a. 1848 b. 1884 c. 1944 d. 1949

67. Which expression represents 70 + 80 + 90? a. LX + LXX + LXXX b. LXX + LXXX + LXXXX c. LCX + LXXX + LXXX d. LXX + LCXX + LXXX


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68. Ronald earns $3225 per month. 12% of his salary is withheld for income tax. Find the amount of his take home per month. a. $2883 b. $2838 c. $2787 d. $2778

69. 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. $3211 b. $3121 c. $3112 d. $3011

70. The following list shows the salaries of four people along with their total deductions for each month. Which one has the greatest take-home amount? a. Salary = $3402; Total Deduction = 14% b. Salary = $3150; Total Deduction = 15% c. Salary = $3655; Total Deduction = 17% d. Salary = $4455; Total Deduction = 24%

71. 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 2010-2011? a. $48,482 b. $46,486 c. $44,462 d. $42,482

72. 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. $8.98 b. $8.68 c. $7.96 d. $6.86


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73. 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. $658.24 b. $678.44 c. $687.24 d. $689.46

74. Different stores offer different prices and discounts for a chair and an ottoman as follows. Which store offers the best purchase price? a. Store A: Original price = $580 with 11% discount b. Store B: Original price = $520 with 9% discount c. Store C: Original price = $490 with 7% discount d. Store D: Original price = $450 with 5% discount

75. 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. 2.4m + 1.8n + 1.24p + 3.92q b. 0.24m + 0.18n + 12.4p + 3.92q c. 0.24m + 0.18n + 1.24p + 3.92q d. 0.24m + 0.18n + 1.24p + 39.2q

76. 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: 1. Electronic withdrawal: $320 2. Electronic withdrawal: $22 3. Electronic withdrawal: $124 a. $3958 b. $3937 c. $3857 d. $3807


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77. 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. $4378 b. $4577 c. $4676 d. $4766

78. 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. $3938 b. $3937 c. $3836 d. $3737

79. 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. $1650 b. $1600 c. $1500 d. $1350


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80. 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. $3802 b. $3383 c. $3083 d. $3080

81. Which expression is equivalent to 3 + 4(9 − 3) + 11? a. 3 + 4 × 9 − 3 + 11 b. 3 + 4 × 9 − 4 × 3 + 11 c. 3 + 4 × 9 + 4 × 3 + 11 d. 3 − 4 × 9 + 4 × 3 + 11

82. Which expression is the translation of “three times a quantity added to 12, divided by 12?” a. (3 + 12x) ÷ 12 b. (3x + 12) ÷ 12 c. 3(x ÷ 12) + 12 d. 3(x + 12 ÷ 12)

83. What is the value of −4[3 − 4(8 + 1) ÷ 3 − 3] + 12? a. 69 b. 63 c. 60 d. 57


28

84. To convert degrees Celsius to degrees Fahrenheit, multiply by 9, divide by 5 and add 32. Write a formula that represents these operations.

a. 95

C + 32.

b. 59

C + 32.

c. 325

C + 9.

d. 329

C + 5.

85. What is the value of 4(29 − 19) ÷ 5 − 4 × 13? a. − 49 b. −44 c. 48 d. 44

86. 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. $153 b. $148 c. $145 d. $143

87. 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. $114.44 b. $112.42 c. $104.42 d. $102.24


29

88. Wendy wants to invite a number of friends to an anniversary party at a restaurant. She would like to invite between 14-18 friends. She checked with different restaurants, and they offered the following packages. Which restaurant offered the lowest quote for each guest? a. Restaurant A: $705 for 15 guests b. Restaurant B: $736 for 16 guests c. Restaurant C: $1020 for 20 guests d. Restaurant D: $1250 for 25 guests

89. 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. $27.14 b. $25.04 c. $24.14 d. $23.04

90. 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. $2414 b. $2214 c. $2142 d. $2042

91. Which list shows the following numbers from the smallest to the greatest?

13

, 56

, 45

, 1415

a. 13

, 56

, 1415

, 45

b. 56

, 13

, 45

, 1415

c. 45

, 13

, 56

, 1415

d. 13

, 45

, 56

, 1415


30

92. Three telecommunication companies plan to lay off some of their workers as listed below: Company A: 70 workers of its 210 workers Company B: 30 workers of its 140 workers Company C: 80 workers of its 200 workers Company D: 60 workers of its 190 workers Which company plans to lay off the highest fraction of it workers? a. Company A b. Company B c. Company C d. Company D

93. Which list shows the following numbers from the greatest to the smallest?

7 9 11 23, , ,8 16 12 24

a. 1112

, 2324

, 78

, 9

16

b. 2324

, 78

, 9

16,

1112

c. 9

16,

2324

, 78

, 1112

d. 2324

, 1112

, 78

, 916

Continue to next page.


31

94. 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. Rachael b. Raymond c. Russ d. Regina

95. Which are the two greatest numbers in the following list?

,17 7 11 1, ,32 12 24 6

a. and 1732

b. 7

12 and

c. 7

12 and

1732

d. 7

12 and

16

1124

1124


32

96. Order the following numbers from the smallest to the greatest:

12.25, 3115

, 899

, 12.025

a. 899

, 3115

, 12.025, 12.25

b. 899

, 12.025, 12.25, 3115

c. 3115

, 899

, 12.025, 12.25

d. 12.25, 899

, 3115

, 12.025

97. 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 work-hours from the lowest to the highest in terms of months. a. June, March, April, May, January, February b. June, March, April, January, May, February c. April, June, January, February, March, May d. April, May, January, February, March, June

98. Find the middle number among the following data?

321.243, , 321.432 , 322.254, 322.245

a. 321.243

b. 5632167

c. 321.432 d. 322.254

5632167


33

99. What is the difference between the smallest and the largest numbers in the following list?

23023, 23.01,17

a. 9.74 b. 9.48 c. 7.72 d. 7.47

100. 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

School C : 79

School D: 1.09 Which school has the highest fraction of female students? a. School A b. School B c. School C d. School D

101. 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. 52 13 1325 4 50

, ,

b. 56 11 1325 4 50

, ,

c. 56 13 1125 4 50

, ,

d. 56 13 1325 4 50

, ,


34

102. Which list represents the equivalents of the following decimal numbers? 4.15, 4.65, 4.25

a. 8325

, 9320

, 174

b. , 9320

, 174

c. , 9325

, 174

d. , 9720

, 174

103. The dimensions of a rectangular tract of land are 723

12 ft. and

5248

ft. Which fractions can be

used to find the area of the land?

a. 28312

and 197

8

b. 28112

and 1978

c. 28312

and 1938

d. 28314

and 197

8

104. Which list represents the equivalents of the following fractions?

84 35 14 35, , ,49 49 21 63

a. 127

, 57

, 23

, 59

b. 59

, 127

, 57

, 23

c. 117

, 57

, 23

, 59

d. 127

, 57

, 23

, 79

832083208320


35

105. 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. 725

, 9

20,

1120

, 34

b. 8

25,

920

, 1720

, 34

c. 8

25,

920

, 1120

, 34

d. 8

25,

920

, 1320

, 34

106. In which number does the digit 9 have the highest place value? a. 3409008 b. 3490806 c. 3400908 d. 3400790

107. 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. two hundred thousand thirty eight, eight hundred fifty seven b. two hundred thirty eight, eight hundred fifty seven c. two hundred thirty eight thousand, eight hundred fifty seven d. two million thirty eight, eight hundred fifty seven

108. Which is the name of the number 45,600,006? a. forty five million, six thousand, sixty b. forty five million, six hundred thousand, sixty c. forty million, forty six hundred thousand, six d. forty five million, six hundred thousand, six


36

109. The exact distance between two islands in the Atlantic Ocean is 440,056 ft. What is the order of magnitude of this number? a. 8 b. 7 c. 6 d. 5

110. 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. 24(34.81) b. 24(12.46) c. 8.23 + 101.52 d. 197.52 + 4.23

111. Which expression is equivalent to 3(12 − 1) + 4(13 + 2)? a. 3 × 12 − 4 × 13 + 4 × 2 − 3 × 1 b. 3 × 12 + 4 × 13 + 4 × 2 − 3 c. 3 × 12 + 4 × 13 + 2 − 1 d. 3 × 12 + 4 × 13 + 4 × 2 − 3 × 1

112. Which operation must be performed first when calculating (129 + 321 × 481 + 2)? a. 129 + 321 b. 481 + 2 c. 481 × 2 d. 321 × 481

113. Which of the following equations is false? a. 21 + (11 + 9) = (21 + 11) + 9 b. 21 × (11 + 9) = (11 + 9) × 21 c. 21 ÷ (11 + 9) = (11 + 9) ÷ 21 d. 21 × (11 − 9) = (11 − 9) × 21


37

114. 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. 6 b. 5 c. 4 d. 3

115. 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. 19(24) + 11 b. 19(11) + 24 c. 19(24 + 11) d. 19(24)(11)

116. Which of the following is the value of 4[12 + 3(1 + 5)] ÷ 144

?

a. 428

17

b. 128

17

c. 427

17

d. 72617

117. If a truck carries a 324

tons load, how many pounds is it hauling, knowing that 1 ton = 2000

pounds? a. 5250 pounds b. 5450 pounds c. 5500 pounds d. 5600 pounds

118. Which of the following is equivalent to

1 16 ÷ 34 8

?


38

a. 8 b. 7 c. 5 d. 2

119. The area of an irregular 4-sided shape is calculated using the formula ( )1 a b + c + d3

, where a, b,

c and d are the side lengths. If, a = 3, b = 4, c = 134

and d = 6, which expression

can be used to calculate the area?

a. 134 64

+ +

b. 133 4 64

+ +

c. 1 134 63 4 + +

d. 114 64

+ +

120. What is the proper procedure to calculate ( ) 512 3 + 4 1 - 7 ÷ 3

12?

a. Simplify inside brackets, multiply by 12, then divide by the mixed number. b. Simplify inside parentheses, multiply by 12, then divide by the mixed number. c. Simplify inside brackets, multiply by 12 by the mixed number, then divide by 12. d. Simplify inside parentheses, multiply by 3 and 12, then divide by the fraction.

121. To calculate the product 3.23 ×

1323

, which two procedures can be used?

a. 3.23 × 3.04348 or 323100

× 703

b. 3.23 × 3.4348 or 323100

× 7023

c. 3.23 × 3.04348 or 32 3100

.

× 7023

d. 3.23 × 3.04348 or 323100

× 7023

122. For a Physics Project, John designed a micro-tool 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 side-


39

lengths repeatedly he found the side-lengths 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. 49a mm b. 51a mm c. 62a mm d. 63a mm

123. To calculate the division 7.73 ÷

773

, which set of the procedures can be used?

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.

124. Find x. 12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = x a. 387 b. 368 c. 312 d. 268

125. In the US, about 45

of the residents are registered to vote. In one elections, 34

of the registered

voters actually voted. What portion of the citizens voted in this election?

a. 34

b. 14

c. 35

d. 15

126. Perform the following calculations:


40

( )

1 3 571.1 1 + 4 ÷11 4 4

a. 2215

b. 2315

c. 1913

d. 1713

127. Calculate the following expression:

121 32 + 3 1+ 1 + 15 3 +3

a. 9.3 b. 9.1 c. 8.9 d. 6.3

128. Cindy measures a side and a diagonal of a square-shaped 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. 1798 ft b. 1789 ft c. 1697 ft d. 1679 ft


41

129. 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. 5.82 ft b. 5.62 ft c. 4.81 ft d. 4.62 ft

130. Michelle wants to find some ordered pairs to fit in the equation y = 3x − 2. She created the following table:

x y 3 7 5 13 7 19 8 21 11 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. 21 must be changed to 22 b. 21 must be changed to 26 c. 31 must be changed to 30 d. 31 must be changed to 33

131. 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. 41% b. 42% c. 45% d. 40%

132. 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. Multiplication b. Division c. Subtraction d. Addition 133. To express the value 0.32 as a percent what operation is needed?


42

a. Multiplication b. Division c. Addition d. Subtraction

134. 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. Addition b. Subtraction c. Multiplication d. Division

135. 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. Multiplication b. Division c. Addition d. Subtraction

136. Which of the following is the best estimation of 2300 × 3209? a. 7360000 b. 7380000 c. 7480000 d. 7408000

137. Mt. Whitney is 14,494 feet above sea-level and Rock Valley is 347 feet below sea-level. Which of the following is the best estimation of the difference in these elevations? a. 14000 b. 14500 c. 15000 ft d. 1480 ft


43

138. Which is the best estimation of 450081505

?

a. 30 b. 29.29 c. 29 d. 28.89

139. 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. 440 ft b. 400 ft c. 385 ft d. 380 ft

140. To find a reasonable estimate of 3300031129

, which fraction is the best choice?

a. 340000

1100

b. 330000

1100

c. 330001100

d. 330000110

141. 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. 300 in. b. 330 in. c. 400 in. d. 450 in.

142. To find a reasonable estimate of 1000.01 × 100, which expression is the best choice? a. 10010 × 100 b. 1000 × 100 c. 1001 × 100 d. 1000 × 101


44

143. Which is a reasonable estimate of the total amount of the following coins, in dollars? 40 quarters 10 dimes 20 nickels 770 pennies a. $20 b. $19 c. $18 d. $17

144. Which ratio is proportional to 1248

?

a. 7

24

b. 5

28

c. 728

d. 628

145. Which proportion is true?

a. 22 1877 64

=

b. 11 1877 63

=

c. 22 1677 63

=

d. 22 1877 63

=

146. 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. 63 b. 65 c. 76 d. 79


45

147. Which number must be placed inside the box 11 =28 35

?

a. 12.25 b. 12.85 c. 13.25 d. 13.75

148. 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. 213 b. 219 c. 231 d. 243

149. 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. If p, then q. b. If q, then not p. c. If q but not p, then q. d. If q but not p, then q.

150. The following simple statements are given: p: Mika likes Ronald q: Ronald likes Mika. Which symbolic statement is true? a. p q∨ b. p q∧ c. p q p∨ ∨ d. p q q∨ →


46

151. 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. q q p→ ∨ b. p q p∨ ∨ c. p q∧ d. p q∨

152. The following statements are given: Elementary schools are closed on Sunday. It is Sunday. Write a conditional statement by combining these statements. a. If elementary schools are closed, then it’s Sunday. b. It is either Sunday or the elementary schools are closed. c. If it is Sunday, then the elementary schools are closed. d. If the elementary schools are closed, then it may not be Sunday.

153. The following statement is given: In any right triangle, the sum of two acute angles is 90º. Which triangle is a right triangle? a. Triangle ABC, in which the difference of two angles is 90º. b. Triangle DEF, in which no angle is obtuse. c. Triangle GHK, in which two angles are acute. d. Triangle LMN, in which one angle is obtained by subtracting the other angle from 90º.


47

154. 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. John is a publisher. b. John may be both an author and a member of the club. c. John may be a published author. d. John is a published author.

155. 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. a is not definitely a member of S. b. a is not a member of S. c. a may be a member of S. d. a is a member of S.

156. 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. John may attend Algebra and/or Geometry class(es). b. John is not attending Algebra class. c. John is not attending Geometry class. d. John is attending both Algebra and Geometry classes.

157. Which general formula can be used for all the numbers in the following series? 2, 6, 12, 20… a. 2n(2n − 1) b. n(n - 1) c. 2n(n + 1) d. n(n + 1)


48

158. 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. 2 b. 3 c. 4 d. None of the above

159. 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. 88 b. 82 c. 76 d. 66

160. If (1 + 2 + 3 + . . . + n)2 = 13 + 23 + 33 + . . . + n3, which expression is equal to ( 1 + 2 + 3 + 4 + . . + 100)2? a. 12 + 22 + 32 + 42 + . . . + 100 b. 13 + 23 + 33 + 43 + . . . + 1003 c. 22(1 + 2 + 3 + 4 + . . . + 100) d. 1 + 2 + 3 + 4 + . . . + 1002

TEAS Practice Exam – Math - Section 2 Algebra

161. Solve 3x + 11 = 31 – x. a. 7 b. 5 c. 4 d. 2


49

162. Sarah and her father together are 47 years old. If her father is 34 years old, what is Sarah’s age? a. 19 b. 17 c. 13 d. 11 163. The ratio of two numbers is 13. If the larger number is 1027, what is the smaller number? a. 79 b. 83 c. 87 d. 89 164. Solve the equation 5x − 11 = 39. a. 14 b. 13 c. 11 d. 10 165. The side-lengths of a triangle are described by x2 + x + 1, 3x − 2, and 3x2 + x. What is the perimeter of the triangle? a. 4x2 + 5x − 1 b. 4x2 + 4x − 1 c. 4x2 + 5x + 3 d. 4x2 + 5x − 2 166. Subtract (3x2 + 1) from (4x3 + 2x2 + x). a. 4x3 − x2 + 2x − 1 b. 4x3 − 2x2 + x − 1 c. 4x3 − x2 + x + 1 d. 4x3 − x2 + x − 1 167. The dimensions of a rectangle are described by (x + 2) and (x + 3). Which of the following describes the area of the rectangle? a. x2 + 5x + 5 b. x2 + 6x + 6 c. x2 + 5x + 6 d. x2 + 6x + 5


50

168. Add (x2 + x) to (8x3 + 2x2 − x − 1). a. 8x3 + 3x − 1 b. 8x3 − 3x2 − 1 c. 8x3 + 3x2 − 1 d. 8x3 + 3x2 − 2x 169. Write an equation: “value of x is two more than three times x.” a. 3x = x + 2 b. 3x = x − 2 c. x = 2 + 3x d. x = 2 − 3x 170. 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. 8x + 3 b. 5x + 3 c. 8x + 5 d. 5x + 8 171. The sum of the right angle and an acute angle in a right triangle is greater than 123º. Which expression represents this relationship? a. x + 90 < 123 b. x + 90 > 123 c. x + 123 > 90 d. x + 123 < 90 172. Which is the translation of the phrase “11 more than the triple of a number?” a. 11x + 3 b. 3x + 11 c. 3(x + 11) d. 3x + 33 173. Which of the following is the solution to the equation |x + 12| = 25? a. 12 or 37 b. 17 or 33 c. 13 or −37 d. −13 or 37


51

174. The temperature on the surface of Mars fits the inequality C + 85 56≤ , in degrees Celsius. What is the range of the temperature? a. −29 ≤ C ≤ −141 b. 29 ≤ C ≤ 141 c. 141 ≤ C ≤ 29 d. −141 ≤ C ≤ −29 175. Which is the solution set to the inequality x 1+ 5 6> ? a. x > −11 or x < −21 b. x > 11 or x < −21 c. x < 11 or x < 21 d. x < 11 or x < 21 176. 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. 9 p 5≥ ≥ − b. 9 p 5≥ > c. 9 p 5> ≥ d. 9 p 5≥ ≥ 177. Solve the equation 3x + 11 = 51 − x. a. 12 b. 10 c. 6 d. 2 178. 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. x = 22 ft b. x = 19 ft c. x = 18 ft d. x = 16 ft


52

179. Solve the inequality 5x − 19 > 3x + 33. a. x > 26 b. x > 28 c. x < 26 d. x < 28 180. If the radius of a circle is doubled, how will its area be changed? a. Increase two times. b. Increased four times. c. Increased by two. d. Increased by four. 181. If x in x(22 − 19) is tripled, how much is the value of the expression changed? a. Will Increase by 6x b. Will increase 6x times c. Will increase by 8x d. Will increase 8x times 182. If x in the expression 12(x + 3) + 9 is increased by 9, how will the value of the expression be changed? a. Will be increased by 132 b. Will be decreased by 132 c. Will be increased by 126 d. Will be decreased by 126 183. A side-length of a square-shape pool is 44 ft. If its length extended to 48 ft, how much will its area be increased? a. 466 ft2 b. 468 ft2 c. 386 ft2 d. 368 ft2


53

184. If x in the expression 3(x + 9) − 12 is decreased by 9, how much will the value of the expression be changed? a. Will be decrease by 62 b. Will be decreased by 51 c. Will be decreased by 43 d. Will be decreased by 27 185. 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. Remove the decimal from the left side. b. Cancel the decimals. c. Multiply all the terms by 10 d. Multiply all the terms by 100.

