English Language for Academic Purposes (EAP)

 EAP Reading Skills  EAP Sentence Meaning

 EAP Listening  EAP Writing

Testing Center
Educational Services Building Room 108

7411 West Broadway Avenue

Brooklyn Park, MN 55445
Placement Testing Hours
Intersection of West Broadway and 85th Avenue
Monday: 9:00 a.m. or 1:00 p.m.
Tuesday: 3:00 p.m. Phone: 763-424-0928
Wednesday: 3:00 p.m. Email: testingcenter@nhcc.edu
Thursday: 9:00 a.m. or 1:00 p.m. Fax: 763-493-0552
 CONTENT
About the EAP Placement Test Page 2
General Test and Review Information Page 3
EAP Reading Comprehension Page 4 – 8
Content Area Page 4
Sample Questions Page 5 – 7
Answer Key / Notes Page 8
EAP Sentence Meaning Page 9 – 14
Content Area Page 9
Sample Questions Page 10 – 13
Answer Key / Notes Page 14
EAP Listening Page 15
EAP Writing Page 16
Common Writing Errors Page 16 – 17
Math Review Page 18
Developmental Math Page 19 – 23
NHCC’s Sample Questions Page 19 – 23
NHCC Answer Key Page 23
Next Generation Advance Algebra and Functions Page 24 – 35
Content Area Page 24
Accuplacer’s Sample Questions Page 25 – 30
Accuplacer Answer Key Page 31
Accuplacer Problem Review Page 31 – 35
Calculus Readiness Page 36 – 42
NHCC’s Sample Questions Page 36 – 42
NHCC Answer Key Page 42

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 About the English Language for Academic Purposes (EAP) Tests
Thank you for choosing to pursue your academic, professional, and personal goals here at North
Hennepin Community College (NHCC). Please read the following information to help you
review for the placement tests.
When students go to college in the U.S., students take placement tests. The purpose of these
tests is for class placement. It is important to try to do your best on these tests. The EAP
placement tests measure a student’s skills in these areas: reading, writing, listening, and
vocabulary. The tests place non-native English speakers into EAP courses at NHCC. All
courses in the EAP program are designed to help students succeed in the United States’ higher
education system. The Testing Advisor will discuss test results and course placements with
students after the placement test.
The contents of this packet are not intended to be exhaustive or to suggest what will be on the
test. Rather, this packet is meant to guide your review of reading, writing, listening, grammar,
vocabulary, and math. Take advantage of the resources outlined and invest the time you need to
assure appropriate course placement.
We wish you success in all your endeavors here at North Hennepin Community College.
Testing Center Staff

Placement
Course placement in Reading, Listening, Vocabulary, Writing, or Math courses will be at either
developmental or college-level. Courses numbered below 1000 are developmental courses
designed to prepare students for success in college-level courses. Developmental credits do not
apply toward a certificate, diploma, or degree. Courses numbered 1000 or above are considered
college-level that meet college-level standards. College credits apply toward the requirements of
a certificate, diploma, or degree.
Guidelines
Students must register for courses according to their placement or for a lower course, but not for
a higher course. Students may retest only once a semester for a $10 fee. Students must complete
each course with a “C” or better before moving to the next level.
Results for the placement test will be available upon completing the test. The Testing Advisor
will explain test results, course placements, the retesting policy, and the next steps in the
enrollment process. Information about Online Orientation will be provided following the
placement test, and students can schedule the Registration Session once a score is received for
the writing placement test. Students will register for courses during their Registration Session.
Placement Test Waiver
You may be eligible for a placement test waiver if you have previously completed college-level
course work. Please contact the Testing Center with questions about eligibility for a placement
test waiver.
© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 General Test & Review Information
How to take the placement test
 First apply to the college – www.nhcc.edu/admissions or in person at the Student Info Desk.
 Schedule an appointment to take the placement test. Call 763-424-0928 to schedule an
appointment. Monday 9:00 or 1:00, Tuesday 3:00, Wednesday 3:00, Thursday 9:00 or 1:00.
 Review! Use this study packet and other recommended resources listed below.
 Show up! Bring photo identification (passport, state ID, driver’s license) to your appointment.
We cannot allow students to test without identification. Arrive at least 15 minutes early to check-
in for your appointment. You will have one hour to write the essay. The other tests are not timed.
However, you should assume that it will take approximately two hours to complete the
computerized test.

Preparing for the Placement Tests

We strongly recommend that you review for the tests, so that your results reflect your true ability.
Here are a few websites to help you review.

 Accuplacer Study App – Create an account and log in to take “ESL Practice Tests”. Practice
the ESL Reading, ESL Listening, and ESL Sentence Meaning tests. Select “Learn as You Go” to
show the correct answer and receive rationale for the answer to each question. For Math, switch
to “Next Generation Practice Tests”, we only use “Advanced Algebra and Functions.”
https://accuplacerpractice.collegeboard.org/login
 Exam English – Use the English TOEFL practice reading, listening, sentence structure, and
vocabulary tests at http://www.examenglish.com/TOEFL/index.php.
 Union Test Prep – Practice the Accuplacer tests for ESL Reading, ESL Sentence Meaning, and
three levels of math. https://uniontestprep.com/accuplacer-test/practice-test
 Study Guide – Under Goals select “College Placement Exams” and “Accuplacer Exams”. View
the lessons under ESL Reading, ESL Listening, ESL Sentence Meaning, Arithmetic, Elementary
Algebra, College Level Math. https://study.com/academy/goal/test-prep.html
 PETT – Practice ESOL Listening tests https://www.seminolestate.edu/adult-ed/els/pett/
 EAP Writing – Review essay organization.
http://writing.umn.edu/sws/assets/pdf/quicktips/academicessaystructures.pdf
 EAP Grammar – Practice grammar exercises at www.englishpage.com
Additional Math resources
 Math Help – Review individual content areas covered in Accuplacer math tests, with online
practice tests and instruction. https://member.mathhelp.com/courses/test_prep/151.
 ARCC Math Videos – Tutorials for different topics on the Math placement test.
http://www.anokaramsey.edu/resources/tutoring-services/tutoring-services/msc-video-modules/.
 Test Prep Review – Online practice tests for Math. Provides additional self-assessment modules.
https://www.mometrix.com/academy/accuplacer-test/next-generation-accuplacer/next-generation-
accuplacer-advanced-algebra-and-function/.
 Khan Academy – Resources with video tutorials of math topics. http://www.khanacademy.org.
 IXL – Review Algebra 1, Algebra 2, Geometry, and Precalculus. https://www.ixl.com/math/.

