ACCUPLACER
®
Sample Questions for Students
© 2016 e College Board. College Board, ACCUPLACER, WritePlacer and the
acorn logo are registered trademarks of the College Board. All other products and
services may be trademarks of their respective owners. Visit the College Board on
the Web: www.collegeboard.org.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
1
Sentence Skills
In an ACCUPLACER® placement test, there are 20
Sentence Skills questions of two types.
• e rst type consists of sentence-correction
questions that require an understanding of
sentence structure. ese questions ask you to
choose the most appropriate word or phrase for
the underlined portion of the sentence.
• e second type consists of construction-shi
questions. ese questions ask that a sentence be
rewritten according to the criteria shown while
maintaining essentially the same meaning as the
original sentence.
Within these two primary categories, the questions
are also classied according to the skills being tested.
Some questions deal with the logic of the sentence,
others with whether or not the answer is a complete
sentence, and still others with the relationship
between coordination and subordination.
Sentence Skills Sample
Questions
Directions for questions 1–11
Select the best version of the underlined part of the
sentence. e rst choice is the same as the original
sentence. If you think the original sentence is best,
choose the rst answer.
1. Stamp collecting being a hobby that is sometimes used in
the schools to teach economics and social studies.
A. being a hobby that is
B. is a hobby because it is
C. which is a hobby
D. is a hobby
2. Knocked sideways, the statue looked as if it would fall.
A. Knocked sideways, the statue looked
B. e statue was knocked sideways, looked
C. e statue looked knocked sideways
D. e statue, looking knocked sideways,
3. To walk, biking, and driving are Pat’s favorite ways of
getting around.
A. To walk, biking, and driving
B. Walking, biking, and driving
C. To walk, biking, and to drive
D. To walk, to bike, and also driving
4. When you cross the street in the middle of the block, this is
an example of jaywalking.
A. When you cross the street in the middle of the block,
this
B. You cross the street in the middle of the block, this
C. Crossing the street in the middle of the block
D. e fact that you cross the street in the middle of the
block
5. Walking by the corner the other day, a child, I noticed, was
watching for the light to change.
A. a child, I noticed, was watching
B. I noticed a child watching
C. a child was watching, I noticed,
D. there was, I noticed, a child watching
6. Going back to his old school, everything there looked
smaller than Don remembered.
A. Going back to his old school,
B. When he went back to his old school,
C. To go back to his old school,
D. As he went back to his old school,
7. Painting, drawing and to sculpt are some of the techniques
artists such as Picasso used to express themselves.
A. Painting, drawing and to sculpt
B. To paint, to draw, and sculpting
C. Painting, drawing, and sculpting
D. To paint, draw, and sculpting
8. Playing sports in school which is an activity meant to teach
teamwork and leadership skills students can use later in life.
A. which is an activity
B. is an activity because it is
C. being an activity which is
D. is an activity
9. Glancing at his watch, Daniel picked up his speed.
A. Glancing at his watch,
B. He glanced at his watch, and
C. To glance at his watch,
D. He glanced at his watch,
10. For a snake, shedding their skin up to eight times a year is
part of a natural process.
A. For a snake, shedding their skin
B. A snake’s shedding its skin
C. When a snake sheds its skin
D. To shed its skin, for snakes
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
2
11. I was surprised by the noise peering through the window to
see who was at the door.
A. I was surprised by the noise peering
B. I was surprised by the noise, peered
C. e noise surprised me, peering
D. Surprised by the noise, I peered
Directions for questions 12–22
Rewrite the sentence in your head following the
directions given below. Keep in mind that your new
sentence should be well written and should have
essentially the same meaning as the original sentence.
12. It is easy to carry solid objects without spilling them, but the
same cannot be said of liquids.
Rewrite, beginning with
Unlike liquids,
e next words will be
A. it is easy to
B. we can easily
C. solid objects can easily be
D. solid objects are easy to be
13. Although the sandpiper is easily frightened by noise and
light, it will bravely resist any force that threatens its nest.
Rewrite, beginning with
e sandpiper is easily frightened by noise and light,
e next words will be
A. but it will bravely resist
B. nevertheless bravely resisting
C. and it will bravely resist
D. even if bravely resisting
14. If he had enough strength, Todd would move the boulder.
Rewrite, beginning with
Todd cannot move the boulder
e next words will be
A. when lacking
B. because he
C. although there
D. without enough
15. e band began to play, and then the real party started.
Rewrite, beginning with
e real party started
e next words will be
A. aer the band began
B. and the band began
C. although the band began
D. the band beginning
16. Chris heard no unusual noises when he listened in the park.
Rewrite, beginning with
Listening in the park,
e next words will be
A. no unusual noises could be heard
B. then Chris heard no unusual noises
C. and hearing no unusual noises
D. Chris heard no unusual noises
17. It is unusual to see owls during the daytime, since they are
nocturnal animals.