186. To solve the equation x 4= 35 9

, what step must be taken first?

a. Divide the fractions by 45. b. Multiply the denominators by 45. c. Cross multiply the proportion. d. Change the mixed number to an improper fraction.

187. To solve equations such as 1 5 1x + =18 12 6

, which step must be followed first in order to make the

solution easier?

a. Move 16

to the left side.

b. Add 16

to the left side.

c. Multiply all the terms by 36. d. Divide all the terms by 36.

188. What are two different methods to verify that 24 3=32 4

?

a. Division and Reducing b. Cross-multiplication and Reducing c. Multiplication and Reducing d. Cross-multiplication and Division


54

189. What are two different methods to find 144 ÷ 24? a. Synthetic Division and Division of Reciprocals b. Synthetic Division and Mixed Numbers c. Division of Fraction and Division of Reciprocals d. Synthetic Division and Reducing a Fraction 190. 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. By multiplying all the terms by 2. b. By replacing x by x + 3. c. By adding 3(3 + x) to both sides. d. By subtracting 3(3 + x) from both sides.

191. Solving the equation

1 1 5=2 7 x

yields 1 5=

14 x. How can you complete the solution?

a. By cross-multiplication b. By division c. By subtraction d. By multiplication 192. 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. Perimeter = 2a + a + 2b + b = 2(a + b) b. Perimeter = 2a + 2a + b + b = 2(a + b) c. Perimeter = a + a + b + b = 2(a + b) d. None of the above


55

193. The sum of interior angles of geometric shapes are calculated as follows:

Triangle: 180(3 − 2) Quadrilateral : 180(4 − 2)

Pentagon : 180(5 − 2) Hexagon : 180 (6 − 2)

Which of the following is a general pattern for finding the sum of the interior angles of a polygon with n sides? a. 180(n + 1) b. 180(2n − 1) c. 180(n − 2) d. 180(2n − 2) 194. The following set of numbers fit the sides of right triangles:

a = 3 b = 4 c = 5 a = 6 b = 8 c = 10 a = 9 b= 12 c = 15 a = 12 b = 16 c = 20

Using this pattern, find a general formula for the sides of right triangles. a. a = n(3), b = n(5), and c = n(6) b. a = n(2), b = n(4), and c = n(5) c. a = n(3), b = n(5), and c = n(7) d. a = n(3), b = n(4), and c = n(5) 195. The following equations are given: (x + 1)(x + 2) = x2 + x(1 + 2) + 1 × 2 (x + 3)(x + 4) = x2 + x(3 + 4) + 3 × 4 (x + 6)(x + 8) = x2 + x(6 + 8) + 6 × 8 (x + 9)(x + 5) = x2 + x(9 + 5) + 9 × 5 Develop a general pattern for the expansion of (x + a)(x + b). a. x2 + x(a + b) + a + b b. x2 + x(ab) + a + b c. x2 + x(a + b) + a × b d. x2 + x(ab) + a × b


56

196. What pattern is used for generating numbers in the series below: 4, 9, 19, 39, 79, . . . , a. Add 1 to each number, then double. b. Double each number, then add 1. c. Subtract 1 from each number, then double. d. Double each number, then add 2. 197. 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. 70 b. 85 c. 89 d. 94 198. Which formula is used to generate the numbers in the series below? 4, 9, 19, 34, 54, . . . , a. 6 added to each term, then 1 is subtracted. b. 5 added to each term, then added 10. c. Multiple of 5 added to each term beginning with 5. d. Multiple of 10 added to each term beginning with 10. 199. The numbers below follow a general pattern. What is the next number in the series? 100, 98, 94, 88, . . . a. 72 b. 78 c. 80 d. 82 200. The relationship between P and n is defined by P = 4n. If n increases, how will P change? a. P will increase. b. P will decrease. c. P first will increase, then will decrease. d. P first will decrease, then will increase.


57

201. The area of a rectangle is A = ab. Given A as a constant, how will b vary if a is doubled? a. b will be decreased by one-half. b. b will be increased by one-half. c. b will be decreased by one-third. d. b will be doubled.

202. The relationship between R and x is defined by 5R =x

. If x increases how will R change?

a. R will increase. b. R will decrease. c. R first will increase, then will decrease. d. R first will decrease, then will increase. 203. 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. If T decreases, then P decreases b. If T stays constant, then P increases. c. If T increases, then P decreases. d. If T increases then P increases. 204. Which function can be described by the given graph below?

a. y = mx + b

b. 54

xy =

c. y = x2 + 3x − 7 d. y = 3x3 + 4x


58

205. Which function represents the graph below?

a. y = 2x + c b. y = 2x3 + 3x + c c. y = 2x + 3x + c d. y = ax2 + bx + c Continue to next page.


59

206. Which graph can represent the path of launching a projectile? a.

b.

c.

d.

207. 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. 90 − x = 32 b. 90 + x = 32 c. 32 − x = 90 d. −32 + x = 90


60

208. Which expression represents the phrase “nine times a number added to 32, subtracted from 193”? a. 222 + 9x b. 222 − 9x c. 160 + 9x d. 161 − 9x 209. The sum of two consecutive even integers is 650. Which equation can be used to find these numbers? a. 2x + 1 = 650 b. 2(x + 1) = 650 c. 2x − 1 = 650 d. 2(x − 1) = 650 210. 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. x + 162 = 290 b. x + 182 = 280 c. x + 172 = 270 d. x − 172 = 265 211. Which statement is true? a. If p: (x − 1)(x + 3) = 0, then q: x = 1. b. If p: (x − 1)(x + 3) = 0, then q: x = −1. c. If p: (x − 1)(x + 3) = 0, then q: x = 3. d. If p: (x − 1)(x + 3) = 0, then q: x = 4.


61

212. An airline made 320 flights in the first three months of the year. The airline predicts the same ratio for the following seasons. Let’s assume the following:

p: Ratio of the number of fights to the number of months during the first three months = 320

3

q: Ratio of the number of fights to the number of months during the first six months = 640

6

Which statement is true? a. If p, then q. b. If p, then not q. c. If q, then not p. d. Ifp q∨ , then not q. 213. 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. q r∨ b. p q∧ c. p q p∨ ∧ d. r q p→ ∧ 214. If (x + 3)(x + 23) = 0, then which statement is true? a. x = −3 or x = −23 b. x = −3 and x = −23 c. x = 3 or x = −23 d. x = 3 and x = −23


62

215. 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. Olivia is a member of the Sport Club. b. Jason is a member of the Hemingway Club. c. Ronald is a member of the Hemingway Club. d. Olivia is a published author.

216. The sum of the numbers 1 + 2 + 3 + 4 + 5 +, . . . , + n is equal to ( )

=n n + 1

S2

. What is the sum of

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15? a. 144 b. 140 c. 120 d. 112 217. The following statements are given:

In all the parallelograms, the diagonals are not equal, but bisect one another. In ABCD, AC = AD. In MNPQ, the diagonals bisect one another and are equal. In RSTU, diagonals pass through the center of the figure. In TVWX, if the point of intersection of the diagonals is called A, then TA = AW and VA = XA. Which of the following statements is true?

a. ABCD is a parallelogram b. MNPQ is a parallelogram. c. RSTU is a parallelogram. d. TVWX is a parallelogram.


63

218. 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. Subtracted zero from both sides. b. Multiply both sides by zero. c. Added zero to both sides. d. Divided both sides by zero. 219. 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. 19 b. 20 c. 23 d. 24 220. 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. 9 b. 8 c. 7 d. 6


64

TEAS Practice Exam – Math - Section 3 Data Interpretation

221. The numbers of hours of sunshine in Roan Mountain during one week of the summer is displayed in the graph below:

Which data table fits the bar graph? a.

b.

c.

d.

0 1 2 3 4 5 6 7 8 9

10

Sun Mon Tue Wed Thu Fri Sat

Day Fri Sat Sun Mon Tue Wed Thu Sunshine 7.0 8.5 8.5 5.2 9.0 6.2 5.5





65

222. 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.

b.

c.

d.

Data Frequency 126 8 127 3 128 6 129 4 130 1

Data Frequency 126 7 127 3 128 5 129 3 130 1

Data Frequency 126 7 127 3 128 5 129 4 130 2

Data Frequency 126 7 127 3 128 5 129 4 130 1


66

223. The percentages of different elements in a chemical substance is shown in the table below.

Carbon 34% Oxygen 26%

Hydrogen 21% Sulfur 12%

Nitrogen 7% Which pie chart represents the data in the table? a. c.

b. d.

Continue to next page.


67

224. The following table shows the number of graduates of Boone Creek High School during years 2004-2011. Which line graph represents the data in the table? (Numbers starting from 1 represent the years 2004, 2005, and so forth.) a. c.

b. d.

Year Number of Graduates 2004 453 2005 571 2006 356 2007 398 2008 433 2009 405 2010 447 2011 511


68

225. The Venn Diagram below displays the number of students attending different classes.

What is total number of students attending Literature class? a. 51 b. 49 c. 43 d. 37 226. The graph below represents the amount of rain during a week of spring in New York, in millimeters.

Which is the best estimate of the range of the data given in the graph? a. 4.2 mm b. 5.6 mm c. 5.9 mm d. 6.2 mm

0 1 2 3 4 5 6 7 8 9

10

Fri Sat Sun Mon Tue Wed Thu


69

227. The following stem - and - leaf graph represents a set of data.

What is the median of the data? a. 46 b. 51 c. 55 d. 58 Use the following information to answer questions 228 and 229. The amounts of money a Telecommunication Company spent on ads for the years 2005-2010 are shown in the table below.

Year Amount (in dollars) 2005 190,000 2006 230,000 2007 110,000 2008 150,000 2009 160,000 2010 180,000

228. In which year was the advertisement cost the highest? a. 2005 b. 2006 c. 2009 d. 2010 229. In which year was the advertisement cost the lowest? a. 2006 b. 2007 c. 2008 d. 2010


70

230. 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 a b c d 1 2 −1 6 −2 9 4 3 −1 3 21 2 9 8 −7

a. Variable a b. Variable b c. Variable c d. Variable d 231. 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 m n p q 11 2 −3 4 −2 26 −4 7 −1 3 2 2 5 8 −1

a. Variable m b. Variable n c. Variable p d. Variable q 232. 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 + 22

?

R m n p q −5 −4 −1 6 1 7 4 3 −1 3 10 6 9 8 −7

a. Variable m b. Variable n c. Variable p d. Variable q


71

233. 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?

a. The sum of the numbers is equal to the area of the circle. b. The sum of the numbers is equal to the circumference of the circle. c. The sum of the numbers is 100% and the total shaded regions is 100% of the circle. d. The sum of the numbers is 100% of the diameter of the circle 234. 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?

a. By the columns below the horizontal line 400,000. b. By the columns below the horizontal line 300,000. c. By the columns below the horizontal line 200,000. d. By the columns below the horizontal line 100,000.

0

100000

200000

300000

400000

500000

600000

700000

Service Percent Army 33% Navy 27%

Marine Corp 12% Air Force 25%

Coastal Guard 3%

State Land Area Alabama 50700

Alaska 573,000 California 155900 Colorado 103700 Maryland 9770

Minnesota 79600


72

235. The bar graph represents the data in the table. How are the areas of the States of Arizona and Montana shown in the graph?

a. By the columns above the horizontal line 100,000. b. By the columns below the horizontal line 100,000. c. By the columns between the horizontal lines 100,000 and 80,000. d. By the columns between the horizontal lines 80,000 and 60,000. Use the following information to answer questions 236 - 240. 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

Science Score

86 76 68 94 92 73

History Score

71 98 86 67 81 92

236. Which student scored lowest grade only in History? a. Student A b. Student B c. Student D d. Student E

0

20000

40000

60000

80000

100000

120000

140000

160000 State Land Area

Arkansas 52000 Arizona 113,650

Connecticut 4850 Michigan 56800 Montana 145550

Minnesota 79600


73

237. What is the difference between the ranges of the scores of the two subjects? a. 1 b. 2 c. 4 d. 5 238. Which student scored the lowest grade only in Science? a. Student A b. Student C c. Student D d. Student E 239. Which student scored the highest in Science and lowest in History? a. Student A b. Student B c. Student D d. Student E 240. What is the difference between the mean of the scores of both subjects? a. 4 b. 3.5 c. 1.5 d. 1


74

Use the following information to answer questions 241 - 245.

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 pull-outs for all groups.

Groups First

Week Second Week

Third Week

Fourth Week

Group A 11 32 20 19 Group B 32 44 9 33 Group C 14 21 21 29 Group D 30 39 11 12

241. In which week was the number of patients who pulled out from the trial the highest? a. First week b. Second week c. Third week d. Fourth week 242. Which group had the highest number of pull outs? a. Group A b. Group B c. Group C d. Group D 243. Which group had the lowest number of pull outs? a. Group A b. Group B c. Group C d. Group D 244. In which week was the number of patients who pulled out from the trial the lowest? a. First week b. Second week c. Third week d. Fourth week


75

245. Which group had the highest pull-out average? a. Group A b. Group B c. Group C d. Group D 246. 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. 3 b. 4 c. 5 d. 6 247. The average of three consecutive integers is 16. What is the smallest integer? a. 15 b. 16 c. 17 d. 18 248. 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. 29 cm b. 30 cm c. 32 cm d. 35 cm 249. Olivia made the following scores in her History tests. What is the average of her scores?

86, 72, 78, 88 a. 81 b. 80 c. 78 d. 75


76

250. What is the mode of the following data?

20, 11, 15, 17, 15, 17, 19, 15, 11, 11, 20, 15 a. 11 b. 15 c. 17 d. 20

251. A 6-sided die is rolled. The probability of getting an odd number is 13

. What does this fraction

represent? a. It means that the chance of an odd number is 3 out of 1. b. It means that the chance of an odd number is 1 out of 3. c. 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 13

.

252. The chance of choosing a member from a sports club as the president is 1131

. What is the chance

of NOT selecting this member?

a. 131

b. 2331

c. 2031

d. 1931

253. A box contains 42 red and green marbles. The probability of choosing a red marble from the box

is 47

. What can be concluded from this fraction?

a. There are 36 red marbles in the box. b. There are 24 red marbles in the box. c. There are 22 red marbles in the box. d. There are 18 red marbles in the box.


77

254. There are 32 students in Algebra class. The chance of choosing a female student is 916

. What

does this fraction represent? a. The number of male students is 14. b. The number of male students is 16. c. The number of male students is 15. d. The number of male students is 12. 255. Box A contains 124 cards marked with positive integers. The chance of choosing an odd integer

is 1231

. What does this fraction represents?

a. There are 42 even integers in the box. b. There are 44 even integers in the box. c. There are 48 even integers in the box. d. There are 76 even integers in the box. 256. What is the probability of getting a three and a heads, if we role a die and toss a coin?

a. 112

b. 14

c. 13

d. 16

257. What chance is there of choosing a number divisible by 5 from the numbers between 53 and 75?

a. 7

18

b. 417

c. 518

d. 4

21


78

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. 35

b. 45

c. 15

d. 23

259. Four coins are flipped together. What is the probability that all four coins come out heads?

a. 15

b. 14

c. 13

d. 12

260. What is the probability of getting a tail and an integer greater than 3, if we role a die and toss a coin?

a. 16

b. 14

c. 13

d. 12


79

TEAS Practice Exam – Math - Section 4 Measurements

261. 1000 mg = ___ g a. 1 b. 10 c. 100 d. 110 262. 160 cm = ____ mm a. 1.6 b. 16 c. 160 d. 1600 263. 109 g = ____kg a. .0109 b. .109 c. 1.09 d. 10.9 264. 4 L = ___ml a. .4 b. 40 c. 400 d. 4000 265. 75 ml = ___L a. .0075 b. .075 c. .75 d. 7.5


80

266. A man weighs 80 kilograms. How much does he weigh in pounds? a. 176 lbs. b. 185 lbs. c. 210 lbs. d. 80 lbs. 267. 54⁰ F = _____⁰ C a. 1.2 b. 10.22 c. 12.22 d. 102.22 268. 32⁰ C = _____⁰ F a. 89.6 b. 88.9 c. 86.9 d. 100 269. A woman weights 132 pounds. What is her weight in kilograms? a. 13,200 b. 1,320 c. 132 d. 60 270. A man is 6’4” in height. How tall is he in centimeters? a. 152 b. 164 c. 193 d. 640 271. Which of the following is equivalent to 3 pounds and 12 ounces? a. 42 ounces b. 48 ounces c. 52 ounces d. 60 ounces


81

272. 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. 10122 grams b. 10312 grams c. 11021 grams d. 13021 grams 273. What is the total, in inches, of 5 yards, 5 feet and 22 inches? a. 262 inches b. 254 inches c. 248 inches d. 234 inches 274. How many miles are in 24,500 kilometers? a. 12,512.5 miles b. 15,312.5 miles c. 15,315.5 miles d. 15,512.5 miles 275. What is the difference between the following lengths, in meters?

M: 12 m, 119 cm N: 1.2 m

a. 1379 cm b. 1289 cm c. 1299 cm d. 1199 cm 276. 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. 4 kg b. 3 kg c. 2 kg d. 1 kg


82

277. 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. 77.3 mm b. 73.7 mm c. 63.7 mm d. 60.3 mm 278. 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. 15 mm b. 14 mm c. 12 mm d. 10 mm 279. 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. 29 miles b. 26 miles c. 24 miles d. 21 miles 280. 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. 24 by 34 b. 21 by 32 c. 26 by 34 d. 21 by 42 281. 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. 12 in. by 13 in. b. 13 in. by 10 in. c. 12 in. by 13 in. d. 15 in. by 10 in.


83

282. How many inches are in one yard? a. 38 inches b. 36 inches c. 34 inches d. 32 inches 283. How many cubic centimeters are in a liter? a. 10 b. 100 c. 1000 d. 10000 284. How many pints are in a gallon? a. 4 b. 5 c. 6 d. 8 285. What is (2 gallons, 8 quarts) in quarts only? a. 10 b. 14 c. 16 d. 20 286. What is (2 decameters, 34 decimeters) in centimeters? a. 2340 cm b. 2420 cm c. 2440 cm d. 2624 cm 287. What is (5 yards, 4 feet) in inches? a. 228 in. b. 218 in. c. 192 in. d. 188 in.


