Texas Success Initiative
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Mathematics

Mathematics Sample Questions
Directions for questions 1–15

The Texas Success Initiative (TSI) Mathematics
and Statistics test contains questions that measureproficiency in four content areas. The four content
areas are as follows:

For each of the questions below, choose the bestanswer from the four choices given. You may use thepaper you received as scratch paper.
1. If 3t − 7 =5t , then 6t =Elementary Algebra and Functions — Topics
covered in this category include:

A.
B.
C.
D.

• Linear equations, inequalities and systems• Algebraic expressions and equations

21
−7
−21
−42

• Word problems and applications
Intermediate Algebra and Functions — Topics
covered in this category include:

2. The variables x and y are directly proportional, and y = 2
when x = 3. What is the value of y when x = 9 ?

• Quadratic and other polynomial expressions,
equations and functions

A. 4
B. 6
C. 8
D. 12

• Expressions, equations and functions involving
powers, roots and radicals• Rational and exponential expressions, equations
and functionsy

Geometry and Measurement — Topics covered inthis category include:C• Plane geometry• Transformations and symmetry• Linear, area and three-dimensional measurements
Data Analysis, Statistics and Probability — Topics
covered in this category include:• Interpreting categorical and quantitative data
• Statistical measures• Probabilistic reasoningOx

3. In the xy -plane above, point C has coordinates (6, 9).
Which of the following is an equation of the line that
contains points O and C ?
A. y= x − 3
B. y= x + 32
x3
3
D. y = x
2
C. y =© 2013 The College Board.

Diagnostic and Placement Test Sample Questions1

4. There are 3 x − 2 trees planted in each row of a rectangularparcel of land. If there are a total of 24 x − 16 trees plantedin the parcel, how many rows of trees are there in the parcel?

9. (3 x 2 y 3 )3 =A. 3x 5 y 6

A. 21x − 18
B. 21x − 14
C. 8x
D. 8

B. 9x 6 y 9
C. 27x 5 y 6
D. 27x 6 y 9

5− x =
4, then x =10. If

5. A group of 18 people ordered soup and sandwiches forlunch. Each person in the group had either one soup or one
sandwich. The sandwiches cost $7.75 each and the soups
cost $4.50 each. If the total cost of all 18 lunches was$113.50, how many sandwiches were ordered?

A. −21
B. −11
C. 1
D. 11

A. 7
B. 8
C. 9
D. 10

11. Ifx −1= 20, then x =x

A. −21
B. −196. Which of the following equations has both 1 and −3 assolutions?

1
19
1
D.
21
C. −

2

A. x − 2 x − 3 =0
B. x 2 + 2 x − 3 =0
C. x 2 − 4 x + 3 =0
D. x 2 + 4 x + 3 =0

12. A ball was kicked into the air from a balcony 20 feetabove the ground, and the ball’s height above theground, in feet, t seconds after the ball wasw kicked wash(t ) =20 − 16t 2 + 32t. What was the maximum height, in
feet, of the ball above the ground after it was kicked?

7. In the xy -plane, what is the y -intercept of the graph of theequation y = 2( x + 3)( x − 4) ?
A. −24B. −12
C. −2
D. 12

8.

A.
B.
C.
D.

x4 − 1 =13. The yard behind the Cindy’s house is rectangular in shapeand has a perimeter of 72 feet. If the length  of the yard
is 18 feet longer than the width w of the yard, what is thearea of the yard, in square feet?

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

32
34
36
40

A. 36
B. 144
C. 243
D. 4864© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
2

City

High
Temperature

A

t°F

B

87°F

C

81°F

D

62°F

E

93°F

14. The table above shows the high temperature last Thursday
for five cities, A through E. If the median of the Thursday
high temperatures for these cities was 81°F, which of thefollowing could NOT have been the high temperature lastThursday for City A ?
A.
B.
C.
D.

85°F
75°F
65°F
55°F

15. There are 20 children in the cast of a class play, and 8 of thechildren are boys. Of the boys, 4 have a speaking part in theplay, and of the girls, 8 do not have a speaking part in theplay. If a child from the cast of the play is chosen at random,
what is the probability that the child has a speaking part?

2
5
1
B.
2
A.

3
5
3
D.
4
C.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
3

Reading

Reading Sample Questions

The Texas Success Initiative (TSI) Reading test
contains questions that measure proficiency in fourcontent areas. The four content areas are as follows:

Directions for questions 1–9
Read the passage and then choose the best answer to thequestion. Answer the question on the basis of what isstated or implied in the passage.

Literary Analysis — Topics covered in this category
include:1. When we think of volcanoes, eruptions, lava, and smokefilled air come to mind—all occurring on land. Most people
are surprised to learn about the prevalence of underwater
volcanoes on our planet. Because the lava and smoke spillingout of an active, underwater volcano is contained by theocean, people generally do not take note of these eruptions.
However, the largest underwater volcanoes are capable ofcreating huge tidal waves, threatening coastal communities.

• Identifying and analyzing ideas in and elements ofliterary texts
Main Idea and Supporting Details — Topics coveredin this category include:• Identifying the main idea of a passage

The main idea of the passage is that
A. traditional volcanoes and underwater volcanoes are
similarB. the lava and smoke from an underwater volcano iscontained by the sea
C. most tidal waves are caused by underwater volcanoes
D. underwater volcanoes receive little attention but can be
dangerous• Comprehending explicit textual information in a
passage
Inferences in a Text or Texts — Topics covered in thiscategory include:• Synthesizing ideas by making a connection orcomparison between two passages• Making an appropriate inference about single
passages

2. In 2010, talk show host Oprah Winfrey and novelist
Jonathan Franzen kissed and made up after a nine-year
feud. In 2001, Franzen was disinvited from appearing on
Winfrey’s TV show to pitch his novel The Corrections after
he made it clear that he was unhappy about the book’s being
chosen for the Oprah Book Club. Describing his work as“in the high-art literary tradition,” Franzen said he didn’t
want to be associated with the Club, which he accused ofoccasionally choosing “schmaltzy, one-dimensional” novels.
But Winfrey is apparently able to forgive and forget: shechose Franzen’s next novel, Freedom, for her book club andsaid of it, “Now you haven’t heard me say this word often,
but this book is a masterpiece.”

