Answer Explanations
SAT Practice Test #2®

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5LSA07

Answer Explanations

SAT Practice Test #2
Section 1: Reading Test
QUESTION 1.
Choice A is the best answer. The narrator admits that his job is “irksome”(line 7) and reflects on the reasons for his dislike. The narrator admits that
his work is a “dry and tedious task” (line 9) and that he has a poor relationship with his superior: “the antipathy which had sprung up between myself
and my employer striking deeper root and spreading denser shade daily,
excluded me from every glimpse of the sunshine of life” (lines 28-31).
Choices B, C, and D are incorrect because the narrator does not become
increasingly competitive with his employer, publicly defend his choice ofoccupation, or exhibit optimism about his job.

QUESTION 2.
Choice B is the best answer. The first sentence of the passage explains thatpeople do not like to admit when they’ve chosen the wrong profession andthat they will continue in their profession for a while before admitting theirunhappiness. This statement mirrors the narrator’s own situation, as thenarrator admits he finds his own occupation “irksome” (line 7) but that hemight “long have borne with the nuisance” (line 10) if not for his poor relationship with his employer.
Choices A, C, and D are incorrect because the first sentence does not discuss
a controversy, focus on the narrator’s employer, Edward Crimsworth, or provide any evidence of malicious conduct.

QUESTION 3.
Choice C is the best answer. The first paragraph shifts from a general dis-cussion of how people deal with choosing an occupation they later regret(lines 1-6) to the narrator’s description of his own dissatisfaction with his
occupation (lines 6-33).
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Choices A, B, and D are incorrect because the first paragraph does not focus
on the narrator’s self-doubt, his expectations of life as a tradesman, or his
identification of alternatives to his current occupation.

QUESTION 4.
Choice A is the best answer. In lines 27-33, the narrator is describing thehostile relationship between him and his superior, Edward Crimsworth.
This relationship causes the narrator to feel like he lives in the “shade” andin “humid darkness.” These words evoke the narrator’s feelings of dismay
toward his current occupation and his poor relationship with his superior—factors that cause him to live without “the sunshine of life.”
Choices B, C, and D are incorrect because the words “shade” and “darkness”
do not reflect the narrator’s sinister thoughts, his fear of confinement, or his
longing for rest.

QUESTION 5.
Choice D is the best answer. The narrator states that Crimsworth dis-

likes him because the narrator may “one day make a successful tradesman” (line 43). Crimsworth recognizes that the narrator is not “inferior
to him” but rather more intelligent, someone who keeps “the padlock ofsilence on mental wealth which [Crimsworth] was no sharer” (lines 44-48).
Crimsworth feels inferior to the narrator and is jealous of the narrator’s
intellectual and professional abilities.
Choices A and C are incorrect because the narrator is not described as exhibiting “high spirits” or “rash actions,” but “Caution, Tact, [and] Observation”(line 51). Choice B is incorrect because the narrator’s “humble background”
is not discussed.

QUESTION 6.
Choice B is the best answer. Lines 61-62 state that the narrator “hadlong ceased to regard Mr. Crimsworth as my brother.” In these lines, theterm “brother” means friend or ally, which suggests that the narrator andCrimsworth were once friendly toward one another.
Choices A, C, and D are incorrect because the narrator originally viewed
Crimsworth as a friend, or ally, and later as a hostile superior; he never viewed
Crimsworth as a harmless rival, perceptive judge, or demanding mentor.

QUESTION 7.
Choice D is the best answer. In lines 61-62, the narrator states that he once

regarded Mr. Crimsworth as his “brother.” This statement provides evidence
that the narrator originally viewed Crimsworth as a sympathetic ally.
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Choices A, B, and C do not provide the best evidence for the claim that
Crimsworth was a sympathetic ally. Rather, choices A, B, and C provide evidence of the hostile relationship that currently exists between the narrator
and Crimsworth.

QUESTION 8.
Choice D is the best answer. In lines 48-53, the narrator states that he exhibited “Caution, Tact, [and] Observation” at work and watched Mr. Crimsworthwith “lynx-eyes.” The narrator acknowledges that Crimsworth was “prepared
to steal snake-like” if he caught the narrator acting without tact or being disrespectful toward his superiors (lines 53-56). Thus, Crimsworth was trying
to find a reason to place the narrator “in a ridiculous or mortifying position”(lines 49-50) by accusing the narrator of acting unprofessionally. The use of
the lynx and snake serve to emphasize the narrator and Crimsworth’s adversarial, or hostile, relationship.

Choices A and B are incorrect because the description of the lynx and snake
does not contrast two hypothetical courses of action or convey a resolution.
Choice C is incorrect because while lines 48-56 suggest that Crimsworth istrying to find a reason to fault the narrator’s work, they do not imply that analtercation, or heated dispute, between the narrator and Crimsworth is likely
to occur.

QUESTION 9.
Choice B is the best answer. Lines 73-74 state that the narrator noticed

there was no “cheering red gleam” of fire in his sitting-room fireplace. The
lack of a “cheering,” or comforting, fire suggests that the narrator sometimes
found his lodgings to be dreary or bleak.
Choices A and D are incorrect because the narrator does not find his living quarters to be treacherous or intolerable. Choice C is incorrect because
while the narrator is walking home he speculates about the presence of a firein his sitting-room’s fireplace (lines 69-74), which suggests that he could notpredict the state of his living quarters.

QUESTION 10.
Choice D is the best answer. In lines 68-74, the narrator states that he did not
see the “cheering” glow of a fire in his sitting-room fireplace. This statement
provides evidence that the narrator views his lodgings as dreary or bleak.

Choices A, B, and C do not provide the best evidence that the narrator views
his lodgings as dreary. Choices A and C are incorrect because they do notprovide the narrator’s opinion of his lodgings, and choice B is incorrect
because lines 21-23 describe the narrator’s lodgings only as “small.”3

QUESTION 11.
Choice D is the best answer. In lines 11-12, the author introduces themain purpose of the passage, which is to examine the “different views on
where ethics should apply when someone makes an economic decision.”
The passage examines what historical figures Adam Smith, Aristotle,
and John Stuart Mill believed about the relationship between ethics
and economics.
Choices A, B, and C are incorrect because they identify certain points
addressed in the passage (cost-benefit analysis, ethical economic behavior, and the role of the free market), but do not describe the passage’s
main purpose.

QUESTION 12.
Choice D is the best answer. In lines 4-5, the author suggests that people

object to criticizing ethics in free markets because they believe free markets are inherently ethical, and therefore, the role of ethics in free markets
is unnecessary to study. In the opinion of the critics, free markets are ethical because they allow individuals to make their own choices about which
goods to purchase and which goods to sell.
Choices A and B are incorrect because they are not objections that criticize
the ethics of free markets. Choice C is incorrect because the author does notpresent the opinion that free markets depend on devalued currency.

QUESTION 13.
Choice A is the best answer. In lines 4-5, the author states that some people
believe that free markets are “already ethical” because they “allow for personal choice.” This statement provides evidence that some people believe
criticizing the ethics of free markets is unnecessary because free markets
permit individuals to make their own choices.

Choices B, C, and D are incorrect because they do not provide the best evidence of an objection to a critique of the ethics of free markets.

QUESTION 14.
Choice B is the best answer. In lines 6-7, the author states that people “haveaccepted the ethical critique and embraced corporate social responsibility.”In this context, people “embrace,” or readily adopt, corporate social responsibility by acting in a certain way.
Choices A, C, and D are incorrect because in this context “embraced” does
not mean lovingly held, eagerly hugged, or reluctantly used.

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QUESTION 15.
Choice C is the best answer. The third and fourth paragraphs of the passage

present Adam Smith’s and Aristotle’s different approaches to defining ethics
in economics. The fifth paragraph offers a third approach to defining ethicaleconomics, how “instead of rooting ethics in character or the consequencesof actions, we can focus on our actions themselves. From this perspective
some things are right, some wrong” (lines 45-48).
Choice A is incorrect because the fifth paragraph does not develop a counterargument. Choices B and D are incorrect because although “character” isbriefly mentioned in the fifth paragraph, its relationship to ethics is examined in the fourth paragraph.

QUESTION 16.
Choice A is the best answer. In lines 57-59, the author states that “Manymoral dilemmas arise when these three versions pull in different directions
but clashes are not inevitable.” In this context, the three different perspectives on ethical economics may “clash,” or conflict, with one another.
Choices B, C, and D are incorrect because in this context “clashes” does notmean mismatches, collisions, or brawls.

QUESTION 17.
Choice C is the best answer. In lines 59-64, the author states, “Take fairtrade coffee . . . for example: buying it might have good consequences, bevirtuous, and also be the right way to act in a flawed market.” The author
is suggesting that in the example of fair trade coffee, all three perspectives
about ethical economics—Adam Smith’s belief in consequences dictating
action, Aristotle’s emphasis on character, and the third approach emphasizing the virtue of good actions—can be applied. These three approaches share“common ground” (line 64), as they all can be applied to the example of fairtrade coffee without contradicting one another.
Choices A, B, and D are incorrect because they do not show how the threedifferent approaches to ethical economics share common ground. Choice A
simply states that there are “different views on ethics” in economics, choice
B explains the third ethical economics approach, and choice D suggests thatpeople “behave like a herd” when considering economics.

QUESTION 18.
Choice C is the best answer. In lines 83-88, the author states that psychol-ogy can help “define ethics for us,” which can help explain why people “reactin disgust at economic injustice, or accept a moral law as universal.”

5Choices A and B are incorrect because they identify topics discussed in the
final paragraph (human quirks and people’s reaction to economic injustice)
but not its main idea. Choice D is incorrect because the final paragraphdoes not suggest that economists may be responsible for reforming thefree market.

QUESTION 19.
Choice A is the best answer. The data in the graph show that in Tanzania

between the years 2000 and 2008, fair trade coffee profits were around$1.30 per pound, while profits of regular coffee were in the approximate
range of 20–60 cents per pound.
Choices B, C, and D are incorrect because they are not supported by information in the graph.

QUESTION 20.
Choice B is the best answer. The data in the graph indicate that between

2002 and 2004 the difference in per-pound profits between fair trade andregular coffee was about $1. In this time period, fair trade coffee was valued at around $1.30 per pound and regular coffee was valued at around20 cents per pound. The graph also shows that regular coffee recorded
the lowest profits between the years 2002 and 2004, while fair tradecoffee remained relatively stable throughout the entire eight-year span
(2000 to 2008).
Choices A, C, and D are incorrect because they do not indicate the greatest
difference between per-pound profits for fair trade and regular coffee.

