Accuplacer ( For nursing school ). Consists of 4 parts: 20 reading questions, 20 math questions, 20 sentence skills questions and 25 algebra questions. (I have attached samples for all of them below ). answere is multiple choice.
ACCUPLACER
REVIEW PACKET
From orientation to graduation…
Department of Advising and Counseling
…a commitment to academic success and student retention.
Community College of Rhode Island
ACCUPLACER REVIEW PACKET
What you should know
Why the Accuplacer Placement Test is Administered
Accuplacer is administered to students to ensure academic success in English (Writing and Comprehension),
Mathematics and Computer Skills, as these courses are foundational to virtually every degree program offered
at the Community College of Rhode Island.
Testing aims for success by revealing each prospective student’s skill level in English Writing, Reading
Comprehension, Mathematics and Computer Skils. Mandatory placements based on test scores correspond to
the skill level of each student. Using these mandatory placements, students will begin classes at a level where
they are more likely to succeed.
The ACCUPLACER ESL assesses your English skills if you have learned English as an additional language to
your native or first language. The ACCUPLACER ESL is divided into five sections. You may be asked to take
more than one of these exams.
Who is Required to Complete Placement Testing?
All students are required to complete placement testing in order to meet certain course prerequisites (please
consult course descriptions in the College Catalog for prerequisite requirements).
Waiver Criteria
The CCRI Advising and Counseling Department will consider students for placement testing waivers based on
certain academic criteria, however waivers are NOT automatically granted to students meeting the criteria
below. Waivers are considered individually after a thorough review of the respective student’s entire academic
record. Students eligible for a waiver from all or part of the Accuplacer exam must meet at least one of the
following criteria:
Students who have completed ACCUPLACER at another institution within the past year
Students who have transfer credits in College-level English and Math classes
If College-level math courses were completed more than TWO years ago, placement testing is strongly
recommended to obtain estimates of current skill levels for advisement purposes.
Students requesting a waiver from ACCUPLACER should contact the Advising and Counseling Department.
Preparing for the Placement Test
Preparation is suggested to insure that test scores accurately represent your current skill levels. Reviewing
basic concepts in reading, grammar, arithmetic and algebra before taking ACCUPLACER should assist you in
preparation for the test.
Making your Appointment for the Accuplacer Assessment
To schedule your appointment for the Accuplacer Assessment, please contact the Advising and Counseling
Department at:
401-825-2301—Warwick Campus
401-333-7159—Lincoln Campus (Office of Student Services)
401-455-6149—Providence Campus
401-851-1631—Newport Campus
Referral Sources for Preparation (available at most libraries and bookstores)
You may find the following resources helpful in your preparation for Accuplacer:
Reading Comprehension and Sentence Skills
GED Review Book
SAT I Review Books (publishers include: Arco, Kaplan, Nova and Barrons)
Arithmetic Review
Essential Mathematics: Basic Math for Everyday Use, Williams and Akins, Barrons
Contemporary’s Building Basic Skills in Mathematics, Contemporary Books
GED Review Book
SAT I Review Books (publishers include: Arco, Kaplan, Nova and Barrons)
Algebra Review
Forgotten Algebra, Bleau, Barrons
Quick Algebra Review: A Self-Teaching Guide, Selby and Slavin, Wiley
SAT I Review Books (publishers include: Arco, Kaplan, Nova and Barrons)
http://www.collegeboard.com/student/testing/accuplacer/preparation-sample.html
Websites
Computer Delivered Testing
Accuplacer is a computer-based test delivered via the Internet. Minimal computer skills are needed to complete
the test. All information is entered by using the mouse and/or the keyboard. A proctor will always be present
to assist with problems that relate to test format or to computer usage. Proctors may not, however, answer
any academic-related questions associated with the test.
Adaptive Testing
The Accuplacer test is an adaptive test. This means that the computer uses your answers to questions to
determine the level of difficulty of each successive question asked. Using this technique, we can determine
your skill level on Math and Reading sections of the test by asking relatively few questions. This portion of
the test is untimed, so that you can give each question as much thought as you wish. Once you
have verified your answer, however, you cannot return to that question.
Administrative Instructions
A photo ID (driver’s license, student ID, etc.) and Receipt of Payment are REQUIRED at the time of check-in.
Before testing begins, a proctor will give administrative instructions to all students who are about to test. These
instructions are also available at each computer station. To eliminate unnecessary noise in the testing room,
you MUST turn off any cell phones and pagers, there is no talking during testing, and you should maintain
silence if you have to leave the room to take a break. Students are not allowed to use a calculator on the math
portion or a dictionary on the essay, reading, or sentence skills portions of the test. If you require special
arrangements, please see the following paragraph on accommodations for students with disabilities. Students
who are caught violating any testing instructions will be asked to leave the lab and will need to make other
arrangements for testing. No food or drink is allowed in the testing lab.
Testing of Students with Disabilities
Students who need Accuplacer testing and are eligible for special accommodations should ensure that the
appropriate documentation, reflecting the specified accommodations, is forwarded to the CCRI Office of
Disability Services at least TWO WEEKS prior to desired testing. Please call Disability Services at 401-8252164 Warwick Campus, or 401-333-7329 Lincoln Campus, or 401-455-6064 Providence Campus, or 401-8511650 Newport County Campus to discuss accommodations and to schedule a testing session where these
accommodations can be used.
Testing Time
You are given 50 minutes to complete the typed essay and 70 minutes to complete the computer skills portion
of the test. The reading, sentence skills, and math portions of the test are un-timed. Generally, students take
2 ½ to 3 hours to complete the full test.
Testing Fee
You will be required to pay a $40 Placement Fee in advance to Accuplacer testing. You must make this
payment at the BURSAR Office. This is a one-time fee and is mandatory of all students completing
Accuplacer testing. It is used to defray the cost of placement materials and programs as well as the cost of the
administration of the mandatory placement tests. This fee is non-refundable.
Review Questions
The following questions are examples of the type of questions you may find on each section of the Accuplacer
test. Simply reviewing these questions does not guarantee an improved Accuplacer score, but may serve as a
useful starting point in beginning your preparation. Reading through each question and thoroughly
understanding how each correct answer was derived will be an excellent starting point in your preparation to
take this test!
WritePlacer
This test measures your ability to write effectively, which is critical to academic success.
You will be allowed 50 minutes to review your directions and type your essay.
Your writing sample will be scored on the basis of how effectively 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. The following five characteristics of writing will
be considered:
Focus
The clarity with which you maintain your main idea or point of view
Organization
The clarity with which you structure your response and present a logical sequence of ideas
Development and Support
The extent to which you elaborate on your ideas and the extent to which you present supporting details
Sentence Structure
The effectiveness of your sentence structure
Mechanical Conventions
The extent to which your writing is free of errors in usage and mechanics
You may not use any books or papers or other reference materials during the test. Remember to review your
writing and make any changes you think will improve what you have written.
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, review, and edit what you have typed. Read the assignment carefully before you begin to
type.
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.
Reading Comprehension
In an ACCUPLACER placement test, there are two primary types of Reading Comprehension questions.
The first type of question consists of a reading passage followed by a question based on the text. Both
short and long passages are provided. The reading passages can also be classified 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.
The second type of question, sentence relationships, presents two sentences followed by a question
about the relationship between these two sentences. The question may ask, for example, if the
statement in the second sentence supports that in the first, 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 Thomas 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: The 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 effective this technique is
and probably recall those names for the rest of your life.
The main idea of the paragraph maintains that the memory
A. always operates at peak efficiency.
B. breaks down under great strain.
C. improves if it is used often.
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. The 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. The president selected Harry L.
Hopkins, who headed the New York relief program, to run FERA. A gifted administrator, Hopkins quickly put
the program into high gear. He gathered a small staff in Washington and brought the state relief
organizations into the FERA system. While the agency tried to provide all the necessities, food came first.
City dwellers usually got an allowance for fuel, and rent for one month was provided in case of eviction.
This passage is primarily about
A. unemployment in the 1930s.
B. the effect 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. The 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.
5
In 1848, Charles Burton of New York City made the first 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. The United States had to wait
another 10 years before it got a carriage factory, and only 75 carriages were sold in the first year.
Even after 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. The shape of the
crystal is determined by temperature, vapor, and wind conditions in the upper atmosphere. Snow crystals
are always symmetrical because these conditions affect all six sides simultaneously.
The purpose of the passage is to present
A. a personal observation.
B. a solution to a problem.
C. actual information.
D. opposing scientific theories.
Directions for questions 7–10
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.