Author’s Use of Language — Topics covered in thiscategory include:• Identifying an author’s purpose, tone andorganization or rhetorical strategies and use ofevidence• Determining the meaning of words in context

The passage implies that Franzen’s criticism of the Oprah
Book Club was motivated primarily by
A. prideB. angerC. insensitivity
D. ignorance© 2013 The College Board.

Diagnostic and Placement Test Sample Questions4

3. The main authors of The Declaration of Independence
and the Constitution are usually thought of as America’s“Founding Fathers.” Other, less known personages also
deserve the title, however, and Noah Webster was oneof these. Through his writings, which include the stillinfluential dictionary that bears his name, Webster sought
to legitimize an “American English” that was independentof British spelling and pronunciation. For instance, Webster
removed the “u” from “colour,” creating the distinct
American version of the word.

6. Television has been the primary source of information andentertainment for most Americans over the last 50 years.
However, with Internet use on the rise year after year, some
may wonder if surfing the net will soon surpass watching
television as Americans’ primary leisure activity. Indeed,some recent surveys show that time spent on the Internet
is now greater than time spent in front of the television.
However, this statistic may not tell the whole story, as 59%
of Americans say they multitask, using the Internet andwatching TV simultaneously.

What is the main purpose of this passage?
A. To praise the Founding Fathers
B. To present information about an important American
C. To define and explain “American English”
D. To distinguish American dictionaries from British
dictionaries

The main idea of the passage is that television
A. is only one of many information sources
B. may have become less popular than the Internet
C. is watched by more people now than ever before
D. focuses more on entertainment than on news

7. Plywood, while not the most pleasing wood to look at, has
become an incredibly important building material in house
construction. It is flexible, inexpensive, and strong. Its
strength is due to layers of thin wood glued on top of eachother with the grain of each layer making a right angle withthe grain of the layer below it. This way of layering the sheetsof wood makes plywood difficult to break.

4. If you are committed to healthy, green living and want to
reduce your environmental footprint, you might consider
expanding your daily diet to include bugs. Supporters of theedible insect initiative rightfully argue that farming insects
has a much lower environmental impact than does raising
livestock since bugs are easier to harvest and require afraction of the water and land space that cattle need. Indeed,
the high-protein, low-fat health benefits of bug-eating havelong been known. For hundreds of years, crickets, silkworms
and even tarantulas have been served roasted, stewed andfried at the dinner tables of many cultures.

According to the passage, the arrangement of the layers ofthin wood explains plywood’s
A. strength
B. costC. attractivenessD. flexibility

Which words best describe the author’s attitude toward the“edible insect initiative”?
A. awe and amazement
B. interest and support
C. disgust and distaste
D. fear and apprehension

8. The 1922 German Expressionist film Nosferatu, directed by
F. W. Murnau, is considered one of the most influential films
in cinematic history—while also being a classic vampire
movie. The film is closely based on Bram Stoker’s 1897 novel,
Dracula; however, the villain in the film is called “Count
Orlok” rather than “Count Dracula.” The reason is thatthe small studio that produced the film, Prana Film, wasunable to secure the rights to Stoker’s novel. In fact, shortly
after finishing Nosferatu, its one and only film, Prana wentbankrupt in order to dodge copyright lawsuits from Stoker’s
widow.

5. Long thought to be a case of mistaken identity, the discoveryof the Bornean rainbow toad by European explorers in 1924
was recently verified by scientists. The explorers had made a
black-and-white sketch of an unusual toad they had foundin the jungles of Southeast Asia, christening it the Bornean
rainbow toad. Skeptical but curious, scientists recently went
to look for the toad—and ended up finding three specimens.

Why does the author say that the vampire in Nosferatu isnamed “Count Orlok” and not “Count Dracula”?
A. To show that the makers of Nosferatu made minorchanges to Stoker’s novel
B. To suggest that the characters in Nosferatu were basedon real people instead of literary characters
C. To criticize Nosferatu for its differences from its source
D. To praise the makers of Nosferatu for their imaginationin recreating Stoker’s novel

The passage implies which of the following about the
Bornean rainbow toad?
A. Some people doubted the existence of the toad.
B. Scientists were confident that they would find the toad.
C. The surviving toads have been relocated to Europe.
D. No human being had seen the toad since 1924.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
5

9. Guillermo Gonzalez Camarena became a successful inventor
at an early age. By the age of seven, he had constructed avariety of electronically-propelled toys to play with; he later
designed and built his own amateur radio and a functioning
telescope. In 1940, when he was only 23, Camarena obtained
the world’s first patent for color television. Camarena’s earlycolor television transmission system was the first one to beapproved by the U.S. Federal Communications Commission.
Other color-television technologies came after Camarena’s
patented invention, but his system is still used by a numberof scientists today.

the use of technology, including computers, a more central
part of children’s lives.
10. The author of Passage 2 probably would respond to the lastsentence of Passage 1 (“Parents . . . every day!”) by
A. asserting that parents should help children find abalance of indoor and outdoor activities
B. claiming that young children often know more about
computers than their parents do
C. pointing out that many children would rather use
technology than play outside
D. arguing that children should be spending more timeusing computers

In sentence 2, the word “functioning” most nearly means
A. performing
B. runningC. working
D. moving

