ACCUPLACER
®
Sample Questions for Students
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© 2012 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 is 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 is 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 classied 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 1–12
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. Since 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
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
2
11. To appear white or colorless, light is actually composed of an
entire spectrum of colors.
A. To appear white or colorless,
B. In appearing white or colorless,
C. As it appears white or colorless,
D. While it appears white or colorless,
12. 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 13–25
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.
13. 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
14. 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
15. 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
16. e band began to play, and then the real party started.
Rewrite, beginning with
e real party started
e next words will be
A. aer the band began
B. and the band began
C. although the band began
D. the band beginning
17. 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
18. 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
19. While bear attacks on humans are extremely rare, most
occur when a mother bear’s cubs are approached.
Rewrite, beginning with
Bear attacks on humans are extremely rare,
e next words will be
A. but approaching a mother bear’s cubs
B. and approaching a mother bear’s cubs
C. even though approaching a mother bear’s cubs
D. nevertheless approaching a mother bear’s cubs
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
3


20. 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
21. 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 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
22. 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
23. Aer 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.
24. Bats see extremely well in the dark; in fact, much better than
humans.
Rewrite, beginning with
Unlike bats,
e next words will be
A. humans can see
B. humans do not see
C. it is not easy to see
D. seeing is dicult
25. 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. aer the big celebration meal
D. although the big celebration meal
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
4
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 classied 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
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 DeQuincey, “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
eective this technique is and probably recall those names
for the rest of your life.
e main idea of the paragraph maintains that the memory
A. always operates at peak eciency.
B. breaks down under great strain.
C. improves if it is used oen.
D. becomes unreliable if it tires.
2. Unemployment was the overriding fact of life when
Franklin D. Roosevelt became president of the United
States on March 4, 1933. An anomaly of the time was that
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 gied
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. unemployment in the 1930s.
B. the eect of unemployment on United States families.
C. President Franklin D. Roosevelt’s presidency.
D. President Roosevelt’s FERA program.
3. It is said that a smile is universally understood. And nothing
triggers a smile more universally than a taste of sugar.
Nearly everyone loves sugar. Infant studies indicate that
humans are born with an innate love of sweets. Based on
statistics, a lot of people in Great Britain must be smiling
because on average, every man, woman, and child in that
country consumes 95 pounds of sugar each year.
From this passage it seems safe to conclude that the English
A. do not know that too much sugar is unhealthy.
B. eat desserts at every meal.
C. are fonder of sweets than most people.
D. have more cavities than any other people.
4. 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.
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
5
5. In 1848, Charles Burton of New York City made the rst
baby carriage, but people strongly objected to the vehicles
because they said the carriage operators hit too many
pedestrians. Still convinced that he had a good idea, Burton
opened a factory in England. He obtained orders for the
baby carriages from Queen Isabella II of Spain, Queen
Victoria of England, and the Pasha of Egypt. e United
States had to wait another 10 years before it got a carriage
factory, and only 75 carriages were sold in the rst year.
Even aer the success of baby carriages in England,
A. Charles Burton was a poor man.
B. Americans were still reluctant to buy baby carriages.
C. Americans purchased thousands of baby carriages.
D. the United States bought more carriages than any other
country.
6. All water molecules form six-sided structures as they freeze
and become snow crystals. e shape of the crystal is
determined by temperature, vapor, and wind conditions in
the upper atmosphere. Snow crystals are always symmetrical
because these conditions aect all six sides simultaneously.
e purpose of the passage is to present
A. a personal observation.
B. a solution to a problem.
C. actual information.
D. opposing scientic theories.
7. In the words of omas DeQuincey, “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 eective
this technique is and probably recall those names for the rest
of your life.
e writer believes people remember names best when they
a. meet new people
b. are intelligent
c. decide to do so
d. are interested in people
8. 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
oen 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 dierent 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 gis 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
A. how people in dierent countries save their money
B. how people in England made pottery centuries ago
C. how a common expression began in a surprising way
D. how an unusual custom got started
9. It is said that a smile is universally understood. And nothing
triggers a smile more universally that the taste of sugar.