7. The 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 first.
B. It states an effect.
C. It gives an example.
D. It analyzes the statement made in the first.
8. Social studies classes focus on the complexity of our social environment.
The 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 first sentence.
B. It makes a contrast.
C. It proposes a solution.
D. It states an effect.
9. 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. They contradict each other.
B. They present problems and solutions.
C. They establish a contrast.
D. They repeat the same idea.
10. 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 first.
B. It explains what is stated in the first.
C. It expands on the first.
D. It draws a conclusion about what is stated in the first.
Sentence Skills
In an ACCUPLACER placement test, there are two types of Sentence Skills questions.
The first type is sentence correction questions that require an understanding of sentence structure.
These questions ask you to choose the most appropriate word or phrase for the underlined portion of
the sentence.
The second type is construction shift questions. These 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 classified 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 others with the relationship between coordination and subordination.
Sentence Skills Sample Questions
Directions for questions 1–5
Select the best version of the underlined part of the sentence. The first choice is the same as the original
sentence. If you think the original sentence is best, choose the first 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. The statue was knocked sideways, looked
C. The statue looked knocked sideways
D. The 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. The 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
Directions for questions 6–10
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.
6. It is easy to carry solid objects without spilling them, but the same cannot be said of liquids.
Rewrite, beginning with
Unlike liquids,
The 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
7. Although the sandpiper is easily frightened by noise and light, it will bravely resist any force that threatens
its nest.
Rewrite, beginning with
The sandpiper is easily frightened by noise and light,
The 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
8. If he had enough strength, Todd would move the boulder.
Rewrite, beginning with
Todd cannot move the boulder
The next words will be
A. when lacking
B. because he
C. although there
D. without enough
9. The band began to play, and then the real party started.
Rewrite, beginning with
The real party started
The next words will be
A. after the band began
B. and the band began
C. although the band began
D. the band beginning
10. Chris heard no unusual noises when he listened in the park.
Rewrite, beginning with
Listening in the park,
The 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
Arithmetic
This test measures your ability to perform basic arithmetic operations and to solve problems that involve
fundamental arithmetic concepts. The Arithmetic test is divided into three types of questions:
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.
Sample Questions
Solve the following problems and select your answer from the choices given. You may use scrap
paper. Remember, no calculators are permitted on Accuplacer.
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
3.
7
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
B.
25N
100
C. ¼ N
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
8. Three 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?
A.
B.
C.
D.
1
3
3
5
1
6
1
8
9. 32 is 40 percent of what number?
A. 12.8
B. 128
C. 80
D. 800
10. 3
1
2
2
3
5
A. 1
B.
C.
1
2
1
15
14
15
D. 1
1
15
Elementary Algebra
There are three types of questions administered in this test.
The first type involves operations with integers and rational numbers, and includes computation with
integers and negative rationals, the use of absolute values, and ordering.
The 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.
The 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.
Sample Questions
Solve the following problems and choose your answer from the choices given. You may use scrap
paper. Remember, no calculators are permitted on Accuplacer.
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 2×2 + 3xy – 4y2 when x = 2 and y = – 4?
A. -80
B. 80
C. -32
D. 32
4. In the figure 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. πR2
B. π(R – 3)2
C. πR2 – π × 32
D. πR2 – π(R – 3)2
5. (3x – 2y)2 =
A. 9×2 – 4y2
B. 9×2 + 4y2
C. 9×2 + 4y2 – 6xy
D. 9×2 + 4y2 – 12xy
2
6. If x > 2, then
A.
B.
C.
D.
x 3
2
x 3
x 2
x 3
x2
3
2
x -x-6
2
x -4
=
7.
4 ( 6)
5
A.
B. –
=
2
5
2
5
C. 2
D. -2
8. If 2x – 3(x + 4) = – 5, then x =
A. 7
B. – 7
C. 17
D. – 17
9. – 3(5 – 6) – 4(2 – 3) =
A. – 7
B. 7
C. – 1
D. 1
10. Which of the following expressions is equivalent to 20 –
4
5
x > 16?
A. x ≤ 5
B. x ≥ 5
C. x ≥ 32½
D. x ≤ 32½
College-Level Mathematics Test
Not all students will take the Accuplacer College-Level Math test. Accuplacer will automatically place you into
the College Level Math test based upon your performance in the Arithmetic and Elementary Algebra sections.
The College-Level Mathematics test measures your ability to solve problems that involve college-level
mathematics concepts. There are six content areas measured on this test: (a) Algebraic Operations—this
includes the simplification of rational algebraic expressions, factoring and expanding polynomials, and
manipulating roots and exponents, (b) Solutions of Equations and Inequalities—this area includes the solution of
linear and quadratic equations and inequalities, systems of equations, and other algebraic equations,
(c) Coordinate Geometry—this presents questions involving plane geometry, the coordinate plane, straight lines,
conics, sets of points in the plane, and graphs of algebraic functions, (d) Applications and other Algebra
Topics—this area contains complex numbers, series and sequences, determinants, permutations and
combinations, factorials, and word problems, (e) Functions—this includes questions involving polynomial,
algebraic, exponential, and logarithmic functions, and (f) Trigonometry—this content area includes
trigonometric functions.
Sample Questions
Solve the problem. Use the paper you were given for scratchwork.
1. 2
5
2
–2
3
2
1
2
A. 2
B. 2
3
2
C. 2
5
D. 2 3
E. 22
2. If a ≠ b and
1
x
1
A.
b
1
a
1
, then x =
b
1
a
ba
B.
1
C.
ab
D.
ab
ab
E.
ab
ab
2
1
3. If 3x 2 x 7 0 , then x =
3
2
A.
20
9
7
B.
9
7
C.
9
D.
8
9
E.
20
9
4. The 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
2
x 1
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 figures below have the respective areas indicated in square yards, how many
yards of fencing are needed to enclose the two regions?
A. 4 130
B. 20 10
C. 24 5
D. 100
E. 104 5
8. If log10x = 3, then x =
A. 3
B. 1,000
10
C.
30
D.
10
E.
3
3
10
125
5
9. If f(x) = 2x + 1 and g(x) =
x 1
, then f(g(x)) =
2
A.
B.
x
x 1
4 x2
C.
D.
4x 2
x 1
5x 1
2
E.
2 x 1x 1
2
10. If θ is an acute angle and sin θ = 1/2, then cos θ =
A. 1
B. 0
1
C.
2
D.
3
2
E. 2
ACCUPLACER WritePlacer ESL
This is to accurately assess your fundamental writing skills. This test measures your ability to write effectively,
which is critical to academic success. Your college will select the topic to be written, and the essay will be either
timed or untimed.
Your writing sample will be scored on the basis of how effectively 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. The following five characteristics of writing will
be considered:
Organization—The clarity with which you structure your response and present a logical sequence of
ideas
Focus—The clarity with which you maintain your main idea or point of view
Vocabulary—The effectiveness of your use of vocabulary
Sentence Structure—The effectiveness of your sentence structure
Mechanical Conventions—The extent to which your writing is free of errors in usage and mechanics
ACCUPLACER ESL Reading Skills Test
The ESL Reading Skills test measures your ability to read English. Specifically, 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). The other half assesses inference skills (main idea, fact
versus opinion, cause/effect logic, identifying irrelevant information, author’s point of view, and applying the
author’s logic to another situation).
Sample Questions
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.
According to the passage, which of the following is true?
A. Television is watched in nearly every country.
B. Not everybody who had a television set could watch the 1998 World Cup finals.
C. Watching television makes people dissatisfied with their own lives.
D. Television was invented in 1980.
2. Janet’s parents bought her a new sports car as a birthday present. It was blue. Janet sold her 7-year-old
blue pickup truck to a high school student. The truck could not go very fast, but the student was happy with
it.
According to the passage, which of these statements is true?
A. Janet bought a pickup truck and a sports car.
B. The pickup truck was faster than the sports car.
C. The high school student traded cars with Janet.
D. The pickup truck was older than the sports car.
3. Some of Edward Weston’s black-and-white photographs of American nature scenes are considered superb
examples of visual art. Indeed, some of his photographs have commanded top prices at art galleries.
Which of the following best characterizes Weston’s photographs?
A. They belong to famous collectors.
B. They have been sold in art galleries for large sums of money.
C. They introduced many Americans to visual art.
D. They contrast American cities with natural settings.
4. Speaking to a group of people can be a frightening experience. Some speakers cope by looking above the
heads of the audience. Others try to imagine that they are talking to a friend. A few try picturing the
audience in some non-threatening way, such as in their pajamas.