11. The author of Passage 1 would most likely criticize theauthor of Passage 2 for
A. overemphasizing the strength of the data about
students’ technological literacy
B. overlooking the drawbacks of increasing the timechildren spend using technology
C. dismissing as unimportant the development that
occurs during outdoor activities
D. exaggerating the proportion of careers that require
knowledge of science and math

Directions for questions 10–11
Read the 2 passages below and then choose the bestanswer to each question. Answer the questions on thebasis of what is stated or implied in the passages.
Passage 1
I recently met a fifth-grade teacher who had asked her
students what they did after school. Most said they stayed
inside and watched TV or spent time on the computer.
Some went to a recreation center for an afterschool
program—where they played computer games. A handfulof students played outside, but most of those were doingorganized sports. It turned out that fewer than 10% of thechildren were enjoying unstructured time outside rather
than concentrating on electronic devices. This is a tragedy!
Now more than ever, kids need opportunities to learn
and develop through outdoor activities—and not just onorganized teams. Parents, limit computer use and encourage
your kids to get outside and play every day!

Directions for questions 12–15
Read the passage below and then choose the best answer
to each question. Answer the questions on the basis ofwhat is stated or implied in the passage.
The narrator of this passage from a short story describes thecabin where her father worked.
I wasn’t sure what this work involved, but it must have been
exciting because the Lab itself was exciting. Anywhere we
didn’t go often was exciting.

Passage 2
There is almost no reliable data about the level oftechnological literacy among children in the United States.
Our students perform relatively poorly on international
tests in science and math, however, and many other Westerncountries teach more about technology than we do. It seems
that American students are not as technologically literate
as their international counterparts. This could put themat a disadvantage when it comes to their careers, because
technology is everywhere, from medical facilities to farms.
Obviously, it is imperative that teachers and parents makeWe would get there in a heavy wooden rowboat, built in thefive-house village half a mile away—our mother would row,
she was quite good at it—or by following a twisty, winding
footpath, over fallen trees and stumps and around boulders
and across wet patches where a few slippery planks were laidacross the sphagnum moss, breathing in the mildew smellof damp wood and slowly decaying leaves. It was too far for
us to walk, our legs were too short, so mostly we went in the
rowboat.
The Lab was made of logs; it seemed enormous, though inthe two photographs of it that survive it looks like a shack. It
did however have a screened porch, with log railings. Inside
it there were things we weren’t allowed to touch—bottles
containing a dangerous liquid in which white grubs floated,their six tiny front legs clasped together like praying fingers,
and corks that smelled like poison and were poison, andtrays with dried insects pinned to them with long, thin pins,© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
6each with a tiny, alluring black knob for a head. All of thiswas so forbidden it made us dizzy.
At the Lab we could hide in the ice house, a dim andmysterious place that was always bigger on the inside thanit was on the outside, and where there was a hush, and a lotof sawdust to keep the blocks of ice cool. Sometimes there
would be a tin of evaporated milk with holes punched in the
top and wax paper stuck over them; sometimes there would
be a carefully hoarded stub of butter or an end of bacon;sometimes there would be a fish or two, pickerel or lake
trout, already filleted, laid out on a chipped enamel pie plate.
What did we do in there? There was nothing to actually do.
We’d pretend we had vanished—that nobody knew where
we were. This in itself was strangely energizing. Then we’dcome out, away from the silence, back into the pine-needle
scent and the sound of waves plocking against the shore, andour mother’s voice calling us, because it was time to get backinto the rowboat and row home.*
12. In line 1, “this work” clearly refers to
A. writing
B. food science
C. photography
D. insect research

13. Details in the passage suggest that the narrator is
A. an adult remembering a recent incident
B. an elderly person remembering middle age
C. an adult recalling a location from childhood
D. a child describing a frightening place

14. The descriptions of the Lab and of the ice house are similarin that both descriptions
A. emphasize cheerful and light-filled surroundings
B. contain images of hiding and concealment
C. highlight the narrator’s misconception of size
D. contrast with descriptions of the narrator’s home

15. When the narrator repeatedly uses the pronouns “we” and“us,” she is most likely speaking of herself and
A. a sibling
B. her mother
C. her father
D. the reader* Margaret Atwood, excerpt from “The Boys at the Lab” from Moral Disorder:
Stories. Copyright © 2006 by O. W. Toad, Ltd. Used by permission of Nan
A. Talese/Doubleday, a division of Random House, Inc. Any third party useof this material, outside of this publication, is prohibited. Interested parties
must apply directly to Random House, Inc. for permission.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
7

Writing

Writing Sample Questions

The Texas Success Initiative (TSI) Writing test
contains questions that measure proficiency in fourcontent areas. The four content areas are as follows:

Directions for questions 1–5
Read the following early draft of an essay and thenchoose the best answer to the question or the bestcompletion of the statement.

Essay Revision — Topics covered in this category
include:(1) Seaweed-based fuel could one day power your car. (2)It is more than just an ingredient in a purifying face mask
or a sushi roll. (3) According to new research, seaweed has
the potential to become an advanced biofuel known asbiobutanol.

• Coherence, organization and word choice.
• Rhetorical effectiveness and use of evidence
Agreement — Topics covered in this category include:(4) In the past, U.S. scientists have looked to the possibilityof algae-based biofuels, but most of these explorations haveshied away from kelp and seaweed. (5) One reason why
seaweed may not have taken off as a potential fuel sourceis the fact that it’s not a major part of American culture.
(6) In contrast, in Asian countries such as Japan, there has
been a long history of seaweed in the cuisine. (7) Japanese
researchers are much more familiar with it and have spentdecades studying its potential uses.

• Subject-verb agreement• Pronoun agreement• Verb tense
Sentence Structure — Topics covered in this category
include:• Comma splices and run-on sentences(8) A second reason for the U.S. avoidance of seaweedbased biofuel is the country’s lack of experience with
seaweed farming. (9) The U.S. is no stranger to seaweed
harvesting. (10) However, for the biobutanol project to beenvironmentally sustainable, seaweed cannot be harvested;
it must be farmed. (11) “One of the challenges of harvestinga natural seaweed bed is you can only [use] a certain percentof the bed if you don’t want to have a negative environmental
impact,” Nikesh Parekh, CEO of Bio Architecture Lab, said.