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 EAP READING TEST
Purpose: The Accuplacer EAP Reading Test measures a student’s understanding of what
they have read.
Length: 20 questions
Format: Multiple choice
You will read short passages of 50 to 90 words. Half of this test
contains comprehension questions (paraphrase, locating information,
vocabulary on a phrase level, and pronoun reference). The other half
assesses inference skills (main idea, fact vs. opinion, cause/effect
logic, identifying irrelevant information, author’s point of view and
applying the author’s logic to another situation).

Helpful tip: During the test, take the time to read each passage and the questions again before
choosing your answer.
Practice test and review websites: Take the reading practice test below. The answers are at the
end of the test. Try more practice tests at:
 https://accuplacerpractice.collegeboard.org/login
 http://www.examenglish.com/TOEFL/TOEFL_reading1.htm
 http://www.examenglish.com/TOEFL/TOEFL_reading2.htm
 http://www.examenglish.com/TOEFL/TOEFL_reading3.htm
 http://www.examenglish.com/TOEFL/toefl_reading.htm
 https://uniontestprep.com/accuplacer-test/practice-test/esl-reading-skills/pages/1

Review websites: Use these resources for helpful study guides and tips.
 https://study.com/academy/course/accuplacer-esl-reading-skills-test-practice-study-
guide.html

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 EAP Reading Skills Sample Questions
Read the information below, then choose the best answer.

1. Television has been introduced to almost every country in the world, reaching a large number
of viewers on every continent. About 600 million people saw the first person walk on the
moon, and a billion people watched the twentieth Olympic Games. Television has in many
ways promoted understanding and cooperation among people. It does this by showing
educational and cultural programs.
From this passage, a reader can most reasonably conclude that the author believes that

A. people spend too much time watching television

B. not every country needs to have television
C. television can unify people from around the world
D. television is as important as schools

2. People have different ways of learning. Some are better at making mental pictures of new
ideas. Others are more comfortable with writing lists of things to memorize. Certain people
can learn best when listening to music, while others need silence to concentrate.
Which of the following is the main idea of the passage?

A. Mental pictures help many to learn.

B. Some people prefer lists to making mental pictures.
C. To learn well you need to be comfortable.
D. Different individuals have different ways of acquiring information.

3. If you hold a piece of copper wire over the flame of a wooden match, heat will be conducted
by the copper wire to your fingers, and you will be forced to drop the wire. You will,
however, still be able to hold the match because wood is a poor conductor of heat.
Which of the following is implied in the passage above?

A. Copper is a good conductor of heat.

B. Wood and copper conduct heat equally.
C. Wood is an excellent conductor of heat.
D. Matches should be made of copper.

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 4. Many people own different pets. Dogs, cats, birds, and fish are common household pets.
Others pets are considered to be exotic animals. These include snakes, lizards, and
hedgehogs.
According to the passage, snakes are

A. uncommon pets
B. likely to be found in a household with dogs
C. found only in zoos
D. not allowed in people’s homes

5. Cesar Chavez was an influential leader for farmworkers. He fought for their rights and
better working conditions. Chavez led many strikes that angered farm owners. Eventually
he succeeded in getting increased wages and better living situations for farmworkers.
The passage indicates that Chavez changed lives by

A. helping to end the farmworkers’ strikes

B. fighting for the rights of farm owners

C. working on the farms every day

D. improving the conditions for farmworkers

6. When cartoonist Charles M. Schulz was a boy in elementary school, other boys teased him
for being small and not very good at sports, and his art teacher told him he had no talent for
drawing. He had few friends and was too shy to talk to a red-haired girl he admired. Later in
life, Schulz used his childhood experiences in his comic strip Peanuts: the strip’s main
character, the sad and lonely Charlie Brown, represents Schulz as a little boy. Peanuts was
unique at the time because it contained no adult characters. Readers fell in love with Charlie
Brown, and Peanuts eventually became one of the most popular comic strips of all time.
What is the main idea of the passage?

A. Peanuts was the world’s most widely read comic strip.

B. Schulz was a very famous cartoonist.

C. Schulz turned the pain of his youth into success as an adult.

D. The comic strip Peanuts featured children as its only characters.

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 7. Money has been used for thousands of years in nearly every culture as a means of
exchange. However, today, the use of cash is becoming less and less common in modern
societies all over the world. Every year, a higher percentage of purchases are made online,
and even in stores customers are now using credit cards more often than cash. Many
people today do all of their banking on the Internet rather than going to the bank in person.

The author of the passage probably assumes that

A. cash will become virtually obsolete in the near future

B. using cash will become popular again
C. paying with credit cards all the time is dangerous
D. societies that do business online will struggle

8. Before giving first aid to an accident victim, you should obtain his or her consent. Asking
for consent takes a simple question. Say to the victim, “I know first aid, and I can help until
an ambulance arrives. Is that okay?”
According to the passage, it is wrong to

A. use first aid on an accident victim without medical training

B. attempt to help an accident victim without permission

C. help a victim before an ambulance arrives

D. call for an ambulance instead of helping the victim

9. Dr. Ellen Ochoa is an inventor and is also the first female Hispanic astronaut. Her
inventions include technology to help robots inspect equipment in space to maintain safety
and quality control on spacecraft. Before retiring, she logged more than 1,000 hours in
space across several space missions.
According to the passage, Dr. Ochoa is the first

A. Hispanic person to travel into space

B. inventor to travel into space
C. woman to travel into space
D. Hispanic woman to travel into space

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 10. Dogs and cats make very different types of pets. Before deciding whether to buy or adopt a
dog or a cat, prospective owners need to carefully consider their own lifestyles and
personalities. Dogs may make more affectionate companions, but they require more care and
attention. They must be taken out several times a day and should not be left alone for more
than a few hours. Larger dogs require significant exercise to remain fit and healthy. Cats are
usually more independent in nature and interact less with their owners. Also, a cat can be left
on its own all day, or even for several days, as long as it has food and clean water to drink.
From this passage, a reader can conclude that

A. owning a cat requires less work than owning a dog

B. people who are away from home during the day should not own a cat
C. people who like to play with their pets should own a cat
D. owning a cat is more responsibility than owning a dog

EAP Reading Skills Answer Key

1 2 3 4 5 6 7 8 9 10
C D A A D C A B D A

Notes

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 SENTENCE MEANING (VOCABULARY) TEST
Purpose: The Accuplacer EAP Sentence Meaning Test measures how well you understand
the meaning of sentences in English.
Length: 20 questions
Format: Multiple choice
The Sentence Meaning test measures your understanding of word meanings in
one- or two-sentence contexts. The sentences are taken from the subject areas of
natural science, history/social studies, arts/humanities, psychology/ human
relations, and practical situations.