The author of the passage assumes that speakers should
A. feel comfortable when addressing an audience.
B. scare the audience.
C. encourage people to talk during the speech.
D. speak only to familiar people.
5. 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.
6. 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 you until an ambulance arrives. Is that
okay?”
“Asking for consent” means asking for
A. permission to help the victim.
B. thanks from the victim.
C. help from onlookers.
D. information about the victim’s injuries.
7. Jane and Paul are busy for 15 hours a day, 5 days a week going to college and working in a restaurant.
They go to sleep at 11 p.m. every day, but on Sunday they take part in dance lessons.
According to the passage, Jane and Paul spend most of their time
A. at home.
B. going to college and working.
C. taking part in dance lessons.
D. sleeping.
8. If you hold a piece of copper wire over the flame of a 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 the match is a poor conductor of heat. Anyone, child or adult, can try this simple experiment.
Which of the following is implied in the passage above?
A. Copper is a good conductor of heat.
B. A match and copper conduct heat equally.
C. A match is an excellent conductor of heat.
D. Matches should be kept out of the reach of small children.
9. 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.
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.
10. Cesar Chavez was an influential leader for farm workers. 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 improved living situations for farm workers.
Chavez changed lives because he
A. helped the farmers get more workers.
B. worked for the farmers.
C. helped work on the farms every day.
D. changed the conditions for the farm workers.
ACCUPLACER ESL Sentence Meaning Test
The 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. The sentences are drawn 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.
Sample Questions
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 ____ Jane’s performance.
A. about
B. at
C. for
D. towards
Each problem contains one or two sentences followed by a question. Choose the correct answer to
the question.
5. 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.
6. 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
7. Janet is never late to meet her friends, and sometimes arrives early.
Which best describes Janet?
A. Lonely
B. Punctual
C. Talkative
D. Tardy
8. 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.
9. 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. Lose her enthusiasm
D. Go to bed
10. This semester many students are enrolled in a new course, African Dance, which is being taught by a firsttime instructor, Sheila Duncan.
How long has the university offered the African dance class?
A. For a short time
B. For many years
C. For an entire school year
D. On and off for a while
ACCUPLACER ESL Language Use Test
The ESL Language Use test measures your proficiency in using correct grammar in English sentences. There are
five 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.
Sample Questions
The sentence below has a blank space. Choose the word or phrase that makes a grammatically
correct sentence.
1. _____ washing her sweater, Mary hung it up to dry.
A. After
B. Before
C. By
D. Until
2. Some day men and women _____ to Mars.
A. will travel
B. will travels
C. will traveling
D. will traveled
3. Water _____ at a temperature of zero degrees Celsius.
A. having frozen
B. freezing
C. freeze
D. freezes
4. _____ get a new haircut?
A. Have you
B. Does you
C. Are you
D. Did you
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. Since my parents always insist that I get a good night’s sleep, they were _____ when I stayed out last night
past my curfew.
A. very happy
B. very relieved
C. very tired
D. very angry
Read the two sentences below and choose the best way of combining them.
7. Her puppy ran out into the street chasing a cat. The owner quickly went to retrieve it.
A. The owner quickly went to retrieve it after a cat was chased into the street by her puppy.
B. The owner quickly retrieved it after her puppy chased a cat into the street.
C. When her puppy ran into the street after a cat, the owner quickly went to retrieve the puppy.
D. Quickly retrieving it, the owner went quickly after her puppy that ran out into the street after a cat.
8. 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.
9. The road was slippery. We put chains on the tires.
A. Although the road was slippery, we put chains on the tires.
B. The road became slippery when we put chains on the tires.
C. We put chains on the tires because the road was slippery.
D. Putting chains on the tires, the road we were on was slippery.
10. Kazuko took her dog for a walk. They went to the park.
A. Kazuko, going to the park, took her dog for a walk.
B. Kazuko took her dog for a walk in 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 they walked.
Answer Key
CLM
READING COMPREHENSION
Question Number
Correct Answer
1
C
2
D
3
C
4
D
5
B
6
C
7
B
8
A
9
D
10
A
Question Number
1
2
3
4
5
6
7
8
9
10
SENTENCE SKILLS
Question Number
Correct Answer
1
D
2
A
3
B
4
C
5
B
6
C
7
A
8
B
9
A
10
D
ESL READING SKILLS
Question Number
Correct Answer
1
A
2
D
3
B
4
A
5
D
6
A
7
B
8
A
9
A
10
D
ARITHMETIC
Correct Answer
B
A
C
C
D
A
B
C
C
C
ESL SENTENCE MEANING
Question Number
Correct Answer
1
D
2
A
3
A
4
A
5
D
6
D
7
B
8
C
9
D
10
A
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
ESL LANGUAGE USE
Question Number
Correct Answer
1
A
2
A
3
D
4
D
5
B
6
D
7
C
8
B
9
C
10
B
Question Number
1
2
3
4
5
6
7
8
9
10
Correct Answer
C
E
E
C
A
E
C
B
A
D
COMPUTER SKILLS PLACEMENT (CSP)
This test consists of 70 questions that test in seven areas. Sample questions include:
CONCEPTS OF INFORMATION TECHNOLOGY
o Hardware and software
o Computer information networks and how they are used
o Use of IT systems in everyday situations
o How personal computers can affect your health and environment
o Security and legal matters affecting computers
FILE MANAGEMENT
o Basic computer operation
o Manage files and directories/folders
o Working with desktop icons and windows
o Understand printing application
o Concepts and treatment of viruses
WORD PROCESSING (Word)
o Create, edit and format a document
o Use pictures, images, charts and tables in a document
o Use mail merge tools and print features
SPREADSHEETS (Excel)
o Design and format a spreadsheet
o Use formulas and functions to generate standard mathematical and logical applications
o Create and revise graphs and charts
DATABASE (Access)
o Understand how to use database applications including tables and forms
o Retrieve information using the query and sort tools
o Create, modify and print reports
PRESENTATION (PowerPoint)
o Design and format presentations using graphics, charts and drawn objects
o Present slide show
INTERNET AND EMAIL
o Understand internet concepts and security terms
o Web search using a browser application and available search engines
o Read, print and send messages, including attachments
o Manage e-mail using folders and address books
There are a combination of multiple choice and “click on the screen” questions.
Basic Concepts:
1. Which of the following is an input device?
o Speakers
o Mouse
o Monitor
o Printer
2. Which of the following has the highest memory capacity?
o Internal hard disk
o Zip disk
o DVD
3. Which of the following is used to measure hard drive capacity?
o bps
o Gigahertz
o Gigabyte
o dpi
4. Which of the following is an output device?
Indicate your answer by clicking on the picture.
Word Processing:
5. Which tab would you click to check the spelling on the document below?
6. After highlighting the passage below, where would you click on the toolbar to double-space it?
Spreadsheets:
7. In Excel, which button below is the AutoSum button?
8. Click on the picture that represents a cell in a worksheet.
9. In Excel, which icon is used to create a hyperlink?
10. You want to set the print area for your spreadsheet. Where can you click to access the print
area tool?
11. Which button should you click to center the text in the selected cell?
Presentations:
12. Which icon will advance to the next slide in PowerPoint?
13. Which icon allows a user to insert a new slide in PowerPoint?
14. If you need to change the slide orientation in PowerPoint, which icon will allow this feature to
occur?
15. Which button would you click to Print the current slideshow?
16. Which button in the toolbar would you click to add a New slide to the presentation?
17. Which button allows you to open “Slideshow View” with one click.
ANSWERS
1. Mouse
2. Internal Hard Disk
3. Gigabyte
Gigabyte refers to a number of bytes that can be stored on a storage device.
Bps is bits per second and is used to measure transmission speeds.
Gigahertz measures processor speed.
Dpi stands for dots per inch and is used to measure resolution of an image.
4. Computer monitor.
The mouse and keyboard are input devices.
The tower contains the processor, hard drive, memory and expansion cards.
5.
The “Review” tab is used to find Spell Check.
6.
The question asks about the “toolbar” so choose the button that affects line spacing.
7.
AutoSum button
8.
9.
A1 Cell address
Hyperlink Icon
10. Page Layout is where you can access the print area tool.
11. Center text.
12.
Space bar
13.
New Slide Icon
14.