QUESTION 21.
Choice C is the best answer. In lines 59-61, the author defines fair tradecoffee as “coffee that is sold with a certification that indicates the farmers
and workers who produced it were paid a fair wage.” This definition suggests that purchasing fair trade coffee is an ethically responsible choice, andthe fact that fair trade coffee is being produced and is profitable suggeststhat ethical economics is still a consideration. The graph’s data support thisclaim by showing how fair trade coffee was more than twice as profitable asregular coffee.
Choice A is incorrect because the graph suggests that people acting on
empathy (by buying fair trade coffee) is productive for fair trade coffee
farmers and workers. Choices B and D are incorrect because the graph does
not provide support for the idea that character or people’s fears factor into
economic choices.

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QUESTION 22.
Choice C is the best answer. The author of Passage 1 indicates that people

can benefit from using screen-based technologies as these technologies
strengthen “certain cognitive skills” (line 3) and the “brain functions related
to fast-paced problem solving” (lines 14-15).
Choice A is incorrect because the author of Passage 1 cites numerous studies
of screen-based technologies. Choice B is incorrect because it is not supported by Passage 1, and choice D is incorrect because while the author
mentions some benefits to screen-based technologies, he does not encourage their use.

QUESTION 23.
Choice A is the best answer. In lines 3-4, the author of Passage 1 pro-vides evidence that the use of screen-based technologies has some positiveeffects: “Certain cognitive skills are strengthened by our use of computers
and the Net.”
Choices B, C, and D are incorrect because they do not provide the best evidence that the use of screen-based technologies has some positive effects.
Choices B, C, and D introduce and describe the author’s reservations about
screen-based technologies.

QUESTION 24.
Choice B is the best answer. The author of Passage 1 cites Patricia

Greenfield’s study, which found that people’s use of screen-based technologies weakened their ability to acquire knowledge, perform “inductive analysis” and “critical thinking,” and be imaginative and reflective(lines 34-38). The author of Passage 1 concludes that the use of screen-based
technologies interferes with people’s ability to think “deeply” (lines 47-50).
Choices A, C, and D are incorrect because the author of Passage 1 does
not address how using the Internet affects people’s health, social contacts,or self-confidence.

QUESTION 25.
Choice C is the best answer. In lines 39-41, the author states, “We knowthat the human brain is highly plastic; neurons and synapses change as
circumstances change.” In this context, the brain is “plastic” because it ismalleable, or able to change.
Choices A, B, and D are incorrect because in this context “plastic” does notmean creative, artificial, or sculptural.

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QUESTION 26.
Choice B is the best answer. In lines 60-65, the author of Passage 2 explains

how speed-reading does not “revamp,” or alter, how the brain processes
information. He supports this statement by explaining how Woody Allen’sreading of War and Peace in one sitting caused him to describe the novel
as “about Russia.” Woody Allen was not able to comprehend the “famously
long” novel by speed-reading it.
Choices A and D are incorrect because Woody Allen’s description of War
and Peace does not suggest he disliked Tolstoy’s writing style or that heregretted reading the book. Choice C is incorrect because the anecdote
about Woody Allen is unrelated to multitasking.

QUESTION 27.
Choice D is the best answer. The author of Passage 2 states that people likenovelists and scientists improve in their profession by “immers[ing] themselves in their fields” (line 79). Both novelists and scientists, in other words,
become absorbed in their areas of expertise.

Choices A and C are incorrect because the author of Passage 2 does notsuggest that novelists and scientists both take risks when they pursue
knowledge or are curious about other subjects. Choice B is incorrect
because the author of Passage 2 states that “accomplished people” don’t
perform “intellectual calisthenics,” or exercises that improve their minds(lines 77-78).

QUESTION 28.
Choice D is the best answer. In lines 83-90, the author of Passage 2 criti-

cizes media critics for their alarmist writing: “Media critics write as if thebrain takes on the qualities of whatever it consumes, the informational
equivalent of ‘you are what you eat.’ ” The author then compares media
critics’ “you are what you eat” mentality to ancient people’s belief that“eating fierce animals made them fierce.” The author uses this analogy todiscredit media critics’ belief that consumption of electronic media alters
the brain.
Choices A, B, and C are incorrect because the final sentence of Passage 2
does not use ornate language, employ humor, or evoke nostalgia for the past.

QUESTION 29.
Choice D is the best answer. The author of Passage 1 argues that online

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and other screen-based technologies affect people’s abilities to think
deeply (lines 47-50). The author of Passage 2 argues that the effects ofconsuming electronic media are less drastic than media critics suggest(lines 81-82).

Choices A and B are incorrect because they discuss points made in the passages
but not the main purpose of the passages. Choice C is incorrect because neither
passage argues in favor of increasing financial support for certain studies.

QUESTION 30.
Choice B is the best answer. The author of Passage 1 cites scientific researchthat suggests online and screen-based technologies have a negative effect on
the brain (lines 25-38). The author of Passage 2 is critical of the researchhighlighted in Passage 1: “Critics of new media sometimes use science itself
to press their case, citing research that shows how ‘experience can change thebrain.’ But cognitive neuroscientists roll their eyes at such talk” (lines 51-54).
Choices A, C, and D are incorrect because they do not accurately describe
the relationship between the two passages. Passage 1 does not take a clinicalapproach to the topic. Passage 2 does not take a high-level view of a finding
examined in depth in Passage 1, nor does it predict negative reactions to thefindings discussed in paragraph 1.

QUESTION 31.
Choice C is the best answer. In Passage 1, the author cites psychologist Patricia

Greenfield’s finding that “‘every medium develops some cognitive skills at theexpense of others’” (lines 29-31). In Passage 2, the author states “If you train people to do one thing (recognize shapes, solve math puzzles, find hidden words),
they get better at doing that thing, but almost nothing else” (lines 71-74). Bothauthors would agree than an improvement in one cognitive area, such as visualspatial skills, would not result in improved skills in other areas.
Choice A is incorrect because hand-eye coordination is not discussed in
Passage 2. Choice B is incorrect because Passage 1 does not suggest that critics of electronic media tend to overreact. Choice D is incorrect because neither passage discusses whether Internet users prefer reading printed texts ordigital texts.

QUESTION 32.
Choice B is the best answer. In Passage 1, the author cites Michael
Merzenich’s claim that when people adapt to a new cultural phenomenon,
including the use of a new medium, we end up with a “different brain”(lines 41-43). The author of Passage 2 somewhat agrees with Merzenich’s
claim by stating, “Yes, every time we learn a fact or skill the wiring of thebrain changes” (lines 54-56).

Choices A, C, and D do not provide the best evidence that the author of
Passage 2 would agree to some extent with Merzenich’s claim. Choices A
and D are incorrect because the claims are attributed to critics of new media.
Choice C is incorrect because it shows that the author of Passage 2 does notcompletely agree with Merzenich’s claim about brain plasticity.

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QUESTION 33.
Choice B is the best answer. In lines 16-31, Stanton argues that men

make all the decisions in “the church, the state, and the home.” This absolute power has led to a disorganized society, a “fragmentary conditionof everything.” Stanton confirms this claim when she states that society needs women to “lift man up into the higher realms of thought andaction” (lines 60-61).
Choices A and D are incorrect because Stanton does not focus on women’slack of equal educational opportunities or inability to hold political positions. Choice C is incorrect because although Stanton implies womenare not allowed to vote, she never mentions that “poor candidates” arewinning elections.

QUESTION 34.
Choice A is the best answer. Stanton argues that women are repressed insociety because men hold “high carnival,” or have all the power, and makethe rules in “the church, the state, and the home” (lines 16-31). Stanton
claims that men have total control over women, “overpowering the feminine
element everywhere” (line 18).
Choices B, C, and D are incorrect because Stanton does not use the term“high carnival” to emphasize that the time period is freewheeling, or unrestricted; that there has been a scandalous decline in moral values; or that thepower of women is growing.

QUESTION 35.
Choice D is the best answer. In lines 16-23, Stanton states that men’s absolute rule in society is “crushing out all the diviner qualities in human nature,”such that society knows very “little of true manhood and womanhood.”
Stanton argues that society knows less about womanhood than manhood,because womanhood has “scarce been recognized as a power until within
the last century.” This statement indicates that society’s acknowledgementof “womanhood,” or women’s true character, is a fairly recent historicaldevelopment.

Choices A, B, and C are incorrect because Stanton describes men’s control ofsociety, their domination of the domestic sphere, and the prevalence of war
and injustice as long-established realities.

QUESTION 36.
Choice B is the best answer. In lines 16-23, Stanton provides evidence forthe claim that society’s acknowledgement of “womanhood,” or women’strue character, is a fairly recent historical development: “[womanhood] has
scarce been recognized as a power until within the last century.”
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Choices A, C, and D are incorrect because they do not provide the best evidence that society’s acknowledgement of “womanhood,” or women’s true
character, is a fairly recent historical development. Rather, choices A, C, andD discuss men’s character, power, and influence.

QUESTION 37.
Choice B is the best answer. In lines 23-26, Stanton states, “Society is but

the reflection of man himself, untempered by woman’s thought; the hardiron rule we feel alike in the church, the state, and the home.” In this context,
man’s “rule” in “the church, the state, and the home” means that men have acontrolling force in all areas of society.
Choices A, C, and D are incorrect because in this context “rule” does notmean a general guideline, an established habit, or a procedural method.

QUESTION 38.
Choice D is the best answer. In lines 32-35, Stanton argues that people use
the term “the strong-minded” to refer to women who advocate for “the rightto suffrage,” or the right to vote in elections. In this context, people use theterm “the strong-minded” to criticize female suffragists, as they believe voting will make women too “masculine.”

Choices A and B are incorrect because Stanton does not suggest that people
use the term “the strong-minded” as a compliment. Choice C is incorrect
because Stanton suggests that “the strong-minded” is a term used to criticize
women who want to vote, not those who enter male-dominated professions.

QUESTION 39.
Choice C is the best answer. In lines 36-39, Stanton states that society

contains hardly any women in the “best sense,” and clarifies that too many
women are “reflections, varieties, and dilutions of the masculine gender.”Stanton is suggesting that there are few “best,” or genuine, women who are
not completely influenced or controlled by men.
Choices A, B, and D are incorrect because in this context “best” does notmean superior, excellent, or rarest.