Rewrite, beginning with
Being nocturnal animals,
e next words will be
A. it is unusual to see owls
B. owls are not usually seen
C. owls during the daytime are
D. it is during the daytime that
18. If I want your opinion, I will ask for it.
Rewrite, beginning with
I won’t ask for your opinion
e next words will be
A. if I want it
B. when I want it
C. although I want it
D. unless I want it
19. It began to rain, and everyone at the picnic ran to the trees
to take shelter.
Rewrite, beginning with
Everyone at the picnic ran to the trees to take shelter
e next words will be
A. beginning to rain
B. when it began to rain
C. although it began to rain
D. and it began to rain
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
3
20. Lucy saw an amazing sight when she witnessed her rst
sunrise.
Rewrite, beginning with
Witnessing her rst sunrise,
e next words will be
A. an amazing sight was seen
B. when Lucy saw an amazing sight
C. Lucy saw an amazing sight
D. seeing an amazing sight
21. Aer three hours of walking the museum, the entire family
felt in need of a rest.
Rewrite, beginning with
e entire family felt in need of a rest
e next words will be
A. walking through the museum for three hours
B. having walked through the museum for three hours
C. and they walked through the museum for three hours
D. despite having walked through the museum for three
hours
22. e big celebration meal was over, and everyone began to
feel sleepy.
Rewrite, beginning with
Everyone began to feel sleepy
e next words will be
A. and the big celebration meal
B. before the big celebration meal
C. aer the big celebration meal
D. although the big celebration meal
Reading Comprehension
In an ACCUPLACER placement test, there are
20 questions of two primary types in Reading
Comprehension.
• e rst type of question consists of a reading
passage followed by a question based on the text.
Both short and long passages are provided. e
reading passages can also be classied according
to the kind of information processing required,
including explicit statements related to the main
idea, explicit statements related to a secondary
idea, application, and inference.
• e second type of question, sentence
relationships, presents two sentences followed by a
question about the relationship between these two
sentences. e question may ask, for example, if
the statement in the second sentence supports that
in the rst, if it contradicts it, or if it repeats the
same information.
Reading Comprehension
Sample Questions
Directions for questions 1–9
Read the statement or passage and then choose the best
answer to the question. Answer the question based on
what is stated or implied in the statement or passage.
1. In the words of omas De Quincey, “It is notorious that
the memory strengthens as you lay burdens upon it.” If,
like most people, you have trouble recalling the names of
those you have just met, try this: e next time you are
introduced, plan to remember the names. Say to yourself,
“I’ll listen carefully; I’ll repeat each person’s name to be
sure I’ve got it, and I will remember.” You’ll discover how
eective this technique is and probably recall those names
for the rest of your life.
e quotation from De Quincey indicates that the memory
A. always operates at peak eciency
B. breaks down under great strain
C. improves if it is used oen
D. becomes unreliable if it tires
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
4
2. Unemployment was the overriding fact of life when
Franklin D. Roosevelt became president of the United States
on March 4, 1933. At the time, the government did not
systematically collect statistics of joblessness; actually it did
not start doing so until 1940. e Bureau of Labor Statistics
later estimated that 12,830,000 persons were out of work in
1933, about one-fourth of a civilian labor force of more than
51 million.
Roosevelt signed the Federal Emergency Relief Act on May
12, 1933. e president selected Harry L. Hopkins, who
headed the New York relief program, to run FERA. A gied
administrator, Hopkins quickly put the program into high
gear. He gathered a small sta in Washington and brought
the state relief organizations into the FERA system. While
the agency tried to provide all the necessities, food came
rst. City dwellers usually got an allowance for fuel, and
rent for one month was provided in case of eviction.
is passage is primarily about
A. methods of estimating unemployment rates in the
1930s
B. the eect of unemployment on United States families
C. President Franklin D. Roosevelt’s presidency
D. the creation of President Roosevelt’s FERA program
3. With varying success, many women around the world
today struggle for equal rights. Historically, women have
achieved greater equality with men during periods of social
adversity. e following factors initiated the greatest number
of improvements for women: violent revolution, world war,
and the rigors of pioneering in an undeveloped land. In all
three cases, the essential element that improved the status
of women was a shortage of men, which required women to
perform many of society’s vital tasks.