Slide Orientation Icon
Accuplacer Test
Study Guide
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1
Table of Contents
ACCUPLACER TEST RESOURCES …………………………………………………………………………………….. 4
READING COMPREHENSION & ENGLISH PROFICIENCY ……………………………………….. 5
STRATEGY 1: FLYING OVER THE PASSAGE ……………………………………………………………………………….. 5
STRATEGY 2: CREATING A TENTATIVE SUMMARY ……………………………………………………………………… 5
STRATEGY 3: OPENINGS AND ENDINGS …………………………………………………………………………………… 6
STRATEGY 4: USING KITCHEN LOGIC ………………………………………………………………………………………. 7
STRATEGY 5: GETTING INTO THE AUTHOR’S MIND …………………………………………………………………… 7
STRATEGY 6: EMOTIONAL WORDS …………………………………………………………………………………………… 8
STRATEGY 7: FINDING THE KEY WORDS ………………………………………………………………………………….. 9
STRATEGY 8: MAKING PROPER INFERENCES …………………………………………………………………………… 11
STRATEGY 9: APPLYING IDEAS FOR GENERALIZATIONS …………………………………………………………… 12
STRATEGY 10: USING CONTEXT CLUES ………………………………………………………………………………… 12
STRATEGY 11: BREAKING DOWN PASSAGE ORGANIZATION ……………………………………………………. 13
STRATEGY 12: FIRST WORD ANALYSIS ………………………………………………………………………………… 15
STRATEGY 13: UNDERSTANDING THE INTIMIDATION………………………………………………………………. 15
STRATEGY 14: FINDING YOUR OPTIMAL PACE ……………………………………………………………………….. 16
STRATEGY 15: DON’T BE A PERFECTIONIST……………………………………………………………………………. 18
STRATEGY 16: FACTUALLY CORRECT, BUT ACTUALLY WRONG ………………………………………………… 19
STRATEGY 17: DIFFERENT VIEWPOINTS ………………………………………………………………………………… 19
STRATEGY 18: EXTRANEOUS INFORMATION ………………………………………………………………………….. 20
SENTENCE SKILLS …………………………………………………………………………………………………………….. 21
STRATEGY 1: APOSTROPHES ………………………………………………………………………………………………….. 21
Possessive Nouns …………………………………………………………………………………………………………. 21
Possessive Personal Pronouns vs. Contractions ……………………………………………………… 21
STRATEGY 2: COMMA ERRORS ……………………………………………………………………………………………… 22
STRATEGY 3: PROBLEMS WITH REFERENCES ………………………………………………………………………….. 24
STRATEGY 4: PROBLEMS WITH AGREEMENT …………………………………………………………………………… 26
STRATEGY 5: LACK OF PARALLELISM ……………………………………………………………………………………… 29
STRATEGY 6: MISCELLANEOUS PROBLEMS ……………………………………………………………………………… 30
ARITHMETIC, ELEMENTARY ALGEBRA, AND COLLEGE-LEVEL MATHEMATICS
REVIEW…………………………………………………………………………………………………………………………………. 35
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NUMBER TYPES ……………………………………………………………………………………………………………………… 35
Integers, Odd and Even Numbers, Prime Numbers, Digits…………………………………… 35
ADDITION AND MULTIPLICATION OF ODD AND EVEN NUMBERS ……………………………………………….. 36
PERCENT ……………………………………………………………………………………………………………………………….. 36
Percent less than 100 ………………………………………………………………………………………………….. 36
Percent Greater than 100 …………………………………………………………………………………………… 36
Percent less than 1 ………………………………………………………………………………………………………. 36
Percent Increase/Decrease…………………………………………………………………………………………. 37
AVERAGE ………………………………………………………………………………………………………………………………. 37
WEIGHTED AVERAGE ……………………………………………………………………………………………………………… 38
Average Speed ……………………………………………………………………………………………………………… 39
PROPERTIES OF SIGNED NUMBERS …………………………………………………………………………………………. 39
FACTORING……………………………………………………………………………………………………………………………. 40
PROBABILITY …………………………………………………………………………………………………………………………. 40
GEOMETRIC FIGURES …………………………………………………………………………………………………………….. 41
GEOMETRIC SKILLS AND CONCEPTS ……………………………………………………………………………………….. 43
Properties of Parallel Lines …………………………………………………………………………………………. 43
Angle Relationships ……………………………………………………………………………………………………… 44
Side Relationships………………………………………………………………………………………………………… 45
AREA AND PERIMETER ……………………………………………………………………………………………………………. 47
Rectangles……………………………………………………………………………………………………………………… 47
Circles …………………………………………………………………………………………………………………………….. 47
Triangles ………………………………………………………………………………………………………………………… 48
VOLUME ………………………………………………………………………………………………………………………………… 48
COORDINATE GEOMETRY ……………………………………………………………………………………………………….. 49
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Accuplacer Test Resources
Free Accuplacer Practice Tests
Financial Aid Facts
http://www.finaidfacts.org
Scholarship Help
http://www.scholarshiphelp.org
Study Tips and Information
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Reading Comprehension & English Proficiency
Strategy 1: Flying Over the Passage
A topic that is hotly debated among test taking circles is whether or
not you should read the reading passages before you read the
question. One theory is that you can save time if you read the
questions first and then go back and read over the passage. Another
theory is that you should read the passage first and then go into the
questions. Both theories have their own individual merit and due to
the differences in ability and preferences among test takers, one
method may work better than another for you.
Our recommended theory is the flyover. You want to spend some time
on the passage, at a bare minimum so that you have a general idea
about what the questions are going to ask and get your mind into the
proper mindset for the series of questions. However, you don’t want
to waste too much time on reading the passage, because much of the
detail will be forgotten by the time you get to the questions anyway.
Therefore, you should fly over the passage. You should read it very
quickly for a high-level overview (hence the flyover) understanding of
what is contained in the passage.
In part, this is a compromise between the theories that gains most of
the benefits of each. You won’t waste time on the details and yet will
have a general idea of what the passage is about and what to expect.
Strategy 2: Creating a Tentative Summary
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After you’ve finished your flyover of the passage, take a few seconds
and compose a tentative mental summary of what you’ve just read.
Try to sort out the details you picked up on and arrange them into a
loose organizational pattern that describes the passage. Remember
that your goal in the flyover is not to check it off of a test-taking list of
things to do. You want there to be some purpose behind the flyover
and having the definite goal of being able to put together a brief
mental summary will allow you to maintain some focus and gain
benefit from the flyover – as opposed to just skimming it for the sake
of skimming it without actually picking up on anything.
As you begin going through the questions and answer choices, if you
get good enough at putting together your mental summaries from
practice, you should be able to eliminate a number of answer choices
that are immediately contrary to your summary. Note, however that if
you find yourself without any good answer choices remaining (because
you’ve eliminated them all) you obviously had to have eliminated the
right answer choice. Don’t hesitate to reopen an answer choice that
you’ve already “eliminated” from consideration and reconsider it as a
possibility. If you think an answer choice contradicts your initial
summary, you’re probably right, but are not infallible.
Strategy 3: Openings and Endings
A main focus of this flyover will be the opening and ending sentences
in each paragraph. These are likely to contain the main ideas of the
paragraphs and should be mentally tagged for future reference. Try to
remember a vague idea of what the different paragraphs are about,
because this will save you time when answering questions later.
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For the most part, make sure you never try to just answer the
questions from this first flyover. Always try to go back and confirm
the answer, as your memory will play tricks on you and the writers of
the test questions may deliberately have planted a trap for you –
remember that they don’t exactly have your best interests at heart.
Strategy 4: Using Kitchen Logic
When a question asks the test taker to identify a main idea, you
should first focus on the opening and ending sentences of the passage
and each individual paragraph. If you can’t find the main idea from
these key sentences, then ask yourself how you would describe the
passage to someone who had never read it. Which words and phrases
would you use to explain the principle ideas of the passage?
This is called “Kitchen Logic” – when you explain something the way
you would if you were talking to your friends and family, while sitting
at your kitchen table. So, when faced with identifying the main idea of
a difficult passage, make it easier on yourself by backing away from
the passage and thinking about it in terms of using easy “kitchen
logic”.
Strategy 5: Getting into the Author’s Mind
A number of questions become much easier when you place yourself
into the mind of the author of the passage. Ask yourself a few
different questions:
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“Why did the author write this passage?”
“What was the author trying to say?”
What angle is the author taking?”
“What is the single most important point the author is trying to
make?”