• Improper punctuation• Fragments and parallelism• Subordination and coordination
Sentence Logic — Topics covered in this category
include:• Correct placement of modifying phrase andclauses(12) Farming enough seaweed to support mass production ofa biofuel would be very expensive initially, but it could pay
off handsomely. (13) They say that the seaweed-based fuelwould work better in automobiles than ethanol and be easierto transport.

• The use of logical transitions

1. In context, which of the following is the best way to revise
and combine sentences 1 and 2 (reproduced below)?
Seaweed-based fuel could one day power your car. It is morethan just an ingredient in a purifying face mask or a sushi roll.
A. Seaweed-based fuel could one day power your car, it ismore than just an ingredient in a purifying face mask
or a sushi roll.
B. Seaweed-based fuel could one day power your car
because it is more than just an ingredient in a purifying
face mask or a sushi roll.
C. Seaweed is more than just an ingredient in a purifying
face mask or a sushi roll; seaweed-based fuel could one
day power your car.
D. Fuel from seaweed could one day power your car so it ismore than just an ingredient in a purifying face maskor sushi roll.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
8

Directions for questions 6–10
Select the best version of the underlined part of thesentence. If you think the original sentence is best,choose the first answer.

2. In context, where would the following sentence best beplaced?
There are a number of possible reasons for this.
A. After sentence 2
B. After sentence 4
C. After sentence 6
D. After sentence 9

6. It is important to learn how to swim, even if one is afraid;
the skill will invariably prove useful later in your life.
A. one is
B. you are
C. everyone is
D. they are

3. In context, which of the following is best to insert at the
beginning of sentence 7 (reproduced below)?
Japanese researchers are much more familiar with it and havespent decades studying its potential uses.

7. In the Roman Empire, the first fish to be brought indoors
was the sea barbel, it was kept under guest beds in small
tanks made of marble.
A. sea barbel, it
B. sea barbel, which
C. sea barbel, but
D. sea barbel and

A. As a result,
B. Ironically,
C. However,D. In addition,

4. In context, which of the following sentences would best be
inserted between sentences 9 and 10?
A. New research shows that seaweed may also possess thepower to repair tissue damage in heart attack patients.
B. Planting a large-scale seaweed farm will likely meetwith stiff opposition.
C. Maine Seaweed Co., for instance, harvests the seaweed
naturally available along the U.S. coast.
D. Some say that seaweed-based fuel may one day be competitive with petroleum.

8. The idea that lightning never strikes the same place twice
is one of the oldest and most well-known weather-related
myths; in fact, lightning strikes the Empire State Building in
New York City about 100 times per year.
A. in fact
B. therefore
C. moreover
D. in contrast

9. Horror films that keep viewers in a state of endless frightand which draw record-breaking crowds.
A. that keep viewers in a state of endless fright and whichdraw
B. keep viewers in a state of endless fright and drawing
C. that keep viewers in a state of endless fright draw
D. that keep viewers in a state of endless fright and theydraw

5. In context, which is the best revision to sentence 13(reproduced below)?
They say that the seaweed-based fuel would work better in
automobiles than ethanol and be easier to transport.
A. Replace “They say” with “Advocates contend”.
B. Replace “would work” with “would be”.
C. Delete “and be easier to transport”.
D. Insert “their” before “automobiles”.

10. According to explorers, a "Lost Falls" resembling New York's
Niagara Falls have been found in Tsangpo River Gorge inthe Himalaya Mountains.
A. have been foundB. has been foundC. having been foundD. being found© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
9

Directions for questions 11–15
Think about how you would rewrite the following
sentence according to the directions given, and thenchoose the best answer. Keep in mind that your revision
should not change the meaning of the original sentence.

14. Carmen created a new piñata by constructing a papier-mâchéfigure and decorating it with brilliantly colored tissue paper.
Rewrite, beginning with
To create a new piñata, …
The next words will be
A. Carmen constructed a papier-mâché figure
B. Carmen, constructing a papier-mâché figure
C. a papier-mâché figure that Carmen had to construct
D. that Carmen would construct a papier-mâché figure for

11. In some places, virtually all the topsoil has washed away,
leaving the subsoils to sustain the crops.
Rewrite, beginning with
In some places, the subsoils must sustain the crops …
The next word will be
A. although
B. because
C. until
D. before

15. If Antarctica’s icebergs could be floated north before
melting, many arid areas would experience relief fromdrought.
Rewrite, beginning with
If they could be floated north before melting, …

12. Hawaii, which consists of eight major islands and manysmaller ones, and which used to be known as the Sandwich
Islands, was admitted to the Union as the fiftieth state in
1959.

The next words will be
A. relief would be brought
B. many arid areas would experience
C. Antarctica’s icebergs would bringD. drought relief would be experienced

Rewrite, beginning with
Formerly known as the Sandwich Islands, and consisting ofeight major and many smaller islands, …
The next words will be
A. Hawaii wasB. in 1959
C. the Union
D. Hawaii, which

13. Facing a 50% cut in funding for the library, the director wasforced to lay off two librarians and sharply reduce hours ofoperation.
Rewrite, beginning with
Funding for the library was cut by 50%, …
The next words will be
A. the director was forced
B. forcing the director
C. this forced the director
D. two librarians were

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
10

Answer Key
Mathematics and Statistics
Question
NumberCorrect
Answer

1

C

Rationale
Choice (C) is correct. If 3t − 7 =5t , then 5t − 3t =−7 , and 2t = −7. Therefore,
6t =(3)(2t ) =(3)(−7) =−21.
Choice (B) is correct. Since the variables x and y are directly proportional, they are related by an2

