Answer Explanations

SAT Practice Test #8
Section 1: Reading Test
QUESTION 1

Choice A is the best answer. The first paragraph explains thenarrator’s love of reading: “Even then my only friends were made of
paper and ink. . . . Where my school friends saw notches of ink on
incomprehensible pages, I saw light, streets, and people.” The fourthparagraph reiterates this love in its description of the bookshop asa “sanctuary” and “refuge.” The shift in focus occurs in the last six
paragraphs, which recount the gift of a book that transforms thenarrator’s love of reading into a desire to write: “I did not think there
could be a better [book] in the whole world and I was beginningto suspect that Mr. Dickens had written it just for me. Soon I wasconvinced that I didn’t want to do anything else in life but learn to dowhat Mr. Dickens had done.” Thus the passage’s overall focus shifts
from the narrator’s love of reading to a specific incident that influences
his decision to become a writer.
Choice B is incorrect because the passage never focuses on the
narrator’s father, who primarily serves to illustrate the narrator’sdetermination to read books despite all obstacles. Choice C is incorrect
because the passage focuses on the narrator’s desire to write rather
than on whatever skill he may have as a writer. Choice D is incorrect
because the passage doesn’t make the narrator’s childhood hardships
its central focus or analyze the effects of those hardships.

QUESTION 2

Choice C is the best answer. In the first paragraph, the third sentence
describes the narrator’s love of reading (“where my school friends saw
notches of ink on incomprehensible pages, I saw light, streets, andpeople”), and the fourth sentence describes the role that reading playedin the narrator’s life (“a safe haven from that home, those streets, andthose troubled days in which even I could sense that only a limited
fortune awaited me”). The remainder of the passage recounts incidents
in which the narrator’s actions arise from his love of, and dependence
on, reading. Thus the third and fourth sentences can be seen as
describing a passion that accounts for those actions.
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Choice A is incorrect because although the narrator’s “school friends”
are mentioned in passing in the third sentence, they aren’t introduced
as proper characters and make no further appearance in the passage.
Choice B is incorrect because the passage doesn’t list the difficult
conditions of the narrator’s childhood until after these sentences.
Choice D is incorrect because the narrator’s aspirations aren’t
discussed until the last paragraph of the passage.

QUESTION 3

Choice C is the best answer. The tenth paragraph shows that upon
returning home, the narrator hides the gift (the “new friend”) that
Sempere had given him: “That afternoon I took my new friend home,
hidden under my clothes so that my father wouldn’t see it.” It can beinferred from this sentence that the narrator’s concern arises from anawareness that his father would disapprove of the gift.
Choice A is incorrect because although the passage discusses thefather’s hostility toward the narrator’s love of reading, there is no
indication that the father is not affectionate to the narrator moregenerally; indeed, the third paragraph depicts the father’s generosity
toward the narrator. Choice B is incorrect because the father’s
generosity toward the narrator, as depicted in the third paragraph,clearly shows that the father encourages unnecessary purchases ofsuch things as candy. Choice D is incorrect because although the firstparagraph shows that the father is hostile toward books in general,
there is no indication in the passage that Dickens or any other author
is a specific object of the father’s disdain.

QUESTION 4

Choice D is the best answer. The previous question asks whichstatement about the narrator’s father would the narrator most likely agreewith. The answer, that his father wouldn’t have approved of Sempere’s gift
to the narrator, is best supported in the tenth paragraph: “That afternoon
I took my new friend home, hidden under my clothes so that my father
wouldn’t see it.” It can be inferred from this sentence that the narrator isaware of his father’s likely disapproval of the gift (the “new friend”).
Choices A, B, and C are incorrect because the cited lines don’t support
the answer to the previous question. Instead, they show the father
giving his own gift to the narrator (choice A) and illustrate how thenarrator was treated when in Sempere’s bookshop (choices B and C).

QUESTION 5

Choice A is the best answer. The last paragraph makes clear the
narrator’s enthusiasm for Charles Dickens’s Great Expectations, andit can be inferred from the last sentence of this paragraph that thisenthusiasm motivated the narrator to aspire to a career as a writer:“Soon I was convinced that I didn’t want to do anything else in life but
learn to do what Mr. Dickens had done.”