QUESTION 40.
Choice A is the best answer. In lines 54-56, Stanton argues that man “mourns,”

or regrets, how his power has caused “falsehood, selfishness, and violence” tobecome the “law” of society. Stanton is arguing that men are lamenting, or
expressing regret about, how their governance has created problems.
Choices B, C, and D are incorrect because Stanton does not suggest that men
are advocating for women’s right to vote or for female equality, nor are they
requesting women’s opinions about improving civic life.

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QUESTION 41.
Choice B is the best answer. In lines 54-56, Stanton provides evidence that

men are lamenting the problems they have created, as they recognize that
their actions have caused “falsehood, selfishness, and violence [to become]the law of life.”
Choices A, C, and D are incorrect because they do not provide the best evidence that men are lamenting the problems they have created. Choice A
explains society’s current fragmentation. Choices C and D present Stanton’s
main argument for women’s enfranchisement.

QUESTION 42.
Choice D is the best answer. In the sixth paragraph, Stanton differentiates

between men and masculine traits. Stanton argues that masculine traits or“characteristics,” such as a “love of acquisition and ­conquest,” serve to “subjugate one man to another” (lines 69-80). Stanton is ­suggesting that somemasculine traits position men within certain power structures.
Choices A and B are incorrect because the sixth paragraph does not primarily establish a contrast between men and women or between the spiritualand material worlds. Choice C is incorrect because although Stanton argues
that not “all men are hard, selfish, and brutal,” she does not discuss what
constitutes a “good” man.

QUESTION 43.
Choice C is the best answer. In the first paragraph, the author identifies thenatural phenomenon “internal waves” (line 3), and explains why they areimportant: “internal waves are fundamental parts of ocean water dynamics, transferring heat to the ocean depths and bringing up cold water frombelow” (lines 7-9).
Choices A, B, and D are incorrect because they do not identify the main
purpose of the first paragraph, as that paragraph does not focus on a scientific device, a common misconception, or a recent study.

QUESTION 44.
Choice B is the best answer. In lines 17-19, researcher Tom Peacockargues that in order to create precise global climate models, scientists must be able to “capture processes” such as how internal waves areformed. In this context, to “capture” a process means to record it for scientific study.
Choices A, C, and D are incorrect because in this context “capture” does notmean to control, secure, or absorb.
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QUESTION 45.
Choice D is the best answer. In lines 17-19, researcher Tom Peacock argues

that scientists need to “capture processes” of internal waves to develop “moreand more accurate climate models.” Peacock is suggesting that studying
internal waves will inform the development of scientific models.
Choices A, B, and C are incorrect because Peacock does not state that monitoring internal waves will allow people to verify wave heights, improve satellite image quality, or prevent coastal damage.

QUESTION 46.
Choice C is the best answer. In lines 17-19, researcher Tom Peacock provides evidence that studying internal waves will inform the development of
key scientific models, such as “more accurate climate models.”

Choices A, B, and D are incorrect because they do not provide the best
evidence that studying internal waves will inform the development of
key scientific models; rather, they provide general information about
internal waves.

QUESTION 47.
Choice A is the best answer. In lines 65-67, the author notes that Tom

Peacock and his team “were able to devise a mathematical model that
describes the movement and formation of these waves.” In this context, theresearchers devised, or created, a mathematical model.
Choices B, C, and D are incorrect because in this context “devise” does notmean to solve, imagine, or begin.

QUESTION 48.
Choice B is the best answer. Tom Peacock and his team created a modelof the “Luzon’s Strait’s underwater topography” and determined that its“distinct double-ridge shape . . . [is] responsible for generating the underwater [internal] waves” (lines 53-55). The author notes that this model
describes only internal waves in the Luzon Strait but that the team’s findings may “help researchers understand how internal waves are generated
in other places around the world” (lines 67-70). The author’s claim suggeststhat while internal waves in the Luzon Strait are “some of the largest in theworld” (line 25) due to the region’s topography, internal waves occurring inother regions may be caused by some similar factors.
Choice A is incorrect because the author notes that the internal waves in theLuzon Strait are “some of the largest in the world” (line 25), which suggeststhat internal waves reach varying heights. Choices C and D are incorrect
because they are not supported by the researchers’ findings.
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QUESTION 49.
Choice D is the best answer. In lines 67-70, the author provides evidence

that, while the researchers’ findings suggest the internal waves in the Luzon
Strait are influenced by the region’s topography, the findings may “helpresearchers understand how internal waves are generated in other places
around the world.” This statement suggests that all internal waves may becaused by some similar factors.
Choices A, B, and C are incorrect because they do not provide the best evidence that internal waves are caused by similar factors but influenced by thedistinct topographies of different regions. Rather, choices A, B, and C reference general information about internal waves or focus solely on those that
occur in the Luzon Strait.

QUESTION 50.
Choice D is the best answer. During the period 19:12 to 20:24, the graphshows the 13°C isotherm increasing in depth from about 20 to 40 meters.
Choices A, B, and C are incorrect because during the time period 19:12 to
20:24 the 9°C, 10°C, and 11°C isotherms all decreased in depth.

QUESTION 51.
Choice D is the best answer. In lines 3-6, the author notes that internal

waves “do not ride the ocean surface” but “move underwater, undetectablewithout the use of satellite imagery or sophisticated monitoring equipment.”
The graph shows that the isotherms in an internal wave never reach theocean’s surface, as the isotherms do not record a depth of 0.
Choice A is incorrect because the graph provides no information aboutsalinity. Choice B is incorrect because the graph shows layers of less densewater (which, based on the passage, are warmer) riding above layers ofdenser water (which, based on the passage, are cooler). Choice C is incorrect because the graph shows that internal waves push isotherms of warmer
water above bands of colder water.

QUESTION 52.
Choice A is the best answer. In lines 7-9, the author notes that internal

waves are “fundamental parts of ocean water dynamics” because they transfer “heat to the ocean depths and brin[g] up cold water from below.” Thegraph shows an internal wave forcing the warm isotherms to depths thattypically are colder. For example, at 13:12, the internal wave transfers “heatto the ocean depths” by forcing the 10°C, 11°C, and 13°C isotherms todepths that typically are colder.

14

Choices B, C, and D are incorrect because the graph does not show how
internal waves affect the ocean’s density, surface temperature, or tide flow.

Section 2: Writing and Language Test
QUESTION 1.
Choice B is the best answer because it provides a noun, “reductions,” yield-

ing a grammatically complete and coherent sentence.
Choices A, C, and D are incorrect because each provides a verb or gerund,while the underlined portion calls for a noun.

QUESTION 2.
Choice B is the best answer because it offers a transitional adverb,“Consequently,” that communicates a cause-effect relationship between
the funding reduction identified in the previous sentence and the staffing
decrease described in this sentence.

Choices A, C, and D are incorrect because each misidentifies the relationship between the preceding sentence and the sentence of which it is a part.

QUESTION 3.
Choice A is the best answer because the singular verb “has” agrees with thesingular noun “trend” that appears earlier in the sentence.
Choices B, C, and D are incorrect because the plural verb “have” does notagree with the singular subject “trend,” and the relative pronoun “which”
unnecessarily interrupts the direct relationship between “trend” and the verb.

QUESTION 4.
Choice A is the best answer because it states accurately why the proposedclause should be added to the sentence. Without these specific examples,
readers have only a vague sense of what “nonprint” formats might be.
Choices B, C, and D are incorrect because each represents a misinterpretation of the relationship between the proposed clause to be added and thesurrounding text in the passage.

QUESTION 5.
Choice D is the best answer because it includes only the preposition andnoun that the sentence requires.
Choices A, B, and C are incorrect because each includes an unnecessary pronoun, either “them” or “their.” The sentence contains no referents that would
circulate e-books.

QUESTION 6.
Choice D is the best answer because the verb form “cataloging” parallels theother verbs in the series.

15

Choices A, B, and C are incorrect because each interrupts the parallel structure in the verb series, either through an incorrect verb form or with anunnecessary subject.

QUESTION 7.
Choice B is the best answer because it consolidates references to the subject,“librarians,” by placing the relative pronoun “whose” immediately following“librarians.” This results in a logical flow of information within the sentence.
Choices A, C, and D are incorrect because each fails to place “librarians” as
the main subject of the sentence without redundancy, resulting in a convoluted sentence whose relevance to the preceding and subsequent sentences
is unclear.

QUESTION 8.
Choice D is the best answer because no conjunction is necessary to com-municate the relationship between the clauses in the sentence. The conjunction “While” at the beginning of the sentence already creates a comparison.
Choices A, B, and C are incorrect because each provides an unnecessary
coordinating conjunction.

QUESTION 9.
Choice B is the best answer because it mentions time periods when thefree services described later in the sentence are particularly useful tolibrary patrons.
Choices A, C, and D are incorrect because each creates redundancy or awkwardness in the remainder of the sentence.

QUESTION 10.
Choice B is the best answer because it is concise; it is also consistent withthe formal language in the rest of the sentence and the passage overall.
Choices A, C, and D are incorrect because each is either unnecessarily
wordy or uses colloquial language that does not correspond with the tone ofthe passage.

QUESTION 11.
Choice C is the best answer because it restates the writer’s primary argu-

ment, which may be found at the end of the first paragraph: “As public
libraries adapt to rapid technological advances in information distribution,librarians’ roles are actually expanding.”

16

Choices A, B, and D are incorrect because they do not paraphrase the­writer’s primary claim.

QUESTION 12.
Choice B is the best answer because it clarifies that the sentence, which

mentions a specific large-scale painting at the Art Institute of Chicago, is an
example supporting the preceding claim about large-scale paintings.
Choices A, C, and D are incorrect because they propose transitional words
or phrases that do not accurately represent the relationship between the preceding sentence and the sentence containing the underlined portion.

QUESTION 13.
Choice D is the best answer because no punctuation is necessary in theunderlined phrase.
Choices A, B, and C are incorrect because each separates parts of the nounphrase “painter Georges Seurat’s 10-foot-wide A Sunday Afternoon on the
Island of La Grande Jatte” from one another with one or more unnecessarycommas.

QUESTION 14.
Choice C is the best answer because it provides the appropriate possessive

form, “its,” and a colon to introduce the identifying phrase that follows.
Choices A, B, and D are incorrect because none contains both the appropriate possessive form of “it” and the punctuation that creates a grammaticallystandard sentence.