Put yourself in the shoes of the author and imagine that you wrote the
passage and try to identify what you were trying to describe and how
you were trying to describe it. If you take on the opinions and ideas
expressed by the author as your own, then it becomes easier to
answer questions that would be easy for the author to answer.
Strategy 6: Emotional Words
Each question will be about a different angle of the passage. For
questions asking about the author’s emotions, find words in the
passage that are adjectives describing emotions.
So, if a question asks what sort of attitude an author had towards the
passage or subject, then look throughout the passage for attitude
words that might convey a positive or negative attitude. Are words
such as brilliant, excited, delightful used, or are words such as
depressive, gloomy, disappointing used?
A lot of questions could be answered correctly simply by going through
and circling all the adjectives in a passage. Without looking at
anything else except for the adjectives in a passage, most questions
about attitude or emotion could be answered correctly.
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Another way of handling these situations is to arrange all of the
answer choices in a list going from most negative to most positive.
Example:
Question: The author’s attitude on this topic is best described as:
A. indignation
B. eagerness
C. impartiality
D. fear
Now arrange these in order from negative to positive:
( – ) indignation, fear, impartiality, eagerness (+)
This will help sort out the different choices and keep you from
overlooking an answer choice and making an easy mistake.
Strategy 7: Finding the Key Words
The strategy of finding certain “give-away” words does not only apply
to adjectives in questions about emotions or attitude. Many questions
about specific details will have key words that hold the “key” to finding
the right part of the passage to look in for the answer.
Rather than answering based on your memory of the passage, you
always want to have support for your answer choice rooted in a
specific part of the passage. To gain that support, it follows that you
have to identify which part of the passage to look in. While reading
back over the entire passage may be the most foolproof method of
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9
finding that important part of the passage, it definitely is not the most
time economical method of finding that part of the passage.
A better route is to find key words in the question or answer choices
that are likely to stand out in the passage and will enable you to
quickly narrow your search down. These key words will be nouns or
verbs in the question or answer choices. Once you’ve identified
possible key words, then you should scan through the passage quickly
looking for either those key words to be repeated in the passage, or
their synonyms to appear in the passage. Once you find a particular
part of the passage that either has the exact key word repeated or a
synonym of the key word, you have probably identified the particular
part of the passage that will contain the support or justification that
you need to correctly answer the question and will allow you to be
confident in your answer choice selection.
One warning that should be made here is that often question writers
may use the exact same word or wording in their answer choices that
are used in the passage, but have done so in such a way as to mislead
you. So, simply because a particular word or phrase appears in an
answer choice and also appears exactly the same in a passage does
not make that answer choice correct. Be sure that you reread the
answer choice and consider the context that it is in, to ensure that you
are not misled by a cheap trick.
In conclusion, always try to connect the question to the right words in
the passage that will allow you to save time in finding the right part of
the passage to look in for the answer and will give you the key to the
correct answer choice.
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Strategy 8: Making Proper Inferences
Questions that ask you to make an inference from the passage will
require you to use your own personal judgment. Anything directly
stated by the author is not an inference. You will need to understand
the main idea of the passage in order to make a proper inference
about the author’s intent and mindset.
The obvious will not be enough to answer an inference question. You
must logically deduce what follows from what the author has stated in
the passage. You are looking for what can be inferred by the passage,
not what is directly stated in the passage.
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11
Strategy 9: Applying Ideas for Generalizations
Generalization questions are similar to inference questions in that you
have to go beyond what is directly stated in the passage by the
author. It helps to put yourself again in the author’s shoes. If you
were the author and believed in what you had just written, how would
you feel about another similar situation? What would either
strengthen or weaken your argument. How would you apply the
information you have just expressed to a completely different
situation?
Strategy 10: Using Context Clues
Context clues are a valuable aide in helping you understand difficult
phrases or words in the passage. A number of questions will ask you
about the meaning of words as they are used in a given passage.
If you already know the definition of the word, or have some
familiarity with it, a common mistake is to go with your first impulse
and choose the answer that you immediately recognize. However, the
reason the test writers may have chosen that particular vocabulary
word is because it is used in an unusual context. Therefore, return to
the passage and find where the word is used and make sure that you
understand how it is being used in the passage.
Once you’ve made your choice of a good definition go back again to
the passage and reread that particular section, but mentally replace
the answer choice you’ve chosen for the word being asked about.
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12
Example:
A passage states: “He was notorious for making decisions on the spur
of the moment…”
Question: Which of the following words, if substituted for the word
“notorious” would introduce the LEAST change in the meaning of the
sentence?
A. evil
B. disturbed
C. famous
D. despised
If you knew that the most common definition for “notorious” meant
being known in an unfavorable sense, then you might be tempted to
choose choice A, “evil.”
But once you review back over the passage, choice C, “famous” fits in
better into the context of the sentence of passage. Read the sentence
again and substitute your chosen answer choice for the word it
replaces. This gives you:
““He was famous for making decisions on the spur of the moment…,”
which makes sense and is correct.
Strategy 11: Breaking Down Passage Organization
In trying to understand the author’s perspective, you will sometimes
be asked about how the passage is organized. Many times, the
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13
simplest way to find the answer is to note how the opening sentence in
a passage or paragraph relates to the rest of the passage. How does
the author’s main idea get developed and broken down into supporting
ideas and statements?
As you go through the answer choices for these organization problems,
quiz yourself on each answer choice.
Example:
Question: Which of the following best describes the organization of the
author’s discussion of this topic?
A. He provides an example – Ask yourself, is there an example in
the question? Don’t work exclusively from your memory. Make
sure you can go back and actually find the example in the
passage.
B. He makes a comparison – Ask yourself, is there a comparison in
the question? Again, go back to the passage and actually find
the comparison being made and verify that it exists.
C. He makes an acknowledgement – Ask yourself, where is the
acknowledgement made and to whom?
D. He discusses a theory – Ask yourself, which theory is being
discussed?
After each of these initial questions, remember that it is not enough
for them simply to be true, they have to answer the question. Simply
because the author provided an example, doesn’t make choice A
correct. The example provided may have been to support a
comparison that he was making and the comparison may be the main
method of organization, which in this case would make answer choice
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14
B correct. So always read all the answer choices and only choose the
one that is the best, not just the first one you read that is factually
correct.
Strategy 12: First Word Analysis
When asked for main ideas that best summarize the passage, an easy
strategy is to look at the first words in each answer choice and without
looking at the rest of the answer choice, see if you could make a
decision based on those first words alone.
Example:
Question: Which of the following best explains the author’s primary
purpose?
A. dispute…
B. describe…
C. condemn…
D. convince…
If you know that the passage is fairly neutral about the subject, then
even if you know nothing else, you can probably eliminate the stronger
verbs used in answer choices A, C, and D, leaving you with “describe”
or answer choice B as being correct.
Strategy 13: Understanding the Intimidation
The test writers will generally choose passages that will be completely
foreign to most test takers. You can’t expect the passages to be on a
topic with which you have any familiarity. If you do happen to come
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15
across a passage that you are familiar with, consider yourself lucky,
but don’t plan on that happening.
The passages will also frequently be drawn from longer passages in
books, articles, journals, etc. Therefore, the passage that you will face
on the test may almost seem out of context and as though it begins in
the middle of a thought process. You won’t have a nice title overhead
explaining the general topic being covered but will immediately be
thrown into the middle of a strange format that you don’t recognize.
Also, while the topics chosen may have originally been interesting
reading in their original state, after a particular section is pulled and
used for the test passage, it will likely be dry and boring.
Getting hit by strange reading topics that you don’t recognize, of which
you may only have a small part of the original selection, and that are
dry and boring can be a bit intimidating if you’re not adequately
prepared. Just remember that the passages themselves will contain
all the information necessary to answer the questions and you don’t
need any prior knowledge of the topic in order to succeed and do well
on the test.
Strategy 14: Finding your Optimal Pace
Everyone reads at a different rate. It will take practice to determine
what is the optimal rate at which you can read fast and yet absorb and
comprehend the information. This is true for both the flyover that you
should initially conduct and then the subsequent reading you will have
to do as you go through and begin answering the questions. However,
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on the flyover, you are looking for only a surface level knowledge and
are not trying to comprehend the minutia of details that will be
contained in the passages.
You can practice with any form of reading material. Read an article at
your normal pace and then after you’re finished, ask yourself some
questions about what you just read and see how well you can
comprehend. Experiment with reading articles faster and slower and
always gauge how well you comprehended what you read at the end.
Train your brain to remember the details and absorb the facts.