84

288. Cindy wants to add some preservative to 0.8 kg dried fruit. What unit of measurement should she use to weigh the preservative? a. Kilogram b. Gram c. Pound d. Liter 289. 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. Liter b. Ton c. Kilogram d. Pound 290. 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. Pound b. Gram c. Ton d. Liter 291. The amount of power (in watts) that a satellite drops depends on the number of days its been on in the sky. The amount of drop in its power supply occurs gradually and is determined by the following formula:

w = 50e−0.004d Assume e is 2.71828183. How much power would a satellite drop after 500 days? a. 5.97 watts b. 6.77 watts c. 7.76 watts d. 8.78 watts


85

292. Physicians use the following formula to determine the gradual absorption of a drug in a patient’s body after h hours:

D = 5e−0.4h When the number of milligrams decreases to 2, the physician must administer the drug again. Assume e is 2.71828183. How much of the drug will be in the patient’s bloodstream after 5 hours? a. 0.68 mg b. 9.92 mg c. 1.22 mg d. 1.46 mg 293. 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. 1 b. 2 c. 3 d. 4 294. What is the volume of a gold bar that is 4.5 cm long, 3.5 cm wide and 2 cm thick? a. 10 cm³ b. 15.75 cm³ c. 20.25 cm³ d. 31.5 cm³ 295. The dimensions of a rectangle are 2 feet and 240 inches. What is the area of the rectangle? a. 5760 in.2 b. 5780 in.2 c. 5860 in.2 d. 5980 in.2 296. 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. 54 ft. b. 60 ft. c. 118 in. d. 120 in.


86

297. 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. 608 m2 b. 612 m2 c. 652 m2 d. 672 m2 298. To measure the volume of a rock, which method is best? a. Using a graduated cylinder half-filled with water b. Using an empty graduated cylinder c. Using a “verinier calipers” d. Using an empty balloon 299. 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. 37 b. 31 c. 27 d. 25 300. One foot-pound(ft-lb) is the amount of energy used to lift a one pound object a distance of 1 foot. One British Thermal Unit (BTU) is the amount of heat needed to raise the temperature of 1 pound of water 1 degree Fahrenheit. These two units are related by the formula 1 BTU = 778 ft-pl. How much is 1945 ft-pl in BTU? a. 2.5 BTU b. 3.5 BTU c. 4 BTU d. 5 BTU


87

TEAS 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


88

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. c - Percent of students that are male = 100% − 45% = 55%

Now, convert 55% to a fraction.

55% = 55 11

100 20=

12. c - Subtract 25

from 11

to obtain the fraction of the members which are not published writers:

1 2 5 - 2 3

- = =1 5 5 5

Now, convert 35

to a percent by converting its denominator to 100:

3 3 × 20 60= = = 60%

5 5 × 20 100

13. b - Since 25% of A is 48, we can find the value of A by multiplying 48 by the reciprocal of 25

100.

So, ( )100= 48 = 192

25A

Multiply 192 by 23

to get the answer.

( )2 192 1283

=

14. a - To find (2x + 3y), simply multiply 60 by the reciprocal of 35

.

(2 + 3 ) = (60) = 10053

x y

Now, multiply 100 by 3.25 to find the solution: 100(3.25) = 325

15. d - First simplify 3

3.25 + = 3.25 + 0.75 = 44

Now, find 25% of 4:


89

( )25(25%)(4) = 4 = 1

100

16. c - First multiply 32002 × 32005 = 1024224010 The factors of the product have a total of 6 decimal digits. So, place a decimal point to the left of the sixth digit from right: 0.32002 × 3200.5 = 1024.224010

17. c - Set up the numerical expression first, and then simplify: Total purchase = 3(12.54) + 2(29.98) = 37.62 + 59.96 = $97.58

18. 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.

19. b - The original division form is as follows:

4.52 2004.52

Multiply both divisor and dividend by 100 to get rid of the decimal digits. Then continue the division:

443474.52 2004.52 = 452 200452 = 452 20045200

-1808

1965

-1808

1572

-1356

2160

-1808

3520

-3164

356


90

Since both dividend and divisor are multiplied by 100, to obtain the real remainder, we must divide the remainder above, 356, by 100. Remainder = 356 ÷ 100 = 3.56 On the other hand, since we added two zeros to the dividend, now we must place a decimal point to the left of the second digit from the left. So, the quotient is 443.47

20. c - 24% is equal to 24

100. To find (m + 2n) multiply 48 by the reciprocal of

24100

.

(m + 2n) = (48) =100 20024

Now, find 25% of 200.

25

(25%) = = 50100

200 200

21. d - Simply find 12% of 3400.

( )( ) ( )1212% 3400 = 3400 = 408

100

So, he spends $408 per month.

22. 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:

10052

5200 52 123.8142= = = = 123.81%1004200 42 1004242

So, the percent of increase was 123.81%.

23. 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:

10040 1 11.119= = = = 11.11%

100360 9 10099

So, the percent of decrease was 11.11%.


91

24. a - 28% is equivalent to the fraction 28 7

=100 25

and 20% is equivalent to the fraction

20 1

=100 5

. To find 20% of A, we must multiply 420 by the reciprocal of the fraction 7

25.

20% of A = 25

420 = 15007

Now, to find A, we must multiply 1500 by the reciprocal of 15

.

A = 5

1500 = 75001

25. b - First find the 32% of 450 to get the discount amount:

Discount = ( )( ) ( )3232% 450 = 450 = 144

100

Subtracting the discount amount from the original price gives the marked down price. Sale Price = $450 − $144 = $306

26. 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.

Discount rate = 66 1

= = 0.25264 4

We know that 0.25 is equal to 25%.

27. d - First find 29% of 2900.

A = 29

2900 = 841100

On the other hand, to find B, we must divide 29 by 290, and then multiply the result by 100.

B = ( )29100

290 = 10

Therefore, A + B = 841 + 10 = 851

28. a - First calculate the marked down price on the first day:

Discount on first day =

15304 = 45.6

100

Marked down price on first day = $304 − $45.6 = $258.4


92

Discount on the second day = 12

258.4 = 31.01100

Marked down price on the second day = $258.4 − $31.01 = $227.39

29. d - First find the division of 32.24 by 24.32, and then multiply the result by 23

.

( ) ( )2 232.24 24.32 = 1.325658 = 0.88

3 3÷

Now add 0.88 to the product of 24 and 32. 0.88 + (24 × 32) = 768.88

30. b - First set the numerical expression in terms of both purchases, and then calculate:

3(12.82) + 5(8.21) = $79.51

31. c - First find 23

the sum of 23 and 32:

( ) ( )2 223 32 55 36 673 3

.+ = =

Now add 36.67 to 2.3 time 3.2: 36.67 + 2.3(3.2) = 44.03

32. b - Find the price of each can using the different pack-prices: $6.24 ÷ 12 = $0.52 $3.92 ÷ 6 = $0.65 Subtract these prices. $0.65 − $0.52 =$0.13

33. a - Convert the first mixed number to an improper fraction.

5 77

12 =6 6

Now, find A − B and A + B.

A − B = 77 7 154 - 7 147

- = =6 12 12 12

A + B = 77 7 154 + 7 161

= =6 12 12 12+

Then find the ratio of these fractions.


93

14714712

161 16112

A BA B−

+ =+

34. d - Simply divide the weight of the flour by the weight of the cake:

2 3 11 23 11 5

3 ÷ 4 = ÷ = × = 0.803 5 3 5 3 23

35. d - Simplify M and N first.

M = 4

1 9 92 - 1 = - = 0

4 4 45

N = 1 4 17 14 85 - 56 29

4 - 2 = - = =4 5 4 5 20 20

Now find M + 2N and 2M + N.

M + 2N = 0 + 29 29220 10

=

2M + N = 2(0) + 29 2920 20

=

Now we can determine the required ratio using the calculated values:

292 10 2292

20

M NM N+

= =+

36. c - Find the values of the expressions1

2 + 33

A

and 1

2 -3

B

using the given

numbers for A and B.

1 1 10 13 10 23

2 + 3 = 2 2 + = + =3 6 3 3 3 3

A

1

2 -3

1 1 1= 2 - =3 3 3

B

Now, divide 233

by 13

:

233

÷ 13

= 23 3 233 1× =


94

37. a - First simplify A and B.

A = 1 1 1 5 7 35

+ 3 = =2 3 2 6 2 12

B = 1 1 1 1 7 7

- 3 = =2 3 2 6 2 12

Now add 3512

and 712

: 35 7 42 1312 12 12 2

+ = =

38. b - Add 2

23

and 2

43

, and simplify the result:

2 2 8 14 22 1

2 + 4 = + = = 73 3 3 3 3 3

Bottles

39. d - Simplify each numerical expression.

K = 2 1 11 9 44 + 27 11

3 + 2 = + = = 53 4 3 4 12 12

L = 13 6 16 5 47 5

1 + 1 = + = = 73 4 3 2 6 6

M = 8 10 8 9 43 1

+ 2 = + = = 73 4 3 2 6 6

N = 1 1

5 + 33

16 7 32 + 21 53 5= + = = = 82 3 2 6 6 6

The mixed number 586

has the greatest whole number part.

40. c - Set up the numerical expression and simplify.

A + 2B − 3C = 5

37

+ 2

2 15

− 1

33

= 267

+ 145

− 1 = 26 × 5 + 14 × 7 - 35

35193 18= = 535 35

41. d - Calculate each sum given in the answer choices and then compare the results:

(a) 2008 and 2009 : 2 1 14 3 17 0 813 7 21 21

.++ = = =

(b) 2009 and 2010 : 1 1 5 7 12 0 347 5 35 35

.++ = = =

(c) 2010 and 2011 : 1 1 1 1 2 0 405 5 5 5

.++ = = =

(d) 2008 and 2011 : 2 1 10 3 13 0 873 5 15 15

.++ = = =

Obviously, the fraction (d) which is the highest number.


95

42. 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

43. 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.

44. 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).

45. b - Combine the given relations in terms of c. (1) a = 2b

Replace b = 2c in (1). (2) a = 2(2c) = 4c

Also, we are given (3) b = 2c

Now, replace (2)-(3) in the choice (b), and simplify.

2 4 2 2 88 8 8

a b c c c c c c+ + + += = =

So, (b) results in a whole number. You can check the other choices similarly. But you will not obtain a whole number.

46. c - Write the ratios as given in the problem.

23

ab=

2

15cb=

Divide these proportions side by side.


96

232

15

abcb

=

2 152 3

abbc

×=

×

15 53

ac= =

47. 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 BCKL LM

=

Now, replace the given values and find the missing length.

12 9 1

18 2KL= =

KL = 24 in.

48. d - Cross-multiply the given proportion first. ad = bc Now cross divide by ab:

ad bc=ab ab

d c=b a

49. c - Find the rate of change for each case, and then compare:

Rate of change in height of Michelle = 108 98 10 2

14 9 5−

= =−

Rate of change in height of Sarah = 92 74 18 4 511 7 4

.−= =

−

Rate of change in height of Joanne = 82 56 26 6 510 6 4

.−= =

−

Rate of change in height of Alison = 108 52 56 6 22

14 5 9.−

= =−

So, Joanne had the highest rate of change

50. c - Set the rate of change as follows:

Rate of change = 540 420 120 122011 2001 10

−= =

−


97

51. 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

52. 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.

53. d - Replace the given values in +-

m nmnp

n p

.

+ 3.2 + 2.2= (3.2)(2.2)(2.1)

- 2.2 - 2.1m n

mnpn p

5.4

= (14.784)0.1

= 798.336

798.3≈

54. 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

55. 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.

56. d -

8 13 10 15

9 4 1 54 7 8 6

4 6 2 9

−

57. c - Because the digit 9 in the subtrahend is greater than the corresponding digit in the minuend.


98

58. a -

2 12 13 14 16

3 3 4 5 62 9 6 5 7

3 7 9 9

−

59. b -

8 13 15 18

9 4 6 87 5 6 9

1 8 9 9

−

60. a - Given π = 3.141592…., then 2π = 6.283184. Rounding this number to ten-thousandth gives 2π = 6.2832

61. d - 99 is the only irrational number whose decimal digits are calculated which includes the same decimal digit as 9.94987.

62. b - Replace the 4-digit value of π and d = 3 in the formula and then round up.

( ) ( )

( )2

3 14153 3 1415 33

3 3 1415 3 1415

12 566

.C .

. .

. ft

= +

= +

=

63. d - 227

is the only fraction that is closest to π .

64. 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

65. 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


99

66. 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

67. 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

68. b - First find 12% of 3225.

Tax = 12(3225)(12%) = (3225)100

= 387 Subtract the tax amount from his earning. 3225 − 387 = 2838

69. a - First find 24% of 4225.

Installment = 24(4225)(24%) = (4225)100

= 1014 Subtract the installment amount from his earning. 4225 − 1014 = 3211

70. d - First find take home amount of each person, and then compare.

(a) Deduction = 14(3402)(14%) = (3402)100

= 476.28 Take-home amount = 3402 − 476.28 = $2925.72

(b) Deduction = 15(3150)(15%) = (3150)100

= $472.5 Take-home amount = 3150 − 472.5 = $2677.5

(c) Deduction = 17(3655)(17%) = (3655)100

= $621.35 Take-home amount = 3655 − 621.35 = $30333.65


100

(d) Deduction = 24(4455)(24%) = (4455)100

= 1069.20 Take-home amount = 4455 − 1069.20 = $3385.80 Among the outcomes, $3385.80 is the greatest.

71. d - Find the amount of tax for 2010 and deduct from income.

Amount of tax for 2010 = 1448200100

= 6748 Amount of take home in 2011 = 48200 − 6748 = $41452 Find the amount of tax for 2011 and deduct from income.


= 8288 Amount of take home in 2011 = 51800 − 8288 = $43,512 Now find the average. (41452 + 43512) ÷ 2 = $42482

72. a - First find the original price of 12 bottles. Price of 12 bottles = 12(0.85) = $10.20

Amount of discount = 1210 20100

.

= 1.224 The prices after discount = 10.20 − 1.224 = $8.98

73. a - The total price of items = 328 + 420 = 748

Find 12% of 748.

Amount of discount = 12748100

= 89.76 Price after discount = 748 − 89.76 = $658.24


101

74. d - Find the sale price for each store. Store A


= 63.80 Price after discount = 580 − 63.80 = 516.20 Store B


= 46.80 Price after discount = 520 − 46.80 = 473.20 Store C


= 34.30 Price after discount = 490 − 34.30 = 455.70 Store D


= 22.50 Price after discount = 450− 22.50 = 427.50 Store D offers the lowest price.

75. 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 76. 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 77. b - Add six times 230 to the original account balance. Balance after six months = 3197 + 6(230) = 4577 78. d - Add all the transactions, and subtract the result from the account balance. Balance after withdrawals = 4531 − (437 + 291 + 29 + 37) = 3737


102

79. c - Deduct the sum of the transactions from the account balance. Account balance after withdrawals = 2024 − (212 + 102 + 210) = 1500 80. 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 81. 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. 82. b - Three times a quantity is 3x. Adding this quantity to 12 gives (3x + 12). Dividing this expression by 12 gives (3x + 12) ÷ 12. 83. 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 84. a - Denote degrees Celsius by C and degrees Fahrenheit by F. Then, multiplying C by 9 gives

9C. Dividing 9C by 5 gives 95

C . Adding 32 to this amount gives 95

C + 32.

85. b - First simplify inside the parentheses. 4(29 − 19) ÷ 5 − 4 × 13 = 4(10) ÷ 5 − 4 × 13 = 40 ÷ 5 − 52 = 8 − 52 = −44 86. d - First determine how many gallons of gas will she use. 1232 ÷ 28 = 44 gallons Cost of gas = 44 × 3.25 = 143 87. a - Total spending = 12(4.25) + 4(12.50) + 42(0.32) = 51 + 50 + 13.44 = 114.44


103

88. 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. 89. 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 90. 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 91. 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:

13

56

45

1415

1×103×10

5×56×5

4 65 6××

14 215 2

××

1030

2530

2430

2830

These fractions can be listed in an ascending order as follows: 1030

, 2430

, 2530

, 2830

Their corresponding fractions are 13

, 45

, 56

, 1415

.

92. c - Find the ratio of each company in decimal forms.

Company A: 70 0 33

210.=

Company B: 30 0 21

140.=

Company C: 80 0 40

200.=

Company D: 60 0 32190

.=

Therefore, Company C is the answer, since 0.40 is greater than all the other numbers.


104

93. d - First multiply the denominator and numerator of each fraction to make their denominators the same.

78

916

1112

2324

7 68 6××

9 3

16 3××

11 412 4

××

23 224 2

××

4248

2748

4448

4648

Arranging these fractions based on their numerators we get 4648

, 4448

, 4248

, 2748

. The

corresponding fractions to these fractions are 2324

, 1112

, 78

, 916

.

94. d - Find the ratio for each novel:

Rachael: 42 0 32130

.=

Raymond: 24 0 18132

.=

Russ: 38 0 30

126.=

Regina: 56 0 39

144.=

Regina has the greatest number. 95. c - Multiply the denominator and numerator of each fraction by a certain number to make all the denominators the same:

1732

7

12

16

17 332 3

××

7 812 8××

1 166 16××

5196

5696

4496

1696

The two greatest fractions are 5696

and 5196

. Their corresponding fractions are 7

12 and

1732

.

96. a - Convert the fractions to decimal numbers:

311 11 0 60 11 605

. .= + =

89 9 899

.=

Here are the numbers from the smallest to the greatest: 9.80, 11.60, 12.025, 12.25

1124

11 424 4

××


105

Replace the equivalents of the decimals 9.80 and 11.60.

899

, 3115

, 12.025, 12.25

97. d - Here is the ascending list along with each month work-hours: 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

98. b - 5632167

= 321 + 0.84 = 321.836

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 5632167

.

99. b - First convert the fraction to a decimal: 230 13 5317

.= . The largest number and the smallest

number are 23.01 and 13.53. Then 23.01 − 13.53 = 9.48

100. b - First convert the fraction to a decimal. 7 0 789

.= . Comparing the numbers shows that 2

is the greatest. So, School B has the highest ratio.