QUESTION 15.
Choice C is the best answer because an analysis of the consequences ofKing Louis XV’s reign is irrelevant to the paragraph.
Choices A, B, and D are incorrect because each represents a misinterpretation of the relationship between the proposed sentence to be added and themain point of the paragraph.

QUESTION 16.
Choice C is the best answer because it provides a coordinating conjunction, “and,” to connect the two verb phrases “are characterized” and“are covered.”

Choices A, B, and D are incorrect because each lacks the conjunction needed
to connect the two verb phrases “are characterized” and “are covered.”

QUESTION 17.
Choice B is the best answer because it offers an example of an additional

household item, a “tea cup,” with a specific measurement that is one-twelfthof its actual size.

17Choices A, C, D are incorrect because, compared to the example preceding
the underlined portion, each is vague and fails to offer a specific measurement of an additional household item.

QUESTION 18.
Choice B is the best answer because it provides correct punctuation andthe coordinating conjunction “but,” which acknowledges the possible
contrast between being “sparsely furnished” and displaying “just as true”
period details.
Choices A, C, and D are incorrect because each communicates an illogicalrelationship between the phrases that precede and follow the underlined
portion.

QUESTION 19.
Choice A is the best answer because it provides a clause that is the mostsimilar to the two preceding clauses, which both end with a reference to a
specific wall.
Choices B, C, and D are incorrect because each deviates from the stylistic
pattern of the preceding two clauses.

QUESTION 20.
Choice D is the best answer because the article “a” requires the singularnoun “visitor,” and the simple present verb “remark” is the appropriate verb
tense in this context.
Choices A, B, and C are incorrect because each contains either a noun orverb that does not fit the context.

QUESTION 21.
Choice D is the best answer because it identifies the drawers, rather thanthe visitor, as being “dotted with pin-sized knobs.”

Choices A, B, and C are incorrect because all three contain dangling modifiers that obscure the relationship between the visitor, the drawers, and thepin-sized knobs.

QUESTION 22.
Choice B is the best answer because paragraph 3 offers an overview of theexhibit and so serves to introduce the specific aspects of particular miniature rooms described in paragraphs 2 and 4.

18

Choices A, C, and D are incorrect because each proposes a placementof paragraph 2 that prevents the passage from developing in a logicalsequence.

QUESTION 23.
Choice A is the best answer because it correctly completes the noun phrase thatbegins with “sea otters,” and directly follows the noun phrase with the verb “help.”
Choices B, C, and D are incorrect because each separates the noun “otters” fromthe verb “help” in a way that results in a grammatically incomplete sentence.

QUESTION 24.
Choice B is the best answer because the data in the chart show lower sea

urchin density in areas where sea otters have lived for two years or less thanin areas where no otters are present.
Choices A, C, and D are incorrect because none accurately describes the datain the chart.

QUESTION 25.
Choice B is the best answer because the conjunctive adverb “however”

accurately communicates the contrast between an environment shaped by
the presence of sea otters, described in the preceding sentence, and an environment shaped by the absence of sea otters, described in this sentence.
Choices A, C, and D are incorrect because each presents a conjunctive adverbthat does not accurately depict the relationship between the preceding sentence and the sentence with the underlined word.

QUESTION 26.
Choice A is the best answer because the additional information usefully

connects the carbon dioxide levels mentioned in this sentence with theglobal warming mentioned in the previous sentence.
Choices B, C, and D are incorrect because each misinterprets the relationshipbetween the proposed information and the main points of the paragraphand the passage.

QUESTION 27.
Choice D is the best answer because it offers the verb “suggests” followed

directly by its object, a that-clause, without interruption.
Choices A, B, and C are incorrect because each contains punctuation that
unnecessarily separates the study from its findings—that is, separates theverb from its object.

QUESTION 28.
Choice A is the best answer because it accurately reflects the fact that sea
urchins “graze voraciously on kelp,” as stated in the first paragraph, and it
also maintains the tone of the passage.

19

Choices B, C, and D are incorrect because each offers a term that does notaccurately describe the behavior of sea otters.

QUESTION 29.
Choice C is the best answer because the possessive singular pronoun “its”

corresponds with the referent “kelp,” which appears later in the sentence,
and with the possessive relationship between the pronoun and the “terrestrial plant cousins.”
Choices A, B, and D are incorrect because none provides a pronoun that isboth singular and possessive.

QUESTION 30.
Choice C is the best answer because it provides the noun “sea otters” toidentify who or what “played a role.”
Choices A, B, and D are incorrect because each provides a pronoun thatmakes no sense in the context of the paragraph and the passage, which
is about the role sea otters play—not the role scientists play or the role
kelp plays.

QUESTION 31.
Choice D is the best answer because sentence 5 indicates that sea otters’

importance in decreasing atmospheric carbon dioxide was not known, andthe sentence to be added indicates that a surprise will follow. Sentence 6 provides that surprise: sea otters have a large impact on the amount of carbon
dioxide kelp can remove from the atmosphere.
Choices A, B, and C are incorrect because each interrupts the logical flow ofideas in the paragraph.

QUESTION 32.
Choice B is the best answer because its clear wording and formal tone cor-

respond with the passage’s established style.
Choices A, C, and D are incorrect because each contains vague language thatis inconsistent with the passage’s clear wording and formal tone.

QUESTION 33.
Choice D is the best answer because it provides punctuation that appropri-

ately identifies “removed” as the definition of “sequestered.”
Choices A, B, and C are incorrect because each contains punctuation that
obscures the relationship between “sequestered,” “removed,” and the textthat follows.
20

QUESTION 34.
Choice D is the best answer because it provides a conjunction that correctly

identifies the relationship between “a practice” and the actions involved in
the practice.
Choices A, B, and C are incorrect because each contains a conjunction that
miscommunicates the relationship between the text that precedes and follows the underlined portion.

QUESTION 35.
Choice A is the best answer because it provides a comma to close theappositive clause “a practice whereby products are designed to have a limited period of usefulness,” which also begins with a comma.
Choices B, C, and D are incorrect because each provides closing punctuation
inconsistent with the punctuation at the beginning of the clause.

QUESTION 36.
Choice D is the best answer because it provides an adjective that accurately
describes the clear “contrast” between products “designed to have a limited
period of usefulness” and those “produced to be durable.”

Choices A, B, and C are incorrect because none provides an adjective thatappropriately modifies “contrast” in the context of the paragraph.

QUESTION 37.
Choice A is the best answer because by mentioning the “specialized” meth-ods used in repair shops, it suggests that repairing goods is seen as a specialty rather than as a common activity. This connects logically with the“rare” repair shops introduced just before the underlined portion.
Choices B, C, and D are incorrect because none provides information that
supports the claim made in the sentence.

QUESTION 38.
Choice B is the best answer because it provides the correct spelling of thenoun “fair,” meaning exhibition, and uses the correct word “than” to create
the comparison between a “fair” and a “café.”
Choices A, C, and D are incorrect because each contains a misspelling ofeither “fair” or “than.”

QUESTION 39.
Choice C is the best answer because it offers a relative pronoun that prop-

erly links the noun “Martine Postma” with the appropriate verb “wanted.”
21

Choices A, B, and D are incorrect because none contains a pronoun that is
appropriate for the referent and placement of the clause.

QUESTION 40.
Choice D is the best answer because it provides the most concise phrasing

and links the sentence appropriately to the previous sentence.
Choices A, B, and C are incorrect because each provides an unnecessary
adverb that obscures the relationship between this sentence and the previous one.

QUESTION 41.
Choice D is the best answer because the gerund “waiting” correspondswith the preposition “for” and the present tense used in the rest of thesentence.
Choices A, B, and C are incorrect because each contains a verb form notused with the preposition “for.”

QUESTION 42.
Choice C is the best answer because it appropriately places sentence 5,

which describes the places Repair Cafés can be found today, between a sentence that gives the first Repair Café’s location and purpose and a statement
about current customers and how they use Repair Cafés.
Choices A, B, and D are incorrect because each creates a paragraph withan inappropriate shift in verb tense and, therefore, an illogical sequenceof information.

QUESTION 43.
Choice C is the best answer because it accurately states that the issue of“corporate and service-based jobs” is not particularly relevant at this pointin the paragraph. The focus here is on repairing objects in a “throwaway culture,” not jobs.

Choices A, B, and D are incorrect because each misinterprets the relationship between the proposed text and the information in the paragraph.

QUESTION 44.
Choice D is the best answer because the phrase “and other countries”

communicates the fact that there are additional items not being namedthat could be added to the list; no other wording is required to clarify
that point.
22

Choices A, B, and C are incorrect because each presents a word or phrasethat results in a redundancy with “and other countries.”

Section 3: Math Test — No Calculator
QUESTION 1.
Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x = _​  4 ​. The value of x can now be
54 ​  ​+ 3 = 11.
substituted into the expression 10x + 3, giving 10 ​ ​ _5Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

()

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,
contradicting the given equation, 5x + 6 = 10. For example, choice A isincorrect because if the value of 10x + 3 were 4, then it would follow thatx = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.
Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Then, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives
5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting
2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Therefore, the solution to thegiven system of equations is (2, −2).
Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. The value of y can thenbe found in the same way as before.
Choices A, C, and D are incorrect because when the given values of x andy are substituted into x + y = 0 and 3x − 2y = 10, either one or both of theequations are not true. These answers may result from sign errors or othercomputational errors.

QUESTION 3.
Choice A is correct. The price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fixed price and 12nh depends on thenumber of landscapers, n, working the job and the number of hours, h, the job
takes those n landscapers. Since nh is the total number of hours of work done
when n landscapers work h hours, the cost of the job increases by $12 for eachhour a landscaper works. Therefore, of the choices given, the best interpretationof the number 12 is that the company charges $12 per hour for each landscaper.
Choice B is incorrect because the number of landscapers that will work eachjob is represented by n in the equation, not by the number 12. Choice C isincorrect because the price of the job increases by 12n dollars each hour,which will not be equal to 12 dollars unless n = 1. Choice D is incorrect
because the total number of hours each landscaper works is equal to h. The
number of hours each landscaper works in a day is not provided.