There are four content areas measured: (a) Particle, Phrasal Verbs, Prepositions of
Direction; (b) Adverbs, Adjectives, Connectives Sequence; (c) Basic Nouns and
Verbs; and (d) Basic and Important Idioms.

Helpful tip: During the test, take the time to read each sentence and the questions again before
choosing your answer.
Practice tests: Take the sentence meaning practice test. The answers are at the end of the test.
Additional online practice tests are listed below:
 https://accuplacerpractice.collegeboard.org/login
 https://uniontestprep.com/accuplacer-test/practice-test/esl-sentence-meaning/pages/1
 http://www.examenglish.com/TOEFL/toefl_structure_1.htm
 http://www.examenglish.com/TOEFL/toefl_structure_2.htm
 http://www.examenglish.com/TOEFL/toefl_structure_3.htm
 http://www.examenglish.com/TOEFL/toefl_structure_4.htm

Grammar review websites: Use these resources for helpful study guides and tips.
 https://study.com/academy/course/accuplacer-esl-sentence-meaning-test-practice-study-
guide.html
 http://www.examenglish.com/grammar/index.html
 https://elt.oup.com/student/practicegrammar/test?cc=us&selLanguage=en
 http://www.roadtogrammar.com/

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 EAP Sentence Meaning Sample Questions
Directions for questions 1–8:

The sentence below has a blank space. Choose the word or phrase that makes the sentence
meaningful and correct.

1. Shikibu Murasaki, who wrote almost a thousand years ago, was one of the world’s _____
novelists.

A. most early

B. too early

C. more early

D. earliest

2. The Chang children _____ their parents by making sandwiches for the whole family.

A. helped out

B. helped with

C. helps for

D. helps to

3. As demonstrated by his last album, which was released after his death, Ibrahim Ferrer _____
one of the most beautiful voices in Latin music.
A. had

B. have

C. have had

D. having

4. After we saw the play, we had different opinions _____ Vincent’s performance.
A. about

B. at

C. for

D. to
© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 5. Having recorded many of the most beloved songs of the 1940’s, jazz singer Ella Fitzgerald
_____ one of the most prominent musical performers of her time.

A. had been

B. has been

C. was

D. will be

6. As we drove through the darkness, we saw another car coming _____ the bend in the road.
A. through

B. under

C. over

D. around

7. Sonia is so determined and stubborn that she never _____ until she gets exactly what she wants.

A. gives up

B. gives out

C. gave in

D. gave away

8. At only 43, John F. Kennedy was the _____ American president ever to be elected.

A. most young

B. more young

C. youngest

D. younger

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 Directions for questions 9–15:

Each problem contains one or two sentences followed by a question. Choose the correct answer
to the question.

9. Elena found a tomato that was much bigger than all the others in the garden.

How did the tomato compare to the others in the garden?

A. It was the smallest.

B. It was not very large.

C. It was larger than some.

D. It was the largest.

10. When the popular entertainer canceled her appearance, the Latin American festival was
postponed indefinitely.
When will the festival likely take place?

A. Tonight

B. Tomorrow

C. Next week

D. Many weeks later

11. Jasmine is never late to meet her friends, and sometimes arrives a few minutes early.

Which best describes Jasmine?

A. Lonely

B. Punctual

C. Talkative

D. Tardy

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 12. Bram Stoker is best known for his classic horror novel Dracula, which was published in 1897.
What did Bram Stoker do?

A. He was a doctor.

B. He was a merchant.

C. He was a writer.

D. He was an engineer.

13. Exhausted from her transatlantic flight, Judy could not stay up past 9 p.m.

What did Judy do at 9 p.m.?

A. Leave work

B. Come home from the airport

C. Get on an airplane

D. Go to bed

14. Eliot sleeps late whenever he can, leaves work early, and never does anything unless he
absolutely has to.
Which best describes Eliot?

A. Boring

B. Lazy

C. Selfish

D. Tired.

15. Juanita rushed to her dance class and burst through the door in the nick of time.

When Juanita got to her dance class, she was

A. very early

B. very late

C. nearly late

D. a little late

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 EAP Sentence Meaning Answer Key
1 2 3 4 5 6 7 8
D A A A C D A C
9 10 11 12 13 14 15
D D B C D B C

Notes

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 EAP LISTENING TEST
Purpose: The Accuplacer EAP Listening Test measures your ability to understand spoken
English in a variety of situations. The conversations may take place at work,
home, or school.
Length: 20 questions
Format: Multiple choice
First, you will listen to a spoken conversation, followed by a spoken question.
The possible answers to the question are spoken and written. You will be asked
to choose the best answer.
Helpful tip: During the test, you have the ability to listen to each section two
more times by clicking on the “play” button next to each section.
The first time the test reads through each section, use that opportunity to select what you think is
the best answer. Select “Play” to repeat the spoken conversation and spoken question, then
determine if you still think the answer you originally selected is correct. You will still have one
more opportunity to listen to the spoken conversation and spoken question before you move on
to the next question. You can change your answer multiple times, but once you submit the
answer and move on to the next question you cannot go back to the previous question. When
you move to the next question it will start the spoken conversation immediately, be prepared.
Practice Tests: Take the listening practice tests below. You can check your answers throughout
the tests.
 https://accuplacerpractice.collegeboard.org/login
 https://uniontestprep.com/accuplacer-test/practice-test/esl-listening/pages/1
 https://www.examenglish.com/TOEFL/TOEFL_listening_conversation1.htm
 https://www.examenglish.com/TOEFL/TOEFL_listening_conversation2.htm
 https://www.examenglish.com/TOEFL/TOEFL_listening_conversation3.htm
 https://www.seminolestate.edu/adult-ed/els/pett/listening
Review websites: Use these resources for helpful study guides and tips.
 http://study.com/academy/course/accuplacer-esl-listening-test-practice-study-guide.html
 http://www.esl-lab.com/

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 WRITING TEST
Purpose: The Writing Test measures your ability to organize and communicate your ideas
effectively in formal writing. The essay you write will decide the level of your
first writing class here at North Hennepin Community College. It is important for
you to do your very best writing.
Length: 60 minutes
Format: Write an essay of 4-5 paragraphs, with an introduction, a body, and a conclusion.
 In your introduction paragraph, include a thesis statement that gives the
main points you will explain in your essay.
 For each body paragraph, include a topic sentence, specific information
about your main point, and a concluding sentence
 Your concluding paragraph should provide a final idea about the main
points in your essay.
Helpful tip: Write as much as you can in the time you have. Organize your ideas clearly and
explain each idea completely. Carefully check your writing for correct grammar, spelling and
punctuation.