Answer Explanations | SAT Practice Test #8

Choice B is incorrect because the passage doesn’t discuss gifts thenarrator has received in the past; although the father sometimes gave
the narrator money to buy sweets and snacks, these weren’t gifts since
the narrator made the purchases himself. Choice C is incorrect because
although it is clear from the passage that Sempere was kind and evenindulgent to the narrator, there is no suggestion that this treatment
was inspired by respect for the narrator. Choice D is incorrect because
there is no suggestion that the narrator took Sempere’s figurative
designation of Dickens as a “lifelong friend” in the ninth paragraph tobe a literal statement.

QUESTION 6

Choice D is the best answer. The previous question asks why thenarrator considers Great Expectations to be the greatest gift he everreceived. The answer, that the book convinced him to become a writer,is best supported by the last sentence of the last paragraph: “Soon I
was convinced that I didn’t want to do anything else in life but learn todo what Mr. Dickens had done.”
Choices A, B, and C are incorrect because the cited lines don’t
support the answer to the previous question. Instead, they explain
the narrator’s interactions with the bookseller (choice A), describe thebook’s physical condition (choice B), and indicate the narrator’s initial,
erroneous assumption that Sempere knew Charles Dickens personally(choice C).

QUESTION 7

Choice D is the best answer. In the fourth paragraph, the narrator
explains that although Sempere normally didn’t charge him for books,
he still left Sempere a few coins as payment: “It was only smallchange—if I’d had to buy a book with that pittance, I would probably
have been able to afford only a booklet of cigarette papers.” These lines
signal the narrator’s awareness that he was paying less for the books
than they were worth.
Choice A is incorrect because the passage states that Sempere didn’t
expect or want the narrator to pay: “He hardly ever allowed me to pay
for the books.” Choice B is incorrect because the fourth paragraphmakes clear that even if Sempere didn’t want the narrator's money, thenarrator would still “leave the coins I’d managed to collect.” Choice C
is incorrect because the third paragraph states that the money withwhich the narrator paid Sempere was originally given to the narrator
by his father.

QUESTION 8

Choice B is the best answer. In the fourth paragraph, the narrator
describes his reluctance to leave Sempere’s bookshop: “When it wastime for me to leave, I would do so dragging my feet, a weight on mysoul.” In this context, “weight” most nearly means burden.

Choices A, C, and D are incorrect because in the context of the narrator
having to do something he doesn’t want to, a “weight” he had to carrymost nearly means a burden, not a bulk (choice A), force (choice C), or
clout (choice D).

QUESTION 9

Choice C is the best answer. When, in the eighth paragraph, thenarrator asks Sempere if the author Charles Dickens is a friend of his,Sempere replies, in the ninth paragraph, that Dickens is a “lifelong
friend. And from now on, he’s your friend too.” Sempere designatedDickens a “friend” of both himself and the narrator, who had neverheard of the author before. This signals that the use of “friend”
in these lines is figurative and emphasizes Sempere’s emotional
connection to Dickens and, more generally, to reading. It also
signals Sempere’s hope that the narrator will come to have a similar
connection to Dickens.
Choices A, B, and D are incorrect because the word “friend” is used inthese lines to emphasize Sempere’s connection to reading, rather thanhis connection to the narrator (choice A), the narrator’s relationships
or home life (choice B), or the narrator’s emotional state or decision
making (choice D).

QUESTION 10

Choice B is the best answer. In the ninth paragraph, Sempere describes
the author Charles Dickens to the narrator: “A lifelong friend. And fromnow on, he’s your friend too.” As the reader can reasonably assume that
Sempere doesn’t actually know Dickens, this description can be read as
signaling Sempere as an avid admirer of Dickens’s work.
Choice A is incorrect because the passage describes Sempere as abookseller, not a writer. Choice C is incorrect because although thepassage implies Sempere feels an emotional connection to Dickens, it
doesn’t suggest that this connection arises from any similarity between
Sempere’s life and that of Dickens. Choice D is incorrect becauseeven if the passage implies that Sempere admires Dickens’s work,
Sempere’s admiration isn’t discussed in relation to that felt by otherreaders of Dickens, nor is Sempere shown to compare himself to othersuch readers.