23

QUESTION 4.
Choice A is correct. If a polynomial expression is in the form (x)2 + 2(x)(y) +(y)2, then it is equivalent to (x + y)2. Because 9a4 + 12a2b2 + 4b4 = (3a2)2 +2(3a2)(2b2) + (2b2)2, it can be rewritten as (3a2 + 2b2)2.
Choice B is incorrect. The expression (3a + 2b)4 is equivalent to the product(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). This product will contain the term
4(3a)3 (2b) = 216a3b. However, the given polynomial, 9a4 + 12a2b2 + 4b4,
does not contain the term 216a3b. Therefore, 9a4 + 12a2b2 + 4b4 ≠ (3a + 2b)4.
Choice C is incorrect. The expression (9a2 + 4b2)2 is equivalent to the
product (9a2 + 4b2)(9a2 + 4b2). This product will contain the term (9a2)(9a2) = 81a4. However, the given polynomial, 9a4 + 12a2b2 + 4b4, does
not contain the term 81a4. Therefore, 9a4 + 12a2b2 + 4b4 ≠ (9a2 + 4b2)2.
Choice D is incorrect. The expression (9a + 4b)4 is equivalent to the product (9a + 4b)(9a + 4b)(9a + 4b) (9a + 4b). This product will contain theterm (9a)(9a)(9a)(9a) = 6,561a4. However, the given polynomial, 9a4 +
12a2b2 + 4b4, does not contain the term 6,561a4. Therefore, 9a4 + 12a2b2 +4b4 ≠ (9a + 4b)4.

QUESTION 5.

_

Choice C is correct.
Since √
​ 2k2 + 17 ​− x = 0, and x = 7, one can_substitute 7 for_x, which gives ​√ 2k2 + 17 ​ − 7 = 0. Adding 7 to each side of ​√2k2 + 17 ​ − 7 = 0__

gives ​√ 2k2 + 17 ​= 7. Squaring each side of ​√ 2k2 + 17 ​= 7 will remove the_ 2square root symbol: ​( ​√2k2 + 17 ​ )​ = (7)2, or 2k2 + 17 = 49. Then subtracting
17 from each side of 2k2 + 17 = 49 gives 2k2 = 49 − 17 = 32, and dividing eachside of 2k2 = 32 by 2 gives k2 = 16. Finally, taking the square root of each sideof k2 = 16 gives k = ±4, and since the problem states that k > 0, it follows thatk = 4.
_

Since the sides of an equation were squared while solving ​√2k2 + 17 ​− 7 = 0,
it is possiblethat an extraneous root was produced. However,substituting 4__2− 7 = 0 confirms that 4 is a solution for k: ​√2(4)2 + 17 ​− 7 =fork in ​√2k + 17 ​__√32 + 17 ​− 7 = ​√49 ​− 7 = 7 − 7 = 0.
Choices A,
B, and D are incorrect because substituting any of these values_
2for k in ​√2k + 17 ​− 7 = 0 does not yield a true statement.

QUESTION 6.
Choice D is correct. Since lines ℓ and k are parallel, the lines have the same slope.
0−2Line ℓ passes through the points (−5, 0) and (0, 2), so its slope is ​ _ ​, which−5 − 02 ​. Since line k has slope ​ _2 ​and passes
2 ​. The slope of line k must also be ​ _is ​ _

24

5
5
5
−4
−0 _
4 ​ = ​ _2 ​.
_​ = ​  2 ​, or ​ _through the points (0, −4) and (p, 0), it follows that ​ 
p 5
5
0−p
4 ​ = ​ _
2 ​by 5p gives 20 = 2p, and therefore, p = 10.
Multiplying each side of ​ _p 5

Choices A, B, and C are incorrect and may result from conceptual or calculation errors.

QUESTION 7.
x
Choice A is correct. Since the numerator and denominator of ​ _2 ​have aa2

xb
common base, it follows by the laws of exponents that this expression can be

2
2
2
2
xa
rewritten as xa − b . Thus, the equation ​ _2 ​ = 16 can be rewritten as xa − b = x16.
bxBecause the equivalent expressions have the common base x, and x > 1,
2

it follows that the exponents of the two expressions must also be equivalent. Hence, the equation a2 − b2 = 16 must be true. The left-hand sideof this new equation is a difference of squares, and so it can be factored:(a + b)(a − b) = 16. It is given that (a + b) = 2; substituting 2 for the factor(a + b) gives 2(a − b) = 16. Finally, dividing both sides of 2(a − b) = 16 by 2
gives a − b = 8.
Choices B, C, and D are incorrect and may result from errors in applying thelaws of exponents or errors in solving the equation a2 − b2 = 16.

QUESTION 8.
Choice C is correct. The relationship between n and A is given by the equation nA = 360. Since n is the number of sides of a polygon, n must be a posi360
tive integer, and so nA = 360 can be rewritten as A = _​  n ​. If the value of A is360
greater than 50, it follows that _​  n ​> 50 is a true statement. Thus, 50n < 360, or360n<_​   ​= 7.2. Since n must be an integer, the greatest possible value of n is 7.
50
Choices A and B are incorrect. These are possible values for n, the number ofsides of a regular polygon, if A > 50, but neither is the greatest possible valueof n. Choice D is incorrect. If A < 50, then n = 8 is the least possible value ofn, the number of sides of a regular polygon. However, the question asks forthe greatest possible value of n if A > 50, which is n = 7.

QUESTION 9.
Choice B is correct. Since the slope of the first line is 2, an equation of thisline can be written in the form y = 2x + c, where c is the y-intercept of theline. Since the line contains the point (1, 8), one can substitute 1 for x and 8
for y in y = 2x + c, which gives 8 = 2(1) + c, or c = 6. Thus, an equation of thefirst line is y = 2x + 6. The slope of the second line is equal to 1 − 2 or −1.
2−1
Thus, an equation of the second line can be written in the form y = −x + d,
where d is the y-intercept of the line. Substituting 2 for x and 1 for y gives
1 = −2 + d, or d = 3. Thus, an equation of the second line is y = −x + 3.
25

Since a is the x-coordinate and b is the y-coordinate of the intersection
point of the two lines, one can substitute a for x and b for y in the two equations, giving the system b = 2a + 6 and b = –a + 3. Thus, a can be found bysolving the equation 2a + 6 = −a + 3, which gives a = −1. Finally, substituting −1 for a into the equation b = –a + 3 gives b = −(−1) + 3, or b = 4.
Therefore, the value of a + b is 3.
Alternatively, since the second line passes through the points (1, 2) and(2, 1), an equation for the second line is x + y = 3. Thus, the intersection
point of the first line and the second line, (a, b) lies on the line with equationx + y = 3. It follows that a + b = 3.
Choices A and C are incorrect and may result from finding the value of onlya or b, but not calculating the value of a + b. Choice D is incorrect and may
result from a computation error in finding equations of the two lines or insolving the resulting system of equations.

QUESTION 10.
Choice C is correct. Since the square of any real number is nonnegative, every

point on the graph of the quadratic equation y = (x − 2)2 in the xy-plane has anonnegative y-coordinate. Thus, y ≥ 0 for every point on the graph. Therefore, theequation y = (x − 2)2 has a graph for which y is always greater than or equal to −1.
Choices A, B, and D are incorrect because the graph of each of these equations in the xy-plane has a y-intercept at (0, −2). Therefore, each of theseequations contains at least one point where y is less than −1.

QUESTION 11.
3 − 5i ​  , multiply the numerator
Choice C is correct. To perform the division _​ 8 + 2i3 − 5i ​ by the conjugate of the denominator, 8 − 2i. Thisand denominator of _​ 8 + 2i− 6i − 40i + (−5i)(−2i)(3− 5i)(8 − 2i) 24__     ​. Since i2 = −1, this can begives ​     = ​  ___
(8 + 2i)(8 − 2i)
82 − (2i)224 − 6i − 40i − 10 _7 23i
14 − 46i
simplified to __​  ​​, which then simplifies to ​ _ ​ − ​ _ ​.
   ​ = ​ 
34 34
64 + 468
Choices A and B are incorrect and may result from misconceptions about
a+b
a
b
a b
fractions. For example, _​  ​ is equal to ​ _ ​ + ​ _ ​ , not ​ _ ​ + ​ _ ​. Choice Dc dc+dc+d c+d
is incorrect and may result from a calculation error.

QUESTION 12.
F
Choice B is correct. Multiplying each side of R = ​ _ ​ by N + F gives

N+F
R(N + F) = F, which can be rewritten as RN + RF = F. Subtracting RFfrom each side of RN + RF = F gives RN = F − RF, which can be factored26

as RN = F(1 − R). Finally, dividing each side of RN = F(1 − R) by 1 − R,
RN
expresses F in terms of the other variables: F = _.
1−R
Choices A, C, and D are incorrect and may result from calculation errors
when rewriting the given equation.

QUESTION 13.
Choice D is correct. The problem asks for the sum of the roots of the quadratic
equation 2m2 − 16m + 8 = 0. Dividing each side of the equation by 2 gives
m2 − 8m + 4 = 0. If the roots of m2 − 8m + 4 = 0 are s1 and s2, then the equation canbe factored as m2 − 8m + 4 = (m − s1)(m − s2) = 0. Looking at the coefficient of x oneach side of m2 − 8m + 4 = (m − s1)(m − s2) gives −8 = −s1 − s2, or s1 + s2 = 8.

Alternatively, one can apply the quadratic formula to either 2m2 − 16m +_8 = 0
8m
or m2 −
√3 and
_4 + 2√3 whose sum is 8.
Choices A, B, and C are incorrect and may result from calculation errors
when applying the quadratic formula or a sign error when determining the

QUESTION 14.
Choice A is correct. Each year, the amount of the radioactive substanceis reduced by 13 percent from the prior year’s amount; that is, each year,
87 percent of the previous year’s amount remains. Since the initial amount2

f(t) = 325(0.87)tt years.

t years, 325(0.87)t

Choice B is incorrect and may result from confusing the amount of the substance remaining with the decay rate. Choices C and D are incorrect and may
result from confusing the original amount of the substance and the decay rate.

QUESTION 15.
Choice D is correct. Dividing 5x − 2 by x + 3 gives:5
x + 3)5x − 2
5x + 15−17
17
5x − 2_can be rewritten as 5 − _.
x+3

5x − 2
Alternatively, _ can be rewritten asx+3(5x + 15) − 15 − 2 __5(x + 3) − 1717
5x − 2 ___=== 5 − _.
x+3
x+3
x+3
x+3

x+3

27

Choices A and B are incorrect and may result from incorrectly canceling out
5x − 2the x in the expression ​ _ ​ . Choice C is incorrect and may result fromx+3
finding an incorrect remainder when performing long division.