101. d - 224 56 4 562 24100 25 4 25

. ×= = =

×

325 25 13 133 25100 25 4 4

. ×= = =

×

26 2 13 130 26

100 50 2 50. ×

= = =×

102. b - 415 5 83 834 15100 5 20 20

. ×= = =

×

465 5 93 934 65100 5 20 20

. ×= = =

×

425 17 25 174 25100 25 4 4

. ×= = =

×

103. a - 7 12 23 7 2832312 12 12

× += =


106

104. a - 84 7 12 1249 7 7 7

×= =

×

35 7 5 549 7 7 7

×= =

×

14 2 7 221 3 7 3

×= =

×

35 7 5 563 7 9 9

×= =

×

105. c - 32 80 32

100 25. = =

45 90 45100 20

. = =

55 110 55100 20

. = =

75 30 75

100 4. = =

106. b - The digit 9 represents the 100,000 place value. 107. c - We can read the number in two parts and then combine them: 238857 = 238000 + 857 = two hundred thirty eight thousand, eight hundred fifty seven 108. 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 109. d - The distance 440,560 is rounded to 400,000 which is equal to 4.0 × 105. So, the order of magnitude is 5. 110. b - Using the Distribution Property we have 24 × 8.23 + 24 × 4.23 = 24(8.23 + 4.23) = 24(12.46) 111. 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)

5 24 8 5 19724 = =8 8 8

× +


107

= 3 × 12 + 4 × 13 + 4 × 2 − 3 112. d - The multiplication must be performed first. 113. 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. 114. 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. 115. 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.

116. a - 4[12 + 3(1 + 5)] ÷ 144

= 4(12 + 3 × 6) ÷ 174

= 4(30) ÷ 174

= 120 4

1 17×

= 48017

= 42817

117. c - Multiply the number of tons by the number of pounds in each ton:

3 112 2000 20004 4× = ×

= 11 2000

4×

= 5500 pounds

118. d - 1 1 25 256 ÷ 34 8 4 8

= ÷

= 25 84 25×

= 2 119. a - Replace the given values in the formula:


108

( ) ( )1 1 1a b + c + d 3 4 3 63 3 4

= + +

= 134 64

+ +

120. a - First convert all the expression inside the brackets to one number, multiply by 12, and then divide by the mixed number.

121. d - First procedure: 3.23 × 1323

= 3.23 × 7023

= 3.23 × 3.04348 = 9.83

Second procedure: 3.23 × 1323

= 323100

× 7023

= 323 70100 23

××

= 9.83 122. d - If a = the shortest side, then Perimeter = a + 2a + 4a + 8a + 16a + 32a = 63a 123. a - Convert the mixed number to a decimal, divide the two decimal numbers 124. 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

125. c - Find 34

of 45

4 3 12 35 4 20 5× = =

126. b - ( ) 1 3 57 11 12 19 571.1 1 + 4 ÷11 4 4 10 11 4 4

= + ÷


109

11 12 19 410 11 4 57

× = + × ×

6 15 3

= +

2315

=

127. a -

1 721 63 32 + 3 1+ 1 + 2 3 11 105 53 +3 3

= + + +

11 72 35 10

= + +

2 33 71 5 10

= + +

20 66 7

10+ +

=

9310

=

= 9.3 128. 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. 129. 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

x = 6013

= 4.62

130. 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. 131. a - Round off 41.33% to 41%.


110

132. d - Area is found by simply adding the areas of all the segments of the shape. 133. a - To convert a decimal to a percent, simply multiply by 100. 134. d - She must find the ratio of two numbers. So, the division operation is needed. 135. b - We must find the ratio of 4589 to 2000. So, the type of the operation is division. 136. a - To estimate the result simply multiply 2300 × 3200 = 7360000 137. 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 138. a - The easiest and simplest way to estimate the result is round the fraction before the division:

45008 45000 301505 1500

≈ =

139. b - Multiply 11 by 39 to find the distance after 39 seconds. 11 × 39 = 429 ft ≈ 400 ft 140. b - The denominator and numerator of the fraction can be rounded off as follows:

330000 3001100

≈

141. c - Round 9 to 10 and 43 to 40. 9 × 43 ≈ 10 × 40 = 400 in. 142. b - Rounding 1000.01 to the nearest unit, we get 1000. So, the expression 1000 × 100 gives the best estimate.


111

143. 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

144. c - 12 748 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.

145. d - Cross multiply the proportion 22 1877 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. 146. a - Set up the proportion and solve for x.

798 383x

=

38x = 3 × 798 38x = 2394 x = 63

147. d - Denote the unknown number inside the box by x. Then 1128 35

x= .

Solve the proportion. 28x = 11 × 35 28x = 385 x = 13.75 148. c - Find 22% of 1050.

( )( ) ( )2222 1050 1050100

% =

2 11 21 50100

× × × =

= 231


112

149. a - Since all the negative numbers are less than zero, q is a consequence of p. Therefore, if p, then q. 150. 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”. 151. 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”. 152. c - Since on Sundays, all the schools are closed, c is a conditional statement. 153. 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 154. d - Since all the members are published author, then John as one of these members must be a published author. 155. 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. 156. a − We do not know whether all the History students are attending Algebra and/or Geometry classes. So, a is a true statement. 157. 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. 158. c - 1 + 2 + 3 + 4 = 10 Replacing 4 in the formula yields 1 + 2 + 3 + 4 = 42 − 4 = 12, which is not true. 159. a - The numbers of bricks starting from the bottom step up to the eighth step are as


113

follows: 18, 16, 14, 12, 10, 8, 6, 4 = 88

This is an arithmetic progression. Use the formula S = ( )12 nn a a+ to find the total number

of bricks.

S = ( )8 18 42

+ = 88

160. b - Using the given formula, (1 + 2 + 3 + 4 + . . . + 100)2 = 13 + 23 + 33 + 43 + . . . + 1003 161. b - Subtract 11 from each side and add x to each side. 3x + 11 −11 + x = 31 − x − 11 + x 4x = 20 x = 5 162. 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

163. a - 1027 131x

=

13x = 1027 x = 79 164. d − Add 11 to each side, and simplify. 5x − 11 + 11 = 39 + 11 5x = 50 x = 10 165. a - Add the given polynomials. (x2 + x + 1) + (3x − 2) + (3x2 + x) = 4x2 + 5x − 1 166. d - (4x3 + 2x2 + x) − (3x2 + 1) = 4x3 + 2x2 + x − 3x2 − 1 = 4x3 − x2 + x − 1 167. c - Multiply the dimensions, and simplify.


114

Area = (x + 2)(x + 3) = x2 + 2x + 3x + 2 × 3 = x2 + 5x + 6 168. c - (x2 + x) + (8x3 + 2x2 − x − 1) = x2 + x + 8x3 + 2x2 − x − 1 = 8x3 + 3x2 − 1 169. c - Three times x is 3x. x is 2 more than 3x. So, x = 2 + 3x 170. 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 + 3 171. b - The measurement of the right angle is 90º. The sum of an acute angle and 90º is greater than 123º. Therefore, x + 90 > 123 172. b - The triple of a number is 3x. 11 more than 3x is 3x + 11. 173. 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. 174. 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 ≤ −29 175. b - x + 5 > 16 can be rewritten in the following forms.


115

(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 < −21 176. 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≥ ≥ 177. 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 = 10 178. 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 179. 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 > 26 180. 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 = ( )2 22r 4 rπ π=


116

S is as four times as A. So, the area increased four times. 181. a - Subtract x(22 − 19) from (3x)(22 − 19). (3x)(22 −19) − x(22 − 19) = 3x(3) − x(3) = 9x − 3x = 6x 182. 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 = 126 183. 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 184. b - 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 + 36 = 51 185. d - Multiplying all the terms by 100, converts the decimals to whole numbers. This way, the calculations become simpler and easier. 186. d - The mixed number must be converted to an improper fraction in order to perform cross multiplication. 187. c - Multiplying all the terms by the least common denominator, 36, converts all the fractions to whole numbers. 188. b - 1. Cross multiply. 2. Reduce the first ratio. 189. d - (1) Divide 144 by 24 using synthetic method. (2) Write the division in the form of a fraction and reduce it. 190. 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. 191. a - Cross multiplying the proportion yields x = 70.


117

192. c - The perimeter is a + a + b + b, (a + a) + (b + b), (2a + 2b), or 2(a + b). 193. c - The formation of each expression indicates that to find the sum of the interior angles of a polygon, we must subtract 2 from the number of the sides, then multiply by 180. So, for an n-gon, we subtract 2 from n, then multiply by 180. 194. 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. 195. c - Examining each equation shows that each product on the left side is equal to the square of x, added to the product of x and the sum of the numbers, added to the product of the numbers. 196. b - Each number is doubled, then added 1 to generate the following number. 197. 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 90-100. 198. c - To generate the numbers in the series, a multiple of 5 is added to each term beginning with 5. 199. c - Starting from 2, the even numbers are subtracted. 200. a - This is a direct variation. Increase in n implies an increase in P. 201. a - Since A is constant, then by doubling “a” we must divide “b” by 2. 202. b - This is an inverse variation. Increase in x implies a decrease in R. 203. c - Since V, product of T and P, is a constant, then if P increases then T must be decreased, and vice versa.


118

204. 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. 205. d - The graph is curved and has two points of intersection with x-axis. Therefore, the quadratic function (d) represents this graph. 206. c - Path of a projectile has only one maximum point. Hence, (c) is the answer. 207. 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. 208. 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. 209. 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. 210. 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. 211. a - Out of the given solutions of x, only x = 1 fits the equation. So, if (x − 1)(x + 3), then x = 1. 212. a - The given ratios are proportional. So, the first ratio implies the second ratio. 213. 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. 214. 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.


119

215. 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. 216. c - Replace n = 15 in the general formula and simplify:

( )15 15 + 1 15 16S = 120

2 2×

= =

217. d - The given equations verify that the distances of A on each diagonal from both vertices are the same. That is, the diagonals bisect one another. 218. 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 non- zero number. 219. d - If we continue the same pattern, we obtain 37 × 18 = 666 37 × 21 = 777 37 × 24 = 888. 220. a - Following the same pattern we obtain (12346 × 9) + 7 = 1111111 (1234567 × 9) + 8 = 11111111 (12345678 × 9) + 9 = 111111111 221. b - Comparing each data point to all the tables shows that the data in (b) fits the graph. 222. d - Checking data from each table one by one with the given set of data indicates that table (d) matches the data set. 223. c - Comparing the table to each pie chart indicates that chart (c) represents the data.


120

224. d - Comparing the data in the table to each graph indicates the line graph (a) represents the table. 225. 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 = 43 226. a - The highest measure is about 9.4 and the lowest is about 5.2. Range = 9.4 −5.2 = 4.2 227. 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. 228. b - Comparing the numbers on the right column shows that 230,000 is the highest. 229. b - Comparing the numbers on the right column shows that 110,000 is the lowest. 230. b - Replacing the values of b for x gives the corresponding values of P given in the table. 231. d - Replacing the values of q for x gives the corresponding values of T given in the table. 232. a - Replacing the values of m for x in R gives the corresponding values of R given in the table. 233. 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. 234. d - By the columns below the horizontal line 200,000. 235. a - The tops of the columns representing these states are above the horizontal line 100,000 236. c - Among the History scores 67 is the lowest. 237. a - Range of scores of History = 98 −67 = 31


121

Range of scores of Science = 94 − 68 = 26 Difference of ranges = 31 − 26 = 5 238. b - Among the Science scores, 68 is the lowest. 239. c - Student D scored 94 in Science and 67 in History. 240. 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 = 1 241. 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. 242. 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. 243. 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. 244. 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. 245. 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


122

246. c -− Arrange the data in ascending order: 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7 The middle number is 5. 247. 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 = 15 248. a - The longest and the shortest heights are 174 and 145. Difference of these heights is 174 − 145 = 29. 249. a - Average score = (86 + 72 + 78 + 88) ÷ 4 = 324 ÷ 4 = 81 250. 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. 251. 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.

252. c - The chance of not getting selected is 1 − 1131

= 31 11 2031 31−

= .

253. b - Multiply the denominator and the numerator of the fraction 47

by 6.

4 6 247 6 42×

=×

. This means that there are 24 red marbles among the total of 42 marbles in the box.

254. a - Multiply the denominator and the numerator of the fraction by 2.


123

9 2 1816 2 32×

=×

. This means that 18 students out of 32 students are female. Then

Number of male students = 32 − 18 = 14

255. d - Multiply the denominator and the numerator of the fraction 1231

by 4.

12 12 4 4831 31 4 124

×= =

×. This means that 48 cards out of 124 cards are marked with odd

integers. So, 124 − 48 = 76 cards are marked with even integers. 256. a - The following is the set of all possible outcomes of this event: S = {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)} The probability of getting a head and a three is 1 out of 12. 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 421

.

258. a - The number of students do not attend Algebra class is 50 − 20 = 30. Therefore, the

chance is 30 350 5

= .

259. a - Here is the sample space: {(T, T, T, T), (H, H, H, H), (T, H, H, H), (T, T, H, H), (T, T, T, H)}

Only one of the sample points is (H, H, H, H). Therefore, the chance is 15

.

260. b - Here are all the outcomes of this event: S = {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)} Sample points (4, T), (5, T), and (6, T) are to be chosen randomly.

The probability of getting one of these points is 3 to 12 or 14

.

261. a – 1000 milligrams equals 1 gram. Milligrams and grams are units of weight in the metric system. 262. 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.


124

263. b – 1 gram equals .001 kilograms. 109 x .001 = .109. Grams and kilograms are units of weight in the metric system. 264. d – I liter equals 1000 milliliters. 4 x 1000 = 4000 milliliters. Liters and milliliters are units of volume in the metric system. 265. b – 1 milliliter equals 1/1000 liter. 75 ÷ 1000 = .075 liters. Liters and milliliters are units of volume in the metric system. 266. 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. 267. 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 = 12.22 268. a – To convert Celsuis to Fahrenheit, first multiply by 9/5 and then add 32. 32 x 9/5 = 288/5 288/5 = 57.6 57.6 + 32 = 89.6 269. 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. 270. 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 = 193.04 271. d - Each pound is equal to 16 ounces. Therefore, 3 pounds + 12 ounces = 3 × 16 + 12 = 48 + 12 = 60 ounces 272. b - One kilogram = 1000 grams Weight of M = 9 × 1000 + 112 = 9112 grams Weight of N = 1200 grams


125

Weight of M and N = 9112 + 1200 = 10312 grams 273. a - One yard = 36 inches 1 foot = 12 inches 5 yards + 5 feet + 22 inches = 5 × 36 + 5 × 12 + 22 = 262 inches 274. 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 275. 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 276. 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 277. 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 278. a - 1 cm = 10 mm Distance = 24 × 10 = 240 mm Distance between each two lines = 240 ÷ 16 = 15 mm 279. c - Denote the real distance by x. Then solve the following proportion.

3 601 2 x.

=

3x = 60(1.2) 3x = 72 x = 24 miles 280. d - Multiply each dimension by the scale factor. 4.2 × 5 = 21 8.4 × 5 = 42


126

281. b - Denote the dimensions after scaling by x and y. Then solve the following proportions:

1 5x 85=

5x = 85 x = 13 in.

1 5y 50=

5y = 50 y = 10 in. 282. b - 1 yard = 3 feet 1 foot = 12 inches 1 yard = 3 × 12 = 36 inches 283. c - One liter is equivalent to 1000 cubic centimeters. 284. d - 1 gallon = 4 quarts 1 quart = 2 pints 1 gallon = 2 × 4 = 8 pints 285. c - 1 gallon = 4 quarts. 2 gallons + 8 quarts = 2 × 4 + 8 = 16 quarts 286. a - 1 decameter = 1000 centimeters 1 decimeter = 10 centimeters 2 dm + 34 dc = 2 × 1000 + 34 × 10 = 2000 + 340 = 2340 cm 287. a - 1 yard = 36 inches 1 foot = 12 inches 5 yards + 4 feet = 5 × 36 + 4 × 12 = 180 + 48 = 228 in. 288. a - Since the preservative is a small portion of the total weight of the product, the preservative must be measured in grams. 289. 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. 290. c - Total weight of the load = 124 × 24 × 340 = 1011840 g


127

= 1011.840 kg = 1.002 tons 291. b - Replace d = 500 in the formula and calculate.

w = 50e−0.004(500) = 50e−2 ≈ 50(2.71828183)−2= ( )2

502 71828183.

= 50(0.1353) = 6.77 watts

292. a - Place h = 5 in D = 5e−0.4h.

D = 5e−0.4(5) = 5e−2 = ≈ 5(2.71828183)−2= ( )2

52 71828183.

= 5(0.1353) = 0.68 mg

293. b – Answering this question is a two step 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.

294. 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 295. a - Area = (2 ft)(240 in) = (2 × 12 in.)(240 in.) = (24 in.)(240 in.) = 5760 in.2 296. 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.)


128

= 24 in. + 25 in. + 36 in. + 35 in. = 120 in. 297. c - 100 square decimeter = 1 square meter Total Area = (232 m2) + (420000 dc2) = (232 m2) + (42000 ÷ 100 m2) = 232 m2 + 420 m2

= 652 m2 298. a - Dropping a rock inside a cylinder half-filled with water increases the level of the water. The difference in the levels of the water represents the volume of the rock.

299. d - Replace F = 77 with F = 9 C + 325

, and solve for C.

77 = 9 C + 325

77 − 32 = 9 C + 325

− 32

45 = 9 C 5

C = 25

300. a - Multiply 1945 ft-pl by the unit fraction 1 BTU778 ft -pl

.

1945 ft-pl × 1 BTU778 ft -pl

= 1945 ft -pl 1 BTU1 778 ft -pl

× = 2.5 BTU


129

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. 3/12 b. 3/4 c. 5/4 d. 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. 1 b. 3/7 c. 1 5/7 d. 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. 5/8 b. 8/10 c. 15/10 d. None of the above.


130

a – To multiply a fraction by another fraction, multiply numerators and denominators: 5/6 x 3/4 = 15/24 = 5/8 4. 348 ÷ 6 = a. 48 b. 58 c. 68 d. 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 – 3 x 4 + 9 = a. 5 b. - 5 c. 65 d. - 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. 28 b. 285 c. 105 d. 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. 39 b. 38 c. - 38 d. 1


131

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. 2/3 ÷ 4/5 = a. 3/5 b. 5/6 c. 6/8 d. 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. 9 b. 40 c. 90 d. 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. 63.08 b. 62.73 c. 63.72 d. 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.


132

11. In Science Hill High School, 45% of students are female. What fraction of the students is male?

a. 1125

b. 1320

c. 1120

d. 9

20

c - Percent of students that are male = 100% − 45% = 55% Now, convert 55% to a fraction.

55% = 55 11

100 20=

12. Two fifths of the members of a Literature Club are published writers. What percent of the members are not published writers? a. 25% b. 40% c. 60% d. 65%

c - Subtract 25

from 11

to obtain the fraction of the members which are not published writers:

1 2 5 - 2 3

- = =1 5 5 5

Now, convert 35

to a percent by converting its denominator to 100:

3 3 × 20 60= = = 60%

5 5 × 20 100

13. If 25% of A is equal to 48, then what is 23

of A?

a. 124 b. 128 c. 142 d. 122


133

b - Since 25% of A is 48, we can find the value of A by multiplying 48 by the reciprocal of 25

100.

So, ( )100= 48 = 192

25A

Multiply 192 by 23

to get the answer.

( )2 192 128

3=

14. If 35

the expression (2x + 3y) is 60, then what is 3.25 times the expression (2x + 3y)?

a. 325 b. 322 c. 314 d. 304

a - To find (2x + 3y), simply multiply 60 by the reciprocal of 35

.