We can conclude from the information in this passage that
A. women today are highly successful in winning equal
rights
B. only pioneer women have been considered equal to
men
C. historically, women have only achieved equality
through force
D. historically, the principle of equality alone has not been
enough to secure women equal rights
4. All water molecules form six-sided structures as they freeze
and become snow crystals. e shape of a snow crystal is
determined by temperature, vapor, and wind conditions in
the upper atmosphere. A snow crystal is always symmetrical
because these conditions aect all six of its sides
simultaneously.
e purpose of the passage is to present
A. a personal observation
B. a solution to a problem
C. factual information
D. opposing scientic theories
5. In the words of omas De Quincey, “It is notorious that
the memory strengthens as you lay burdens upon it.” If,
like most people, you have trouble recalling the names of
those you have just met, try this: e next time you are
introduced, plan to remember the names. Say to yourself,
“I’ll listen carefully; I’ll repeat each person’s name to be sure
I have it, and I will remember.” You’ll discover how eective
this technique is and probably recall those names for the rest
of your life.
e passage suggests that people remember names best
when they
A. meet new people
B. are intelligent
C. decide to do so
D. are interested in people
6. Many people have owned, or have heard of, traditional
“piggy banks,” coin banks shaped like pigs. A logical theory
about how this tradition started might be that because pigs
oen symbolize greed, the object is to “fatten” one’s piggy
bank with as much money as possible.
However, while this idea makes sense, it is not the correct
origin of the term. e genesis of the piggy bank is the old
English word “pygg,” which was a common kind of clay
hundreds of years ago in England. People used pots and jars
made out of this red “pygg” clay for many dierent purposes
in their homes. Sometimes they kept their money in one of
the pots, and this was known as a pygg bank. Over the years,
because “pygg” and “pig” sounded the same, glaziers began
making novelty banks out of pottery in the shape of a pig as
a kind of joke. ese banks were given as gis and exported
to countries where people spoke other languages and where
no one had ever heard of pygg clay. e tradition caught on
all over the world, and today piggy banks come in all colors
and are made of all kinds of materials, including plastic.
is passage is mainly about how
A. people in dierent countries save their money
B. people in England made pottery centuries ago
C. a common term originated in a surprising way
D. an unusual custom got started
7. e wheel is considered one of the most important
mechanical inventions of all time. Many technologiessince
the invention of the wheel have been based on its principles,
and since the industrial revolution, the wheel has been
a basic element of nearly every machine constructed by
humankind. No one knows the exact time and place of the
invention of the wheel, but its beginnings can be seen across
many ancient civilizations.
e passage suggests that the wheel is an important
invention because it
A. is one of the world’s oldest inventions
B. forms the basis of so many later inventions
C. can be traced to many ancient cultures
D. is one the world’s most famous inventions
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
5
8. Samuel Morse, best known today as the inventor of
Morse Code and one of the inventors of the telegraph,
was originally a prominent painter. While he was always
interested in technology and studied electrical engineering
in college, Morse went to Paris to learn from famous artists
of his day and later painted many pictures that now hang
in museums, including a portrait of former President John
Adams. In 1825, Morse was in Washington, D.C., painting
a portrait of the Marquis de Lafayette when a messenger
arrived on horseback to tell him that his wife was gravely
ill back at his home in Connecticut. e message had taken
several days to reach him because of the distance. Morse
rushed to his home as fast as he could, but his wife had
already passed away by the time he arrived. Grief-stricken,
he gave up painting and devoted the rest of his life to nding
ways to transmit messages over long distances faster.
Morse le the art world and helped to invent the telegraph
because he
A. was tired of painting
B. wanted to communicate with people far away
C. experienced a personal tragedy in his life
D. was fascinated by science
9. Leonardo da Vinci is not only one of the most famous
artists in history, but he was also a botanist, a writer, and
an inventor. Even though most of his inventions were
not actually built in his lifetime, many of today’s modern
machines can be traced back to some of his original designs.
e parachute, the military tank, the bicycle, and even the
airplane were foretold in the imaginative drawings that can
still be seen in the fragments of da Vinci’s notebooks. Over
500 years ago, this man conceived ideas that were far ahead
of his time.
e author of this passage is praising da Vinci primarily
for his
A. artistic talent
B. intelligence
C. foresight
D. fame
Directions for questions 10–18
For the questions that follow, two underlined sentences
are followed by a question or statement. Read the
sentences, then choose the best answer to the question or
the best completion of the statement.
10. e Midwest is experiencing its worst drought in 15 years.
Corn and soybean prices are expected to be very high this
year.
What does the second sentence do?
A. It restates the idea found in the rst.
B. It states an eect.
C. It gives an example.
D. It analyzes the statement made in the rst.
11. Social studies classes focus on the complexity of our social
environment.
e subject combines the study of history and the social
sciences and promotes skills in citizenship.
What does the second sentence do?
A. It expands on the rst sentence.
B. It makes a contrast.
C. It proposes a solution.
D. It states an eect.
12. Knowledge of another language fosters greater awareness of
cultural diversity among the peoples of the world.