QUESTION 16.
The correct answer is 3, 6, or 9. Let x be the number of $250 bonuses

awarded, and let y be the number of $750 bonuses awarded. Since $3000 inbonuses were awarded, and this included at least one $250 bonus and one$750 bonus, it follows that 250x + 750y = 3000, where x and y are positive
integers. Dividing each side of 250x + 750y = 3000 by 250 gives x + 3y = 12,
where x and y are positive integers. Since 3y and 12 are each divisible by 3,
it follows that x = 12 − 3y must also be divisible by 3. If x = 3, then y = 3; if
x = 6, then y = 2; and if x = 9, then y = 1. If x = 12, then y = 0, but this is notpossible since there was at least one $750 bonus awarded. Therefore, the possible numbers of $250 bonuses awarded are 3, 6, and 9. Any of the numbers
3, 6, or 9 may be gridded as the correct answer.

QUESTION 17.
The correct answer is 19. Since 2x(3x + 5) + 3(3x + 5) = ax2 + bx + c for all val-ues of x, the two sides of the equation are equal, and the value of b can be determined by simplifying the left-hand side of the equation and writing it in thesame form as the right-hand side. Using the distributive property, the equation
becomes (6x2 + 10x) + (9x + 15) = ax2 + bx + c. Combining like terms gives
6x2 + 19x + 15 = ax2 + bx + c. The value of b is the coefficient of x, which is 19.

QUESTION 18.
The correct answer is 12. Angles ABE and DBC are vertical angles and thus

have the same measure. Since segment AE is parallel to segment CD, angles
A and D are of the same measure by the alternate interior angle theorem.
Thus, by the angle-angle theorem, triangle ABE is similar to triangle DBC,
with vertices A, B, and E corresponding to vertices D, B, and C, respectively.
8
10 _EB  ​ or ​ _ ​ = ​   ​. It follows that CB = 4, and so CE = CB + BE =Thus, _​  AB ​= ​_
5 CB
DB CB
4 + 8 =12.

QUESTION 19.
The_
correct answer is 6. By the distance formula, the length of radius OA__
1 ​. Therefore, the measure ofis ​ (​√3 ​)2 + 12 ​= ​√3 + 1 ​= 2. Thus, sin(∠AOB) = ​ _

√

2
π
π
∠AOB is 30°, which is equal to 30​ _​  ​  = _​   ​radians. Hence, the value of a is 6.
180 6

( )

QUESTION 20.
1
The correct answer is ​ _ ​or .25. In order for a system of two linear equations
428

to have infinitely many solutions, the two equations must be equivalent.

Thus, the equation ax + by = 12 must be equivalent to the equation 2x +8y = 60. Multiplying each side of ax + by = 12 by 5 gives 5ax + 5by = 60,
which must be equivalent to 2x + 8y = 60. Since the right-hand sides of
5ax + 5by = 60 and 2x + 8y = 60 are the same, equating coefficients gives8a8
2 ​  ​÷ ​ ​ _2 ​, and 5b = 8, or b = ​ _ ​. Therefore, the value of ​ _​ = ​ ​ _ ​  ​,
5a = 2, or a = ​ _
5
5
5
5
b
1 ​or its equivalent decimal, .25, may
1 ​. Either the fraction ​ _which is equal to ​ _44
be gridded asthe correct answer.

() ()Alternatively, since ax + by = 12 is equivalent to 2x + 8y = 60, the equationax + by =12 is equal to 2x + 8y = 60 multiplied on each side by the same constant. Since multiplying 2x + 8y = 60 by a constant does not change the ratioa 2 _of the coefficient of x to the coefficient of y, it follows that ​ _​ = ​ _ ​ = ​  1 ​.
b 8 4

Section 4: Math Test — Calculator
QUESTION 1.
Choice C is correct. Since the musician earns $0.09 for each download,

the musician earns 0.09d dollars when the song is downloaded d times.
Similarly, since the musician earns $0.002 each time the song is streamed,
the musician earns 0.002s dollars when the song is streamed s times.
Therefore, the musician earns a total of 0.09d + 0.002s dollars when the songis downloaded d times and streamed s times.
Choice A is incorrect because the earnings for each download and the earnings for time streamed are interchanged in the expression. Choices B and D
are incorrect because in both answer choices, the musician will lose money
when a song is either downloaded or streamed. However, the musician only
earns money, not loses money, when the song is downloaded or streamed.

QUESTION 2.
Choice B is correct. The quality control manager selects 7 lightbulbs at

random for inspection out of every 400 lightbulbs produced. A quan20,000 ​= 50 batches of 400 lightbulbs.
tity of 20,000 lightbulbs is equal to ​ _400
Therefore, at the rate of 7 lightbulbs per 400 lightbulbs produced, the quality
control manager will inspect a total of 50 × 7 = 350 lightbulbs.
Choices A, C, and D are incorrect and may result from calculation errors or
misunderstanding of the proportional relationship.

QUESTION 3.
Choice A is correct. The value of m when l is 73 can be found by ­substituting

the 73 for l in l = 24 + 3.5m and then solving for m. The resulting e­ quation is
73 = 24 + 3.5m; subtracting 24 from each side gives 49 = 3.5m. Then, ­dividing
each side of 49 = 3.5m by 3.5 gives 14 = m. Therefore, when l is 73, m is 14.

29

Choice B is incorrect and may result from adding 24 to 73, instead of subtracting 24 from 73, when solving 73 = 24 + 3.5m. Choice C is incorrect
because 73 is the given value for l, not for m. Choice D is incorrect andmay result from substituting 73 for m, instead of for l, in the equationl = 24 + 3.5m.

QUESTION 4.
Choice C is correct. The amount of money the performer earns is directly

proportional to the number of people who attend the performance. Thus, by
the definition of direct proportionality, M = kP, where M is the amount ofmoney the performer earns, in dollars, P is the number of people who attend
the performance, and k is a constant. Since the performer earns $120 when
8 people attend the performance, one can substitute 120 for M and 8 for P,
giving 120 = 8k. Hence, k = 15, and the relationship between the number ofpeople who attend the performance and the amount of money, in dollars,
the performer earns is M = 15P. Therefore, when 20 people attend the performance, the performer earns 15(20) = 300 dollars.
Choices A, B, and D are incorrect and may result from either misconceptions about proportional relationships or computational errors.

QUESTION 5.
Choice C is correct. If 43% of the money earned is used to pay for costs, thenthe rest, 57%, is profit. A performance where 8 people attend earns the performer $120, and 57% of $120 is $120 × 0.57 = $68.40.
Choice A is incorrect. The amount $51.60 is 43% of the money earned froma performance where 8 people attend, which is the cost of putting on theperformance, not the profit from the performance. Choice B is incorrect. It
is given that 57% of the money earned is profit, but 57% of $120 is not equal
to $57.00. Choice D is incorrect. The profit can be found by subtracting 43%
of $120 from $120, but 43% of $120 is $51.60, not $43.00. Thus, the profit is$120 − $51.60 = $68.40, not $120 − $43.00 = $77.00.

QUESTION 6.
Choice B is correct. When 4 times the number x is added to 12, the result is

12 + 4x. Since this result is equal to 8, the equation 12 + 4x = 8 must be true.
Subtracting 12 from each side of 12 + 4x = 8 gives 4x = −4, and then dividing
both sides of 4x = −4 by 4 gives x = −1. Therefore, 2 times x added to 7, or
7 + 2x, is equal to 7 + 2(−1) = 5.
Choice A is incorrect because −1 is the value of x, not the value of 7 + 2x.
Choices C and D are incorrect and may result from calculation errors.

30

QUESTION 7.
Choice D is correct. The x-intercepts of the parabola represented by

y = x2 − 6x + 8 in the xy-plane are the values of x for which y is equal to 0.
The factored form of the equation, y = (x − 2)(x − 4), shows that y equals 0 if
and only if x = 2 or x = 4. Thus, the factored form, y = (x − 2)(x − 4), displays
the x-intercepts of the parabola as the constants 2 and 4.
Choices A, B, and C are incorrect because none of these forms shows thex-intercepts 2 and 4 as constants or coefficients.

QUESTION 8.
Choice D is correct. Since a player starts with k points and loses 2 points

each time a task is not completed, the player’s score will be k − 2n after ntasks are not completed (and no additional points are gained). Since a player
who fails to complete 100 tasks has a score of 200 points, the equation
200 = k − 100(2) must be true. This equation can be solved by adding 200 toeach side, giving k = 400.
Choices A, B, and C are incorrect and may result from errors in setting up
or solving the equation relating the player’s score to the number of tasks theplayer fails to complete. For example, choice A may result from subtracting
200 from the left-hand side of 200 = k − 100(2) and adding 200 to the righthand side.

QUESTION 9.
Choice A is correct. Since x is the number of 40-pound boxes, 40x is thetotal weight, in pounds, of the 40-pound boxes; and since y is the number of 65-pound boxes, 65y is the total weight, in pounds, of the 65-poundboxes. The combined weight of the boxes is therefore 40x + 65y, and thetotal number of boxes is x + y. Since the forklift can carry up to 45 boxes or
up to 2,400 pounds, the inequalities that represent these relationships are
40x + 65y ≤ 2,400 and x + y ≤ 45.
Choice B is incorrect. The second inequality correctly represents the maximum number of boxes on the forklift, but the first inequality divides, rather
than multiplies, the number of boxes by their respective weights. Choice C isincorrect. The combined weight of the boxes, 40x + 65y, must be less than orequal to 2,400 pounds, not 45; the total number of boxes, x + y, must be lessthan or equal to 45, not 2,400. Choice D is incorrect. The second inequality
correctly represents the maximum weight, in pounds, of the boxes on theforklift, but the total number of boxes, x + y, must be less than or equal to 45,
not 2,400.

31

QUESTION 10.
Choice B is correct. It is given that g(3) = 2. Therefore, to find the value off(g(3)), substitute 2 for g(3): f(g(3)) = f(2) = 3.
Choices A, C, and D are incorrect and may result from misunderstandings
about function notation.

QUESTION 11.
Choice B is correct. Tony reads 250 words per minute, and he plans to readfor 3 hours, which is 180 minutes, each day. Thus, Tony is planning to read
250 × 180 = 45,000 words of the novel per day. Since the novel has 349,168
349,168
words, it will take Tony ​ _ ​≈ 7.76 days of reading to finish the novel.
45,000That is, it will take Tony 7 full days of reading and most of an 8th day of reading to finish the novel. Therefore, it will take Tony 8 days to finish the novel.
Choice A is incorrect and may result from an incorrect calculation or incorrectly using the numbers provided in the table. Choice C is incorrect andmay result from taking the total number of words in the novel divided by
the rate Tony reads per hour. Choice D is incorrect and may result from taking the total number of words in the novel divided by the number of pages
in the novel.