Essay organization: http://writing.umn.edu/sws/assets/pdf/quicktips/academicessaystructures.pdf

Review grammar: www.englishpage.com

Common Writing Errors

SINGULAR AND PLURAL NOUNS ARTICLES
Incorrect: She needs two book for this class.
Incorrect: We saw good movie yesterday.
Correct: She needs two book s for this class.
Correct: We saw a good movie yesterday.

POSSESSIVE NOUNS WORD FORM

Incorrect: John notebook is on the table. Incorrect: I saw a beauty picture.

Correct: John ’s notebook is on the table. Correct: I saw a beautiful picture.

WORD CHOICE SUBJECT/VERB AGREEMENT

Incorrect: I like to drive my horse. Incorrect: He like to study at the library.

Correct: I like to ride my horse. Correct: He like s to study at the library.

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 VERB FORM VERB TENSE
Incorrect: They are study English. Incorrect: We study for the test yesterday.

Correct: They are studying English. Correct: We studied for the test yesterday.

PREPOSITIONS WORD ORDER

Incorrect: We started studying 6:00 p.m. Incorrect: I saw five times that movie.

Correct: We started studying at 6:00 p.m. Correct: I saw that movie five times.

REPEATED SUBJECT MISSING SUBJECT OR VERB

Incorrect: My friend she wants to go to school. Incorrect: Took his mother to the doctor.

Correct: My friend she wants to go to school. Correct: He took his mother to the doctor.

SPELLING CAPITALIZATION
Incorrect: I recieved the gift from my family. Incorrect: We are studying english.

Correct: I received the gift from my family. Correct: We are studying English.

PUNCTUATION: RUN-ON PUNCTUATION: COMMA-SPLICE

Incorrect: We enjoyed reading the book we Incorrect: We enjoyed reading the book, we
recommended it to our friends. recommended it to our friends.

Correct: We enjoyed reading the book. We Correct: We enjoyed reading the book. We
recommended it to our friends. recommended it to our friends.

PUNCTUATION: FRAGMENT CONJUNCTIONS/TRANSITIONS

Incorrect: Before I go to school. I eat breakfast. Weak: Traffic was bad. They arrived late.

Correct: Before I go to school, I eat breakfast. Better: Traffic was bad, so they arrived late.

© 2016 The College Board ACCUPLACER SAMPLE QUESTIONS

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 Math Placement Test
Structure
The math placement test is designed to measure student’s understanding of content areas in Arithmetic,
Algebra, Geometry, Functions and Trigonometry. The test begins with the ACCUPLACER Next
Generation Advanced Algebra and Functions test, which has 20 questions, and will either place students
into a College Math class based on that score, or require additional tests for placement. An Advanced
Algebra and Functions score of less than 235, will start the Developmental Math test with 18 questions.
An Advanced Algebra and Functions score of more than 261, will start the Calculus Readiness test with
10 questions. Test scores and placement are available immediately after completing the test. The
Testing Advisor will explain test results and course placements to each student.
Guidelines
The placement test is not timed. Students are not permitted to use a personal calculator, a calculator
tool on the computer or the Internet. The ACCUPLACER calculator is the only calculator students may
use, and it only appears on certain questions.
A calculator button will be displayed right next to the Accessibility button on the toolbar.

The sample questions in this packet are not intended to be exhaustive, but to aid the student’s review of
certain math concepts. The first set of problems was developed by faculty at NHCC, including a review
section, which explains how to solve the problems. The second set of questions is from College Board,
the creators of the ACCUPLACER. To aid study, external study resources and practice questions are
listed on the previous page.
Students are highly encouraged to review for the math placement test before taking it. Take advantage
of the resources and references provided by the Testing Center, as well as others you are aware of that
may help your performance on the test.

18
 Developmental Math Practice Questions
Calculators not allowed
1. Simplify: -7 – (-4) 2. Simplify: -7 + (-4)
a. 3 a. 3
b. -3 b. -3
c. -11 c. -11
d. 11 d. 11
e. 28 e. 28

3. Simplify: 10 – (-5) 4. Simplify: -10 + 5

a. 15 a. 15
b. 5 b. 5
c. -5 c. -5
d. -2 d. -2
e. -15 e. -15

5. Simplify: -30 ÷ (-5) 6. Simplify: -35 ÷ 7

a. -35 a. -28
b. -6 b. -6
c. -5 c. -5
d. 5 d. 5
e. 6 e. 6

8 2 2 1
7. Simplify: − 8. Simplify: 1 +
3 3 3 3
a. 6 a. 6
10 10
b. b.
3 3
c. 2 c. 2
d. 1 d. 1
5 5
e. e.
3 3

19
 3 1 2 2
9. Simplify: + 10. Simplify: +
4 3 15 3
4 4
a. a.
7 5
2 2
b. b.
7 9
2 4
c. c.
3 18
13 4
d. d.
12 15
5 5
e. e.
12 12

4 7 5 6
11. Simplify:  12. Simplify: 
7 16 9 25
11 11
a. a.
23 23
11 11
b. b.
4 4
64 2
c. c.
49 15
5 5
d. d.
4 4
1 1
e. e.
4 4

13. Simplify: 1000 × 0.0372 14. Simplify: 0.0372 ÷ 100

a. 3.72 a. 3.72
b. 0.000372 b. 0.000372
c. 0.00372 c. 0.00372
d. 372 d. 372
e. 37.2 e. 37.2

20
15. Simplify: 3 – 1.75 16. Simplify: 5.8 + 3.55
a. 4.75 a. 9.35
b. 1.75 b. 4.13
c. 1.25 c. 1.25
d. 1.72 d. 8.35
e. 0.75 e. 11.15