Individuals who have foreign language skills can appreciate
more readily other peoples’ values and ways of life.
How are the two sentences related?
A. ey contradict each other.
B. ey present problems and solutions.
C. ey establish a contrast.
D. ey repeat the same idea.
13. While most people think of dogs as pets, some dogs are bred
and trained specically for certain types of work.
e bloodhound’s acute sense of smell and willing
personality make it ideal for tracking lost objects or people.
What does the second sentence do?
A. It makes a contrast.
B. It restates an idea found in the rst.
C. It states an eect.
D. It gives an example.
14. Paris, France, is a city that has long been known as a center
of artistic and cultural expression.
In the 1920s, Paris was home to many famous artists
and writers from around the world, such as Picasso and
Hemingway.
What does the second sentence do?
A. It reinforces the rst.
B. It states an eect.
C. It draws a conclusion.
D. It provides a contrast.
15. Studies show that the prevalence of fast-food restaurants
corresponds with the rates of obesity in both children and
adults.
Obesity is now on the rise in countries where fast-food
restaurants are becoming more common.
How do the two sentences relate?
A. ey express roughly the same idea.
B. ey contradict each other.
C. ey present problems and solutions.
D. ey establish a contrast.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
6
16. Compared with the rest of the country, North Dakota has
a thriving economy, making it a place where more people
want to live.
With temperatures in January ranging from 2 to 17 degrees
Fahrenheit, winters in North Dakota are viewed by some
prospective residents as inhospitable.
What does the second sentence do?
A. It reinforces the rst.
B. It explains what is stated in the rst.
C. It contradicts the rst.
D. It analyzes a statement made in the rst.
17. Some stores are testing a new checkout system that allows
shoppers to use their mobile phones to scan items as they
walk through stores and pay at self-service kiosks, skipping
the cashiers’ lines.
e new mobile checkout system reduces long lines and
customer wait times in stores.
What does the second sentence do?
A. It expands on the rst.
B. It states an eect.
C. It contrasts with the rst.
D. It gives an example.
18. According to the American Sleep Disorders Association, the
average teenager needs around 9.5 hours of sleep per night,
possibly because critical growth hormones are released
during sleep.
e average adult requires between six and eight hours of
sleep per night for optimal health and productivity.
How do the two sentences relate?
A. ey establish a contrast.
B. ey contradict each other.
C. ey reinforce each other.
D. ey provide a problem and solution.
WritePlacer
®
is test measures your ability to write eectively,
which is critical to academic success.
Your writing sample will be scored on the basis of
how eectively it communicates a whole message to
the readers for the stated purpose. Your score will be
based on your ability to express, organize and support
your opinions and ideas, not the position you take on
the essay topic. e following ve characteristics of
writing will be considered:
• Focus — e clarity with which you maintain
your main idea or point of view
• Organization — e clarity with which you
structure your response and present a logical
sequence of ideas
• Development and Support — e extent to which
you elaborate on your ideas and the extent to
which you present supporting details
• Sentence Structure — e eectiveness of your
sentence structure
• Mechanical Conventions — e extent to which
your writing is free of errors in usage and
mechanics
WritePlacer Sample Topic
Prepare a multiple-paragraph writing sample of about
300–600 words on the topic below. You should use the
time available to plan, write, review and edit what you
have written. Read the assignment carefully before you
begin to write.
Some schools require each student to participate in an
organized school sport chosen by the student. People at
these schools argue that athletics is an important part
of the educational experience and that there should be a
rule requiring participation. Others argue that students
should be free to decide whether or not they wish to
participate in organized school sports. Write an essay
for a classroom instructor in which you take a position
on whether participation in organized school athletics
should be required. Be sure to defend your position
with logical arguments and appropriate examples. Your
essay must be 300–600 words in length.
Arithmetic
ere are 17 questions administered on the
Arithmetic test, divided into the following content
areas:
• Operations with whole numbers and
fractions. Topics include addition, subtraction,
multiplication, division, recognizing equivalent
fractions and mixed numbers, and estimating.
• Operations with decimals and percents. Topics
include addition, subtraction, multiplication,
and division with decimals; percent problems;
recognition of decimals; percent equivalencies;
and estimating.
• Applications and problem solving. Topics include
rate, percent and measurement problems; simple
geometry problems; and distribution of a quantity
into its fractional parts.
Arithmetic Sample Questions
For each of the questions below, choose the best answer
from the four choices given. You may use the paper you
received as scratch paper.
1. 2.75 + 0.003 + 0.158 =
A. 0.436
B. 2.911
C. 2.938
D. 4.36
2. 7.86 × 4.6 =
A. 36.156
B. 36.216
C. 351.56
D. 361.56
7
3. =
20
A. 0.035
B. 0.35
C. 0.858
D. 3.5
4.