QUESTION 12.
Choice D is correct. Since there were 175,000 tons of trash in the landfill

on January 1, 2000, and the amount of trash in the landfill increased by
7,500 tons each year after that date, the amount of trash, in tons, in the landfill y years after January 1, 2000 can be expressed as 175,000 + 7,500y. The
landfill has a capacity of 325,000 tons. Therefore, the set of years where theamount of trash in the landfill is at (equal to) or above (greater than) capacity is described by the inequality 175,000 + 7,500y ≥ 325,000.
Choice A is incorrect. This inequality does not account for the 175,000 tonsof trash in the landfill on January 1, 2000, nor does it accurately account forthe 7,500 tons of trash that are added to the landfill each year after January
1, 2000. Choice B is incorrect. This inequality does not account for the
175,000 tons of trash in the landfill on January 1, 2000. Choice C is incorrect. This inequality represents the set of years where the amount of trash in
the landfill is at or below capacity.

QUESTION 13.
Choice D is correct. Survey research is an efficient way to estimate the pref-

erences of a large population. In order to reliably generalize the results ofsurvey research to a larger population, the participants should be randomly
selected from all people in that population. Since this survey was conducted32

with a population that was not randomly selected, the results are not reliably representative of all people in the town. Therefore, of the given factors,
where the survey was given makes it least likely that a reliable conclusion canbe drawn about the sports-watching preferences of all people in the town.
Choice A is incorrect. In general, larger sample sizes are preferred oversmaller sample sizes. However, a sample size of 117 people would haveallowed a reliable conclusion about the population if the participants had
been selected at random. Choice B is incorrect. Whether the population islarge or small, a large enough sample taken from the population is reliably
generalizable if the participants are selected at random from that population. Thus, a reliable conclusion could have been drawn about the population if the 117 survey participants had been selected at random. Choice C
is incorrect. When giving a survey, participants are not forced to respond.
Even though some people refused to respond, a reliable conclusion could
have been drawn about the population if the participants had been selected
at random.

QUESTION 14.
Choice C is correct. According to the graph, the horizontal line that repre-

sents 550 billion miles traveled intersects the line of best fit at a point whose
horizontal coordinate is between 2000 and 2005, and slightly closer to 2005
than to 2000. Therefore, of the choices given, 2003 best approximates theyear in which the number of miles traveled by air passengers in Country X
was estimated to be 550 billion.
Choice A is incorrect. According to the line of best fit, in 1997 the estimated number of miles traveled by air passengers in Country X was about
450 billion, not 550 billion. Choice B is incorrect. According to the lineof best fit, in 2000 the estimated number of miles traveled by air passengers in Country X was about 500 billion, not 550 billion. Choice D isincorrect. According to the line of best fit, in 2008 the estimated numberof miles traveled by air passengers in Country X was about 600 billion,
not 550 billion.

QUESTION 15.
Choice A is correct. The number of miles Earth travels in its one-year orbitof the Sun is 580,000,000. Because there are about 365 days per year, the580,000,000 ​≈ 1,589,041. There arenumber of miles Earth travels per day is ​ _365
1,589,041 ​≈ 66,210 miles per hour.
24 hours in one day, so Earth travels at ​ _24
Therefore, of the choices given, 66,000 miles per hour is closest to the average speed of Earth as it orbits the Sun.

Choices B, C, and D are incorrect and may result from calculation errors.
33

QUESTION 16.
Choice B is correct. According to the table, there are 18 + 7 = 25 graduates

who passed the bar exam, and 7 of them did not take the review course.
Therefore, if one of the surveyed graduates who passed the bar exam ischosen at random, the probability that the person chosen did not take the7review course is ​ _ ​.
25
Choices A, C, and D are incorrect. Each of these choices represents a different probability from the conditional probability that the question asks for.
Choice A represents the following probability. If one of the surveyed graduates who passed the bar exam is chosen at random, the probability that the18
person chosen did take the review course is ​ _ ​ . Choice C represents the25
following probability. If one of the surveyed graduates is chosen at random,25
the probability that the person chosen passed the bar exam is ​ _ ​. Choice D
200
represents the following probability. If one of the surveyed graduates is chosen at random, the probability that the person chosen passed the exam and7
took the review course is ​ _ ​.
200

QUESTION 17.
Choice C is correct. To find the atomic weight of an unknown element thatis 20% less than the atomic weight of calcium, multiply the atomic weight, in
amu, of calcium by (1 − 0.20): (40)(1 − 0.20) = (40)(0.8) = 32.

Choice A is incorrect. This value is 20% of the atomic weight of calcium, notan atomic weight 20% less than that atomic weight of calcium. Choice B isincorrect. This value is 20 amu less, not 20% less, than the atomic weight ofcalcium. Choice D is incorrect. This value is 20% more, not 20% less, than
the atomic weight of calcium.

QUESTION 18.
Choice C is correct. The mean and median values of a data set are equal
when there is a symmetrical distribution. For example, a normal distribution is symmetrical. If the mean and the median values are not equal,
then the distribution is not symmetrical. Outliers are a small group ofvalues that are significantly smaller or larger than the other values in thedata. When there are outliers in the data, the mean will be pulled in theirdirection (either smaller or larger) while the median remains the same.
The example in the question has a mean that is larger than the median,and so an appropriate conjecture is that large outliers are present in thedata; that is, that there are a few homes that are valued much more than
the rest.

Choice A is incorrect because a set of home values that are close to eachother will have median and mean values that are also close to each other.
34

Choice B is incorrect because outliers with small values will tend to makethe mean lower than the median. Choice D is incorrect because a set of data
where many homes are valued between $125,000 and $165,000 will likely
have both a mean and a median between $125,000 and $165,000.

QUESTION 19.
Choice B is correct. The median of a data set is the middle value when

the data points are sorted in either ascending or descending order. There
are a total of 600 data points provided, so the median will be the average of the 300th and 301st data points. When the data points are sorted
in order: Values 1 through 260 will be 0.
 Values 261 through 450 will be 1.
 Values 451 through 540 will be 2.
 Values 541 through 580 will be 3.
 Values 581 through 600 will be 4.

Therefore, both the 300th and 301st values are 1, and hence the median is 1.
Choices A, C, and D are incorrect and may result from either a calculation
error or a conceptual error.

QUESTION 20.
Choice C is correct. When survey participants are selected at random

from a larger population, the sample statistics calculated from the survey
can be generalized to the larger population. Since 10 of 300 students surveyed at Lincoln School have 4 siblings, one can estimate that this sameratio holds for all 2,400 students at Lincoln School. Also, since 10 of 300
students surveyed at Washington School have 4 siblings, one can estimatethat this same ratio holds for all 3,300 students at Washington School.
10
Therefore, approximately ​  _  ​× 2,400 = 80 students at Lincoln School
30
10
and _
​   ​× 3,300 = 110 students at Washington School are expected to have30
4 siblings. Thus, the total number of students with 4 siblings at Washington
School is expected to be 110 − 80 = 30 more than the total number of students with 4 siblings at Lincoln School.
Choices A, B, and D are incorrect and may result from either conceptual or calculation errors. For example, choice A is incorrect; even though
there is the same ratio of survey participants from Lincoln School andWashington School with 4 siblings, the two schools have a different total
number of students, and thus, a different expected total number of students with 4 siblings.
35

QUESTION 21.
Choice D is correct. The difference between the number of hours the projecttakes, y, and the number of hours the project was estimated to take, x, is|y − x|. If the goal is met, the difference is less than 10, which can be represented as |y − x| < 10 or −10 < y − x < 10.
Choice A is incorrect. This inequality states that the estimated number ofhours plus the actual number of hours is less than 10, which cannot betrue because the estimate is greater than 100. Choice B is incorrect. Thisinequality states that the actual number of hours is greater than the estimated number of hours plus 10, which could be true only if the goal ofbeing within 10 hours of the estimate were not met. Choice C is incorrect.
This inequality states that the actual number of hours is less than the estimated number of hours minus 10, which could be true only if the goal ofbeing within 10 hours of the estimate were not met.

QUESTION 22.
P
4πr
P ​. Then dividing
multiply each side of the equation by r2. This yields r2I = ​ _4πeach side of r2I = _​  P ​ by I gives r2 = _​  P ​.
4π
4πI
Choices A, C, and D are incorrect and may result from algebraic errors during the rearrangement of the formula.
Choice B is correct. To rearrange the formula I = ​ _2 in terms of r2, first

QUESTION 23.
Choice A is correct. If IA is the intensity measured by Observer A froma distance of rA and IB is the intensity measured by Observer B fromP ​, the intena distance of rB, then IA =16IB. Using the formula I = ​  _4π2
P  ​, which can also be written insity measured by Observer A is IA = ​  _4πrA2
P  ​  ​. Setting the right-hand sides of theseterms of IB as IA = 16IB = 16 ​ ​ _4πrB2
P  ​  ​, which relates
P  ​= 16 ​ ​ _two equations equal to each other gives ​ _
4πrA2
4πrB2
the distance of Observer A from the radio antenna to the distance ofP ​ and
Observer B from the radio antenna. Canceling the common factor ​ _4π
rearranging the equation gives rB2 = 16rA2. Taking the square root of each

( )

( )

side of rB2 = 16rA2 gives rB = 4rA, and then dividing each side by 4 yields
1 ​rA = _​ 1 ​ r . Therefore, the distance of Observer A from the radio antenna is ​ _4 B
4the distance of Observer B from the radio antenna.
Choices B, C, and D are incorrect and may result from errors in deriving or

( )

P =
​ (16) ​ _using the formula _​ ​  P 2 ​  .​
4πrA2
4πrB
36

QUESTION 24.
Choice A is correct. The equation of a circle with center (h, k) and radius r

is (x − h)2 + (y − k)2 = r2. To put the equation x2 + y2 + 4x − 2y = −1 in thisform, complete the square as follows:

x2 + y2 + 4x − 2y = −1
(x2 + 4x) + (y2 − 2y) = −12
(x + 4x + 4) −4 + (y2 − 2y + 1) − 1 = −1
(x + 2)2 + (y − 1)2 − 4 − 1 = −1
(x + 2)2 + (y − 1)2 = 4 = 22

Therefore, the radius of the circle is 2.
Choice C is incorrect because it is the square of the radius, not the radius.
Choices B and D are incorrect and may result from errors in rewriting the
given equation in standard form.