(2 + 3 ) = (60) = 10053

x y

Now, multiply 100 by 3.25 to find the solution: 100(3.25) = 325

15. What is 25% of

33.25 +

4?

a. 5 b. 4 c. 3 d. 1

d - First simplify 3

3.25 + = 3.25 + 0.75 = 44

Now, find 25% of 4:

( )25(25%)(4) = 4 = 1

100

16. What is the product of 0.32002 × 3200.5? a. 1042.242010 b. 1204.224010 c. 1024.224010 d. 102.4224010


134

c - First multiply 32002 × 32005 = 1024224010 The factors of the product have a total of 6 decimal digits. So, place a decimal point to the left of the sixth digit from right: 0.32002 × 3200.5 = 1024.224010 17. 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. $78.97 b. $87.79 c. $97.58 d. $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 18. 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 2010-2011, to the nearest hundredth? a. $19.19 b. $19.91 c. $91.19 d. $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. 19. What is the quotient of the division 2004.52 ÷ 4.52 to the nearest hundredth? a. 424.37 b. 443.47 c. 483.47 d. 524.73 b - The original division form is as follows:

4.52 2004.52

Multiply both divisor and dividend by 100 to get rid of the decimal digits. Then continue the division:


135

443474.52 2004.52 = 452 200452 = 452 20045200

-1808

1965

-1808

1572

-1356

2160

-1808

3520

-3164

356

Since both dividend and divisor are multiplied by 100, to obtain the real remainder, we must divide the remainder above, 356, by 100. Remainder = 356 ÷ 100 = 3.56 On the other hand, since we added two zeros to the dividend, now we must place a decimal point to the left of the second digit from the left. So, the quotient is 443.47 20. If 24% of the expression (m + 2n) is 48, then what is 25% of (m + 2n)? a. 40 b. 48 c. 50 d. 56

c - 24% is equal to 24

100. To find (m + 2n) multiply 48 by the reciprocal of

24100

.

(m + 2n) = (48) =100 20024

Now, find 25% of 200.

25

(25%) = = 50100

200 200

21. John spends 12% of his salary on groceries each month. If his monthly salary is $3400, how much does he spend on groceries? a. $448 b. $424 c. $412 d. $408


136

d - Simply find 12% of 3400.

( )( ) ( )1212% 3400 = 3400 = 408

100

So, he spends $408 per month. 22. 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. 103.81% b. 111.38% c. 113.18% d. 123.81% 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:

10052

5200 52 123.8142= = = = 123.81%1004200 42 1004242

So, the percent of increase was 123.81%. 23. 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. 11.11% b. 12.21% c. 14.11% d. 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:

10040 1 11.119= = = = 11.11%

100360 9 10099

So, the percent of decrease was 11.11%.


137

24. If 28% of 20% of A is 420, what is A? a. 7500 b. 7700 c. 7850 d. 8500

a - 28% is equivalent to the fraction 28 7

=100 25

and 20% is equivalent to the fraction

20 1

=100 5

. To find 20% of A, we must multiply 420 by the reciprocal of the fraction 7

25.

20% of A = 25

420 = 15007

Now, to find A, we must multiply 1500 by the reciprocal of 15

.

A = 5

1500 = 75001

25. A washing machine is marked down 32% from its original price of $450. What is the sale price of the washing machine? a. $360 b. $306 c. $300 d. $266 b - First find the 32% of 450 to get the discount amount:

Discount = ( )( ) ( )3232% 450 = 450 = 144

100

Subtracting the discount amount from the original price gives the marked down price. Sale Price = $450 − $144 = $306 26. 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. 32% b. 29% c. 27% d. 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


138

then convert the result to a percent.

Discount rate = 66 1

= = 0.25264 4

We know that 0.25 is equal to 25%. 27. A is 29% of 2900, and B% of 290 is 29. What is A + B? a. 812 b. 831 c. 841 d. 851 d - First find 29% of 2900.

A = 29

2900 = 841100

On the other hand, to find B, we must divide 29 by 290, and then multiply the result by 100.

B = ( )29100

290 = 10

Therefore, A + B = 841 + 10 = 851 28. 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. $227.39 b. $244.43 c. $264.23 d. $268.43 a - First calculate the marked down price on the first day:

Discount on first day =

15304 = 45.6

100

Marked down price on first day = $304 − $45.6 = $258.4

Discount on the second day = 12

258.4 = 31.01100

Marked down price on the second day = $258.4 − $31.01 = $227.39

29. What is the result of adding 23

the division of 32.24 by 24.32 to the product of 24 and 32?

a. 779.79 b. 777.39 c. 769.93 d. 768.88


139

d - First find the division of 32.24 by 24.32, and then multiply the result by 23

.

( ) ( )2 232.24 24.32 = 1.325658 = 0.88

3 3÷

Now add 0.88 to the product of 24 and 32. 0.88 + (24 × 32) = 768.88 30. 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. $88.51 b. $79.51 c. $76.15 d. $67.51 b - First set the numerical expression in terms of both purchases, and then calculate: 3(12.82) + 5(8.21) = $79.51

31. Add 2.3 times 3.2 to 23

the sum of 23 and 32.

a. 48.33 b. 46.33 c. 44.03 d. 42.03

c - First find 23

the sum of 23 and 32:

( ) ( )2 223 32 55 36 673 3

.+ = =

Now add 36.67 to 2.3 time 3.2: 36.67 + 2.3(3.2) = 44.03 32. 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. $0.23 b. $0.13 c. $0.11 d. $0.10 b - Find the price of each can using the different pack-prices: $6.24 ÷ 12 = $0.52 $3.92 ÷ 6 = $0.65 Subtract these prices. $0.65 − $0.52 =$0.13


140

33. Given A = 5

126

and B = 7

12, what is

-A BA + B

?

a. 147161

b. 157151

c. 137161

d. 129161

a - Convert the first mixed number to an improper fraction.

5 77

12 =6 6

Now, find A − B and A + B.

A − B = 77 7 154 - 7 147

- = =6 12 12 12

A + B = 77 7 154 + 7 161

= =6 12 12 12+

Then find the ratio of these fractions.

14714712

161 16112

A BA B−

+ =+

34. To make 3

45

cakes, 2

33

pounds of flour is needed. How much flour is needed to make one cake?

a. 0.08 pound b. 0.68 pound c. 0.78 pound d. 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 = ÷ = × = 0.803 5 3 5 3 23


141

35. Find the ratio of M + 2N to 2M + N, if M =

1 52 - 1

4 4 and N =

1 44 - 2

4 5.

a. 6 b. 5 c. 3 d. 2 d - Simplify M and N first.

M = 4

1 9 92 - 1 = - = 0

4 4 45

N = 1 4 17 14 85 - 56 29

4 - 2 = - = =4 5 4 5 20 20

Now find M + 2N and 2M + N.

M + 2N = 0 + 29 29220 10

=

2M + N = 2(0) + 29 2920 20

=

Now we can determine the required ratio using the calculated values:

292 10 2292

20

M NM N+

= =+

36. Given A = 1

26

and B = 13

, divide

12 + 3

3A by

12 -

3B .

a. 29 b. 26 c. 23 d. 22

c - Find the values of the expressions1

2 + 33

A

and 1

2 -3

B

using the given numbers for A and B.

1 1 10 13 10 23

2 + 3 = 2 2 + = + =3 6 3 3 3 3

A

1

2 -3

1 1 1= 2 - =3 3 3

B

Now, divide 233

by 13

:

233

÷ 13

= 23 3 233 1× =


142

37. Given A and B below, what is the sum of A and B?

A =

1 1 1+ 3

2 3 2

B = −

1 1 13

2 3 2

a. 132

b. 13

12

c. 172

d. 1122

a - First simplify A and B.

A = 1 1 1 5 7 35

+ 3 = =2 3 2 6 2 12

B = 1 1 1 1 7 7

- 3 = =2 3 2 6 2 12

Now add 3512

and 712

: 35 7 42 1312 12 12 2

+ = =

38. I n the process of film development, photographers use a chemical called “stop bath.” A

photographer used 2

23

bottles of stop bath for the first group of rolls of film and 2

43

bottles of 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. 293

b. 192

c. 173

d. 164

b - Add 2

23

and 2

43

, and simplify the result:

2 2 8 14 22 1

2 + 4 = + = = 73 3 3 3 3 3

Bottles

39. The sum of which numerical expression has the greatest whole number part?


143

K = 2 1

3 + 23 4

L = 13 6

1 + 13 4

M = 8 10

+ 23 4

N = 1 1

5 + 33 2

a. K b. L c. M d. N d - Simplify each numerical expression.

K = 2 1 11 9 44 + 27 11

3 + 2 = + = = 53 4 3 4 12 12

L = 13 6 16 5 47 5

1 + 1 = + = = 73 4 3 2 6 6

M = 8 10 8 9 43 1

+ 2 = + = = 73 4 3 2 6 6

N = 1 1

5 + 33

16 7 32 + 21 53 5= + = = = 82 3 2 6 6 6

The mixed number 586

has the greatest whole number part.

40. Given A, B, and C below, find A + 2B − 3C.

A = 5

37

B = 2

15

C = 13

a. 13

835

b. 3

635

c. 18

535

d. 1

521

c - Set up the numerical expression and simplify.


144

A + 2B − 3C = 5

37

+ 2

2 15

− 1

33

= 267

+ 145

− 1 = 26 × 5 + 14 × 7 - 35

35193 18= = 535 35

41. A house built on ground sank every year according to the following list:

2008: 23

in.

2009: 17

in.

2010: 15

in.

2011: 15

in.

In which of the following combination of years did the house sink the most? a. 2008 and 2009 b. 2009 and 2010 c. 2010 and 2011 d. 2008 and 2011 d - Calculate each sum given in the answer choices and then compare the results:

(a) 2008 and 2009 : 2 1 14 3 17 0 813 7 21 21

.++ = = =

(b) 2009 and 2010 : 1 1 5 7 12 0 347 5 35 35

.++ = = =

(c) 2010 and 2011 : 1 1 1 1 2 0 405 5 5 5

.++ = = =

(d) 2008 and 2011 : 2 1 10 3 13 0 873 5 15 15

.++ = = =

Obviously, the fraction (d) which is the highest number. 42. 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. A b. B c. C d. D c - Calculate each sum.


145

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 43. 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 Income Spending January $3420 $2970 February $2927 $2212 March $3189 $3020 April $3024 $2730

a. January and February b. February and March c. March and April d. January and March 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. 44. 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. 9 cases of soda, and 4 bags of potato chips b. 7 cases of soda, and 5 bags of potato chips c. 6 cases of soda, and 11 bags of potato chips d. 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


146

Since $57 is less than $65, then the correct answer is (b). 45. A, b, c, and d are whole numbers such that a = 2b and b = 2c. Which expression is definitely a whole number?

a. 2

a b c+ +

b. 28

a b c+ +

c. 2

10a b c+ +

d. 2

12a b c+ +

b - Combine the given relations in terms of c.

(1) a = 2b Replace b = 2c in (1).

(2) a = 2(2c) = 4c Also, we are given

(3) b = 2c Now, replace (2)-(3) in the choice (b), and simplify.

2 4 2 2 88 8 8

a b c c c c c c+ + + += = =

So, (b) results in a whole number. You can check the other choices similarly. But you will not obtain a whole number.

46. The ratio of a to b is 23

and the ratio of c to b is 215

. What is the ratio of a to c?

a. 143

b. 145

c. 5 d. 3 c - Write the ratios as given in the problem.

23

ab=

2

15cb=

Divide these proportions side by side.

232

15

abcb

=


147

2 152 3

abbc

×=

×

15 53

ac= =

47. 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. 32 in. b. 24 in. c. 20 in. d. 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. Set the proportional relationship among the dimensions of the rectangles.

AB BCKL LM

=

Now, replace the given values and find the missing length.

12 9 118 2KL

= =

KL = 24 in.

48. Which statement is true given the proportion a c=b d

?

a. a c=d b

b. d b=a c

c. c b=d c

d. d c=b a

d - Cross-multiply the given proportion first. ad = bc Now cross divide by ab:

ad bc=ab ab

d c=b a


148

49. Which of the following quantities has the highest rate of change? a. Increase of the height of Michelle from 98 cm at the age of 9 to 108 cm at the age of 14 b. Increase of the height of Sarah from 74 cm at the age of 7 to 92 cm at the age of 11 c. Increase of the height of Joanne from 56 cm at the age of 6 to 82 cm at the age of 10 d. 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:

Rate of change in height of Michelle = 108 98 10 214 9 5

−= =

−

Rate of change in height of Sarah = 92 74 18 4 511 7 4

.−= =

−

Rate of change in height of Joanne = 82 56 26 6 510 6 4

.−= =

−

Rate of change in height of Alison = 108 52 56 6 22

14 5 9.−

= =−

So, Joanne had the highest rate of change 50. 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. $18.00 b. $17.00 c. $12.00 d. $11.00 c - Set the rate of change as follows:

Rate of change = 540 420 120 122011 2001 10

−= =

−

51. 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. 251.3 b. 219.7 c. 205.5 d. 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


149

52. 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. 0.272 in. b. 0.377 in. c. 0.389 in. d. 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.

53. Given m = 3.2, n = 2.2, and p = 2.1, what is the value of

+-

m nmnp

n p to the nearest tenth?

a. 798.5 b. 789.3 c. 798.5 d. 798.3

d - Replace the given values in +-

m nmnp

n p

.

+ 3.2 + 2.2= (3.2)(2.2)(2.1)

- 2.2 - 2.1m n

mnpn p

5.4

= (14.784)0.1

= 798.336

798.3≈

54. 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. 0.10 b. 0.11


150

c. 0.15 d. 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 55. 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. 30 in. b. 31 in. c. 32 in. d. 34 in. 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. 56. Which of the following formats of subtraction is arranged properly using the regrouping method for 9415 − 4786?


151

a.

8 13 11 15

9 4 1 54 7 8 6−

b.

8 12 10 15

9 4 1 54 7 8 6−

c.

8 13 10 5

9 4 1 54 7 8 6−

d.

8 13 10 15

9 4 1 54 7 8 6−

d -

8 13 10 15

9 4 1 54 7 8 6

4 6 2 9

−

57. Which subtraction can be performed using the regrouping method? a. 43,0987 − 34,0765 b. 20,007 − 10,003 c. 34,087 − 32,986 d. 54,983 − 44,572 c - Because the digit 9 in the subtrahend is greater than the corresponding digit in the minuend. 58. 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. 3799 ft2 b. 3898 ft2 c. 3978 ft2 d. 3988 ft2

a -

2 12 13 14 16

3 3 4 5 62 9 6 5 7

3 7 9 9

−


152

59. 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. 1879 gallons b. 1899 gallons c. 1989 gallons d. 1999 gallons

b -

8 13 15 18

9 4 6 87 5 6 9

1 8 9 9

−

60. Convert 2π to a decimal number rounded to the nearest ten-thousandth. a. 6.2832 b. 6.3832 c. 6.6821 d. 6.8861 a - Given π = 3.141592…., then 2π = 6.283184. Rounding this number to ten-thousandth gives 2π = 6.2832 61. An irrational number is rounded to 9.94987. This number is between 6 and 10. Find the irrational number. a. 28 b. 39 c. 98 d. 99 d - 99 is the only irrational number whose decimal digits are calculated which includes the same decimal digit as 9.94987.

62. The circumference of an irregular closed curve is determined using the formula π= 3π +3

C d ,

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. 14.556 ft2 b. 12.566 ft2 c. 10.862 ft2


153

d. 10.266 ft2 b - Replace the 4-digit value of π and d = 3 in the formula and then round up.

( ) ( )

( )2

3 14153 3 1415 33

3 3 1415 3 1415

12 566

.C .

. .

. ft

= +

= +

=

63. Which fraction is approximately equal to π ?

a. 327

b. 317

c. 297

d. 227

d - 227

is the only fraction that is closest to π .

64. What year is the Arabic numeral MMXII? a. 2008 b. 2009 c. 2011 d. 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 65. Which numeral represents the Roman expression XXXI + XXIV? a. 55 b. 52 c. 45 d. 43 a - Replace the following equivalents in the expressions:


154

X = 10 I = 1 IV = 4 XXXI + XXIV = (10 + 10 + 10 + 1) + (10 + 10 + 4) = 31 + 24 = 55 66. John was born in the year MCMXLIX. Convert his birth year to an Arabic Numeral. a. 1848 b. 1884 c. 1944 d. 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 67. Which expression represents 70 + 80 + 90? a. LX + LXX + LXXX b. LXX + LXXX + LXXXX c. LCX + LXXX + LXXX d. 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 68. Ronald earns $3225 per month. 12% of his salary is withheld for income tax. Find the amount of his take home per month. a. $2883 b. $2838 c. $2787 d. $2778 b - First find 12% of 3225.


155

Tax = 12(3225)(12%) = (3225)100

= 387 Subtract the tax amount from his earning. 3225 − 387 = 2838 69. 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. $3211 b. $3121 c. $3112 d. $3011 a - First find 24% of 4225.

Installment = 24(4225)(24%) = (4225)100

= 1014

Subtract the installment amount from his earning. 4225 − 1014 = 3211 70. The following list shows the salaries of four people along with their total deductions for each month. Which one has the greatest take-home amount? a. Salary = $3402; Total Deduction = 14% b. Salary = $3150; Total Deduction = 15% c. Salary = $3655; Total Deduction = 17% d. Salary = $4455; Total Deduction = 24% d - First find take home amount of each person, and then compare.

(a) Deduction = 14(3402)(14%) = (3402)100

= 476.28

Take-home amount = 3402 − 476.28 = $2925.72

(b) Deduction = 15(3150)(15%) = (3150)100

= $472.5

Take-home amount = 3150 − 472.5 = $2677.5

(c) Deduction = 17(3655)(17%) = (3655)100

= $621.35

Take-home amount = 3655 − 621.35 = $30333.65

(d) Deduction = 24(4455)(24%) = (4455)100

= 1069.20

Take-home amount = 4455 − 1069.20 = $3385.80


156

Among the outcomes, $3385.80 is the greatest. 71. 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 2010-2011? a. $48,482 b. $46,486 c. $44,462 d. $42,482 d - Find the amount of tax for 2010 and deduct from income.


= 6748

Amount of take home in 2011 = 48200 − 6748 = $41452 Find the amount of tax for 2011 and deduct from income.


= 8288

Amount of take home in 2011 = 51800 − 8288 = $43,512 Now find the average. (41452 + 43512) ÷ 2 = $42482 72. 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. $8.98 b. $8.68 c. $7.96 d. $6.86 a - First find the original price of 12 bottles. Price of 12 bottles = 12(0.85) = $10.20

Amount of discount = 1210 20100

.

= 1.224

The prices after discount = 10.20 − 1.224 = $8.98 73. 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?


157

a. $658.24 b. $678.44 c. $687.24 d. $689.46 a - The total price of items = 328 + 420 = 748 Find 12% of 748.