With practice, you will find the pace that you should maintain on the
test while going back through passages. It should be a comfortable
rate. This is not a speed reading exercise. If you have a good pace,
and don’t spend too much time on any question, you should have a
sufficient amount of time to read the different sections of the passages
at a comfortable rate. The two extremes you want to avoid are the
dumbfounded mode, in which you are lip reading every word
individually and mouthing each word as though in a stupor, and the
overwhelmed mode, where you are panicked and are buzzing back and
forth through the passage in a frenzy and not comprehending
anything.
You must find your own pace that is relaxed and focused, allowing you
to have time for every question and give you optimal comprehension.
Note that you are looking for optimal comprehension, not maximum
comprehension. If you spent hours on each word and memorized the
passage, you would have maximum comprehension. That isn’t the
goal though, you want to optimize how much you comprehend with
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how much time you spend reading. Practice will allow you to
determine that optimal rate.
Strategy 15: Don’t be a Perfectionist
If you’re a perfectionist, this may be one of the hardest strategies, and
yet one of the most important. The test you are taking is timed, and
you cannot afford to spend too much time on any one question.
If you are working on a problem and you’ve got your answer split
between two possible answer choices, and you’re going back through
the passage and reading it over and over again in order to decide
between the two, you can be in one of the most frustrating situations
possible. You feel that if you just spent one more minute on the
problem, that you would be able to figure the right answer out and
decide between the two. Watch out! You can easily get so absorbed
in that problem that you loose track of time, get off track and end up
spending the rest of the test playing catch up because of all the
wasted time, which may leave you rattled and cause you to miss even
more questions that you would have otherwise.
Therefore, unless you will only be satisfied with a perfect score and
your abilities are in the top .1% strata of test takers, you should not
go into the test with the mindset that you’ve got to get every question
right. It is far better to accept that you will have to guess on some
questions and possibly get them wrong and still have time for every
question, than to work on every problem until you’re absolutely
confident in your answer and then run out of time on the last few
problems.
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Strategy 16: Factually Correct, but Actually Wrong
A favorite ploy of question writers is to write answer choices that are
factually correct on their own, but fail to answer the question, and so
are actually wrong.
When you are going through the answer choices and one jumps out for
being factually correct, watch out. Before you mark it as your answer
choice, first make sure that you go back to the question and confirm
that the answer choice answers the question being asked.
Strategy 17: Different Viewpoints
Some passages will express the author’s viewpoint on a topic, along
with the viewpoint of other experts or other individuals. This can lead
to trouble in answering questions though. If asked for the viewpoint of
the author, you might go back to the passage, find where a certain
viewpoint is expressed, answer the question based on what you read
and move on.
For most passages, that would be fine, but when other viewpoints
besides the author’s are expressed, you have to discern who is
expressing their opinion in the passage. Make sure that if multiple
individuals are giving their viewpoint on a topic, that you sort them out
for any questions and associate the right viewpoint with the right
individual.
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19
Strategy 18: Extraneous Information
Some answer choices will seem to fit in and answer the question being
asked. They might even be factually correct. Everything seems to
check out, so what could possibly be wrong?
Does the answer choice actually match the passage, or is it based on
extraneous information not even contained in the passage. Just
because an answer choice seems right, don’t assume that you
overlooked information while reading the passage. Always try to go
back and find the support for the answer choice in the passage. Your
mind can easily play tricks on you and make you think that you read
something or that you overlooked a phrase.
Unless you are behind on time, always go back to the passage and
make sure that the answer choice “checks out.”
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Sentence Skills
Strategy 1: Apostrophes
An apostrophe is used to form a possessive or a contraction. Check
for the following common apostrophe errors. The bracketed
parenthetical demonstrates the correct use.
Possessive Nouns
1.
Singular possessive nouns. Use ‘s to show that a singular noun
is possessive [the defendant’s motion]. You can apply this rule
even when the singular noun already ends in “s” (Charles’s
costume) though many writers add only the apostrophe [Charles’
shoes].
2.
Plural possessive nouns not ending in “s.” Use ‘s to show that a
plural noun not ending in “s” is possessive [the children’s toy].
3.
Plural possessive nouns ending in “s.” Add only an apostrophe
to make plural nouns possessive [the boys’ game].
4.
Nouns that are not possessive. Do not add an apostrophe to a
noun that is not possessive [the teachers (not teacher’s or
teachers’) have claimed; the Joneses (not Jones’ or Jones’s) did
not attend].
Possessive Personal Pronouns vs. Contractions
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Apostrophe errors with possessive personal pronouns are common
because possessive personal pronouns indicate possession and we are
used to using apostrophes to indicate possession. Also possessive
personal pronouns are easily confused with contractions. Here are the
basic rules:
5.
Possessive personal pronouns. Do not add an apostrophe to a
possessive pronoun [the problem is hers (not her’s); the
corporation must disclose its (not it’s) assets.]
6.
Contractions. Do use an apostrophe in a contraction (it’s time to
go; you’re the one).
* Watch especially for errors in using “it’s” or “its.” Remember that
“it’s” means “it is” and “its” indicates ownership. Confusing
these two words is the most common apostrophe error.
Strategy 2: Comma Errors
Commas are also major troublemakers. Watch for these situations:
1.
Use a comma to separate two independent clauses joined with
a coordinating conjunction (and, or, but, nor, so, for). [The
child agreed, but the parent objected].
2.
Use a semicolon or a period, not a comma, to separate two
independent clauses not joined by a coordinating conjunction
[The child agreed; however, the parent objected.]. The
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following transitional words and phrases are conjunctive
adverbs, not conjunctions:
accordingly
however
consequently
also
on the other hand
moreover
for example
otherwise
for instance
similarly
furthermore
therefore
hence
thus
Therefore, do not use a comma to separate two independent clauses
on either side of one of these words.
Incorrect:
The city must increase its tax base, however, the citizens
must be able to accept the additional tax burden.
Correct:
The city must increase its tax base; however, the citizens
must be able to accept the additional tax burden.
3.
Conjunctive adverbs signal the relationship between the point(s)
made in the material before their sentence and the material of
that sentence. The words and phrases in the list above are
examples. When you begin an independent clause with a
conjunctive adverb or when you use it in the middle of a
sentence, set it off with a comma.
Moreover, the defendant has not yet established a proper foundation
for this testimony.
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The student, moreover, has not yet turned in an acceptable project to
meet his assignment’s requirements.
4.
Use commas to set off the year if you also identify the day [The
birth of Norma Kelly on June 2, 1974, brought the . . . .], but
omit the commas otherwise [The birth of Norma Kelly in June
1974 brought . . . .].
5.
Use commas to separate three or more simple items in a list. If
the descriptions of the items are long or complex, use
semicolons to separate them.
6.
Use a comma to separate two independent clauses connected by
a coordinating conjunction unless the two independent clauses
are short and simple:
Correct:
The sunlight helped the flowers to grow, but they require
frequent watering in order to stay alive.
Correct:
Yours is timely and mine is late.
Strategy 3: Problems With References
A referent is a word or phrase that refers to something else (an
antecedent). Problems with referents can cause confusion and,
sometimes, unintended humor. Problems with references occur
primarily (1) when sentences have more than one possible antecedent
(often caused by placing the referent too far from the intended
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antecedent); or (2) when the antecedent is only implied. Here are
examples problems with references.
More than one possible antecedent
The doctors told their patients that they had serious problems.
[Who had problems?]
To prevent children from sucking their thumbs, some parents soak
them in tabasco sauce. [Do the parents soak the children or the
thumbs?]
The corporate officers had failed to disclose the serious conflicts of
interest caused by their ownership of several of T&J’s suppliers. The
possibility of a bankruptcy was a disaster for them.
[Was the possibility a disaster for the officers, the conflicts, or the
suppliers?]
Referring to an antecedent that is only implied:
The corporate officers had failed to disclose the serious conflict of
interest raised by the possible bankruptcy of T&J’s primary supplier.
This was a disaster for the officers.
[What was a disaster — the failure to disclose, the conflict, or the
possible bankruptcy?]
Notice that the confusing reference in this last example is caused by
using “this” alone. Using the pronoun “this” or “that” without a noun
following immediately is usually inadvisable. Here, for instance, the
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confusion could be resolved easily by adding the clarifying noun after
“this”:
The corporate officers had failed to disclose the serious conflict of
interest raised by the possible bankruptcy of T&J’s primary supplier.
This failure was a disaster for the officers.