B

equation y = kx, where k is a constant. It is given that y = 2 when x = 3, and so 2 = k (3), which

222(9) 6.
gives k = . Therefore, y = x, and so when x = 9, the value of y =is y =
3
3
3
y

C

3

D
x

O

Choice (D) is correct. The coordinates of point O are (0, 0), and the coordinates of point C are(6, 9). It follows that the slope of the line that contains these two points is

9−0 3
= .
6−0 2

The y -intercept of any line through point O is 0. Therefore, an equation of the line that contains
points O and C is y =3x.
2

Choice (D) is correct. Since there are 3 x − 2 trees planted in each row of the parcel, and a total of

4D

24 x − 16 trees planted in the parcel, it follows that the number of rows in the parcel iswhich can be rewritten as

8 ( 3x − 2 )3x − 2© 2013 The College Board.

24 x − 16,
3x − 2= 8.

Diagnostic and Placement Test Sample Questions
11

Choice (D) is correct. Let n be the number of sandwiches ordered. Then 18 − n was the number ofsoups ordered. Since the sandwiches cost $7.75 each, the soups cost $4.50 each and the total cost5Dof all 18 lunches was $113.50, the equation 113.5 = 7.75n + 4.5(18 − n) holds. Multiplying out
32.5=
n = 10.
= 7.75n + 81 − 4.5n, which simplifies to 32.5 = 3.25n, or
this equation gives 113.5
3.25
Therefore, 10 sandwiches were ordered.

6

B

Choice (B) is correct. A quadratic equation that has both 1 and −3 as solutions is

7A( x − 1)( x + 3) =0. Multiplying this equation out gives the equation x 2 + 2 x − 3 =0.
Choice (A) is correct. The y -intercept of the graph of an equation is the y -coordinate of
the point in the xy -plane where the graph intersects the y -axis. Thus the y -intercept canbe found by setting x = 0 and solving the equation y = 2( x + 3)( x − 4) for y. Therefore,y=2(0 + 3)(0 − 4) =−24 is the y -intercept of the graph of y = 2( x + 3)( x − 4).

8A

Choice (A) is correct. The expression x 4 − 1 is the difference of the squares x 4 = ( x 2 ) 2 and 1 = 12 ,and so it can be factored as x 4 − 1= ( x 2 − 1)( x 2 + 1). The factor x 2 − 1 is also a difference of squares,( x 2 − 1)( x 2 + 1) =( x + 1)( x − 1)( x 2 + 1).
and so x 4 − 1 =Choice (D) is correct. By definition, (3 x 2 y 3 )3 is equivalent to (3 x 2 y 3 )(3 x 2 y 3 )(3 x 2 y 3 ).

9D

By the commutative law of multiplication, this expression is equivalent to(3)(3)(3)( x 2 x 2 x 2 )( y 3 y 3 y 3 ). Since (3)(3)(3) = 27, x 2 x 2 x 2 = ( x ⋅ x) ⋅ ( x ⋅ x) ⋅ ( x ⋅ x) = x 6 andy 3 y 3 y 3 = ( y ⋅ y ⋅ y ) ⋅ ( y ⋅ y ⋅ y ) ⋅ ( y ⋅ y ⋅ y ) = y 9 , it follows that (3 x 2 y 3 )3 = 27 x 6 y 9 .

10B

Choice (B) is correct. Squaring both sides of the equation 5 − x =4 gives 5 − x =16, and so
x = −11. Substituting −11 for x in the original equation, one can see that −11 is a solution of theequation. Therefore, the value of x is −11.

11C

Choice (C) is correct. If

x −1
1= 20, then x − 1 =20 x. It follows that −1 =19 x, or x = − .
19xChoice (C) is correct. The equation h(t ) =20 − 16t 2 + 32t is equivalent to h(t ) =20 − 16t (t − 2).

12C

It follows that h(t ) = 20 when t = 0 and t = 2. Thus the maximum value of this quadratic
2−0function occurs when t is halfway between t = 0 and t = 2, which is when=t = 1.
2
Therefore, the maximum height, in feet, of the ball above the ground after it was kicked wash(1) =
20 − 16(1) 2 + 32(1) =36.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
12

Choice (C) is correct. If the length  of the yard is 18 feet longer than the width w of the

13

C

yard, then w=  − 18, and so the perimeter P, which is =P 2( + w), can be rewritten as2( +  − 18)= 2(2 − 18). Since the perimeter of the yard is 72 feet, it follows that 2 − 18 =36,
and so  = 27 and w = 27 − 18 = 9. Therefore, the area of the yard is (27)(9) = 243 square feet.

14

A

City

High
Temperature

A

t°F

B

87°F

C

81°F

D

62°F

E

93°F

Choice (A) is correct. If the median of the Thursday high temperatures for the five cities was 81°F,
then when the five high temperatures are listed in order from greatest to least (or least to greatest),
81°F must be the third temperature in the list. Since the three greatest known high temperaturesare 93°F, 87°F and 81°F, the unknown high temperature for City A must be less than or equalto 81°F. Of the given choices, only 85°F is NOT less than or equal to 81°F, and therefore only
85°F could NOT have been the high temperature last Thursday for City A.
Choice (A) is correct. Of the 20 children, 8 are boys and so 20 − 8 =12 are girls. Of the boys,

15

A

4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play, so

12 − 8 =4 girls do have a speaking part. Therefore, 4 + 4 =8 of the children have a speaking part.
It follows that if a child from the cast of the play is chosen at random, the probability that the child8 2= .
has a speaking part is
20 5