= 89.76

Price after discount = 748 − 89.76 = $658.24 74. Different stores offer different prices and discounts for a chair and an ottoman as follows. Which store offers the best purchase price? a. Store A: Original price = $580 with 11% discount b. Store B: Original price = $520 with 9% discount c. Store C: Original price = $490 with 7% discount d. Store D: Original price = $450 with 5% discount d - Find the sale price for each store.

Store A: Amount of discount = 11580100

= 63.80. Price after discount = 580 − 63.80 = 516.20

Store B: Amount of discount = 9520100


Store C: Amount of discount = 7490100


Store D: Amount of discount = 5450100

= 22.50. Price after discount = 450− 22.50 = 427.50

Store D offers the lowest price. 75. 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?


158

a. 2.4m + 1.8n + 1.24p + 3.92q b. 0.24m + 0.18n + 12.4p + 3.92q c. 0.24m + 0.18n + 1.24p + 3.92q d. 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 76. 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: 1. Electronic withdrawal: $320 2. Electronic withdrawal: $22 3. Electronic withdrawal: $124 a. $3958 b. $3937 c. $3857 d. $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 77. 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. $4378 b. $4577 c. $4676 d. $4766 b - Add six times 230 to the original account balance. Balance after six months = 3197 + 6(230) = 4577 78. 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


159

Withdrawal: $37 Find her account balance at the end of her trip? a. $3938 b. $3937 c. $3836 d. $3737 d - Add all the transactions, and subtract the result from the account balance. Balance after withdrawals = 4531 − (437 + 291 + 29 + 37) = 3737 79. 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. $1650 b. $1600 c. $1500 d. $1350 c - Deduct the sum of the transactions from the account balance. Account balance after withdrawals = 2024 − (212 + 102 + 210) = 1500 80. 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?


160

a. $3802 b. $3383 c. $3083 d. $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 81. Which expression is equivalent to 3 + 4(9 − 3) + 11? a. 3 + 4 × 9 − 3 + 11 b. 3 + 4 × 9 − 4 × 3 + 11 c. 3 + 4 × 9 + 4 × 3 + 11 d. 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. 82. Which expression is the translation of “three times a quantity added to 12, divided by 12?” a. (3 + 12x) ÷ 12 b. (3x + 12) ÷ 12 c. 3(x ÷ 12) + 12 d. 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. 83. What is the value of −4[3 − 4(8 + 1) ÷ 3 − 3] + 12? a. 69 b. 63 c. 60 d. 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


161

= 48 + 12 = 60 84. To convert degrees Celsius to degrees Fahrenheit, multiply by 9, divide by 5 and add 32. Write a formula that represents these operations.

a. 95

C + 32.

b. 59

C + 32.

c. 325

C + 9.

d. 329

C + 5.

a - Denote degrees Celsius by C and degrees Fahrenheit by F. Then, multiplying C by 9 gives

9C. Dividing 9C by 5 gives 95

C . Adding 32 to this amount gives 95

C + 32.

85. What is the value of 4(29 − 19) ÷ 5 − 4 × 13? a. − 49 b. −44 c. 48 d. 44 b - First simplify inside the parentheses. 4(29 − 19) ÷ 5 − 4 × 13 = 4(10) ÷ 5 − 4 × 13 = 40 ÷ 5 − 52 = 8 − 52 = −44 86. 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. $153 b. $148 c. $145 d. $143 d - First determine how many gallons of gas will she use. 1232 ÷ 28 = 44 gallons Cost of gas = 44 × 3.25 = 143


162

87. 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. $114.44 b. $112.42 c. $104.42 d. $102.24 a - Total spending = 12(4.25) + 4(12.50) + 42(0.32) = 51 + 50 + 13.44 = 114.44 88. Wendy wants to invite a number of friends to an anniversary party at a restaurant. She would like to invite between 14-18 friends. She checked with different restaurants, and they offered the following packages. Which restaurant offered the lowest quote for each guest? a. Restaurant A: $705 for 15 guests b. Restaurant B: $736 for 16 guests c. Restaurant C: $1020 for 20 guests d. Restaurant D: $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. 89. 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. $27.14 b. $25.04


163

c. $24.14 d. $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 90. 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. $2414 b. $2214 c. $2142 d. $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 91. Which list shows the following numbers from the smallest to the greatest?

13

, 56

, 45

, 1415

a. 13

, 56

, 1415

, 45

b. 56

, 13

, 45

, 1415

c. 45

, 13

, 56

, 1415


164

d. 13

, 45

, 56

, 1415

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:

13

56

45

1415

1×103×10

5×56×5

4 65 6××

14 215 2

××

1030

2530

2430

2830

These fractions can be listed in an ascending order as follows:

1030

, 2430

, 2530

, 2830

Their corresponding fractions are 13

, 45

, 56

, 1415

.

92. Three telecommunication companies plan to lay off some of their workers as listed below: Company A: 70 workers of its 210 workers Company B: 30 workers of its 140 workers Company C: 80 workers of its 200 workers Company D: 60 workers of its 190 workers Which company plans to lay off the highest fraction of it workers? a. Company A b. Company B c. Company C d. Company D c - Find the ratio of each company in decimal forms.

Company A: 70 0 33

210.=

Company B: 30 0 21

140.=

Company C: 80 0 40

200.=

Company D: 60 0 32

190.=

Therefore, Company C is the answer, since 0.40 is greater than all the other numbers.


165

93. Which list shows the following numbers from the greatest to the smallest?

7 9 11 23, , ,8 16 12 24

a. 1112

, 2324

, 78

, 9

16

b. 2324

, 78

, 9

16,

1112

c. 9

16,

2324

, 78

, 1112

d. 2324

, 1112

, 78

, 9

16

d - First multiply the denominator and numerator of each fraction to make their denominators the same.

78

9

16

1112

2324

7 68 6××

9 3

16 3××

11 412 4

××

23 224 2

××

4248

2748

4448

4648

Arranging these fractions based on their numerators we get 4648

, 4448

, 4248

, 2748

. The

corresponding fractions to these fractions are 2324

, 1112

, 78

, 9

16.

94. 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


166

Raymond: 24 pages Russ: 38 pages Regina: 56 pages Which student left the largest fraction of the novel unread? a. Rachael b. Raymond c. Russ d. Regina d - Find the ratio for each novel:

Rachael: 42 0 32

130.=

Raymond: 24 0 18

132.=

Russ: 38 0 30

126.=

Regina: 56 0 39

144.=

Regina has the greatest number. 95. Which are the two greatest numbers in the following list?

,17 7 11 1, ,32 12 24 6

a. and 1732

b. 7

12 and

1124

1124


167

c. 7

12 and

1732

d. 7

12 and

16

c - Multiply the denominator and numerator of each fraction by a certain number to make all the denominators the same:

1732

7

12

16

17 332 3

××

7 8

12 8××

1 166 16××

5196

5696

4496

1696

The two greatest fractions are 5696

and 5196

. Their corresponding fractions are 7

12 and

1732

.

96. Order the following numbers from the smallest to the greatest:

12.25, 3115

, 899

, 12.025

a. 899

, 3115

, 12.025, 12.25

b. 899

, 12.025, 12.25, 3115

c. 3115

, 899

, 12.025, 12.25

d. 12.25, 899

, 3115

, 12.025

a - Convert the fractions to decimal numbers:

311 11 0 60 11 605

. .= + =

89 9 899

.=

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.

899

, 3115

, 12.025, 12.25

97. John worked the following number of hours per month during the first six months of the year.

1124

11 424 4

××


168

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 work-hours from the lowest to the highest in terms of months. a. June, March, April, May, January, February b. June, March, April, January, May, February c. April, June, January, February, March, May d. April, May, January, February, March, June d - Here is the ascending list along with each month work-hours: 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 98. Find the middle number among the following data?

321.243, , 321.432 , 322.254, 322.245

a. 321.243

b. 5632167

c. 321.432 d. 322.254

b - 5632167

= 321 + 0.84 = 321.836

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 5632167

.

99. What is the difference between the smallest and the largest numbers in the following list?

23023, 23.01,17

a. 9.74 b. 9.48 c. 7.72 d. 7.47

5632167


169

b - First convert the fraction to a decimal: 230 13 5317

.= . The largest number and the

smallest number are 23.01 and 13.53. Then 23.01 − 13.53 = 9.48 100. 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

School C : 79

School D: 1.09 Which school has the highest fraction of female students? a. School A b. School B c. School C d. School D

b - First convert the fraction to a decimal. 7 0 789

.= . Comparing the numbers shows that 2

is the greatest. So, School B has the highest ratio. 101. 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. 52 13 1325 4 50

, ,


170

b. 56 11 1325 4 50

, ,

c. 56 13 1125 4 50

, ,

d. 56 13 1325 4 50

, ,

d - 224 56 4 562 24100 25 4 25

. ×= = =

×

325 25 13 133 25100 25 4 4

. ×= = =

×

26 2 13 130 26

100 50 2 50. ×

= = =×

102. Which list represents the equivalents of the following decimal numbers? 4.15, 4.65, 4.25

a. 8325

, 9320

, 174

b. , 9320

, 174

c. , 9325

, 174

d. , 9720

, 174

b - 415 5 83 834 15100 5 20 20

. ×= = =

×

465 5 93 934 65100 5 20 20

. ×= = =

×

425 17 25 174 25100 25 4 4

. ×= = =

×

103. The dimensions of a rectangular tract of land are 723

12 ft. and

5248

ft. Which fractions can be

used to find the area of the land?

a. 28312

and 197

8

832083208320


171

b. 28112

and 197

8

c. 28312

and 193

8

d. 28314

and 197

8

a - 7 12 23 7 28323

12 12 12× +

= =

104. Which list represents the equivalents of the following fractions?

84 35 14 35, , ,49 49 21 63

a. 127

, 57

, 23

, 59

b. 59

, 127

, 57

, 23

c. 117

, 57

, 23

, 59

d. 127

, 57

, 23

, 79

a - 84 7 12 1249 7 7 7

×= =

×

35 7 5 549 7 7 7

×= =

×

14 2 7 221 3 7 3

×= =

×

35 7 5 563 7 9 9

×= =

×

105. 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?

5 24 8 5 19724 = =8 8 8

× +


172

a. 7

25,

920

, 1120

, 34

b. 8

25,

920

, 1720

, 34

c. 8

25,

920

, 1120

, 34

d. 8

25,

920

, 1320

, 34

c - 32 80 32

100 25. = =

45 90 45

100 20. = =

55 110 55

100 20. = =

75 30 75

100 4. = =

106. In which number does the digit 9 have the highest place value? a. 3409008 b. 3490806 c. 3400908 d. 3400790 b - The digit 9 represents the 100,000 place value. 107. 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. two hundred thousand thirty eight, eight hundred fifty seven b. two hundred thirty eight, eight hundred fifty seven c. two hundred thirty eight thousand, eight hundred fifty seven d. two million thirty eight, eight hundred fifty seven c - We can read the number in two parts and then combine them: 238857 = 238000 + 857 = two hundred thirty eight thousand, eight hundred fifty seven 108. Which is the name of the number 45,600,006? a. forty five million, six thousand, sixty b. forty five million, six hundred thousand, sixty


173

c. forty million, forty six hundred thousand, six d. forty five 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 109. The exact distance between two islands in the Atlantic Ocean is 440,056 ft. What is the order of magnitude of this number? a. 8 b. 7 c. 6 d. 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.

110. 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. 24(34.81) b. 24(12.46) c. 8.23 + 101.52 d. 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) 111. Which expression is equivalent to 3(12 − 1) + 4(13 + 2)? a. 3 × 12 − 4 × 13 + 4 × 2 − 3 × 1 b. 3 × 12 + 4 × 13 + 4 × 2 − 3 c. 3 × 12 + 4 × 13 + 2 − 1 d. 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 − 3 112. Which operation must be performed first when calculating (129 + 321 × 481 + 2)? a. 129 + 321


174

b. 481 + 2 c. 481 × 2 d. 321 × 481 d - The multiplication must be performed first. 113. Which of the following equations is false? a. 21 + (11 + 9) = (21 + 11) + 9 b. 21 × (11 + 9) = (11 + 9) × 21 c. 21 ÷ (11 + 9) = (11 + 9) ÷ 21 d. 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. 114. 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. 6 b. 5 c. 4 d. 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. 115. 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. 19(24) + 11 b. 19(11) + 24 c. 19(24 + 11) d. 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.

116. Which of the following is the value of 4[12 + 3(1 + 5)] ÷ 144

?

a. 428

17

b. 128

17


175

c. 427

17

d. 726

17

a - 4[12 + 3(1 + 5)] ÷ 144

= 4(12 + 3 × 6) ÷ 174

= 4(30) ÷ 174

= 120 4

1 17×

= 48017

= 428

17

117. If a truck carries a 324

tons load, how many pounds is it hauling, knowing that 1 ton = 2000

pounds? a. 5250 pounds b. 5450 pounds c. 5500 pounds d. 5600 pounds c - Multiply the number of tons by the number of pounds in each ton:

3 112 2000 20004 4× = ×

= 11 2000

4×

= 5500 pounds

118. Which of the following is equivalent to

1 16 ÷ 34 8

?

a. 8 b. 7 c. 5 d. 2


176

d - 1 1 25 256 ÷ 34 8 4 8

= ÷

= 25 84 25×

= 2

119. The area of an irregular 4-sided shape is calculated using the formula ( )1 a b + c + d3

, where a, b,

c and d are the side lengths. If, a = 3, b = 4, c = 134

and d = 6, which expression

can be used to calculate the area?

a. 134 64

+ +

b. 133 4 64

+ +

c. 1 134 63 4 + +

d. 114 64

+ +

a - Replace the given values in the formula:

( ) ( )1 1 1a b + c + d 3 4 3 63 3 4

= + +

= 134 64

+ +

120. What is the proper procedure to calculate ( ) 512 3 + 4 1 - 7 ÷ 3

12?

a. Simplify inside brackets, multiply by 12, then divide by the mixed number. b. Simplify inside parentheses, multiply by 12, then divide by the mixed number. c. Simplify inside brackets, multiply by 12 by the mixed number, then divide by 12. d. 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.

121. To calculate the product 3.23 ×

1323

, which two procedures can be used?


177

a. 3.23 × 3.04348 or 323100

× 703

b. 3.23 × 3.4348 or 323100

× 7023

c. 3.23 × 3.04348 or 32 3100

.

× 7023

d. 3.23 × 3.04348 or 323100

× 7023

d - First procedure: 3.23 × 1323

= 3.23 × 7023

= 3.23 × 3.04348 = 9.83

Second procedure: 3.23 × 1323

= 323100

× 7023

= 323 70100 23

××

= 9.83 122. For a Physics Project, John designed a micro-tool 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 side-lengths repeatedly he found the side-lengths 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. 49a mm b. 51a mm c. 62a mm d. 63a mm d - If a = the shortest side, then Perimeter = a + 2a + 4a + 8a + 16a + 32a = 63a

123. To calculate the division 7.73 ÷

773

, which set of the procedures can be used?

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.


178

a - Convert the mixed number to a decimal, divide the two decimal numbers 124. Find x. 12[32 − 12(12 − 11) + 12] + 12 ÷ (21 − 17) = x a. 387 b. 368 c. 312 d. 268 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

125. In the US, about 45

of the residents are registered to vote. In one elections, 34

of the registered

voters actually voted. What portion of the citizens voted in this election?

a. 34

b. 14

c. 35

d. 15

c - Find 34

of 45

4 3 12 35 4 20 5× = =

126. Perform the following calculations:

( )

1 3 571.1 1 + 4 ÷11 4 4

a. 2215


179

b. 2315

c. 1913

d. 1713

b - ( ) 1 3 57 11 12 19 571.1 1 + 4 ÷11 4 4 10 11 4 4

= + ÷

11 12 19 410 11 4 57

× = + × ×

6 15 3

= +

2315

=

127. Calculate the following expression:

121 32 + 3 1+ 1 + 15 3 +3

a. 9.3 b. 9.1 c. 8.9 d. 6.3

a -

1 721 63 32 + 3 1+ 1 + 2 3 11 105 53 +3 3

= + + +

11 72 35 10

= + +

2 33 71 5 10

= + +

20 66 7

10+ +

=

9310

=

= 9.3


180

128. Cindy measures a side and a diagonal of a square-shaped 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. 1798 ft b. 1789 ft c. 1697 ft d. 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. 129. 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. 5.82 ft b. 5.62 ft c. 4.81 ft d. 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

x = 6013

= 4.62

130. Michelle wants to find some ordered pairs to fit in the equation y = 3x − 2. She created the following table:

x y 3 7 5 13


181

7 19 8 21 11 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. 21 must be changed to 22 b. 21 must be changed to 26 c. 31 must be changed to 30 d. 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. 131. 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. 41% b. 42% c. 45% d. 40% a - Round off 41.33% to 41%. 132. 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. Multiplication b. Division c. Subtraction d. Addition d - Area is found by simply adding the areas of all the segments of the shape. 133. To express the value 0.32 as a percent what operation is needed? a. Multiplication b. Division c. Addition d. Subtraction


182

a - To convert a decimal to a percent, simply multiply by 100. 134. 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. Addition b. Subtraction c. Multiplication d. Division d - She must find the ratio of two numbers. So, the division operation is needed. 135. 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. Multiplication b. Division c. Addition d. Subtraction b - We must find the ratio of 4589 to 2000. So, the type of the operation is division. 136. Which of the following is the best estimation of 2300 × 3209? a. 7360000 b. 7380000 c. 7480000 d. 7408000 a - To estimate the result simply multiply 2300 × 3200 = 7360000 137. Mt. Whitney is 14,494 feet above sea-level and Rock Valley is 347 feet below sea-level. Which of the following is the best estimation of the difference in these elevations? a. 14000 b. 14500 c. 15000 ft d. 1480 ft


183

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

138. Which is the best estimation of 450081505

?

a. 30 b. 29.29 c. 29 d. 28.89 a - The easiest and simplest way to estimate the result is round the fraction before the division:

45008 45000 301505 1500

≈ =

139. 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. 440 ft b. 400 ft c. 385 ft d. 380 ft b - Multiply 11 by 39 to find the distance after 39 seconds. 11 × 39 = 429 ft ≈ 400 ft

140. To find a reasonable estimate of 330003

1129, which fraction is the best choice?

a. 340000

1100

b. 330000

1100

c. 330001100


184

d. 330000

110

b - The denominator and numerator of the fraction can be rounded off as follows:

330000 300

1100≈

141. 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. 300 in. b. 330 in. c. 400 in. d. 450 in. c - Round 9 to 10 and 43 to 40. 9 × 43 ≈ 10 × 40 = 400 in. 142. To find a reasonable estimate of 1000.01 × 100, which expression is the best choice? a. 10010 × 100 b. 1000 × 100 c. 1001 × 100 d. 1000 × 101 b - Rounding 1000.01 to the nearest unit, we get 1000. So, the expression 1000 × 100 gives the best estimate. 143. Which is a reasonable estimate of the total amount of the following coins, in dollars? 40 quarters 10 dimes 20 nickels 770 pennies a. $20 b. $19 c. $18


185

d. $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

144. Which ratio is proportional to 1248

?

a. 7

24

b. 5

28

c. 7

28

d. 6

28

c - 12 748 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. 145. Which proportion is true?

a. 22 1877 64

=

b. 11 1877 63

=

c. 22 1677 63

=

d. 22 1877 63

=

d - Cross multiply the proportion 22 1877 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.