The three primary strategies for solving reference problems are: (1)
repeating the antecedent (as in the prior example); (2) re-arranging
the material to place the referent close to the antecedent; or (3) rearranging the material to eliminate the need for the referent. For
instance, here is another possible solution to the reference problem
above:
The possibility of a bankruptcy was a disaster for the corporate
officers. They had failed to disclose the serious conflicts of interest
caused by their ownership of several of T&J’s suppliers.
Strategy 4: Problems With Agreement
Here are the most common errors in agreement:
1.
The following indefinite pronouns are singular and take a
singular verb:
anyone
Anyone is welcome.
each
Each is an expert.
either
Either supports the argument.
everyone
Everyone has problems.
neither
Neither sings in tune.
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The singular verb is correct even when the indefinite pronoun is
followed by a prepositional phrase with a plural noun:
Each of these peaceful alternatives was [not “were”] ignored.
Either of the twins is [not “are”] available.
However, the following indefinite pronouns are either singular or
plural, depending on the nouns or pronouns they refer to:
all
any
none
some
For example:
All [singers] are permitted . . . .
All of the money is counted . . . .
None of them are satisfied . . . .
None of the royalty was present . . . .
2.
“The court” is a singular term, taking a singular pronoun:
The court overruled the traditional rule originally announced in
December. It [not “They”] held that . . . .
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3.
This same kind of error can slip in when referring to any
institution or business:
He said that he is very grateful to St. Catherine’s Hospital. They
treated him with respect.
The problem sometimes occurs because the writer is avoiding the
awkwardness of attributing a human action to an “it.” For instance, in
the St. Catherine’s example, the writer is probably avoiding “It treated
him with respect.” That problem can usually be solved by changing
the antecedent to the humans who actually performed the action:
He said that he is very grateful to the staff at St. Catherine’s Hospital.
They treated him with respect.
4.
Watch for both verb agreement and pronoun agreement when a
singular subject is modified by a phrase or clause containing a
plural noun:
The confidence of several families was [not were] attained.
Each of the groups agrees [not agree] to resolve the problem
peacefully.
Every student who had already taken both courses is [not are]
excused from this requirement.
5.
Use a possessive pronoun before a gerund phrase. A gerund is
an “ing” verb that serves as a noun. The gerund can stand alone
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or can begin a gerund phrase, but either way, the word or
phrase functions as a noun:
Running is good for you.
Coming to work late can result in disciplinary action.
Since a gerund or gerund phrase functions as a noun, it takes a
possessive pronoun:
We’ll go to their house for the party instead of their [not them] coming
to ours.
Strategy 5: Lack of Parallelism
Where possible, similar ideas should be expressed in a similar
(parallel) structure and grammatical form. Parallelism makes for
easier reading and clearer meanings. It also improves sentence
rhythm and cuts down on verbiage.
Parallel structure:
Parallelism makes for easier reading and clearer meanings.
“easier reading” and “clearer meanings” are parallel.
Non-parallel structure:
Problems occur when the business conceals relevant documents or by
deluging the auditors with irrelevant documents.
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In the non-parallel example, the writer identifies two situations in
which problems occur; however, the two situations are phrased in
non-parallel structure. A parallel structure would be:
Problems occur when the business conceals relevant documents or
when they deluge the auditors with irrelevant documents.
Now that the structure is parallel, extra words can go:
Problems occur when the business conceals relevant documents or
deluge the auditors with irrelevant documents.
Parallel structure is especially important in a list.
When the new commander arrived at the post, he immediately posted
a new list of orders: no leaves were to be granted, and no leniency
was to be given.
Strategy 6: Miscellaneous Problems
1.
Use the subjective case for a pronoun that functions as the
subject of an understood verb. The subjective case is the form
the pronoun takes when used as the subject of the sentence
(“I,” “we,” “they”). For example, consider these two sentences:
The corporation’s president worked harder than me.
The corporation’s president worked harder than I.
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Which is correct? The second version is correct, because “I” is the
subject of an understood verb “worked.” In other words, the sentence
is actually a shortened version of “The corporation’s president worked
harder than I worked.”
This is an easy mistake to make because the correct case may sound
wrong. If so, the best solution is to add the understood verb or to rephrase the sentence completely to avoid the awkwardness.
2.
Use the subjective case for a pronoun that functions as the
complement of a subject. A pronoun is a subjective complement
when it actually equals the subject of the sentence. For
example, consider these two sentences:
The person least anxious after the test was her.
The person least anxious after the test was she.
Which is correct? The second version is correct, because the pronoun
in the predicate, “she,” actually equals the subject, “the person least
anxious after the test.” In other words, the sentence is like an algebra
equation: The person least anxious after the test = she. In a
sentence like this one, the noun or pronoun in the predicate functions
like the subject of the sentence. The sentence should read the same
as if you turned it around:
She was the person least anxious after the test.
Once again, this is an easy mistake to make because the correct case
may sound wrong. In spoken English we often hear “It’s him,” or “It’s
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me.”
Again, the best solution may be to reverse the sentence or to
re-phrase the sentence completely to avoid the awkwardness.
3.
Use “try to” and “sure to” rather than “try and” or “sure and.”
Incorrect:
Ms. Thompson wanted to try and finish the project by
Friday.
Correct:
Ms. Thompson wanted to try to finish the project by
Friday.
Incorrect:
Be sure and pick up the baby from daycare.
Correct:
Be sure to pick up the baby from daycare.
This rule makes sense if you think about it. The proper function of the
word “and” is to connect two different things. Thus, the “and” in the
first sentence should mean that Ms. Thompson wanted to do two
different things, but she didn’t; she only wanted to do one thing –
finish the project. The same is true for the third sentence. The “and”
seems to tell the reader that the sentence is an instruction to do two
different things, but it isn’t. The reader is only to do one thing – pick
up the baby.
4.
“Hopefully” is an adverb that explains how someone does
something, as in “She asked hopefully.” Often “hopefully” is
misused in this or a similar fashion: “Hopefully the storm will
pass.” This use actually asserts that the storm’s passing will be
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full of hope. The writer actually means “I hope that the storm
will pass.”
5.
Watch out for one more common error with adverbs: the
difference between “I feel bad” and “I feel badly.” In the first
sentence, the writer is commenting on how she feels, either
physically (perhaps she has the flu) or emotionally (perhaps she
is sad). The first sentence is the proper use of “bad” as an
adjective.
However, the second sentence uses “bad” in its form as an adverb.
The writer is commenting on her ability to feel; perhaps her fingers are
numb. Sometimes writers use the adverbial form “badly” when they
mean “bad,” perhaps believing that “badly” sounds more elevated.
6.
Watch for errors in using “myself” instead of using “I” or “me.”
“Myself” is used as a reflective pronoun or as a device for
emphasis.
Correct:
I injured myself.
used as a reflective pronoun
Correct:
I will draft the interrogatory answers myself.
used for emphasis
Each time “myself” is used, test the use by asking whether “I” or “me”
could substitute for “myself.” If so, using “myself” is incorrect.
Incorrect:
Ms. Alpha and myself will meet you for lunch.
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Incorrect:
If you have any questions about this demonstration,
contact Mr. Jones or myself.
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Arithmetic, Elementary Algebra, and CollegeLevel Mathematics Review
The Mathematics tests measures a test taker’s ability to solve
problems representing some of the key concepts in mathematics.
Some problems will only test one concept, while others will involve
multiple concepts integrated together in a single problem.
The problems will have few technical terms, aside from basics, such as
area, perimeter, integer, and ratio, which are expected to be common
mathematical knowledge. All figures shown will be drawn accurately
and lie in a single plane, unless noted otherwise.
Number Types
Integers, Odd and Even Numbers, Prime Numbers, Digits
Integers…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …
Consecutive Integers: Integers that follow in sequence; for
example, 22, 23, 24, 25. Consecutive Integers can be more
generally represented by n, n + 1, n + 2, n + 3, …
Odd Numbers…, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, …
Even Numbers…, -8, -6, -4, -2, 0, 2, 4, 6, 8, … (Note: zero is
an even number)
Prime Numbers…, 2, 3, 4, 7, 11, 13, 17, 19, … (Note 1 is not a
prime and 2 is the only even prime)
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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Addition and Multiplication of Odd and Even Numbers
Addition
Multiplication
even + even = even
even x even = even
odd + odd = even
even x odd = even
even + odd = odd
odd x odd = odd
Percent
Percent means hundredths or number out of 100. For example, 40
percent means 40/100 or .40 or 2/5.