17. Simplify: 2 + 2 × 4 – 3 18. Simplify: 24 ÷ 2 × 6 – 4

a. 13 a. -2
b. 4 b. 24
c. 9 c. 6
d. 7 d. -18
e. 15 e. 68

19. Simplify: 7 – (2 + 9) 20. Simplify: 7 – 8(3 – 5) + 15

a. 14 a. 38
b. -4 b. 17
c. 18 c. 6
d. 4 d. 4
e. -14 e. -14

1 1
21. Evaluate the expression ab 22. Evaluate the expression h( B + b)
3 2
when a = 5 and b = 6 and simplify when h = 7, B = 3, b = 5 and simplify
a. 10 a. 14
b. 20 b. 20
c. 1 c. 28
11 1
d. d. 11
3 2

e. 80 e. 80

21
 −b + b2 − 4ac
23. Evaluate the expression (a + b)2 24. Evaluate
2a
when a = 5 and b = 3 and simplify when a = 3, b = -5, c = -2 and simplify
a. 34 a. 1
b. 64 b. 2
c. 225 c. 3
d. 16 d. 6
e. 45 e. 9

25. Simplify: (2 – 5)2 + 9 ÷ 3 26. Simplify: 15 – (9 – 6)2 + 45 ÷ 15

a. -6 a. -99
b. 0 b. 0
c. 6 c. 9
d. 12 d. 12
e. 2 e. 2

27. Simplify: 4(x – 2) – 3(x – 1) 28. Simplify: -3(y + 5) + 4(y – 5)

a. 7x – 11 a. 7y – 5
b. 7x – 8 b. 7y – 35
c. x – 11 c. y–5
d. x–5 d. 35y
e. x–3 e. y – 35

29. Simplify: 3a + 2b – 5a – 4a + 2b + 3 30. Simplify: -5x + 9y – 5x – 8 + 3x + 7

a. -12a + 4b + 3 a. -7x + 9y – 1
b. -6a + 4b + 3 b. 3x + 9y + 15
c. 3a + 6b + 3 c. -7x – 1
d. -a + 7b d. -7x + 9y – 15
e. ab e. 12xy – 1

22
31. Solve: 2(a + 5) = -4(a – 4) 32. Solve: 4 – 3(x + 8) = 2(x + 5)
a. a=4 a. x=6
b. a=1 b. x=2
c. a=2 c. x = -6
1 d. x = -2
d. a=
3 18
e. x=
e. a = -1 5

33. Solve: 2x – 1 = 5x + 8 34. Solve: -2(w – 1) = 8 – 3(w + 2)

a. x=3 a. w=4
b. x = -2 b. w = -4
c. x=1 12
c. w=
1 5
d. x=
3 d. w=0
e. x = -3 e. w = -2

35. Solve: 2 + x + 7x = 7 – 2x + 10 36. Solve: y + 7 – 3y = 7 – 5y + 10

a. x = 15 a. x = 15
2 10
b. x= b. y=
3 3
c. x=3 c. x=3
3 3
d. x= d. x=
2 2
e. x = -1 e. x = -1

Developmental Math Answer Key

1 2 3 4 5 6 7 8 9 10 11 12
B C A C E C C C D A E C

13 14 15 16 17 18 19 20 21 22 23 24
E B C A D E B A A C B B

25 26 27 28 29 30 31 32 33 34 35 36
D C D E B A B C E D D B

23
 ACCUPLACER Advanced Algebra and Functions
Sample Questions
The Next-Generation Advanced Algebra and Functions placement test is a computer adaptive
assessment of test-takers’ ability for selected mathematics content. Questions will focus on a
range of topics, including a variety of equations and functions, including linear, quadratic,
rational, radical, polynomial, and exponential. Questions will also delve into some geometry and
trigonometry concepts. In addition, questions may assess a student’s math ability via
computational or fluency skills, conceptual understanding, or the capacity to apply mathematics
presented in a context. All questions are multiple choice in format and appear discretely (stand
alone) across the assessment. The following knowledge and skill categories are assessed:

 Linear equations
 Linear applications
 Factoring
 Quadratics
 Functions
 Radical and rational equations
 Polynomial equations
 Exponential and logarithmic equations
 Geometry concepts
 Trigonometry

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

24
Advanced Algebra and Functions Sample Questions
Choose the best answer. If necessary, use the paper you were given.

1. Function g is defined by g(x) = 3(x+ 8). What is the value of g(12)?

A. –4
B. 20
C. 44
D. 60

2. Which of the following is an equation of the line that

passes through the point (0, 0) and is perpendicular
to the line shown above?
5
A. y = 4 x
5
B. y = 4 x +3
4
C. y = - 5 x
4
D. y = - 5 x + 3

3. The surface area of a right rectangular prism can be found by finding the sum of the area of
each of the faces of the prism. What is the surface area of a right rectangular prism with
length 4 centimeters (cm), width 9 cm, and height 3 cm? (Area of a rectangle is equal to
length times width.)

A. 75 cm2
B. 108 cm2
C. 120 cm2
D. 150 cm2

4. Which of the following expressions is equivalent to (x + 7)(x 2 - 3x + 2)?

A. x 3 - 3x 2 + 2x + 14
B. x 3 + 4x 2 - 19x + 14
C. x 3 - 3x + 14
D. x 2 - 2x + 9

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

25
5. The graph below shows the cost, in dollars, of apples as a function of the number of pounds
of apples purchased at a particular grocery store. The equation above defines the cost C, in
dollars, for p pounds of pears at the same store. Which of the following statements accurately
compares the cost per pound of apples and the cost per pound of pears at this store?

A. Apples cost approximately $0.07 less per pound than pears do.
B. Apples cost approximately $0.04 less per pound than pears do.
C. Apples cost approximately $0.73 less per pound than pears do.
D. Apples cost approximately $0.62 more per pound than pears do.

6. Which of the following is the graph of a function where y= f(x)?

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

26
7. Which of the following expressions is equivalent to 3x2+ 6x– 24?

A. 3(x + 2)(x – 4)
B. 3(x – 2)(x + 4)
C. (x + 6)(x – 12)
D. (x – 6)(x + 12)

8. A biologist puts an initial population of 500 bacteria into a growth plate. The population is
expected to double every 4 hours. Which of the following equations gives the expected
number of bacteria, n, after x days? (24 hours = 1 day)

A. n = 500(2)x

B. n = 500(2)6x

C. n = 500(6)x

D. n = 500(6)2x

9. x2+ 5x– 9 = 5
Which of the following values of x satisfies the equation above?

A. 7
B. 3
C. -2
D. -7

10. The graph of y = f(x) is shown in the xy-plane.

Which of the following equations could define f(x)?