186

146. 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. 63 b. 65 c. 76 d. 79 a − Set up the proportion and solve for x.

798 38

3x=

38x = 3 × 798 38x = 2394 x = 63

147. Which number must be placed inside the box 11 =28 35

?

a. 12.25 b. 12.85 c. 13.25 d. 13.75

d - Denote the unknown number inside the box by x. Then 1128 35

x= .

Solve the proportion. 28x = 11 × 35 28x = 385 x = 13.75 148. 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. 213 b. 219 c. 231 d. 243 c - Find 22% of 1050.


187

( )( ) ( )2222 1050 1050100

% =

2 11 21 50100

× × × =

= 231 149. 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. If p, then q. b. If q, then not p. c. If q but not p, then q. d. 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. 150. The following simple statements are given: p: Mika likes Ronald q: Ronald likes Mika. Which symbolic statement is true? a. p q∨ b. p q∧ c. p q p∨ ∨ d. p q q∨ → 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”. 151. 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. q q p→ ∨


188

b. p q p∨ ∨ c. p q∧ d. 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”. 152. The following statements are given: Elementary schools are closed on Sunday. It is Sunday. Write a conditional statement by combining these statements. a. If elementary schools are closed, then it’s Sunday. b. It is either Sunday or the elementary schools are closed. c. If it is Sunday, then the elementary schools are closed. d. 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. 153. The following statement is given: In any right triangle, the sum of two acute angles is 90º. Which triangle is a right triangle? a. Triangle ABC, in which the difference of two angles is 90º. b. Triangle DEF, in which no angle is obtuse. c. Triangle GHK, in which two angles are acute. d. Triangle LMN, in which one angle is obtained by subtracting the other angle from 90º. 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 154. 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. John is a publisher. b. John may be both an author and a member of the club.


189

c. John may be a published author. d. 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. 155. 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. a is not definitely a member of S. b. a is not a member of S. c. a may be a member of S. d. 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. 156. 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. John may attend Algebra and/or Geometry class(es). b. John is not attending Algebra class. c. John is not attending Geometry class. d. John is attending both Algebra and Geometry classes. a - We do not know whether all the History students are attending Algebra and/or Geometry classes. So, a is a true statement. 157. Which general formula can be used for all the numbers in the following series? 2, 6, 12, 20… a. 2n(2n − 1) b. n(n - 1) c. 2n(n + 1) d. n(n + 1)


190

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. 158. 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. 2 b. 3 c. 4 d. None of the above c - 1 + 2 + 3 + 4 = 10 Replacing 4 in the formula yields 1 + 2 + 3 + 4 = 42 − 4 = 12, which is not true. 159. 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. 88 b. 82 c. 76 d. 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 = ( )12 nn a a+ to find the total number

of bricks.

S = ( )8 18 42

+ = 88

160. If (1 + 2 + 3 + . . . + n)2 = 13 + 23 + 33 + . . . + n3, which expression is equal to (1 + 2 + 3 + 4 + . . . + 100)2?


191

a. 12 + 22 + 32 + 42 + . . . + 100 b. 13 + 23 + 33 + 43 + . . . + 1003 c. 22(1 + 2 + 3 + 4 + . . . + 100) d. 1 + 2 + 3 + 4 + . . . + 1002 b - Using the given formula, (1 + 2 + 3 + 4 + . . . + 100)2 = 13 + 23 + 33 + 43 + . . . + 1003

TEAS Practice Exam – Math - Section 2 Algebra

161. Solve 3x + 11 = 31 – x. a. 7 b. 5 c. 4 d. 2 b - Subtract 11 from each side and add x to each side. 3x + 11 −11 + x = 31 − x − 11 + x 4x = 20 x = 5 162. Sarah and her father together are 47 years old. If her father is 34 years old, what is Sarah’s age? a. 19 b. 17 c. 13 d. 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 = 13 163. The ratio of two numbers is 13. If the larger number is 1027, what is the smaller number? a. 79 b. 83 c. 87 d. 89


192

a - 1027 13

1x=

13x = 1027 x = 79 164. Solve the equation 5x − 11 = 39. a. 14 b. 13 c. 11 d. 10 d - Add 11 to each side, and simplify. 5x − 11 + 11 = 39 + 11 5x = 50 x = 10 165. The side-lengths of a triangle are described by x2 + x + 1, 3x − 2, and 3x2 + x. What is the perimeter of the triangle? a. 4x2 + 5x − 1 b. 4x2 + 4x − 1 c. 4x2 + 5x + 3 d. 4x2 + 5x − 2 a - Add the given polynomials. (x2 + x + 1) + (3x − 2) + (3x2 + x) = 4x2 + 5x − 1 166. Subtract (3x2 + 1) from (4x3 + 2x2 + x). a. 4x3 − x2 + 2x − 1 b. 4x3 − 2x2 + x − 1 c. 4x3 − x2 + x + 1 d. 4x3 − x2 + x − 1 d - (4x3 + 2x2 + x) − (3x2 + 1) = 4x3 + 2x2 + x − 3x2 − 1 = 4x3 − x2 + x − 1 167. The dimensions of a rectangle are described by (x + 2) and (x + 3). Which of the following describes the area of the rectangle? a. x2 + 5x + 5 b. x2 + 6x + 6


193

c. x2 + 5x + 6 d. x2 + 6x + 5 c - Multiply the dimensions, and simplify. Area = (x + 2)(x + 3) = x2 + 2x + 3x + 2 × 3 = x2 + 5x + 6 168. Add (x2 + x) to (8x3 + 2x2 − x − 1). a. 8x3 + 3x − 1 b. 8x3 − 3x2 − 1 c. 8x3 + 3x2 − 1 d. 8x3 + 3x2 − 2x c - (x2 + x) + (8x3 + 2x2 − x − 1) = x2 + x + 8x3 + 2x2 − x − 1 = 8x3 + 3x2 − 1 169. Write an equation: “value of x is two more than three times x.” a. 3x = x + 2 b. 3x = x − 2 c. x = 2 + 3x d. x = 2 − 3x c - Three times x is 3x. x is 2 more than 3x. So, x = 2 + 3x 170. 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. 8x + 3 b. 5x + 3 c. 8x + 5 d. 5x + 8 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 + 3 171. The sum of the right angle and an acute angle in a right triangle is greater than 123º. Which expression represents this relationship? a. x + 90 < 123 b. x + 90 > 123 c. x + 123 > 90


194

d. 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 > 123 172. Which is the translation of the phrase “11 more than the triple of a number?” a. 11x + 3 b. 3x + 11 c. 3(x + 11) d. 3x + 33 b - The triple of a number is 3x. 11 more than 3x is 3x + 11. 173. Which of the following is the solution to the equation |x + 12| = 25? a. 12 or 37 b. 17 or 33 c. 13 or −37 d. −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. 174. The temperature on the surface of Mars fits the inequality C + 85 56≤ , in degrees Celsius. What is the range of the temperature? a. −29 ≤ C ≤ −141 b. 29 ≤ C ≤ 141 c. 141 ≤ C ≤ 29 d. −141 ≤ C ≤ −29


195

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 ≤ −29 175. Which is the solution set to the inequality x 1+ 5 6> ? a. x > −11 or x < −21 b. x > 11 or x < −21 c. x < 11 or x < 21 d. 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 < −21 176. 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. 9 p 5≥ ≥ − b. 9 p 5≥ > c. 9 p 5> ≥ d. 9 p 5≥ ≥


196

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≥ ≥ 177. Solve the equation 3x + 11 = 51 − x. a. 12 b. 10 c. 6 d. 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 = 10 178. 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. x = 22 ft b. x = 19 ft c. x = 18 ft d. 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 2x = 32 x = 16 ft 179. Solve the inequality 5x − 19 > 3x + 33. a. x > 26 b. x > 28 c. x < 26


197

d. 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 > 26 180. If the radius of a circle is doubled, how will its area be changed? a. Increase two times. b. Increased four times. c. Increased by two. d. 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 by S. Then S = ( )2 22r 4 rπ π= S is as four times as A. So, the area increased four times. 181. If x in x(22 − 19) is tripled, how much is the value of the expression changed? a. Will Increase by 6x b. Will increase 6x times c. Will increase by 8x d. 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 182. If x in the expression 12(x + 3) + 9 is increased by 9, how will the value of the expression be changed? a. Will be increased by 132 b. Will be decreased by 132 c. Will be increased by 126 d. 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)


198

= 12x + 144 + 9 − 12x − 27 = 126 183. A side-length of a square-shape pool is 44 ft. If its length extended to 48 ft, how much will its area be increased? a. 466 ft2 b. 468 ft2 c. 386 ft2 d. 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 184. If x in the expression 3(x + 9) − 12 is decreased by 9, how much will the value of the expression be changed? a. Will be decrease by 62 b. Will be decreased by 51 c. Will be decreased by 43 d. Will be decreased by 27 b - 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 + 36 = 51 185. 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. Remove the decimal from the left side. b. Cancel the decimals. c. Multiply all the terms by 10 d. Multiply all the terms by 100. d − Multiplying all the terms by 100, converts the decimals to whole numbers. This way, the calculations become simpler and easier.


199

186. To solve the equation x 4= 35 9

, what step must be taken first?

a. Divide the fractions by 45. b. Multiply the denominators by 45. c. Cross multiply the proportion. d. 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.

187. To solve equations such as 1 5 1x + =

18 12 6, which step must be followed first in order to make the

solution easier?

a. Move 16

to the left side.

b. Add 16

to the left side.

c. Multiply all the terms by 36. d. Divide all the terms by 36. c - Multiplying all the terms by the least common denominator, 36, converts all the fractions to whole numbers.

188. What are two different methods to verify that 24 3=32 4

?

a. Division and Reducing b. Cross-multiplication and Reducing c. Multiplication and Reducing d. Cross-multiplication and Division b - 1. Cross multiply. 2. Reduce the first ratio. 189. What are two different methods to find 144 ÷ 24? a. Synthetic Division and Division of Reciprocals b. Synthetic Division and Mixed Numbers c. Division of Fraction and Division of Reciprocals d. Synthetic Division and Reducing a Fraction d - (1) Divide 144 by 24 using synthetic method. (2) Write the division in the form of a fraction and reduce it.


200

190. 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. By multiplying all the terms by 2. b. By replacing x by x + 3. c. By adding 3(3 + x) to both sides. d. 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.

191. Solving the equation

1 1 5=2 7 x

yields 1 5=

14 x. How can you complete the solution?

a. By cross-multiplication b. By division c. By subtraction d. By multiplication a - Cross multiplying the proportion yields x = 70. 192. 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. Perimeter = 2a + a + 2b + b = 2(a + b) b. Perimeter = 2a + 2a + b + b = 2(a + b) c. Perimeter = a + a + b + b = 2(a + b) d. None of the above c - The perimeter is a + a + b + b, (a + a) + (b + b), (2a + 2b), or 2(a + b). 193. The sum of interior angles of geometric shapes are calculated as follows:

Triangle: 180(3 − 2) Quadrilateral : 180(4 − 2)

Pentagon : 180(5 − 2) Hexagon : 180 (6 − 2)

Which of the following is a general pattern for finding the sum of the interior angles of a polygon with n sides?


201

a. 180(n + 1) b. 180(2n − 1) c. 180(n − 2) d. 180(2n − 2) c - The formation of each expression indicates that to find the sum of the interior angles of a polygon, we must subtract 2 from the number of the sides, then multiply by 180. So, for an n-gon, we subtract 2 from n, then multiply by 180. 194. The following set of numbers fit the sides of right triangles:

a = 3 b = 4 c = 5 a = 6 b = 8 c = 10 a = 9 b= 12 c = 15 a = 12 b = 16 c = 20

Using this pattern, find a general formula for the sides of right triangles. a. a = n(3), b = n(5), and c = n(6) b. a = n(2), b = n(4), and c = n(5) c. a = n(3), b = n(5), and c = n(7) d. a = n(3), b = n(4), and c = n(5) 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. 195. The following equations are given: (x + 1)(x + 2) = x2 + x(1 + 2) + 1 × 2 (x + 3)(x + 4) = x2 + x(3 + 4) + 3 × 4 (x + 6)(x + 8) = x2 + x(6 + 8) + 6 × 8 (x + 9)(x + 5) = x2 + x(9 + 5) + 9 × 5 Develop a general pattern for the expansion of (x + a)(x + b). a. x2 + x(a + b) + a + b


202

b. x2 + x(ab) + a + b c. x2 + x(a + b) + a × b d. x2 + x(ab) + a × b c - Examining each equation shows that each product on the left side is equal to the square of x, added to the product of x and the sum of the numbers, added to the product of the numbers. 196. What pattern is used for generating numbers in the series below: 4, 9, 19, 39, 79, . . . , a. Add 1 to each number, then double. b. Double each number, then add 1. c. Subtract 1 from each number, then double. d. Double each number, then add 2. b - Each number is doubled, then added 1 to generate the following number. 197. 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. 70 b. 85 c. 89 d. 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 90-100. 198. Which formula is used to generate the numbers in the series below? 4, 9, 19, 34, 54, . . . , a. 6 added to each term, then 1 is subtracted. b. 5 added to each term, then added 10. c. Multiple of 5 added to each term beginning with 5. d. Multiple of 10 added to each term beginning with 10. c - To generate the numbers in the series, a multiple of 5 is added to each term beginning with 5.


203

199. The numbers below follow a general pattern. What is the next number in the series? 100, 98, 94, 88, . . . a. 72 b. 78 c. 80 d. 82 c - Starting from 2, the even numbers are subtracted. 200. The relationship between P and n is defined by P = 4n. If n increases, how will P change? a. P will increase. b. P will decrease. c. P first will increase, then will decrease. d. P first will decrease, then will increase. a - This is a direct variation. Increase in n implies an increase in P. 201. The area of a rectangle is A = ab. Given A as a constant, how will b vary if a is doubled? a. b will be decreased by one-half. b. b will be increased by one-half. c. b will be decreased by one-third. d. b will be doubled. a - Since A is constant, then by doubling “a” we must divide “b” by 2.

202. The relationship between R and x is defined by 5R =x

. If x increases how will R change?

a. R will increase. b. R will decrease. c. R first will increase, then will decrease. d. R first will decrease, then will increase. b - This is an inverse variation. Increase in x implies a decrease in R.


204

203. 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. If T decreases, then P decreases b. If T stays constant, then P increases. c. If T increases, then P decreases. d. 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. 204. Which function can be described by the given graph below?

a. y = mx + b

b. 54

xy =

c. y = x2 + 3x − 7 d. 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. 205. Which function represents the graph below?


205

a. y = 2x + c b. y = 2x3 + 3x + c c. y = 2x + 3x + c d. y = ax2 + bx + c d - The graph is curved and has two points of intersection with x-axis. Therefore, the quadratic function (d) represents this graph. Continue to the next page. 206. Which graph can represent the path of launching a projectile? a.


206

b.

c.

d.

c - Path of a projectile has only one maximum point. Hence, (c) is the answer. 207. 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. 90 − x = 32 b. 90 + x = 32 c. 32 − x = 90 d. −32 + x = 90 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.


207

208. Which expression represents the phrase “nine times a number added to 32, subtracted from 193”? a. 222 + 9x b. 222 − 9x c. 160 + 9x d. 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. 209. The sum of two consecutive even integers is 650. Which equation can be used to find these numbers? a. 2x + 1 = 650 b. 2(x + 1) = 650 c. 2x − 1 = 650 d. 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. 210. 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. x + 162 = 290 b. x + 182 = 280 c. x + 172 = 270 d. 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. 211. Which statement is true? a. If p: (x − 1)(x + 3) = 0, then q: x = 1.


208

b. If p: (x − 1)(x + 3) = 0, then q: x = −1. c. If p: (x − 1)(x + 3) = 0, then q: x = 3. d. 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. 212. An airline made 320 flights in the first three months of the year. The airline predicts the same ratio for the following seasons. Let’s assume the following:

p: Ratio of the number of fights to the number of months during the first three months = 320

3

q: Ratio of the number of fights to the number of months during the first six months = 640

6

Which statement is true? a. If p, then q. b. If p, then not q. c. If q, then not p. d. Ifp q∨ , then not q. a - The given ratios are proportional. So, the first ratio implies the second ratio. 213. 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. q r∨ b. p q∧ c. p q p∨ ∧ d. 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. 214. If (x + 3)(x + 23) = 0, then which statement is true?


209

a. x = −3 or x = −23 b. x = −3 and x = −23 c. x = 3 or x = −23 d. 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. 215. 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. Olivia is a member of the Sport Club. b. Jason is a member of the Hemingway Club. c. Ronald is a member of the Hemingway Club. d. 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.

216. The sum of the numbers 1 + 2 + 3 + 4 + 5 +, . . . , + n is equal to ( )

=n n + 1

S2

. What is the sum of

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15? a. 144 b. 140 c. 120 d. 112 c - Replace n = 15 in the general formula and simplify:

( )15 15 + 1 15 16S = 120

2 2×

= =

217. The following statements are given:


210

In all the parallelograms, the diagonals are not equal, but bisect one another. In ABCD, AC = AD. In MNPQ, the diagonals bisect one another and are equal. In RSTU, diagonals pass through the center of the figure. In TVWX, if the point of intersection of the diagonals is called A, then TA = AW and VA = XA.

Which of the following statements is true?

a. ABCD is a parallelogram b. MNPQ is a parallelogram. c. RSTU is a parallelogram. d. TVWX is a parallelogram.

d - The given equations verify that the distances of A on each diagonal from both vertices are the same. That is, the diagonals bisect one another.

218. 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. Subtracted zero from both sides. b. Multiply both sides by zero. c. Added zero to both sides. d. 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. x − 1 = 0 does not allow us to divide both sides by 0. We can only divide by any non- zero number. 219. Consider the pattern among the following equations:


211

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. 19 b. 20 c. 23 d. 24 d - If we continue the same pattern, we obtain 37 × 18 = 666 37 × 21 = 777 37 × 24 = 888. 220. 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. 9 b. 8 c. 7 d. 6 a - Following the same pattern we obtain (12346 × 9) + 7 = 1111111 (1234567 × 9) + 8 = 11111111 (12345678 × 9) + 9 = 111111111

TEAS Practice Exam – Math - Section 3 Data Interpretation


212

221. The numbers of hours of sunshine in Roan Mountain during one week of the summer is displayed in the graph below:

Which data table fits the bar graph? a.

b.

c.

d.

b - Comparing each data point to all the tables shows that the data in (b) fits the graph. 222. Which frequency table represents the following data:

126, 129, 126, 126, 126, 128, 126, 126, 129, 129,

0 1 2 3 4 5 6 7 8 9

10

Sun Mon Tue Wed Thu Fri Sat






213

127, 130, 127, 127, 128, 128, 128, 129, 128 , 126 a.

b.

c.

d.

d - Checking data from each table one by one with the given set of data indicates that table (d) matches the data set. 223. The percentages of different elements in a chemical substance is shown in the table below.