QUESTION 11

Choice B is the best answer. The first paragraph describes thewidespread practice of not reporting null results, or results in which
researchers fail to see an effect that should be detectable. The second
through sixth paragraphs discuss a study that examined how scientists
have dealt with null results. The seventh and eighth paragraphs
discuss the negative consequences that null results pose for future
research and the possible creation of a registry for all data produced byresearch studies, reported and unreported alike, as a remedy for thoseAnswer Explanations | SAT Practice Test #8

consequences. Therefore, the purpose of the passage as a whole is toexplain a common practice in the reporting of research studies andsummarize a study that provides support for a change to that practice.
Choice A is incorrect because the passage doesn’t dispute a widely
held belief about the publication of social science research; rather, itsuggests a solution to deal with a long-debated problem. Choice C isincorrect because while the passage hints at possible shortcomings inresearch trials, it doesn’t describe them in detail; because it addresses
other kinds of research besides medical trials; and because it doesn’tcall for a government database, specifically. Choice D is incorrect
because the passage calls for changes to the reporting of research
results, rather than to research methodology itself, and because it
doesn’t address the publishers of research at all.

QUESTION 12

Choice D is the best answer. The second paragraph states that “TESS
allows scientists to order up Internet-based surveys.” In the context
of the service that the TESS program provides to scientists, “allows”
most nearly means enables.
Choices A, B, and C are incorrect because in the context of thepassage’s discussion of TESS, “allows” most nearly means enables,
not admits (choice A), tolerates (choice B), or grants (choice C).

QUESTION 13

Choice D is the best answer. The fifth paragraph of the passage
addresses the “statistical strength” of certain scientific findings. In thiscontext, “strength” most nearly means significance, or importance.
Choices A, B, and C are incorrect because in the context of thestatistical importance of scientific findings, “strength” most nearlymeans significance, not attribution (choice A), exertion (choice B), or
toughness (choice C).

QUESTION 14

Choice A is the best answer. The seventh paragraph discusses thenegative consequences of not publishing null results, emphasizingthat “worse, if researchers publish significant results from similar
experiments in the future, they could look stronger than they should
because the earlier null studies are ignored.” In other words, failing to
document null results means that the results of later, related studies
will not be as accurate as they appear.
Choices B, C, and D are incorrect because the passage does notindicate that failing to document null results can cause promisingareas of research to be overlooked (choice B), cause errors in datacollection practices that lead to null results being overlooked(choice C), or lessen bias against null results (choice D).

QUESTION 15

Choice D is the best answer. The previous question asks what thepassage indicates could result from failing to document null results.
The answer, that the results of future studies will be misleading,is best supported in the seventh paragraph: “Worse, if researchers
publish significant results from similar experiments in the future, they
could look stronger than they should because the earlier null studies
are ignored.”
Choices A, B, and C are incorrect because the cited lines don’t
support the answer to the previous question. Instead, choice A
suggests how the findings of a study about null results may
affect existing beliefs about such results; choice B explains
how infrequently null results had been written up, according to
Malhotra’s study; and choice C illustrates a problem resulting fromthe failure to document null results, but one that is unrelated to thefact that this documentation failure may make the results of future,
related studies appear more valid than they are.

QUESTION 16

Choice B is the best answer. The last two sentences of the seventh
paragraph identify a particular research scenario that Malhotra
uncovered in his study: “Even more troubling to Malhotra was the factthat two scientists whose initial studies ‘didn’t work out’ went on to
publish results based on a smaller sample. ‘The non-TESS versionof the same study, in which we used a student sample, did yieldfruit,’ noted one investigator.” Since Malhotra especially objected tothese researchers’ suppression of data that produced null results andtheir subsequent publication of related data that were statisticallysignificant, it can be inferred that the hypothetical situation to which
he would most strongly object is one in which researchers publish
their study results in a journal but exclude the portion of data that
produced null results.
Choices A and D are incorrect because the seventh paragraph,
which identifies a research scenario that Malhotra disapproved of,provides no basis for an inference that he would especially object
to a team’s insisting on publishing null results in a top journal
only (choice A) or a team’s expanding the scope of a study that had
produced null results (choice D). Choice C is incorrect because
although the first sentence of the seventh paragraph indicates
Malhotra’s concern that failing to publish null results can meanthat other researchers unwittingly replicate strategies that produced
null results in prior studies, the paragraph goes on to identify
other scenarios as being “worse” and “even more troubling” from
Malhotra’s perspective.