A. 0.105
B. 0.501
C. 0.015
D.
Which of the following is the least?
0.15
5. All of the following are ways to write 25 percent of N
EXCEPT
A. (0.25)N
25
B. N
100
1
C. N
4
D. 25N
6. Which of the following is closest to 27.8 × 9.6?
A. 280
B. 300
C. 2,800
D. 3,000
7. A soccer team played 160 games and won 65 percent of
them. How many games did the team win?
A. 94
B. 104
C. 114
D. 124
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
7
8. ere are 3 people who work full-time and are to work
together on a project, but their total time on the project is to
be equivalent to that of only one person working full-time. If
one of the people is budgeted for
1
of his time to the project
2
and a second person for
1
3
of her time, what part of the third
worker’s time should be budgeted to this project?
1
A.
8
1
B.
6
1
C.
3
3
D.
5
9. 32 is 40% of what number?
A. 12.8
B. 128
C. 80
D. 800
10. 3
1
3
– 2
2
=
5
1
A.
15
14
B.
15
C. 1
15
1
D. 1
2
1
11. 2
1
2
+ 4
2
=
3
A. 6
1
6
B. 6
5
6
C. 7
1
6
D. 7
5
6
12. What is
1,345
rounded to the nearest integer?
99
A. 12
B. 13
C. 14
D. 15
13. ree of four numbers have a sum of 22. If the average of
the four numbers is 8, what is the fourth number?
A. 4
B. 6
C. 8
D. 10
14. 46.2 × 10
–2
=
A. 0.0462
B. 0.462
C. 4.62
D. 462
15. If
3
÷
1
= n, then n is between
2 4
A. 1 and 3
B. 3 and 5
C. 5 and 7
D. 7 and 9
16. What is 12% of 120?
A. 10
B. 14.4
C. 18.4
D. 28.8
17. A box in a college bookstore contains books, and each book
in the box is a history book, an English book or a science
book. If
1
of these books are history books and
1
are
3 6
English books, what fraction of the books are science books?
1
A.
3
1
B.
2
2
C.
3
3
D.
4
18. e measures of two angles of a triangle are 35° and 45°.
What is the measure of the third angle of the triangle?
A. 95°
B. 100°
C. 105°
D. 110°
19. Erica bought 3
1
2
yards of fabric. If she uses
2
3
of the fabric to
make a curtain, how much will she have le?
A.
1
yard
6
1
B.
3
yard
C. 1
1
yards
6
D. 2
1
yards
3
20. Jen wants to tile the oor of her kitchen. e oor is
rectangular and measures 12 feet by 8 feet. If it costs $2.50
per square foot for the materials, what is the total cost of the
materials for tiling the kitchen oor?
A. $160
B. $200
C. $220
D. $240
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
8
A. πR
2
B. π(R – 3)
2
C. πR
2
– π × 3
2
D. πR
2
– π(R – 3)
2
A. 9x
2
– 4y
2
B. 9x
2
+ 4y
2
C. 9x
2
– 6xy + 4y
2
D. 9x
2
– 12xy + 4y
2
Elementary Algebra Elementary Algebra
Sample Questions
ere are 12 questions administered on the Elementary
Algebra test, divided into the following content areas:
• Numbers and quantities. Topics include integers
and rational numbers, computation with
integers and negative rationals, absolute value,
and ordering.
• Algebraic expressions. Topics include evaluation
of simple formulas and expressions, adding
and subtracting monomials and polynomials,
multiplying and dividing monomials and
polynomials, evaluating positive rational roots
and exponents, simplifying algebraic fractions,
and factoring.
• Problem solving. Topics include translating
written phrases into algebraic expressions,
solving linear equations and inequalities,
quadratic equations (by factoring), and verbal
problems presented in an algebraic context.
For each of the questions below, choose the best answer
from the four choices given. You may use the paper you
received as scratch paper.
1. If A represents the number of apples purchased at 15 cents
each, and B represents the number of bananas purchased
at 10 cents each, which of the following represents the total
value of the purchases in cents?
A. A + B
B. 25(A + B)
C. 10A + 15B
D. 15A + 10B
2. √2 × √ 15 = ?
A. √17
B. √30
C. 17
D. 30
3. What is the value of the expression 2x
2
+ 3xy – 4y
2
when
x = 2 and y = –4?
A. –80
B. –32
C. 32
D. 80
4. In the gure below, both circles have the same center, and
the radius of the larger circle is R. If the radius of the smaller
circle is 3 units less than R, which of the following represents
the area of the shaded region?