A. f(x) = x2 – 2x – 8
B. f(x) = –x2 + 2x – 8
C. f(x) = (x – 2)(x + 4)
D. f(x) = –(x – 1)2 – 9

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

27
11. Which of the following best describes the range of y = –2x4 + 7
A. y ≤ –2
B. y ≥ 7
C. y ≤ 7
D. All real numbers

12. For which of the following equations is x = 6 the only solution?

A. (6x) 2 = 0
B. (x – 6)2 = 0
C. (x + 6)2 = 0
D. (x – 6)(x + 6) = 0

13. If f(x) = x2 + 3x + 1, what is f(x + 2)?

A. x2 + 3x + 3
B. (x + 2)2 + 3(x + 2) + 1
C. (x + 2)(x2 + 3x + 1)
D. x2 + 3x + 9

14. What, if any, is a real solution to √5𝑥 + 1 + 9 = 3 ?

1
A. −
5
B. 7
143
C.
5
D. There is no real solution

3 5 𝑥
15. If 𝑥 ≠ −2 and 𝑥 ≠ − , what is the solution to = ?
2 𝑥+2 2𝑥−3
A. 3 and 5
3
B. 2 and −
2
3
C. -2 and
2
D. -3 and -5

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

28
16. Triangle JKL and triangle PQR are shown above. If ∠J is congruent to ∠P, which of the
following must be true in order to prove that triangles JKL and PQR are congruent?

A. ∠L ≅ ∠R and JL = PR
B. KL = QR and PR = JL
C. JK = PQ and KL = QR
D. ∠K ≅ ∠Q and ∠L ≅ ∠R

17. In the function f(x) = a(x + 2)(x – 3)b, a and b are both integer constants and b is positive. If
the end behavior of the graph of y = f(x) is positive for both very large negative values of x,
and very large positive values of x, what is true about a and b?

A. a is negative, and b is even.

B. a is positive, and b is even.
C. a is negative, and b is odd.
D. a is positive, and b is odd.

18. Which of the following equations is equivalent to 25x = 7?

7
A. 𝑥 = log 2 ( )
5
log2 7
B. 𝑥 =
5
log7 2
C. 𝑥 =
5
log7 5
D. 𝑥 =
2

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

29
 𝑥−𝑦
19. If x > 0 and y > 0, which of the following expressions is equivalent to ?
√𝑥−√𝑦
𝑥−𝑦
A.
√𝑥−𝑦

B. √𝑥 − 𝑦

C. √𝑥 + √𝑦

D. 𝑥 √𝑥 + 𝑦√𝑦

5
20. In triangle ABC, angle C is a right angle. If cos A = what is the value of cos B?
8
3
A.
8
5
B.
8

√39
C.
8

√89
D.
8

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

30
 Accuplacer Advanced Algebra and Functions Answer Key
1 2 3 4 5 6 7 8 9 10
D A D B A C B B D A

11 12 13 14 15 16 17 18 19 20
C B B D A A D B C C

Rationales
1. Choice D is correct. The value of g(12) can be found by substituting 12 for x in the equation
for g(x). This yields g(12) = 3(12 + 8), which is equivalent to 3(20) or 60. Choice A is
incorrect. This answer represents the value of x in the equation 12 = 3(x + 8). Choice B is
incorrect. This answer represents the value of the expression in parentheses. Choice C is
incorrect. This answer is a result of incorrectly distributing the 3 through the expression in
parentheses: g(12) = 3(12) + 8.

2. Choice A is correct. The slopes of perpendicular lines are negative reciprocals of each other.
4 4 5
The slope of the line in the graph is − 5. The negative reciprocal of − 5 is 4. A line that passes
5 5
through the point (0, 0) has a y-intercept of 0. Therefore, the equation y = 4 𝑥 + 0, or y = 4 𝑥,
is correct. Choice B is incorrect because it is an equation of a line that is perpendicular to the
line shown, but it does not pass through the origin. Choice C is incorrect because this
equation is parallel to the line shown, not perpendicular. Choice D is incorrect because it is
the equation of the line shown in the graph.

3. Choice D is correct. The surface area of the rectangular prism is the total area of each of the
faces of the prism and can be written as 2(length × width) + 2(height × width) + 2(length ×
height), which is 2(4 cm × 9 cm) + 2(3 cm × 9 cm) + 2(4 cm × 3 cm), or 150 cm2. Choice A
is incorrect because it is half the surface area of the prism. Choice B is incorrect because it is
the volume of the prism. Choice C is incorrect because it is 30 units less than the surface area
of the prism described.

4. Choice B is correct. Using the distribution property, the given expression can be rewritten as
x(x2) + x(−3x) + x(2) + 7(x2) + 7(−3x) + 7(2). Further simplifying results in x3 − 3x2 + 2x +
7x2 − 21x + 14. Finally, adding like terms yields x3 + 4x2 − 19x + 14. Choices A, C, and D are
incorrect because they each result from errors made when performing the necessary
distribution and adding like terms.

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

31
5. Choice A is correct. The cost per pound of apples can be determined by the slope of the
graph as about $1.33 per pound. The cost per pound of pears can be determined by the slope
7 7
of the line defined by the equation C = 5 𝑝. The slope of the line defined by C is 5, so the cost
per pound of pears is $1.40. Therefore, the apples cost approximately $0.07 less per pound
than pears do. Choice B is incorrect. This is the result of misreading the cost per pound of
apples as $0.67 and the cost per pound of pears as $0.71 and then finding the difference
between the two values. Choice C is incorrect. This is the result of misreading the cost per
pound of apples from the graph as $0.67 and then subtracting the cost per pound of pears,
$1.40. Choice D is incorrect. This is the result of misreading the cost per pound of pears as
$0.71 and then subtracting this value from the cost per pound of apples, $1.33.

6. Choice C is correct. A function has one output for each input. Each x-value on this graph
corresponds to only one y-value. Choices A, B, and D are incorrect because each has x-values
that correspond to more than one y-value.

7. Choice B is correct. The expression 3(x − 2)(x + 4) can be expanded by first multiplying
(x − 2) by 3 to get (3x − 6) and then multiplying (3x − 6) by (x + 4) to get 3x2 + 6x − 24.
Choice A is incorrect because it is equivalent to 3x2 − 6x − 24. Choice C is incorrect because
it is equivalent to x2 − 6x − 72. Choice D is incorrect because it is equivalent to x2 + 6x − 72.

8. Choice B is correct. An exponential function can be written in the form y = abt where a is
the initial amount, b is the growth factor, and t is the time. In the scenario described, the
variable y can be substituted with n, the total number of bacteria, and the initial amount is
given as 500, which yields n = 500bt. The growth factor is 2 because the population is
described as being expected to double, which gives the equation n = 500(2)t. The population
is expected to double every 4 hours, so for the time to be x days, x must be multiplied by 6
(the number of 4-hour periods in 1 day). This gives the final equation n = 500(2)6x. Choices
A, C, and D are incorrect. Choice A does not account for the six 4-hour periods per day,
choice C uses the number of time periods per day as the growth rate, and choice D uses the
number of time periods per day as the growth rate and multiplies the exponent by the actual
growth rate.