Answer Explanations | SAT Practice Test #8

QUESTION 17

Choice C is the best answer. The previous question asks about which
hypothetical situation Malhotra would most strongly object to. The
answer, that he would most strongly object to researchers’ reporting
their findings but failing to disclose the null results, is best supported
at the end of the seventh paragraph: “Even more troubling to Malhotra
was the fact that two scientists whose initial studies ‘didn’t work out’
went on to publish results based on a smaller sample. ‘The non-TESS
version of the same study, in which we used a student sample, did
yield fruit,’ noted one investigator.”
Choices A, B, and D are incorrect because the cited lines don’t support
the answer to the previous question about which situation Malhotra
would most strongly object to. Instead, they cite another researcher’s
attitude toward null results from his or her own study (choice A),
compare the publication rate for studies that produce null resultswith that for studies that produce statistically significant results(choice B), and describe the recommendation by Malhotra and his teamfor the creation of a database to remedy problems resulting from thenonpublication of null results (choice D).

QUESTION 18

Choice B is the best answer. After describing problems that could
arise from the failure to report null results, the passage shifts in thelast paragraph to a potential solution to such problems: “A registry fordata generated by all experiments would address these problems, theauthors argue.” The paragraph goes on to imply that a registry could
solve such problems by deterring the suppression of null results.
Choice A is incorrect because the last paragraph proposes a “registryfor data” rather than a future research project. Choice C is incorrect
because the summary of the results of Malhotra’s study occurs in
the fifth paragraph, not in the last. Choice D is incorrect because thelast paragraph of the passage does not mention reexamining results
already obtained in social science trials.

QUESTION 19

Choice C is the best answer. The far left bar of the graph pertains tosocial science studies that produced strong results. This bar showsthat approximately 20 percent (or two full increments of 10 percent) ofsuch studies were published in a top journal.
Choice A is incorrect because the graph shows that approximately
5 percent of social science studies that produced strong results were
unwritten, rather than over 50 percent. Choice B is incorrect because
the graph shows that about 30 percent of social science studies that
produced strong results were unpublished but written, rather than
50 percent. Choice D is incorrect because the graph shows that slightly
over 40 percent of social science studies that produced strong results
were published in a non-top journal, rather than almost 80 percent.

QUESTION 20

Choice A is the best answer. The middle bar of the graph pertains tosocial science studies that produced mixed results. The top 50 percentof this bar represents studies that were published. The bottom
50 percent of this bar represents studies that were either unpublishedor went unwritten. Since each of the two categories accounts for
50 percent of the total, it can be said that studies with mixed results
were just as likely to be published as they were to be left either
unpublished or unwritten.
Choice B is incorrect because the graph indicates that roughly
42 percent of social science studies produced strong results androughly 22 percent produced null results; together, these twopercentages far exceed the 36 percent accounted for by studies that
produced mixed results. Choice C is incorrect because the graphshows that roughly 12 percent of studies that produced mixed
results were published in top journals, well less than the percentage
published in non-top journals (approximately 38 percent). Choice D
is incorrect because the graph indicates that studies that produced
strong results accounted for approximately 42 percent of all studies,while those that produced mixed results only accounted for around36 percent of all studies.

QUESTION 21

Choice C is the best answer. The first sentence of the fifth paragraphstates, “Not unexpectedly, the statistical strength of the findings madea huge difference in whether they were ever published.” This statement
is supported by the graph, which shows that more than 60 percent ofsocial science studies that produced strong results were published,
while only about 50 percent of studies with mixed results and about
20 percent of studies with null results were published.
Choices A, B, and D are incorrect because none of the cited lines
contain information that is represented by the data in the graph.
Instead, they recount scientists’ explanations for why they didn’t
publish their null results (choices A and B) and highlight claims about
the importance of Malhotra’s study (choice D).