5. (3x – 2y)
2
=
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
9
10x
6
+ 8x
4
=
2x
2
A. 9x
12
B. 14x
4
C. 5x
4
+ 4x
2
D. 5x
3
+ 2x
2
A. 2p + 1 exercises per hour
B. 3p – 1 exercises per hour
2
C.
3
p exercises per hour
3
D.
2
p exercises per hour
5 3
2
2
– 2
2
=
1
A. 2
2
B. 2
3
C. 2
2
5
D. 2
3
E. 2
2
College-Level Mathematics
18.
ere are 20 questions administered on the College-
Level Mathematics test, divided into the following
content areas:
19. A rectangular yard has area 96 square feet. If the width of
the yard is 4 feet less than the length, what is the perimeter,
in feet, of the yard?
A. 40
B. 44
C. 48
D. 52
20. On Monday, it took Helen 3 hours to do a page of science
homework exercises. e next day she did the same number
of exercises in 2 hours. If her average rate on Monday was p
exercises per hour, what was her average rate the next day, in
terms of p?
• Algebraic operations. Topics include simplifying
rational algebraic expressions, factoring and
expanding polynomials, and manipulating roots
and exponents.
• Solutions of equations and inequalities. Topics
include solving linear and quadratic equations
and inequalities, systems of equations and other
algebraic equations.
• Coordinate geometry. Topics include plane
geometry, the coordinate plane, straight lines,
conics, sets of points in the plane, and algebraic
function graphs.
• Functions. Topics include polynomial, algebraic,
exponential, and logarithmic functions.
• Trigonometry. Topics include trigonometric
functions.
• Applications and other topics. Topics include
complex numbers, series and sequences,
determinants, permutations and combinations,
factorials, and word problems.
College-Level Mathematics
Sample Questions
For each of the questions below, choose the best answer
from the ve choices given. You may use the paper you
received as scratch paper.
1.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
11
1
a ≠ b and
x
1
+
a
1
=
b
, then x =
1
1
A. –
b
a
B. b – a
1
C.
ab
a – b
D.
ab
ab
E.
a – b
1
3x
2
– 2x + 7 = 0, then x –
3
)
2
=
20
A.
9
7
B.
9
7
C. –
9
8
D. –
9
20
E. –
9
A. 4√130
B. 20√10
C. 24√5
D. 100
E. 104√5
125
5
A. 3
10
B. 1,000
C. 30
10
D.
3
3
E.
10
x –1
f (x) = 2x + 1 and g(x) = , then f (g(x)) =
2
A. x
x –1
B.
4x + 2
4x +2
C.
x –1
5x +1
D.
2
(2x + 1)(x – 1)
E.
2
A. –1
B. 0
1
C.
2
√3
D.
2
E. 2
2. If
3. I
f (
4. e graph of which of the following equations is a straight
line parallel to the graph of y = 2x ?
A. 4x – y = 4
B. 2x – 2y = 2
C. 2x – y = 4
D. 2x + y = 2
E. x – 2y = 4
5. An equation of the line that contains the origin and the
point (1, 2) is
A. y = 2x
B. 2y = x
C. y = x –1
D. y = 2x +1
E.
y
= x –1
2
6. An apartment building contains 12 units consisting of
one- and two-bedroom apartments that rent for $360 and
$450 per month, respectively. When all units are rented,
the total monthly rental is $4,950. What is the number of
two-bedroom apartments?
A. 3
B. 4
C. 5
D. 6
E. 7
7. If the two square regions in the gures below have the
respective areas indicated in square yards, how many yards
of fencing are needed to enclose the two regions? (Assume
the regions are fenced separately.)
8. If log
10
x = 3, then x =
9. If
10. If θ is an acute angle and sin θ =
2
1
, then cos θ =
11. 5y(2y – 3) + (2y – 3) =
A. (5y + 1) (2y + 3)
B. (5y + 1) (2y – 3)
C. (5y – 1) (2y + 3)
D. (5y – 1) (2y – 3)
E. 10y (2y – 3)
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
12
A. –3 < x < 3
B. x < –3 or x > 3
C. x = –3 or x = 3
D. 0 < x < 6
E. For no real numbers x
1 29
A.
2
5
17
B.
2
1
29
C.
2
5
17
D.
2
5
29
E.
2
A. –
r
s
B.
r
s
C. rs
D. r
E. −s
f (x) =
3x – 1
and f
–1
f
–1
(3)?
1
A.
3
2
B.
3
C. 1
D. 2
7
E.
3
+ 2 for n = 0, 1, 2, ... . a
n + 1
= 2a
n
f (x) =
(
1
)
x
3
A. f (a) + f (b) = 3
B. f (a) +
1
= f (b)
3
C. f (a) = f (b)
D. f (a) < f (b)
E. f (a) > f (b)
12. For what real numbers x is the value of x
2
– 6x + 9 negative?