Reading
Question
Number1

Correct
AnswerRationaleD

Choice (D) is correct. The main idea of the passage is that underwater volcanoes receive little
attention but can be dangerous. The author explains that while “people generally do not takenote” of underwater eruptions because “the lava and smoke . . . is contained by the ocean,” such
eruptions are dangerous because they are “capable of creating huge tidal waves, threatening coastal
communities.” Choice (A) is incorrect because the passage highlights differences, not similarities,
between traditional and underwater volcanoes. Choice (B) is incorrect because although thepassage notes that the lava and smoke from underwater volcanoes is contained by the sea, that fact
is not the main idea; it supports the larger point about what people notice. Choice (C) is incorrect
because the passage does not indicate that most tidal waves are caused by underwater eruptions.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
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2

3

4

5

6

7

A

Choice (A) is correct. The author of the passage states that Franzen refers to his own work as
belonging to a “high-art literary tradition” and to Oprah’s book club choices as being “schmaltzy,”or overly sentimental, and “one-dimensional.” These details suggest that Franzen felt that his own
book is of higher quality than other books chosen for the book club. In other words, Franzen’s
criticism of the Oprah Book Club was motivated by his pride, or his sense of self-importance.
Choices (B) and (C) are incorrect because there is no indication in the passage that Franzen felt
any anger or was trying to be insensitive. Choice (D) is incorrect because there is no indicationthat Franzen’s comments about Oprah’s choices were ignorant or uninformed.

B

Choice (B) is correct. The author discusses Noah Webster and the idea that he deserves the titleof Founding Father. The author clearly considers Webster important, citing his “still-influential
dictionary” and his attempt to “legitimize an ‘American English.’” Choice (A) is incorrect because
although the author mentions that the Founding Fathers authored certain documents, he or she
offers no specific praise of the Founding Fathers. Choices (C) and (D) are incorrect; although
the author mentions Webster’s attempt “to legitimize an ‘American English’” and to create an
American English dictionary, neither of these points is the main focus of the passage.

B

Choice (B) is correct. The author of the passage is interested in and supportive of the edible insect
initiative. He or she addresses the reader directly, urging, “you might consider expanding yourdaily diet to include bugs.” The author also shows support for the edible insect movement bystating that advocates of the movement “rightfully” argue that “farming insects has a much lower
environmental impact than does raising livestock.” Choice (A) is incorrect because although theauthor expresses support for the edible insect initiative, he or she does not speak with awe andamazement, or great wonder. Choices (C) and (D) are incorrect because the author is positive
about the movement, showing interest and support rather than fear or disgust.

A

Choice (A) is correct. The author suggests that some people doubted the existence of the Bornean
rainbow toad: they “thought [it] to be a case of mistaken identity” and were “skeptical.” In otherwords, some people thought the “European explorers” were documenting another, already known
kind of toad, and had not discovered a new toad. This is supported by the fact that the discovery
was not “verified” for many years. Choices (B), (C), and (D) are incorrect: the author suggeststhat scientists did not expect to find the Bornean rainbow toad, there is no indication that the
recently-found toads were taken to Europe, and it is unlikely that no human being—including
non-scientists—had seen any specimen of the toad since 1924.

B

Choice (B) is correct. The main idea of the passage is that television may have become less popularthan the Internet. The author points out that “Internet use” is “on the rise,” and that some people
wonder if using the Internet will soon become “Americans’ primary leisure activity.” The author
points out that surfing the net might already be more popular than watching television, as“recent surveys show that time spent on the Internet is now greater than time spent in front of
the television”—though some people use the Internet and watch TV at the same time. Choices(A), (C), and (D) are incorrect: it might be true that television is just one of many information
sources, but the author does not address this, and he or she also does not indicate that television iswatched by more people now than ever before, or that television programs tend to focus more on
entertainment than on news.

A

Choice (A) is correct. The passage indicates that the arrangement of the layers of thin wood—“withthe grain of each layer making a right angle with the grain of the layer below it”—is what “makes
plywood difficult to break.” In other words, the arrangement of the layers explains plywood’s
strength. Choices (B), (C), and (D) are incorrect: the author describes plywood as “inexpensive,”“not the most pleasing wood to look at,” and “flexible,” but he or she does not connect any of thesefacts to the layering of sheets of wood.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
14

8

9

10

11

12

13

A

Choice (A) is correct. The author points out that the film Nosferatu is “closely based on”—but notexactly the same as—“Bram Stoker’s 1897 novel, Dracula.” He or she explains that the vampire in
Nosferatu is “called ‘Count Orlok’ rather than ‘Count Dracula’” in order to show that the makers
of Nosferatu made minor changes to Stoker’s novel as a result of being “unable to secure the rights”
to Dracula. Choices (B), (C), and (D) are incorrect because the author does not indicate that thecharacters in Nosferatu were based on real people, and he or she neither criticizes Nosferatu forits differences from Dracula nor praises the makers of the film for their imagination in recreating
Stoker’s novel.

C

Choice (C) is correct. The author speaks of Camarena’s successful inventions. In this context,“functioning” means “working”; the author is indicating that Camarena built a telescope that
actually worked. He or she is not indicating that the telescope was performing, running, ormoving.

D

Rationale: Choice (D) is correct. The author of Passage 2 believes that American students should
be more technologically literate and suggests that “the use of technology, including computers,”
should be “a more central part of children’s lives.” Therefore, he or she almost certainly would saythat instead of limiting computer use, parents should encourage children to spend more time using
computers. Choices (A), (B), and (C) are incorrect because the author of Passage 2 does not discuss
outdoor activities, adults’ computer knowledge, or children’s recreational preferences.