QUESTION 22

Choice A is the best answer. The first paragraph explains that in the
nanoworld, salt can be seen “stretching like taffy.” The third paragraphnotes that while this elasticity was expected in metals, it wasn’t
imagined for salt: “But scientists don’t expect this superplasticity in arigid, crystalline material like salt.” The rest of the passage explores
this unexpected behavior of salt. Therefore it can be said that one of
the central ideas of the passage is that materials don’t always behave
as scientists might expect them to.

Answer Explanations | SAT Practice Test #8

Choices B, C, and D are incorrect because the passage focuses on theunexpected way that salt reacts in the nanoworld, not on the role of
inputs and outputs in systems (choice B), the relative strengths andweaknesses of models (choice C), or how the properties of systems
differ from the properties of their parts (choice D).

QUESTION 23

Choice D is the best answer. The first five paragraphs introduce salt’s
ability to stretch “like taffy to more than twice its length.” In the fifth
paragraph, the passage shifts into an explanation of how “Moore andhis colleagues discovered salt’s stretchiness.” The last paragraphspeculates about the possible application of this discovery: “The work
also suggests new techniques for making nanowires, which are often
created through nano-imprinting techniques.” The passage’s overall
structure can therefore be seen as consisting of an introduction to aninteresting salt property, followed by a description of how the property
was discovered, followed by a speculation regarding applications of
this property.
Choice A is incorrect because the passage discusses only one way
in which salt differed from researchers’ expectations. Choice B isincorrect because the passage begins not with a hypothesis about
salt’s behavior but with an explanation of its behaviors. Choice C isincorrect because the passage discusses complementary observationsof salt crystals rather than two experiments involving salt that yieldseemingly conflicting results.

QUESTION 24

Choice A is the best answer. That Moore’s group was surprised toobserve salt stretching is most directly suggested by the last sentenceof the third paragraph: “But scientists don’t expect this superplasticity
in a rigid, crystalline material like salt, Moore says.”
Choices B, C, and D are incorrect because the cited lines don’t support
the idea that Moore’s group was surprised to observe salt stretching.
Instead, they explain how the group happened upon their observation(choice B), the measures the group took to investigate the stretching
further (choice C), and how common salt is in nature (choice D).

QUESTION 25

Choice B is the best answer. The first sentence of the fourth paragraphstates, “This unusual behavior highlights that different forces rule thenanoworld.” In this context, to “rule” most nearly means to control.
Choices A, C, and D are incorrect because in the context of a discussionof forces that operate on the nanoworld, to “rule” most nearly means tocontrol, not to mark (choice A), declare (choice C), or restrain (choice D).

QUESTION 26

Choice D is the best answer. The first sentence of the sixth paragraphidentifies “electrostatic forces, perhaps good old van der Waals
interactions” as the potential cause of the initial attraction between the
microscope tip and the salt.
Choices A, B, and C are incorrect because the first sentence of thesixth paragraph clearly identifies the potential cause of the initialattraction between the microscope tip and the salt as van der Waals
interactions, not as gravity (choice A), nano-imprinting (choice B), or
surface tension (choice C).

QUESTION 27

Choice B is the best answer. The sixth paragraph says that “several
mechanisms might lead to” salt’s elasticity. In this context, the phrase“lead to” most nearly means result in.
Choices A, C, and D are incorrect because in the context of somethingcausing salt molecules to exhibit elasticity, the phrase “lead to” mostnearly means result in, not guide to (choice A), point toward (choice C),
or start with (choice D).