13. A root of x
2
– 5x – 1 = 0 is
14. In the xy-plane, the graph of y = x
2
and the circle with
center (0, 1) and radius 3 have how many points of
intersection?
A. None
B. One
C. Two
D. ree
E. More than three
15.
y
x
(0, r)
0
(s, 0)
If an equation of the linear function in the gure above is
y = mx + b, then m =
16
. One ordering of the letters T, U, V, and W from le to right
is UTVW. What is the total number of orderings of these
letters from le to right, including UTVW?
A. 8
B. 12
C. 16
D. 20
E. 24
17. If is the inverse of f, wh
at is the value of
2
18. e sequence {a
n
} is dened by a
o
= 1 and
What is the value
of a
3
?
A. 8
B. 10
C. 16
D. 20
E. 22
19. From 5 employees at a company, a group of 3 employees will
be chosen to work on a project. How many dierent groups
of 3 employees can be chosen?
A. 3
B. 5
C. 6
D. 10
E. 15
20. If and a < b, which of the following must be
true?
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
13
ESL Reading Skills
e ESL Reading Skills test measures your ability
to read English. Specically, it assesses your
comprehension of short passages. It contains brief
passages of 50 words or less and moderate length
passages of 50 to 90 words. Half of this test contains
straightforward comprehension items (paraphrase,
locating information, vocabulary on a phrase level,
and pronoun reference). e other half assesses
inference skills (main idea, fact versus opinion,
cause/eect logic, identifying irrelevant information,
author’s point of view and applying the author’s logic
to another situation).
ESL 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 rst 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 dierent 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. Dierent individuals have dierent ways of acquiring
information.
3. If you hold a piece of copper wire over the ame of a wooden
match, heat will be conducted by the copper wire to your
ngers, 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.
4. Many people own dierent pets. Dogs, cats, birds, and sh
are common household pets. Others pets are considered
to be exotic animals. ese 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 inuential 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.
e passage indicates that Chavez changed lives by
A. helping to end the farmworkers’ strikes
B. ghting 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
Shulz 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. e comic strip Peanuts featured children as its only
characters.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
14
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 oen than cash. Many people
today do all of their banking on the Internet rather than
going to the bank in person.
e 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 rst 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 rst aid, and I can help
until an ambulance arrives. Is that okay?”
According to the passage, it is wrong to
A. use rst 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 rst female
Hispanic astronaut. Her inventions include technology to
help robots inspect equipment in space to maintain safety
and quality control on spacecra. Before retiring, she
logged more than 1,000 hours in space across several space
missions.
According to the passage, Dr. Ochoa is the rst
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
10. Dogs and cats make very dierent 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 aectionate
companions, but they require more care and attention. ey
must be taken out several times a day and should not be
le alone for more than a few hours. Larger dogs require
signicant exercise to remain t and healthy. Cats are
usually more independent in nature and interact less with
their owners. Also, a cat can be le 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
ESL Sentence Meaning
e ESL Sentence Meaning test measures how well
you understand the meaning of sentences in English.
It assesses the understanding of word meanings in
one- or two-sentence contexts. e sentences are
drawn from the subject areas of natural science,
history/social studies, arts/humanities, psychology/
human relations, and practical situations. ere 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.
ESL Sentence Meaning
Sample Questions
Directions for questions 1–8
e 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. e 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 aer
his death, Ibrahim Ferrer one of the most beautiful
voices in Latin music.
A. had
B. have
C. have had
D. having
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
15
4. Aer we saw the play, we had dierent opinions
Vincent’s performance.
A. about
B. at
C. for
D. to
5. Having recorded many of the most beloved songs of the
1940s, 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
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 indenitely.
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
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 ight, 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. Selsh
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
16
ESL Language Use
e ESL Language Use test measures your prociency
in using correct grammar in English sentences. ere
are ve content areas measured on this test: (a) Nouns,
Pronouns, Pronoun Case Structure; (b) Subject-Verb
Agreement; (c) Comparatives, Adverbs, Adjectives;
(d) Verbs; and (e) Subordination/Coordination.
ESL Language Use Sample
Questions
Directions for questions 1–10
e sentence below has a blank space. Choose the word
or phrase that makes a grammatically correct sentence.
1. washing his sweater, Jacob hung it up to dry.
A. Aer
B. Before
C. By
D. Until
2. Dr. O’Hara is certain that some day, men and women will
to Mars.
A. travel
B. travels
C. traveling
D. traveled
3. Water at a temperature of zero degrees Celsius.
A. having frozen
B. freezing
C. freeze
D. freezes
4. you get a new haircut?
A. Have
B. Does
C. Are
D. Did
5. Jacques Cousteau will be remembered for his inventions and
for to marine science.