9. Choice D is correct. Subtracting 5 from both sides of the equation gives x2 + 5x − 14 = 0.

The left-hand side of the equation can be factored, giving (x + 7)(x − 2) = 0. Therefore, the
solutions to the quadratic equation are x = −7 and x = 2. Choice A is incorrect because 72 +
5(7) − 9 is not equal to 5. Choice B is incorrect because 32 + 5(3) − 9 is not equal to 5.
Choice C is incorrect because (−2)2 + 5(−2) − 9 is not equal to 5.

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

32
10. Choice A is correct. The graph of y = f(x) crosses the x-axis at x = −2 and x = 4, crosses the
y-axis at y = 8, and has its vertex at the point (1, −9). Therefore, the ordered pairs (−2, 0), (4
0) , , (0, −8), and (1, −9) must satisfy the equation for f(x). Furthermore, because the graph
opens upward, the equation defining f(x) must have a positive leading coefficient. All of
these conditions are met by the equation f(x) = x2 − 2x − 8. Choice B is incorrect. The points
(−2, 0), (4, 0), (0, −8), and (1, −9), which are easily identified on the graph of y = f(x), do not
all satisfy the equation f(x) = − x2 + 2x − 8; only (0, −8) does. Therefore f(x) = −x2 + 2x − 8
cannot define the function graphed. Furthermore, because the graph opens upward, the
equation defining y = f(x) must have a positive leading coefficient, which f(x) = −x2 + 2x − 8
does not. Choice C is incorrect. The points (−2, 0), (4, 0), (0, −8), and (1, −9), which are
easily identified on the graph of y = f(x), do not all satisfy the equation f(x) = (x − 2)(x + 4);
only (0, −8) does. Therefore, f(x) = (x − 2)(x + 4) cannot define the function graphed. Choice
D is incorrect. Though the vertex (1, −9) does satisfy the equation f(x) = −(x − 1)2 − 9, the
points (−2, 0), (4, 0), and (0, −8) do not. Therefore, f(x) = −(x − 1)2 − 9 cannot define the
function graphed. Furthermore, because the graph opens upward, the equation defining y =
f(x) must have a positive leading coefficient, which f(x) = −(x − 1)2 − 9 does not.

11. Choice C is correct. The range of a function describes the set of all outputs, y, that satisfy
the equation defining the function. In the xy-plane, the graph of y = −2x4 + 7 is a U-shaped
graph that opens downward with its vertex at (0, 7). Because the graph opens downward, the
vertex indicates that the maximum value of y is 7. Therefore, the range of the function
defined by y = −2x4 + 7 is the set of y-values less than or equal to 7. Choices A, B, and D are
incorrect in that choice A doesn’t cover the entire range, while choices B and D include
values that aren’t part of the range.

12. Choice B is correct. The only value of x that satisfies the equation (x − 6)2 = 0 is 6. Choice
A is incorrect because x = 0 is the only solution to the equation (6x)2 = 0. Choice C is
incorrect because x = −6 is the only solution to the equation (x + 6)2 = 0. Choice D is
incorrect because although x = 6 is a solution to the equation (x − 6)(x + 6) = 0, x = −6 is
another solution to the equation.

13. Choice B is correct. Substituting x + 2 for x in the original function gives f(x + 2) = (x + 2)2
+ 3(x + 2) + 1. Choice A is incorrect. This is f(x) + 2. Choice C is incorrect. This is (x +
2)f(x). Choice D is incorrect. This is f(x) + 23.

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

33
14. Choice D is correct. Subtracting 9 from both sides of the equation yields 5x +1 = −6, and
there are no real values of x that result in the square root of a number being negative, so the
equation has no real solution. Choices A and C are incorrect due to computational errors in
solving for x and not checking the solution in the original equation. Choice B is incorrect
because it is the extraneous solution to the equation.

15. Choice A is correct. To solve the equation for x, cross multiply to yield x(x + 2) = 5(2x − 3).
Simplifying both sides of the new equation results in x2 + 2x = 10x − 15. Next, subtract 10x
from both sides of the equation and add 15 to both sides of the equation to yield x2 − 8x + 15
= 0. By factoring the left-hand side, the equation can be rewritten in the form (x − 3)(x − 5) =
0. It follows, therefore, that x = 3 and x = 5. Choices B, C, and D are possible results from
mathematical errors when solving the equation for x.

16. Choice A is correct. If two angles and the included side of one triangle are congruent to
corresponding parts of another triangle, the triangles are congruent. Since angles J and L are
congruent to angles P and R, respectively, and the side lengths between each pair of angles,
JL and PR, are also equal, then it can be proven that triangles JKL and PQR are congruent.
Choices B and C are incorrect because only when two sides and the included angle of one
triangle are congruent to corresponding parts of another triangle can the triangles be proven
to be congruent, and angles J and P are not included within the corresponding pairs of sides
given. Further, side-side-angle congruence works only for right triangles, and it is not given
that triangles JKL and PQR are right triangles. Choice D is incorrect because the triangles
can only be proven to be similar (not congruent) if all three sets of corresponding angles are
congruent.

17. Choice D is correct. A polynomial function of even degree with a positive leading
coefficient will have positive end behavior for both very large negative values of x and very
large positive values of x. For a polynomial function in the form f(x) = a (x + 2)(x − 3)b to be
of even degree with a positive leading coefficient, a must be positive and b must be odd.
Choice A is incorrect. If a is negative and b is even, the polynomial function will be of odd
degree, with a negative leading coefficient. This results in positive end behavior for very
large negative values of x and negative end behavior for very large positive values of x.
Choice B is incorrect. If a is positive and b is even, the polynomial function will be of odd
degree with a positive leading coefficient. This results in negative end behavior for very large
negative values of x and positive end behavior for very large positive values of x. Choice C is
incorrect. If a is negative and b is odd, the polynomial function will be of even degree with a
negative leading coefficient. This results in negative end behavior on both sides of the
function.
ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

34
18. Choice B is correct. By definition, if (b)x = y, where b > 0 and b ≠ 1, then x = logb y.
Therefore, the given equation 25x = 7 can be rewritten in the form log2 7 = 5x. Next, solving
log2 7
for x by dividing both sides of the equation by 5 yields = x. Choices A, C, and D are
5
incorrect because they are the result of misapplying the identity, which states that if (b)x = y,
where b > 0 and b ≠ 1, then x = logb y