Percent less than 100
Problem 1: If the sales tax on a $30 item is $1.80, what is the sales
tax rate?
Solution: $1.80 = n/100 x $30
n = 6, so 6% is the sale tax rate
Percent Greater than 100
Problem 2: What number is 250% of 2?
Solution: n = 250/100 x 2
n = 5, so 5 is the number
Percent less than 1
Problem 3: 3 is 0.2 percent of what number?
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Solution: 3 = 0.2/100 x n
n = 1,500, so 1,500 is the number
Percent Increase/Decrease
Problem 4: If the price of a computer was decreased from $1,000 to
$750, by what percent was the price decreased?
Solution: The price decrease is $250. The percent decrease is the
value of n in the equation 250/1000 = n/100. The value of n is 25, so
the price was decreased by 25%.
Notes: n% increase means increase/original = n/100;
n% decrease means decrease/original = n/100.
Average
An average is a statistic that is used to summarize data. The most
common type of average is the arithmetic mean. The average
(arithmetic mean) of a list of n numbers is equal to the sum of the
numbers divided by n. For example, the mean of 2, 3, 5, 7, and 13 is
equal to
2 + 3 + 5 + 7 + 13 / 5 = 6
When the average of a list of n numbers is given, the sum of the
numbers can be found. For example if the average of six numbers is
12, the sum of these six numbers is 12 x 6, or 72.
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The median of a list of numbers is the number in the middle when the
numbers are ordered from greatest to least or from least to greatest.
For example, the median of 3, 8, 2, 6, and 9 is 6 because when the
numbers are ordered, 2, 3, 6, 8, 9, the number in the middle is 6.
When there is an even number of values, the median is the same as
the mean of the two middle numbers. For example, the median of 6,
8, 9, 13, 14, and 16 is
9 + 13 / 2 = 11
The mode of a list of numbers is the number that occurs most often in
the list.
For example, 7 is the mode of 2, 7, 5, 8, 7, and 12.
The
numbers 10, 12, 14, 16, and 18 have no mode and the numbers 2, 4,
2, 8, 2, 4, 7, 4, 9, and 11 have two modes, 2 and 4.
Note: The mean, median, and mode can each be considered an
average.
On the test, the use of the word average refers the
arithmetic mean and is indicated by “average (arithmetic mean).” The
exception is when a question involves average speed (see problem 2
below).
Questions involving the median and mode will have those
terms stated as part of the question’s text.
Weighted Average
Problem 1: In a group of 10 students, 7 are 13 years old and 3 are
17 years old. What is the average (arithmetic mean) age of these 10
students?
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Solution: The solution is not the average of 13 and 17, which is 15.
In this case the average is
7(13) + 3(17) / 10 = 91 + 51 / 10 = 14.2 years
The expression “weighted average” comes from the fact that 13 gets a
weight factor of 7, whereas 17 gets a weight factor of 3.
Average Speed
Problem 2: Jane traveled for 2 hours at a rate of 70 kilometers per
hour and for 5 hours at a rate of 60 kilometers per hour. What was
her average speed for the 7-hour time period?
Solution: In this situation, the average speed is:
Total Distance/Total Time
The total distance is 2(70) + 5(60) = 440 km.
The total time is 7 hours. Thus the average speed was
440/7 = 62 6/7 kilometers per hour.
Note: In this example the average speed is not the average of the two
separate speeds, which would be 65.
Properties of Signed Numbers
positive x negative = negative
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negative x negative = positive
negative x positive = negative
positive x positive = positive
Factoring
You may need to apply these types of simple factoring:
x^2 + 2x = x(x + 2)
x^2 – 1 = (x + 1) (x – 1)
x^2 + 2x +1 = (x + 1) (x + 1) = (x + 1)^2
x^2 – 3x – 4 = (x – 4)(x + 1)
Probability
Probability refers to the chance that a specific outcome can occur. It
can be found by using the following definition when outcomes are
equally likely.
Number of ways that a specific outcome can occur
Total number of possible outcomes
For example, if a jar contains 13 red marbles and 7 green marbles, the
probability that a marble selected from the jar at random will be green
is
7 / 7 +13 = 7/20 = or 0.35
If a particular outcome can never occur, its probability is 0. If an
outcome is certain to occur, its probability is 1. In general, if p is the
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probability that a specific outcome will occur, values of p fall in the
range 0 < p < 1. Probability may be expressed as either a decimal or
a fraction.
Geometric Figures
Figures that accompany problems are intended to provide information
useful in solving the problems. They are drawn as accurately as
possible EXCEPT when it is stated in a particular problem that the
figure is not drawn to scale. In general, even when figure is not drawn
to scale, the relative positions of points and angles may be assumed to
be in the order shown. Also, line segments that extend through points
and appear to lie on the same line may be assumed to be on the same
line. The text “Note: Figure not drawn to scale.” is included on the
test when degree measures may not be accurately shown and specific
lengths may not be drawn proportionally. The following examples
illustrate the way different figures can be interpreted.
Example 1
Since UY and VX are line segments, angels UWV and XWY are vertical
angles. Therefore, you can conclude that c° = d°. Even though the
figure is drawn to scale, you should NOT make any other assumptions
without additional information. For example, you should NOT assume
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41
that VW = WY or that the angle at vertex Y is a right angle even
though they may look that way in the figure.
Example 2
A question may refer to a triangle such as XWZ above. Although the
note indicates that the figure is not drawn to scale, you may assume
that:
(1)
XWY and YWZ are triangles.
(2)
Y is between X and Z.
(3)
X, Y, and Z are points on a line.
(4)
The length of XY is less than the length of XZ.
(5)
The measure of angle XWY is less than the measure of
angle XWZ.
You may not assume the following:
(1)
The length of XY is less than the length of YZ.
(2)
The measures of angles WXY and WYX are equal.
(3)
The measure of angle XWY is greater than the measure of
angle WYX.
(4)
Angle XWZ is a right angle.
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Geometric Skills and Concepts
Properties of Parallel Lines
1. If two parallel lines are cut by a third line, the alternate interior
angles are equal.
a° = b° and d° = c°
2. If two parallel lines are cut by a third line, the corresponding
angles are equal.
a° = b° and d° = c°
Note: Words like “alternate interior” or “corresponding” are
generally not used on the test, but you do need to know which
angles involving parallel lines are equal.
3. If two parallel lines are cut by a third line, the sum of the interior
angles on the same side of the third line is 180 degrees.
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a° + b° = 180°, because a° + c° = 180° and b° = c°
Angle Relationships
1. The sum of the interior angles of a triangle is 180 degrees.
a° = 70° (Because 70° + 40° + a° = 180°.)
2. When two lines intersect, vertical angles are equal.
a=b
3. A straight angle measures 180 degrees.
a° = 60 (Because a° + 120° = 180°.)
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4. The sum of the two acute angles in a right triangle is 90
degrees.
x = 15 (Because 2x + 4x = 90.)
5. The sum of the interior angles of a polygon can be found by
drawing all diagonals of the polygon from one vertex and
multiplying the number of triangles formed by 180 degrees.
Since the polygon is divided into 3 triangles, the sum of the angles
is 3 x 180° or 540°.
Side Relationships
1. Pythagorean Theorem: In any right triangle, a2 + b2 = c2, where
c is the length of the longest side and a and b are the lengths of
the two shorter sides.
a=5
(By the Pythagorean Theorem,
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a2= 32 + 42
a2 = 9 = 16
a2 = 25
a = square root of 25 = 5
2. In any equilateral triangle, all sides are equal and all angles are
equal.
a=b=5
(Because the measure of the unmarked angle is 60°, the measure
of all angles of the triangle are equal, and therefore, the lengths of
all sides of the triangle are equal.)
3. In an isosceles triangle, the angles opposite equal sides are
equal. Also the sides opposite equal angles are equal.
If A = B, then a° = b°. Also, if a° = b°, then A = B.
4. In any triangle, the longest side is opposite the largest angle (
and the shortest side is opposite the smallest angle.)
A>B>C
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5. Two polygons are similar if the lengths of their corresponding
sides are in the same ratio and their corresponding angles are
equal.
If polygons ABCD and EFGH are similar, and if BC and FG are
corresponding sides, then BC = 3 and FG = 2.
Therefore, the ratio is 3:2 and since AB = 6, EF = 4
Area and Perimeter
Rectangles
Area of a rectangle = length x width = l x w
Perimeter of a rectangle = 2(l + w) = 2l x 2w
Area = 5x X 8x = 40×2
Perimeter = …
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