B

Choice (B) is correct. The author of Passage 1 finds it very troubling that so many children spend
their time on computers and other electronic devices instead of playing outside. The author of
Passage 2, on the other hand, thinks technology should be an even bigger part of children’s lives
than it already is. It is likely that the author of Passage 1 would criticize the author of Passage 2 for
failing to think about the drawbacks of this increased time spent on technology—such as a decreased
amount of time to spend “learn[ing] and develop[ing] through outdoor activities.” Choice (A) is
incorrect because the author of Passage 2 states that there is very little “reliable data,” and choice (C)is incorrect because he or she does not discuss and dismiss development during outdoor activities.
Choice (D) is incorrect because the author of Passage 1 makes no mention of careers, and there is no
indication that the author of Passage 2 is exaggerating when speaking of careers.

D

Choice (D) is correct. In the first part of the passage, the narrator refers to “this work,” saying that“it must have been exciting because the Lab itself was exciting.” While she isn’t “sure what thiswork involved,” she describes the Lab very fully: the mysterious journey to get to it, its exterior,then its contents (“bottles containing a dangerous liquid in which white grubs floated . . . trays
with dried insects”) and other aspects of her father’s work. The narrator never directly states what
“this work” is, but these and other elements of the passage imply that it involves scientific researchwith such insects as the grubs. Choices (A), (B), and (C) are incorrect because there is no indicationin the passage that the narrator’s father is involved in writing, food science, or photography.

C

Choice (C) is correct. The narrator uses the past tense throughout the passage, signaling to thereader that the events described occurred in the past. And the passage contains numerous hints
that the narrator is describing her childhood self: “our mother would row” and “our legs were too
short,” for example. It is reasonable to assume that the narrator is an adult recalling a location(and events) from childhood. Choices (A) and (B) are incorrect because the incidents described areclearly not recent, nor do the events recalled happen to a middle-aged person. And although theplace has elements of scariness about it, the person describing it is clearly not a child; therefore,
choice (D) is incorrect.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
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14

15

C

Choice (C) is correct. When describing the Lab, the narrator states that “it seemed enormous,
though in the two photographs of it that survive it looks like a shack.” When describing the ice
house, she states that it “was always bigger on the inside than it was on the outside.” Both thesedescriptions emphasize misconceptions about the size of a place. The first misconception occurs
because of a child’s natural perception that a place is larger than it is in reality, and is correctedby an adult viewing of photographs; the second plays on a child’s mistaken perception of the sizeof a place based on its exterior. Choices (A) and (D) are incorrect because there are no cheerfuland light-filled surroundings in the passage, nor is there a description of the narrator’s home. And
although the narrator does speak of hiding and concealing herself in the ice house, she does not
speak of doing so in the Lab itself; therefore, choice (B) is incorrect.

A

Choice (A) is correct. In lines 3-4, when referring to the journey to the Lab, the narrator states,“our mother would row.” At the end of the passage—after she has described repeated adventures atthe Lab while accompanied by at least one other person—she recalls hearing “our mother’s voice
calling us, because it was time to get back into the rowboat and row home.” It is clear that thenarrator’s companion shared a mother and a home with the narrator—in other words, the otherperson is the narrator’s sibling. Choices (B) and (D) are incorrect because the narrator’s motheris clearly differentiated from the companion in the passage and the reader does not participate in
the events described in the passage. Although the narrator is describing the place where her father
worked, there is no indication that her father was the other person accompanying her; indeed, it isunlikely that the narrator’s father’s legs would be “too short” for the walk, and he might not hidewith a small child inside an ice house. Therefore, choice (C) is incorrect.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
16

Writing
Question
Number1

2

3

4

Correct
AnswerRationale

C

Choice (C) is correct. The new sentence must be a logical and grammatical combination of theexisting sentences, which indicate that “Seaweed-based fuel could one day power your car” andthat “It” (presumably, seaweed) “is more than just an ingredient in a purifying face mask or a sushi
roll.” Only (C) properly orders the two claims, first expressing that “Seaweed is more than just an
ingredient . . .” and then, following a correct use of a semicolon to join two related independent
clauses, narrowing the focus to “seaweed-based fuel.” The other choices introduce errors: choice(A) creates a comma splice (two independent clauses joined by only a comma), choice (B) provides
an illogical cause-effect statement, and choice (D) contains a vague pronoun (“it”).

B

Choice (B) is correct. The new sentence, “There are a number of possible reasons for this,” needs
to fit logically and grammatically between two existing sentences. Sentence 4 states that American
scientists have “shied away from,” or ignored, kelp and seaweed as possible biofuels. Sentence 5
notes “One reason why seaweed may not have taken off as a fuel source.” Later in the passage,
sentence 8 provides “A second reason for the U.S. avoidance of seaweed-based biofuel.” The new
sentence fits logically and grammatically between sentences 4 and 5 because it introduces thereasons for “this” (American scientists’ neglect of kelp and seaweed as potential fuel sources)—
reasons that are provided in the following sentences. On the contrary, if choices (A), (C), or (D)were chosen as the answer, “this” would refer to other things for which no reasons are given.

A

Choice (A) is correct. The inserted word or phrase must properly link sentence 7 with the sentencesthat come before it in the passage. Sentences 5 and 6 suggest that unlike the U.S., where seaweed
has not been considered a potential fuel source because U.S. scientists are not familiar with it,
Japan has “a long history of seaweed in the cuisine.” Sentence 7 states that “Japanese researchers
are much more familiar with it and have spent decades studying its potential uses.” Only thephrase “As a result” properly links sentence 7 with what has come before: in the context of thepassage, Japanese scientists’ familiarity with seaweed is clearly a result of its history as a food intheir culture. Choices (B) and (C) suggest a contrast between sentences 6 and 7 that does not exist,
and choice (D) suggests that sentence 7 simply adds more information to sentence 6 rather thanshowing the proper cause-effect relationship.