Nearly everyone loves sugar. Infant studies indicate that
humans are born with an innate love of sweets. Based on
statistics, a lot of people in Great Britain must be smiling
because on average, every man, woman and child in that
country consumes 95 pounds of sugar each year.
is passage implies that the writer thinks that 95 pounds of
sugar per person per year is
A. a surprisingly large amount
B. a surprisingly small amount
C. about what one would expect
D. an unhealthy amount
10. e wheel has been used by humans since nearly the
beginning of civilization and is considered one of the most
important mechanical inventions of all time. Most primitive
technologiessince 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.
According to this passage, the wheel is an important
invention because
a. it is one of the world’s oldest inventions
b. it forms the basis of so many later inventions
c. it is an invention that can be traced to many cultures
d. it is one the world’s most famous inventions
11. 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
A. because he was tired of painting
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
6
B. because he wanted to communicate with people far
away
C. because of a personal tragedy in his life
D. because he was fascinated by science
12. Leonardo DaVinci is not only one of the most famous artists
in history, 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 Leonardo’s notebooks. Over 500 years ago,
this man conceived ideas that were far ahead of his time.
e author of this passage is praising Leonardo DaVinci for
his:
A. artistic talent
B. intelligence
C. vision
D. fame
Directions for questions 13–22
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.
13. 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 eect.
C. It gives an example.
D. It analyzes the statement made in the rst.
14. 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 eect.
15. 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.
16. Serving on a jury is an important obligation of citizenship.
Many companies allow their employees paid leaves of
absence to serve on juries.
What does the second sentence do?
A. It reinforces what is stated in the rst.
B. It explains what is stated in the rst.
C. It expands on the rst.
D. It draws a conclusion about what is stated in the rst.
17. While most people think of dogs as pets, some dogs are bred
and trained specically for certain types of work.
e bloodhound’s acute sense of smell and willing
personality make it ideal for tracking people missing in the
woods.
What does the second sentence do?
A. It makes a contrast.
B. It restates an idea found in the rst.
C. It states an eect.
D. It gives an example.
18. Paris, France, is a city that has always been known as a
center of artistic and cultural expression.
In the 1920s, Paris was home to many artists and writers
from around the world who became famous, such as Picasso
and Hemingway.
What does the second sentence do?
A. It reinforces the rst.
B. It states an eect.
C. It draws a conclusion.
D. It provides a contrast.
19. 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 outside the U.S.,
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.
20. Compared with the rest of the country, North Dakota has
a thriving economy, making it a place where more people
want to live.
Winters in North Dakota are inhospitable, with average
temperatures in January ranging from 2 degrees Fahrenheit
to 17 degrees.
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.
21. 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 is intended to reduce long
lines and customer wait times in stores.
What does the second sentence do?
A. It expands on the rst.
B. It states an eect.
C. It contrasts with the rst.
D. It gives an example.
22. 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.
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
7
Arithmetic
is test measures your ability to perform basic
arithmetic operations and to solve problems that
involve fundamental arithmetic concepts. ere are 17
questions on the Arithmetic tests, divided into three
types.
• Operations with whole numbers and fractions:
Topics included in this category are 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, fraction and percent
equivalencies, and problems involving estimation
are also given.
• 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 + .003 + .158 =
A. 4.36
B. 2.911
C. 0.436
D. 2.938
2. 7.86 × 4.6 =
A. 36.156
B. 36.216
C. 351.56
D. 361.56
7
3. =
20
A. 0.035
B. 0.858
C. 0.35
D. 3.5
4. Which of the following is the least?
A. 0.105
B. 0.501
C. 0.015
D. 0.15
5. All of the following are ways to write 25 percent of N
EXCEPT
A. 0.25 N
25N
B.
100
1
C. N
4
D. 25 N
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 it win?
A. 94
B. 104
C. 114
D. 124
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
8
8. ree people who work full-time 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 one-half of his time to the project and
a second person for one-third of her time, what part of the
third worker’s time should be budgeted to this project?
1
A.
3
3
B.
5
1
C.
6
1
D.
8
9. 32 is 40 percent of what number?
A. 12.8
B. 128
C. 80
D. 800
10. 3
1
3
– 2
2
=
5
A. 1
1
2
1
B.
15
14
C.
15
D. 1
15
1
1 2
11.
2 + 4 =
2 3
A.
6
1
6
B.
6
5
6
C.
D.