A. dedication
B. his dedication
C. being dedicated
D. his being dedicated
6. e children, who were tired of traveling, kept asking,
“When we get to the hotel?”
A. have
B. will
C. did
D. are
7. Galileo is most famous that Earth revolves around
the Sun, rather than the other way around.
A. for having discovered
B. for discovery
C. his discovery
D. in discovering
8. Men and women sometimes have diculty understanding
each other because they dierently.
A. communicate
B. communicated
C. have communicated
D. communicates
9. you can speak more than one language, you have
the opportunity to make more new friends.
A. So
B. Before
C. When
D. ough
10. Light faster than sound, which is why you see
lightning before you hear the thunder.
A. traveling
B. travels
C. having traveled
D. will travel
Directions for questions 11–15
Read the two sentences below and choose the best way
of combining them.
11. Lisa plays the piano. Her sister Kelly plays the piano, too.
A. Lisa and her sister Kelly plays the piano.
B. Both Lisa and her sister Kelly play the piano.
C. Lisa plays the piano and Kelly plays the piano.
D. Lisa and Kelly too play the piano.
12. Kazuko took her dog for a walk. ey went to the park.
A. Kazuko, going to the park, took her dog for a walk.
B. Kazuko took her dog for a walk to the park.
C. Kazuko took her dog for a walk because they went to
the park.
D. Kazuko and her dog went to the park, where she and
the dog walked.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
17
13. We knew it might get chilly at the football game. We brought
along some extra blankets.
A. We knew it might get chilly at the football game when
we brought along some extra blankets.
B. Bringing along some extra blankets, we knew it might
get chilly at the football game.
C. We brought along some extra blankets because we
knew it might get chilly at the football game.
D. It got chilly at the football game and we brought along
some extra blankets.
14. Juan loves to play baseball. His friend Miguel enjoys
baseball, too.
A. Both Juan and his friend Miguel enjoy playing baseball.
B. Juan and his friend Miguel enjoys playing baseball.
C. Juan enjoys playing baseball and his friend Miguel, too.
D. Juan loves baseball and Miguel too enjoys baseball.
15. Wolves are pack animals. ey are rarely spotted alone.
A. Wolves are rarely spotted alone if they are pack ani-
mals.
B. Being pack animals, wolves are rarely spotted alone.
C. Aer being pack animals, wolves are rarely spotted
alone.
D. Wolves are rarely spotted alone, although they are pack
animals.
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
18
Answer Key
SENTENCE SKILLS
QUESTION
NUMBER
CORRECT
ANSWER
1 D
2 A
3 B
4 C
5 B
6 B
7 C
8 D
9 A
10 B
11 D
12 C
13 A
14 B
15 A
16 D
17 B
18 D
19 B
20 C
21 B
22 C
READING COMPREHENSION
QUESTION
NUMBER
CORRECT
ANSWER
1 C
2 D
3 D
4 C
5 C
6 C
7 B
8 C
9 C
10 B
11 A
12 D
13 D
14 A
15 A
16 C
17 B
18 A
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
19
Answer Key
ARITHMETIC
QUESTION
NUMBER
CORRECT
ANSWER
1 B
2 A
3 B
4 C
5 D
6 A
7 B
8 B
9 C
10 B
11 C
12 C
13 D
14 B
15 C
16 B
17 B
18 B
19 C
20 D
ELEMENTARY ALGEBRA
QUESTION
NUMBER
CORRECT
ANSWER
1 D
2 B
3 A
4 D
5 D
6 B
7 A
8 B
9 D
10 A
11 B
12 C
13 B
14 C
15 C
16 A
17 A
18 C
19 A
20 D
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
20
Answer Key
COLLEGE-LEVEL MATHEMATICS
QUESTION
NUMBER CORRECT ANSWER
1 C
2 E
3 E
4 C
5 A
6 E
7 C
8 B
9 A
10 D
11 B
12 E
13 E
14 C
15
"
16 E
17 E
18 E
19 D
20 E
ESL READING SKILLS
QUESTION
NUMBER CORRECT ANSWER
1 C
2 D
3 A
4 A
5 D
6 C
7 A
8 B
9 D
10 A
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
21
© 2016 The College Board. ACCUPLACER SAMPLE QUESTIONS
22
ESL SENTENCE MEANING
QUESTION
NUMBER CORRECT ANSWER
1 D
2 A
3 A
4 A
5 C
6 D
7 A
8 C
9 D
10 D
11 B
12 C
13 D
14 B
15 C
ESL LANGUAGE USE
QUESTION
NUMBER CORRECT ANSWER
1 A
2 A
3 D
4 D
5 B
6 B
7 A
8 A
9 C
10 B
11 B
12 B
13 C
14 A
15 B
Answer Key