19. Choice C is correct. Since x > 0 and y > 0, x can be rewritten as (√𝑥 )2 and y can be
𝑥−𝑦 (√𝑥 )2 −(√𝑦 )2
rewritten as (√𝑦 )2. It follows, then, that can be rewritten as . Because the
√𝑥− √ 𝑦 √𝑥− √𝑦
(√𝑥 + √𝑦)(√𝑥 − √𝑦)
numerator is a difference of two squares, it can be factored as . Finally,
√𝑥 − √𝑦

dividing the common factors of (√𝑥 − √𝑦) in the numerator and denominator yields √𝑥 +
𝑥−𝑦 √𝑥 + √𝑦
√𝑦. Alternatively, if √𝑥 − is multiplied by , which is equal to 1, and therefore does
√𝑦 √𝑥 + √𝑦
(𝑥 − 𝑦) (√𝑥 + √𝑦)
not change the value of the original expression, the result is ( , which is
√𝑥 − √𝑦)(√𝑥 + √𝑦)
𝑥 √ 𝑥 + 𝑥 √ 𝑦 − 𝑦√ 𝑥 − 𝑦 √ 𝑦 (𝑥 − 𝑦) (√𝑥 + √𝑦)
equivalent to . This can be rewritten as , which can be
𝑥 − √𝑥𝑦 + √𝑥𝑦− 𝑦 (𝑥 − 𝑦)

simplified to √𝑥 + √𝑦. Choice A is incorrect and may be the result of incorrectly

𝑥−𝑦
combining √𝑥 − √𝑦. Choice B is incorrect because it is equivalent to . Choice D is
√𝑥 − 𝑦
incorrect and may be the result of misusing the conjugate strategy. Instead of multiplying the
numerator and denominator by the quantity (√𝑥 + √𝑦), they may have been multiplied by
(√𝑥 − √𝑦) and then improperly distributed.

20. Choice C is correct. If triangle ABC is defined as a right triangle, where angle C is the right
angle, then the cosine of angle A (cos A) is defined as the ratio
the length of the side adjacent to angle A 5
. Since this ratio is defined as 8, then the length of the side
the length of the hypotenuse
opposite angle A, which is also the side adjacent to angle B, can be derived from the
Pythagorean theorem: a2 + 52 = 82 , where a represents the length of the side opposite angle
A. Solving for a yields a2 = 64 − 25 = 39, so a = √39. Then, to determine the cosine of angle
the length of the side adjacent to angle B √39
B, use the same ratio in relation to angle B: cosB = = .
the length of the hypotenuse 8

Choice A and D are incorrect and likely results from an error in finding the length of side
̅̅̅̅. Choice B is incorrect and is the value of cos A and sin B.
𝐶𝐵

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

35
 Calculus Readiness Practice Test
Calculators not allowed

Function Questions

1. If f  m   m3  2m2  m , then f  2  

a) -2
b) 14
c) -16
d) -18
e) None of these

2. If r t   2t 2  7t  4 , then r  1  

a) 5
b) -13
c) -9
d) -5
e) None of these

x
3. If f  x   2x  3 and g  x   , then g  f  2   
x 1
a) 7
3
b)
4

4
c)
3

5
d)
4

7
e)
6

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

36
 x 1
4. If f  x   and g  x   x 2  1 , then g  f  1   
x
3
a)
2
2
b)
3

c) 5
d) 2
e) None of these

5. Let f  x   2 x  3 . The domain (set of inputs) of the function f is the set of all
numbers x such that
a) x 0
b) x 2

3
c) x
2
2
d) x
3

e) None of these

1
6. Let f  x   . The domain (set of inputs) of the functions is the set of all
3 x
numbers x such that
a) x 3

b) x 0

c) x  3

d) x  3

e) x3

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

37
Logarithms Questions

7. For x  0 , log  10 x  x  1   

a) 10log  x  log  x  1 

b) 1  log  x   log  x  1 

c) log 10x   log  x  1 

d) 10  log  x   log  x  1 

e) None of these

  t  1 2 
8. For t > 0, log  =
 t 
 

log  t  1 
2

a)
log  t 

2 log  t  1 
b)
log  t 

1
c) log  
3

d) 2log t  1   log t 

e) 2log t  1   log t 

9. If x  log 3 50 , then x is a number such that

a) 1 x2
b) 2 x 3

c) 3 x 4

d) 4 x 5

e) x 5
ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

38
 2a
10. If log 2 a  2.1 and log 2 b  1.5 , then log 2 
b
a) can’t be determined from the given information
b) 0.6
c) 2.6
d) 1.6
e) 3.6

11. If log2  3x  5  3 , then x =

8
a)
3

2
b)
3

1
c)
3

14
d)
3

13
e)
3

12. If log3  2x  1   2 , then x =

a) 5
3
b)
2
7
c)
2
d) 3

1
e)
2
ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

39
Trigonometry Questions
13. In the figure here (not drawn to scale), what is the value of tan A ?
3
a)
5
4
b)
5
5
c)
3
5
d)
4
3
e)
4

2
14. If  is an acute angle with sin   , what is the value of cos ?
3
1
a)
3
5
b)
3

7
c)
3

5
d)
3

2
e)
3

 
15. What is the value of sin    cos   ?
2
a) -1
b) 0
c) 1
d) 2
e) cannot be determined without a calculator
ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

40
16. What is the value of sin2  2  cos2 2 ?

a) 4
b) 0
c) 1

2
d)
2
e) None of these

1 
17. If sin  x   with 0  x  , then cos  2x  
2 2

3
a)
2
b) 0

1
c)
2
d) 1
e) None of these

2 
18. If sin  x   with 0  x  , what is the value of tan  x  ?
2 2

a) 3

1
b)
3

c) 1
2
d)
2

e) None of these

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

41
19. The curve shown here could be a portion of the graph of y =

a) sin  x 

b) cos  x 

c)  sin  x 

d) cos  2x 

e) sin  2x 

20. The curve above could be a portion of the graph of y =

a) cos x
b) sin x
c) -cos x
d) -sin x
e) none of these

Accuplacer Calculus Readiness Answer Key

1 2 3 4 5 6 7 8 9 10
D A E C C E B E C D

11 12 13 14 15 16 17 18 19 20
E A E D B C C C E A

ACCUPLACER Next-Generation Advanced Algebra and Functions © 2017 The College Board.

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