QUESTION 25.
Choice A is correct. In the xy-plane, the slope m of the line thatpasses through the points (x1, y1) and (x2, y2) is given by the formulay2 − y1m = ​ _
x2 − x1. Thus, if the graph of the linear function f has intercepts at(a, 0) and (0, b), then the slope of the line that is the graph of y = f(x) is
0−b
b
m=_
​ 
 ​ = − ​ _a ​. It is given that a + b = 0, and so a = −b. Finally, substituting
a−0
b
b
_
−b for a in m = − ​ _a ​gives m = −  −b ​= 1, which is positive.
Choices B, C, and D are incorrect and may result from a conceptual misunderstanding or a calculation error.

QUESTION 26.
Choice D is correct. The definition of the graph of a function f in the xy-

plane is the set of all points (x, f (x)). Thus, for −4 ≤ a ≤ 4, the value of f(a)is 1 if and only if the unique point on the graph of f with x-coordinate a
has y-coordinate equal to 1. The points on the graph of f with x-coordinates
3
3
−4, _
​   ​, and 3 are, respectively, (−4, 1),​ ​ _ ​, 1 ​, and (3, 1). Therefore, all of the2
2values of f given in I, II, and III are equal to 1.

( )Choices A, B, and C are incorrect because they each omit at least one valueof x for which f(x) = 1.

QUESTION 27.
Choice D is correct. According to the graph, in the interval from 0 to 10 min-utes, the non-insulated sample decreased in temperature by about 18°C,
while the insulated sample decreased by about 8°C; in the interval from 10
to 20 minutes, the non-insulated sample decreased in temperature by about
9°C, while the insulated sample decreased by about 5°C; in the interval
37

from 40 to 50 minutes, the non-insulated sample decreased in temperature
by about 1°C, while the insulated sample decreased by about 3°C; and in
the interval from 50 to 60 minutes, the non-insulated sample decreased intemperature by about 1°C, while the insulated sample decreased by about
2°C. The description in choice D accurately summarizes these rates of temperature change over the given intervals. (Note that since the two samplesof water have equal mass and so must lose the same amount of heat to coolfrom 60°C to 25°C, the faster cooling of the non-insulated sample at the startof the cooling process must be balanced out by faster cooling of the insulated sample at the end of the cooling process.)
Choices A, B, and C are incorrect. None of these descriptions accurately
compares the rates of temperature change shown in the graph for the
10-minute intervals.

QUESTION 28.
Choice B is correct. In the xy-plane, the slope m of the line that passesy2 − y1through the points (x1, y1) and (x2, y2) is m = _x − x . Thus, the slope of the
2

1

2−0
 ​, which simplifies to _​ 2 ​ = _​ 1 ​.
line through the points C(7, 2) and E(1, 0) is _
​ 

7−1
6 3
1 ​. The other diagonal of the square is
Therefore, diagonal AC has a slope of ​ _3
a segment of the line that passes through points B and D. The diagonals of asquare are perpendicular, and so the product of the slopes of the diagonals
is equal to −1. Thus, the slope of the line that passes through B and D is −3
1 ​(−3) = −1. Hence, an equation of the line that passes through B andbecause ​ _3
D can be written as y = −3x + b, where b is the y-intercept of the line. Sincediagonal BD will pass through the center of the square, E(1, 0), the equation
0 = −3(1) + b holds. Solving this equation for b gives b = 3. Therefore, an
equation of the line that passes through points B and D is y = −3x + 3, which
can be rewritten as y = −3(x − 1).
Choices A, C, and D are incorrect and may result from a conceptual error ora calculation error.

QUESTION 29.
Choice B is correct. Substituting 3 for y in y = a​ x​2​ + b gives 3 = a​ x​2​ + b, which

can be rewritten as 3 − ​b = ax​2​. Since y = 3 is one of the equations in thegiven system, any solution x of 3 − b = ax2 corresponds to the solution (x, 3)of the given system. Since the square of a real number is always nonnegative, and a positive number has two square roots, the equation 3 − b = ax2
will have two solutions for x if and only if (1) a > 0 and b < 3 or (2) a < 0 andb > 3. Of the values for a and b given in the choices, only a = −2, b = 4 satisfy
one of these pairs of conditions.

38

Alternatively, if a = −2 and b = 4, then the second equation would be
y = −2x2 + 4. The graph of this quadratic equation in the xy-plane is a parabola with y-intercept (0, 4) that opens downward. The graph of the first equation, y = 3, is the horizontal line that contains the point (0, 3). As shown
below, these two graphs have two points of intersection, and therefore,
this system of equations has exactly two real solutions. (Graphing showsthat none of the other three choices produces a system with exactly tworeal solutions.)
y
4
3
2
1
–2

–1

O

1

2

x

Choices A, C, and D are incorrect and may result from calculation or conceptual errors.

QUESTION 30.
Choice A is correct. The regular hexagon can be divided into 6 equilat-eral triangles of side length a by drawing the six segments from the center of the regular_ hexagon to each of its 6 vertices. Since the area of thehexagon_is 384​√3 ​square inches, the area of each equilateral triangle will_384​√3 ​be ​ _ ​= 64​√3 ​square inches.
6
Drawing any altitude of an equilateral triangle divides it into two 30°-60°-90°
triangles. If the side length of the equilateral triangle is a, then the hypotenuse of each 30°-60°-90° triangle is a, and the altitude of the equilateraltriangle will be the side opposite the 60° angle in each of_the 30°-60°-90°​√3 ​triangles. Thus, the altitude of the equilateraltriangleis ​ _ ​a, and the area
_
_
2
​√
​√
3 ​
3 ​ 2
1
_
_
_
of the equilateral triangle is ​   ​(a) ​ ​   ​a = ​   ​a . Since the area of each42_ 2
4_  ​(64​ _equilateral triangle is 64​√3 ​square inches, it follows that a2 = ​ _
√3 ​)
​√3 ​
= 256 square inches. And since the area of the square with side length a is a2,( )it follows that the square has area 256 square inches.
Choices B, C, and D are incorrect and may result from calculation or conceptual errors.

39

QUESTION 31.
The correct answer is 14. Since the coastal geologist estimates that thecountry’s beaches are eroding at a rate of 1.5 feet every year, they will erodeby 1.5x feet in x years. Thus, if the beaches erode by 21 feet in x years, the21  ​= 14. Therefore,
equation 1.5x = 21 must hold. The value of x is then ​ _1.5
according to the geologist’s estimate, it will take 14 years for the country’s
beaches to erode by 21 feet.

QUESTION 32.
The correct answer is 7. There are 60 minutes in each hour, and so there

are 60h minutes in h hours. Since h hours and 30 minutes is equal to
450 minutes, it follows that 60h + 30 = 450. This equation can be simplified
420
to 60h = 420, and so the value of h is ​ _ ​= 7.
60

QUESTION 33.
The correct answer is 11. It is given that the function f(x) passes throughthe point (3, 6). Thus, if x = 3, the value of f(x) is 6 (since the graph of f
in the xy-plane is the set of all points (x, f(x)). Substituting 3 for x and 6
for f(x) in f(x) = 3x2 − bx + 12 gives 6 = 3(3)2 − b(3) + 12. Performing theoperations on the right-hand side of this equation gives 6 = 3(9) − 3b + 12 =27 − 3b + 12 = 39 −3b. Subtracting 39 from each side of 6 = 39 − 3b gives−33 = −3b, and then dividing each side of −3b = −33 by −3 gives the valueof b as 11.

QUESTION 34.
The correct answer is 105. Let D be the number of hours Doug spent in thetutoring lab, and let L be the number of hours Laura spent in the tutoringlab. Since Doug and Laura spent a combined total of 250 hours in the tutoring lab, the equation D + L = 250 holds. The number of hours Doug spent in
the lab is 40 more than the number of hours Laura spent in the lab, and so
the equation D = L + 40 holds. Substituting L + 40 for D in D + L = 250 gives(L + 40) + L = 250, or 40 + 2L = 250. Solving this equation gives L = 105.
Therefore, Laura spent 105 hours in the tutoring lab.

QUESTION 35.
The correct answer is 15. The amount, a, that Jane has deposited after t fixed40

weekly deposits is equal to the initial deposit plus the total amount of money
Jane has deposited in the t fixed weekly deposits. This amount a is given to
be a = 18t + 15. The amount she deposited in the t fixed weekly deposits isthe amount of the weekly deposit times t; hence, this amount must be givenby the term 18t in a = 18t + 15 (and so Jane must have deposited 18 dollars
each week after the initial deposit). Therefore, the amount of Jane’s original
deposit, in dollars, is a − 18t = 15.

QUESTION 36.
The correct answer is 32. Since segments LM and MN are tangent to thecircle at points L and N, respectively, angles OLM and ONM are right angles.
Thus, in quadrilateral OLMN, the measure of angle O is 360° − (90° + 60°
120 1 ​of the+ 90°) = 120°. Thus, in the circle, central angle O cuts off ​ _ ​ = ​ _360 3
1
circumference; that is, minor arc 
LN ​ is ​ _ ​of the circumference. Since the3
1 ​× 96 = 32.
circumference is 96, the length of minor arc 
LN ​ is ​ _3

QUESTION 37.
The correct answer is 3284. According to the formula, the number of plants

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3000
one year from now will be 3000 + 0.2(3000)​ 1 − ​ _ ​  ​, which is equal to4000
3150. Then, using the formula again, the number of plants two years from3150
now will be 3150 + 0.2(3150)​ 1− ​ _ ​ ​, which is 3283.875. Rounding this4000
value to the nearest whole number gives 3284.

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QUESTION 38.
The correct answer is 7500. If the number of plants is to be increased

from 3000 this year to 3360 next year, then the number of plants that theenvironment can support, K, must satisfy the equation 3360 = 3000 +3000​  ​. Dividing both sides of this equation by 3000 gives 1.12 =​ 0.2(3000)​ 1 − _
K
3000
3000
​  ​, and therefore, it must be true that 0.2​ 1 −  ​ _​  ​= 0.12, or​ 
1 + 0.2​ 1 − _
K
K
3000
3000
3000
​= 0.6. It follows that _​= 0.4, and so K = _​ ​   ​ = 7500.
equivalently, 1 − _
​ 
0.4
K
K

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