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
÷=n
15. If
3 1
,
then
n
is between
24
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 one-third of these books are history books and
one-sixth are 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°
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
9
19. Erica bought
3
1
yards of fabric. If she uses
2
of the fabric
2
3
to make a curtain, how much will she have le?
1
A.
yd.
6
1
B. yd.
3
C.
1
1
yd.
6
2
1
D. yd.
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
Elementary Algebra
A total of 12 questions of three types are administered
in this test.
• e rst type involves operations with integers
and rational numbers, and includes computation
with integers and negative rationals, the use of
absolute values, and ordering.
• e second type involves operations with algebraic
expressions using evaluation of simple formulas
and expressions, and adding and subtracting
monomials and polynomials. Questions involve
multiplying and dividing monomials and
polynomials, the evaluation of positive rational
roots and exponents, simplifying algebraic
fractions, and factoring.
• e third type of question involves translating
written phrases into algebraic expressions and
solving equations, inequalities, word problems,
linear equations and inequalities, quadratic
equations (by factoring), and verbal problems
presented in an algebraic context.
Elementary Algebra
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. 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. √30
D. √17
3. What is the value of the expression 2x
2
+ 3xy – 4y
2
when x =
2 and y = - 4?
A. -80
B. 80
C. -32
D. 32
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?
A. πR
2
B. π(R – 3)
2
C. πR
2
– π × 3
2
D. πR
2
– π(R - 3)
2
5. (3x – 2y)
2
=
A. 9x
2
– 4y
2
B. 9x
2
+ 4y
2
C. 9x
2
+ 4y
2
– 6xy
D. 9x
2
+ 4y
2
– 12xy
– x – 6
6. If x > 2, then
x
2
=
x
2
– 4
x – 3
A.
2
x – 3
B.
x – 2
x – 3
C.
x + 2
3
D.
2
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
10
-5
4 – (-6)
13. For which of the following equations are x = 5 and x = –5
7. =
both solutions?
2
A.
2
5
A. x2 –
x 5x 25 = 0−−
2
B. –
2
5
B.
x + 25 = 0
C. 2
2
C.
x + 10x − 25 = 0
D. – 2
2
D.
x − 25 = 0
8. If 2x – 3(x + 4) = – 5, then x =
u 5u u
14. If
x ≠ 0,
then
+− =
A. 7
x x 5x
B. – 7
C. 17
7x
A.
D.
-17
5u
9. – 3(5 – 6) – 4(2 – 3) =
B.
5u
7x
A. –7
29u
B. 7
C.
C. –1
5x
D. 1
31u
D.
5x
10. Which of the following expressions is equivalent
to 20 –
4
5
x > 16?
A. x ≤ 5
15.
B. x ≥ 5
C. x ≥ 32½
e solution set of which of the following inequalities is
D. x ≤ 32½
graphed on the number line above?
2 − ≥ 3
to greatest?
B.
x 56
11. Which of the following lists of numbers is ordered from least
A.
x 4 −
2 +≤
C.
3x 15−≤
1 3 2 3
A.
−− , ,,
D.
4x −≥ 17
3 5 3 5
3 1 3 2
B.
−− , ,,
16.
2x + 6y = 5
5 3 5 3
x + 3y = 2
1 3 3 2
C.
−− , ,,
How many solutions
( )
,xy
are there to the system of
3 5 5 3
equations above?
3 1 2 3
A. None
D.
, ,,−−
5 3 3 5
B. One
C. Two
D. More than two
12. If
5t +=2 6,
then
t =
17. Which of the following is a factor of both
2
x 6x −−
and
2
5x 6?x −+
A. 8
A.
x − 3
5
B.
B.
x + 3
4
C.
x − 2
4
D.
x + 2
C.
5
D. –8
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
11
6 4
10x + 8x
18.
=
2
2x
9x
12
A.
B.
14x
4
C.
5x
4
+ 4x
2
3 2
D.
5x + 2x
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?
A.
2
(
p + 1
)
exercises per hour
B.