C

Choice (C) is correct. The new sentence needs to fit logically and grammatically between sentence
9 (“The U.S. is no stranger to seaweed harvesting”) and sentence 10 (“However, for the biobutanol
project to be environmentally sustainable, seaweed cannot be harvested; it must be farmed”). The
only sentence that provides a direct link back to sentence 9 and forward to sentence 10 is choice(C): “Maine Seaweed Co., for instance, harvests the seaweed naturally available along the U.S.
coast.” This sentence provides the example of Maine Seaweed, a seaweed-harvesting company, tosupport the claim in sentence 9 that the U.S. is familiar with seaweed harvesting. And sentence
10 seems to refer back to the work of Maine Seaweed in stating that “However . . . seaweed cannot
be harvested; it must be farmed.” Neither choice (A), choice (B), nor choice (D) offers the same
explicit, logical link to sentences 9 and 10.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
17

5

6

7

8

9

10

11

A

Choice (A) is correct. It is unclear to whom the pronoun “They” in sentence 13 refers. In fact, there
are no plural nouns in the sentences that come before sentence 13 to which “They” could possiblyrefer. “They” must, therefore, be replaced with a plural noun describing the people who “say thatthe seaweed-based fuel would work better in automobiles than ethanol and be easier to transport.”
These people clearly support the use of seaweed as a biofuel, so it would be appropriate to refer tothem as “Advocates.” In addition, they are making an argumentative claim, so it would be more
precise to state that they “contend” than that they “say” what follows. None of the other threepotential revisions—choices (B), (C), and (D)—solves the problem presented by “They,” and each is
unnecessary.

B

Choice (B) is correct. It avoids the pronoun agreement errors of the other options by providing thesecond-person pronoun “you” to be consistent with the second-person pronoun “your” that follows
it (“in your life”). The third-person pronouns “one,” “everyone” and “they,” in choices (A), (C) and(D), respectively, are not consistent with the second-person pronoun “your.”B

Choice (B) is correct. It avoids the comma-splice error of the original sentence by replacing the
pronoun “it” with the relative pronoun “which,” thus making the second independent clause into
a dependent clause. Two independent clauses (“the first fish to be brought indoors was the sea
barbel” and “it was kept under guest beds in small tanks made of marble”) cannot be joined byonly a comma. Choice (C) is incorrect, because there is no contrast between the idea that “the firstfish to be brought indoors was the sea barbel” and the fact that the sea barbel “was kept underguest beds.” Choice (D) results in awkward phrasing: “. . . the first fish to be brought indoors was
the sea barbel and was kept under guest beds . . . ”

A

Choice (A) is correct. It avoids the illogical phrasing of the other options by providing the phrase“in fact,” which is used in this context to introduce evidence validating a previous statement. In
this sentence, the information in the second clause (“lightning strikes the Empire State Building. . . about 100 times per year”) offers evidence confirming the truth of the statement made in thefirst clause (“The idea that lightning never strikes the same place twice” is a “well-known” yet false
belief). Options (B), (C) and (D), while grammatically correct, result in illogical phrasing because
they do not indicate the relationship specified by the information in the sentence.

C

Choice (C) is correct. It avoids the sentence-fragment error of the original sentence by providing
the main verb “draw” to agree with the subject “horror films” and to carry out the action of thesentence. In addition, choice (C) appropriately provides the relative clause “that keep viewers ina state of endless fright” to modify the noun phrase that precedes it, “horror films.” None of theother options results in a complete sentence.

B

Choice (B) is correct. It avoids the subject-verb agreement error of the original sentence by
providing the singular verb phrase “has been found” to carry out the action of the sentence.
Choices (C) and (D) result in sentence fragments; they provide participial verb forms (“having
been found,” “being found”), not main verbs.

B

Choice (B) is correct. The sentence should be rewritten “In some places, the subsoils must sustain
the crops because virtually all the topsoil has washed away.” Choice (B) avoids the errors of theother options and appropriately provides the causal link needed to explain why the subsoils mustsustain the crops. None of the other options can express the causal relationship between the twoideas (“virtually all the topsoil has washed away” and “the subsoils must sustain the crops”) in thesentence.

© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
18

12

13

14

15

A

Choice (A) is correct. The sentence should be rewritten “Formerly known as the Sandwich Islands,
and consisting of eight major and many smaller islands, Hawaii was admitted to the Union as thefiftieth state in 1959.” Choice (A) avoids the modification errors of choices (B) and (C) by placing
the subject, “Hawaii,” directly after the phrases modifying it, “Formerly known as the Sandwich
Islands” and “consisting of eight major and many smaller islands.” Choice (D) also avoids themodification errors but results in a sentence fragment; there is no main verb to carry out the actionof the sentence, only the relative clause beginning “which.”

B

Choice (B) is correct. The sentence should be rewritten “Funding for the library was cut by 50%,
forcing the director to lay off two librarians and sharply reduce hours of operation.” Each of theother choices results in a comma splice, with two independent clauses improperly joined by only acomma. Choice (B) avoids the comma-splice error by providing the participial phrase “forcing thedirector to lay off two librarians . . . ” to join the independent clause “Funding for the library was
cut by 50%.”A

Choice (A) is correct. The sentence should be rewritten “To create a new piñata, Carmen
constructed a papier-mâché figure and decorated it with brilliantly colored tissue paper.” Choice(A) avoids the errors of the other options by providing the past tense verb “constructed” to serve as
one of the two main verbs in the sentence. Each of the other options results in a sentence fragmentwith no main verb to carry out the action of the sentence.

C

Choice (C) is correct. The sentence should be rewritten “If they could be floated north before
melting, Antarctica’s icebergs would bring many arid areas relief from drought.” Choice (C) avoids
the modification and pronoun errors of the other options by providing the appropriate subject,“Antarctica’s icebergs,” immediately after the dependent clause that modifies it, “If they could befloated north before melting.” Choices (A) and (D) do not clearly establish that “they” refers to“Antarctica’s icebergs,” and choice (B) illogically implies that “many arid areas” “could be floatednorth before melting.”© 2013 The College Board.

Diagnostic and Placement Test Sample Questions
19