Data Frequency 126 8 127 3 128 6 129 4 130 1

Data Frequency 126 7 127 3 128 5 129 3 130 1

Data Frequency 126 7 127 3 128 5 129 4 130 2

Data Frequency 126 7 127 3 128 5 129 4 130 1


214

Carbon 34% Oxygen 26%

Hydrogen 21% Sulfur 12%

Nitrogen 7% Which pie chart represents the data in the table? a. c.

b. d.

c - Comparing the table to each pie chart indicates that chart (c) represents the data. 224. The following table shows the number of graduates of Boone Creek High School during years 2004-2011.


215

Which line graph represents the data in the table? (Numbers starting from 1 represent the years 2004, 2005, and so forth.)

a. c.

b. d.

d - Comparing the data in the table to each graph indicates the line graph (a) represents the table. 225. The Venn Diagram below displays the number of students attending different classes.

Year Number of Graduates 2004 453 2005 571 2006 356 2007 398 2008 433 2009 405 2010 447 2011 511


216

What is total number of students attending Literature class? a. 51 b. 49 c. 43 d. 37 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 Continue to the next page. 226. The graph below represents the amount of rain during a week of spring in New York, in millimeters.


217

Which is the best estimate of the range of the data given in the graph? a. 4.2 mm b. 5.6 mm c. 5.9 mm d. 6.2 mm a - The highest measure is about 9.4 and the lowest is about 5.2. Range = 9.4 −5.2 = 4.2 227. The following stem - and - leaf graph represents a set of data.

What is the median of the data? a. 46 b. 51 c. 55 d. 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 228 and 229.

0 1 2 3 4 5 6 7 8 9

10

Fri Sat Sun Mon Tue Wed Thu


218

The amounts of money a Telecommunication Company spent on ads for the years 2005-2010 are shown in the table below.

Year Amount (in dollars) 2005 190,000 2006 230,000 2007 110,000 2008 150,000 2009 160,000 2010 180,000

228. In which year was the advertisement cost the highest? a. 2005 b. 2006 c. 2009 d. 2010 b - Comparing the numbers on the right column shows that 230,000 is the highest. 229. In which year was the advertisement cost the lowest? a. 2006 b. 2007 c. 2008 d. 2010 b - Comparing the numbers on the right column shows that 110,000 is the lowest. 230. 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?


219

P a b c d 1 2 −1 6 −2 9 4 3 −1 3 21 2 9 8 −7

a. Variable a b. Variable b c. Variable c d. Variable d b - Replacing the values of b for x gives the corresponding values of P given in the table. 231. 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 m n p q 11 2 −3 4 −2 26 −4 7 −1 3 2 2 5 8 −1

a. Variable m b. Variable n c. Variable p d. Variable q d - Replacing the values of q for x gives the corresponding values of T given in the table. 232. 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 m n p q −5 −4 −1 6 1 7 4 3 −1 3 10 6 9 8 −7

a. Variable m b. Variable n c. Variable p d. Variable q a - Replacing the values of m for x in R gives the corresponding values of R given in the table.


220

233. 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?

a. The sum of the numbers is equal to the area of the circle. b. The sum of the numbers is equal to the circumference of the circle. c. The sum of the numbers is 100% and the total shaded regions is 100% of the circle. d. 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. Continue to the next page. 234. 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?

Service Percent Army 33% Navy 27%

Marine Corp 12% Air Force 25%

Coastal Guard 3%


221

a. By the columns below the horizontal line 400,000. b. By the columns below the horizontal line 300,000. c. By the columns below the horizontal line 200,000. d. By the columns below the horizontal line 100,000. d - By the columns below the horizontal line 200,000. Continue to the next page. 235. The bar graph represents the data in the table. How are the areas of the States of Arizona and Montana shown in the graph?

0

100000

200000

300000

400000

500000

600000


Alabama 50700 Alaska 573,000

California 155900 Colorado 103700 Maryland 9770

Minnesota 79600


222

a. By the columns above the horizontal line 100,000. b. By the columns below the horizontal line 100,000. c. By the columns between the horizontal lines 100,000 and 80,000. d. 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 Use the following information to answer questions 236 through 240. 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

Science Score

86 76 68 94 92 73

History Score

71 98 86 67 81 92

236. Which student scored lowest grade only in History? a. Student A b. Student B c. Student D d. Student E c - Among the History scores 67 is the lowest. 237. What is the difference between the ranges of the scores of the two subjects?

0

20000

40000

60000

80000

100000

120000

140000


Arkansas 52000 Arizona 113,650

Connecticut 4850 Michigan 56800 Montana 145550

Minnesota 79600


223

a. 1 b. 2 c. 4 d. 5 a - Range of scores of History = 98 −67 = 31 Range of scores of Science = 94 − 68 = 26 Difference of ranges = 31 − 26 = 5 238. Which student scored the lowest grade only in Science? a. Student A b. Student C c. Student D d. Student E b - Among the Science scores, 68 is the lowest. 239. Which student scored the highest in Science and lowest in History? a. Student A b. Student B c. Student D d. Student E c - Student D scored 94 in Science and 67 in History. 240. What is the difference between the mean of the scores of both subjects? a. 4 b. 3.5 c. 1.5 d. 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 241and 245.


224

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 pull-outs for all groups.

Groups First Week

Second Week

Third Week

Fourth Week

Group A 11 32 20 19 Group B 32 44 9 33 Group C 14 21 21 29 Group D 30 39 11 12

241. In which week was the number of patients who pulled out from the trial the highest? a. First week b. Second week c. Third week d. 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. 242. Which group had the highest number of pull outs? a. Group A b. Group B c. Group C d. Group D 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. 243. Which group had the lowest number of pull outs? a. Group A b. Group B c. Group C d. Group D a - Number of patients pulled out from Group A = 11 + 32 + 20 + 19 = 82


225

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. 244. In which week was the number of patients who pulled out from the trial the lowest? a. First week b. Second week c. Third week d. 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. 245. Which group had the highest pull-out average? a. Group A b. Group B c. Group C d. 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 = 23 246. 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. 3 b. 4 c. 5 d. 6 c - Arrange the data in ascending order: 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7


226

The middle number is 5. 247. The average of three consecutive integers is 16. What is the smallest integer? a. 15 b. 16 c. 17 d. 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 = 15 248. 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. 29 cm b. 30 cm c. 32 cm d. 35 cm a - The longest and the shortest heights are 174 and 145. Difference of these heights is 174 − 145 = 29. 249. Olivia made the following scores in her History tests. What is the average of her scores?

86, 72, 78, 88 a. 81 b. 80 c. 78 d. 75 a - Average score = (86 + 72 + 78 + 88) ÷ 4 = 324 ÷ 4 = 81 250. What is the mode of the following data?


227

20, 11, 15, 17, 15, 17, 19, 15, 11, 11, 20, 15 a. 11 b. 15 c. 17 d. 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.

251. A 6-sided die is rolled. The probability of getting an odd number is 13

. What does this fraction

represent? a. It means that the chance of an odd number is 3 out of 1. b. It means that the chance of an odd number is 1 out of 3. c. 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 13

.

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.

252. The chance of choosing a member from a sports club as the president is 1131

. What is the chance

of NOT selecting this member?

a. 1

31

b. 2331

c. 2031

d. 1931

c - The chance of not getting selected is 1 − 1131

= 31 11 20

31 31−

= .


228

253. A box contains 42 red and green marbles. The probability of choosing a red marble from the box

is 47

. What can be concluded from this fraction?

a. There are 36 red marbles in the box. b. There are 24 red marbles in the box. c. There are 22 red marbles in the box. d. There are 18 red marbles in the box.

b - Multiply the denominator and the numerator of the fraction 47

by 6.

4 6 247 6 42×

=×

. This means that there are 24 red marbles among the total of 42 marbles

in the box.

254. There are 32 students in Algebra class. The chance of choosing a female student is 9

16. What

does this fraction represent? a. The number of male students is 14. b. The number of male students is 16. c. The number of male students is 15. d. The number of male students is 12. a - Multiply the denominator and the numerator of the fraction by 2.

9 2 18

16 2 32×

=×

. This means that 18 students out of 32 students are female. Then

Number of male students = 32 − 18 = 14 255. Box A contains 124 cards marked with positive integers. The chance of choosing an odd integer

is 1231

. What does this fraction represents?

a. There are 42 even integers in the box. b. There are 44 even integers in the box. c. There are 48 even integers in the box. d. There are 76 even integers in the box.

d - Multiply the denominator and the numerator of the fraction 1231

by 4.

12 12 4 4831 31 4 124

×= =

×. This means that 48 cards out of 124 cards are marked with odd

integers. So, 124 − 48 = 76 cards are marked with even integers.


229

256. What is the probability of getting a three and a heads, if we role a die and toss a coin?

a. 1

12

b. 14

c. 13

d. 16

a - The following is the set of all possible outcomes of this event: S = {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)} The probability of getting a head and a three is 1 out of 12. 257. What chance is there of choosing a number divisible by 5 from the numbers between 53 and 75?

a. 7

18

b. 4

17

c. 518

d. 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?


230

a. 35

b. 45

c. 15

d. 23

a - The number of students do not attend Algebra class is 50 − 20 = 30. Therefore, the

chance is 30 350 5

= .

259. Four coins are flipped together. What is the probability that all four coins come out heads?

a. 15

b. 14

c. 13

d. 12

a - Here is the sample space: {(T, T, T, T), (H, H, H, H), (T, H, H, H), (T, T, H, H), (T, T, T, H)}

Only one of the sample points is (H, H, H, H). Therefore, the chance is 15

.

260. What is the probability of getting a tail and an integer greater than 3, if we role a die and toss a coin?

a. 16

b. 14

c. 13

d. 12

b - Here are all the outcomes of this event:


231

S = {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)} Sample points (4, T), (5, T), and (6, T) are to be chosen randomly.

The probability of getting one of these points is 3 to 12 or 14

.

TEAS Practice Exam – Math - Section 4 Measurements

261. 1000 mg = ___ g a. 1 b. 10 c. 100 d. 110 a – 1000 milligrams equals 1 gram. Milligrams and grams are units of weight in the metric system. 262. 160 cm = ____ mm a. 1.6 b. 16 c. 160 d. 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. 263. 109 g = ____kg a. .0109 b. .109 c. 1.09 d. 10.9 b – 1 gram equals .001 kilograms. 109 x .001 = .109. Grams and kilograms are units of weight in the metric system. 264. 4 L = ___ml


232

a. .4 b. 40 c. 400 d. 4000 d – I liter equals 1000 milliliters. 4 x 1000 = 4000 milliliters. Liters and milliliters are units of volume in the metric system. 265. 75 ml = ___L a. .0075 b. .075 c. .75 d. 7.5 b – 1 milliliter equals 1/1000 liter. 75 ÷ 1000 = .075 liters. Liters and milliliters are units of volume in the metric system. 266. A man weighs 80 kilograms. How much does he weigh in pounds? a. 176 lbs. b. 185 lbs. c. 210 lbs. d. 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. 267. 54⁰ F = _____⁰ C a. 1.2 b. 10.22 c. 12.22 d. 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 = 12.22 268. 32⁰ C = _____⁰ F


233

a. 89.6 b. 88.9 c. 86.9 d. 100 a – To convert Celsuis to Fahrenheit, first multiply by 9/5 and then add 32. 32 x 9/5 = 288/5 288/5 = 57.6 57.6 + 32 = 89.6 269. A woman weights 132 pounds. What is her weight in kilograms? a. 13,200 b. 1,320 c. 132 d. 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. 270. A man is 6’4” in height. How tall is he in centimeters? a. 152 b. 164 c. 193 d. 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 = 193.04 271. Which of the following is equivalent to 3 pounds and 12 ounces? a. 42 ounces b. 48 ounces c. 52 ounces d. 60 ounces d - Each pound is equal to 16 ounces. Therefore, 3 pounds + 12 ounces = 3 × 16 + 12


234

= 48 + 12 = 60 ounces 272. 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. 10122 grams b. 10312 grams c. 11021 grams d. 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 273. What is the total, in inches, of 5 yards, 5 feet and 22 inches? a. 262 inches b. 254 inches c. 248 inches d. 234 inches a - One yard = 36 inches 1 foot = 12 inches 5 yards + 5 feet + 22 inches = 5 × 36 + 5 × 12 + 22 = 262 inches 274. How many miles are in 24,500 kilometers? a. 12,512.5 miles b. 15,312.5 miles c. 15,315.5 miles d. 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 275. What is the difference between the following lengths, in meters?


235

M: 12 m, 119 cm N: 1.2 m

a. 1379 cm b. 1289 cm c. 1299 cm d. 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 276. 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. 4 kg b. 3 kg c. 2 kg d. 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 277. 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. 77.3 mm b. 73.7 mm c. 63.7 mm d. 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 278. 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?


236

a. 15 mm b. 14 mm c. 12 mm d. 10 mm a - 1 cm = 10 mm Distance = 24 × 10 = 240 mm Distance between each two lines = 240 ÷ 16 = 15 mm 279. 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. 29 miles b. 26 miles c. 24 miles d. 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 280. 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. 24 by 34 b. 21 by 32 c. 26 by 34 d. 21 by 42 d - Multiply each dimension by the scale factor. 4.2 × 5 = 21 8.4 × 5 = 42 281. 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. 12 in. by 13 in.


237

b. 13 in. by 10 in. c. 12 in. by 13 in. d. 15 in. by 10 in. b - Denote the dimensions after scaling by x and y. Then solve the following proportions:

1 5x 85=

5x = 85 x = 13 in.

1 5y 50=

5y = 50 y = 10 in. 282. How many inches are in one yard? a. 38 inches b. 36 inches c. 34 inches d. 32 inches b - 1 yard = 3 feet 1 foot = 12 inches 1 yard = 3 × 12 = 36 inches 283. How many cubic centimeters are in a liter? a. 10 b. 100 c. 1000 d. 10000 c - One liter is equivalent to 1000 cubic centimeters. 284. How many pints are in a gallon? a. 4 b. 5


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c. 6 d. 8 d - 1 gallon = 4 quarts 1 quart = 2 pints 1 gallon = 2 × 4 = 8 pints 285. What is (2 gallons, 8 quarts) in quarts only? a. 10 b. 14 c. 16 d. 20 c - 1 gallon = 4 quarts. 2 gallons + 8 quarts = 2 × 4 + 8 = 16 quarts 286. What is (2 decameters, 34 decimeters) in centimeters? a. 2340 cm b. 2420 cm c. 2440 cm d. 2624 cm a − 1 decameter = 1000 centimeters 1 decimeter = 10 centimeters 2 dm + 34 dc = 2 × 1000 + 34 × 10 = 2000 + 340 = 2340 cm 287. What is (5 yards, 4 feet) in inches? a. 228 in. b. 218 in. c. 192 in. d. 188 in. a - 1 yard = 36 inches 1 foot = 12 inches 5 yards + 4 feet = 5 × 36 + 4 × 12 = 180 + 48 = 228 in. 288. Cindy wants to add some preservative to 0.8 kg dried fruit. What unit of measurement should she use to weigh the preservative? a. Kilogram


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b. Gram c. Pound d. Liter a - Since the preservative is a small portion of the total weight of the product, the preservative must be measured in grams. 289. 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. Liter b. Ton c. Kilogram d. 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. 290. 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. Pound b. Gram c. Ton d. Liter c - Total weight of the load = 124 × 24 × 340 = 1011840 g = 1011.840 kg = 1.002 tons 291. The amount of power (in watts) that a satellite drops depends on the number of days its been on in the sky. The amount of drop in its power supply occurs gradually and is determined by the following formula:


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w = 50e−0.004d Assume e is 2.71828183. How much power would a satellite drop after 500 days? a. 5.97 watts b. 6.77 watts c. 7.76 watts d. 8.78 watts b - Replace d = 500 in the formula and calculate.

w = 50e−0.004(500) = 50e−2 ≈ 50(2.71828183)−2= ( )2

502 71828183.

= 50(0.1353) = 6.77 watts

292. Physicians use the following formula to determine the gradual absorption of a drug in a patient’s body after h hours:

D = 5e−0.4h When the number of milligrams decreases to 2, the physician must administer the drug again. Assume e is 2.71828183. How much of the drug will be in the patient’s bloodstream after 5 hours? a. 0.68 mg b. 9.92 mg c. 1.22 mg d. 1.46 mg a - Place h = 5 in D = 5e−0.4h.

D = 5e−0.4(5) = 5e−2 = ≈ 5(2.71828183)−2= ( )2

52 71828183.

= 5(0.1353) = 0.68 mg

293. 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. 1 b. 2 c. 3 d. 4 b – Answering this question is a two step process. First, you must convert 2 grams to milligrams (mg).

There are 1000 mg in a gram, so 2 x 1000 = 2000 mg.


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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.

294. What is the volume of a gold bar that is 4.5 cm long, 3.5 cm wide and 2 cm thick? a. 10 cm³ b. 15.75 cm³ c. 20.25 cm³ d. 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 295. The dimensions of a rectangle are 2 feet and 240 inches. What is the area of the rectangle? a. 5760 in.2 b. 5780 in.2 c. 5860 in.2 d. 5980 in.2 a - Area = (2 ft)(240 in) = (2 × 12 in.)(240 in.) = (24 in.)(240 in.) = 5760 in.2 296. 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. 54 ft. b. 60 ft. c. 118 in. d. 120 in. d - Replace the given measures in the equation below: AE = AB + BC + CD + DE = (2 ft) + (25 in.) + (3 ft) + (35 in.)


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= (2 × 12 in.) + (25 in.) + (3 × 12 in.) + (35 in.) = 24 in. + 25 in. + 36 in. + 35 in. = 120 in. 297. 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. 608 m2 b. 612 m2 c. 652 m2 d. 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 298. To measure the volume of a rock, which method is best? a. Using a graduated cylinder half-filled with water b. Using an empty graduated cylinder c. Using a “verinier calipers” d. Using an empty balloon a - Dropping a rock inside a cylinder half-filled with water increases the level of the water. The difference in the levels of the water represents the volume of the rock. 299. 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. 37 b. 31 c. 27 d. 25

d - Replace F = 77 with F = 9 C + 325

, and solve for C.

77 = 9 C + 325

77 − 32 = 9 C + 325

− 32

45 = 9 C 5


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C = 25 300. One foot-pound(ft-lb) is the amount of energy used to lift a one pound object a distance of 1 foot. One British Thermal Unit (BTU) is the amount of heat needed to raise the temperature of 1 pound of water 1 degree Fahrenheit. These two units are related by the formula 1 BTU = 778 ft-pl. How much is 1945 ft-pl in BTU? a. 2.5 BTU b. 3.5 BTU c. 4 BTU d. 5 BTU

a - Multiply 1945 ft-pl by the unit fraction 1 BTU778 ft -pl

.

1945 ft-pl × 1 BTU778 ft -pl

= 1945 ft -pl 1 BTU1 778 ft -pl

× = 2.5 BTU


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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 birds-eye-view 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


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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,


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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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Answer Bubble Sheet


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