3
(
p − 1
)
exercises per hour
2
C.
p
exercises per hour
3
3
D.
p
exercises per hour
2
College-Level Mathematics
Test
e College-Level Mathematics test measures your
ability to solve problems that involve college-level
mathematics concepts. ere are six content areas
measured on this test: (a) Algebraic Operations,
(b) Solutions of Equations and Inequalities,
(c) Coordinate Geometry, (d) Applications and other
Algebra Topics, (e) Functions and (f) Trigonometry.
e Algebraic Operations content area includes
the simplication of rational algebraic expressions,
factoring and expanding polynomials, and
manipulating roots and exponents. e Solutions
of Equations and Inequalities content area includes
the solution of linear and quadratic equations and
inequalities, systems of equations, and other algebraic
equations. e Coordinate Geometry content area
presents questions involving plane geometry, the
coordinate plane, straight lines, conics, sets of points
in the plane, and graphs of algebraic functions. e
Functions content area includes questions involving
polynomial, algebraic, exponential and logarithmic
functions. e Trigonometry content area includes
trigonometric functions. e Applications and
other Algebra Topics content area contains complex
numbers, series and sequences, determinants,
permutations and combinations, factorials, and word
problems. A total of 20 questions are administered on
this test.
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.
5 3
1. 2
2
–2
2
1
A. 2
2
B. 2
3
C. 2
2
5
D. 2
3
E. 2
2
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
12
2. If a ≠ b and
1
+
1
=
1
b
, then x =
x a
1 1
A. –
b a
B. b – a
1
C.
ab
a – b
D.
ab
ab
E.
a – b
1
3. If 3x
2
– 2x + 7 = 0, then (x –
3
)
2
=
20
A.
9
7
B.
9
7
C. -
9
8
D. -
9
20
E. -
9
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?
125
5
A. 4√130
B. 20√10
C. 24√5
D. 100
E. 104√5
8. If log
10
x = 3, then x =
A. 3
10
B. 1,000
C. 30
10
D.
3
3
E.
10
x –1
9. If 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
10. If θ is an acute angle and sin θ =
1
2
, then cos θ =
A. -1
B. 0
1
C.
2
√3
D.
2
E. 2
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)
12. For what real numbers x is x
2
– 6x + 9 negative?
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
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
13
13. A root of x
2
– 5x – 1 = 0 is
1
−
2
9
A.
2
5
−
1
7
B.
2
1
+
2
9
C.
2
5
+
1
7
D.
2
5
+
2
9
E.
2
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.
If an equation of the linear function in the gure above is
y = mx + b, then m =
r
A.
−
s
r
B.
s
C. rs
D. r
E. −s
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
x − 1
−1
17. If
fx
( )
=
3
and
f
is the inverse of
f,
what is the
2
−1
value of
(
3?f
)
1
A.
3
2
B.
3
C. 1
D. 2
7
E.
3
18. e sequence
{ }
a
is dened by
a = 1
and
n
0
a = 2a + 2
for
n = 0, 1, 2, ... .
What is the value of
n+1 n
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 dierent groups
of 3 employees can be chosen?
A. 3
B. 5
C. 6
D. 10
E. 15
x
=
<
3
20. If
fx
( )
1
and
ab,
which of the following must be
true?
A.
(
+ fb
)
= 3 fa
) (
1
fb
B.
fa
( )
+=
( )
3
fa=
)
C.
( ) (
fb
fa<
)
D.
( ) (
fb
fa>
) (
E.
(
fb
)
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
14
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 D
13 C
14 A
15 B
16 A
17 D
18 B
19 A
20 D
21 B
22 C
23 B
24 B
25 C
READING COMPREHENSION
QUESTION
NUMBER
CORRECT
ANSWER
1 C
2 D
3 C
4 D
5 B
6 C
7 C
8 C
9 A
10 B
11 C
12 C
13 B
14 A
15 D
16 A
17 D
18 A
19 A
20 C
21 B
22 A
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
22
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 A
16 E
17 E
18 E
19 D
20 E
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
24
Answer Key
ARITHMETIC
QUESTION
NUMBER
CORRECT
ANSWER
1 B
2 A
3 C
4 C
5 D
6 A
7 B
8 C
9 C
10 C
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 C
3 A
4 D
5 D
6 B
7 D
8 B
9 B
10 A
11 B
12 C
13 D
14 C
15 C
16 A
17 A
18 C
19 A
20 D
© 2012 The College Board. ACCUPLACER SAMPLE QUESTIONS
25