QUESTION 28

Choice A is the best answer. The first paragraph of the passage
makes clear that salt exhibits elasticity (“stretching like taffy”) in the
nanoworld, and the eighth paragraph explains that salt possesses somedegree of elasticity in the macroworld as well: “Huge undergrounddeposits of salt can bend like plastic, but water is believed to playa role at these scales.” Thus flexibility describes the relationshipbetween salt’s behavior in both the nanoworld and the macroworld.
Choice B is incorrect because the third paragraph explains that“scientists don’t expect” salt’s flexibility in the nanoworld, not thatthey do expect it; moreover, there is no indication that salt’s flexibility
in the macroworld is surprising. Choice C is incorrect because thepassage doesn’t make clear whether nanowires were first observedin the nanoworld or the macroworld. Choice D is incorrect because
the passage does not examine the interaction of salt and water in
the nanoworld or suggest that such interaction causes salt to haveproperties that are different from those it possesses in the macroworld.

QUESTION 29

Choice D is the best answer. The previous question asks about which
description of the relationship between salt behavior in the nanoworld
and in the macroworld can be inferred from the passage. The answer, thatsalt is flexible or elastic in both worlds, is best supported in the eighth
paragraph: “Huge underground deposits of salt can bend like plastic, butwater is believed to play a role at these scales.” These lines suggest thatin the macroworld, as in the nanoworld, salt possesses flexibility.

Answer Explanations | SAT Practice Test #8

Choices A, B, and C are incorrect because the cited lines don’t support
the answer to the previous question. Instead, they highlight theprevalence of nanowires (choice A), identify which forces dominate
the nanoworld (choice B), and offer a tentative explanation for an
observation discussed in the passage (choice C).

QUESTION 30

Choice C is the best answer. The lower graph, which shows the “tipmoving away from salt surface,” indicates that when the microscope
tip was 15 nanometers from the surface, the force on the tip was
approximately 0.75 micronewtons.
Choices A, B, and D are incorrect because the graph shows that whenthe microscope tip was 15 nanometers from the salt surface, the force
on the tip was approximately 0.75 micronewtons, not 0 micronewtons(choice A), 0.25 micronewtons (choice B), or 1.25 micronewtons(choice D).

QUESTION 31

Choice D is the best answer. The bottom graph illustrates the processdescribed in the first sentence of the seventh paragraph of the passage:“as the microscope pulls away from the salt, the salt stretches.” On thegraph, the stretching of the salt is represented by the amount of force,in micronewtons, exerted on the microscope tip as the tip moves awayfrom the salt surface. The graph shows that force was exerted on the
tip until the tip reached point T at approximately 22 nanometers fromthe salt surface; from point T on, the force was 0 micronewtons. It canbe inferred that since no force is being exerted after point T, point T is
the point at which a salt nanowire breaks.
Choices A, B, and C are incorrect because the labels P, Q, and R all
appear on the top graph, which represents data on the movement of
the microscope tip toward the salt surface. As the fifth sentence of thefifth paragraph explains, when the microscope tip moved toward thesalt, “the salt actually stretched out to glom on to the microscopetip.” Therefore, the first graph shows the salt attaching itself to themicroscope tip and forming nanowires, not the breaking of a nanowire.

QUESTION 32

Choice B is the best answer. In the first paragraph of Passage 1,
Douglas argues that throughout the period in which the United States
had both free and slave states, the nation as a whole “increased fromfour millions to thirty millions of people . . . extended our territory
from the Mississippi to the Pacific Ocean . . . acquired the Floridas
and Texas . . . [and had] risen from a weak and feeble power to become
the terror and admiration of the civilized world.” It can reasonably beinferred that Douglas cites such growth in territory and population
to make the point that the division into free and slave states was
obviously not a threat to the country’s health or survival.

Choice A is incorrect because although it can be inferred that Douglas
would argue for continued expansion of the United States, he cites
the expansion it has already undergone as support for perpetuating
the division into free and slave states. Choice C is incorrect because
although Douglas implies that basic facts pertaining to the historical
growth of the nation cast doubt on Lincoln’s political agenda, hedoesn’t imply that Lincoln is unaware of those facts. Choice D isincorrect because although Douglas notes that the United States is
globally perceived to be powerful, he doesn’t imply that this perception
can be accounted for by the nation’s record of growth.

QUESTION 33

Choice C is the best answer. In the second paragraph of Passage 1,
Douglas uses a rhetorical question to stress that the division into slaveand free states has existed since the beginning of the United States:“I now come back to the question, why cannot this Union exist forever,divided into Free and Slave States, as our fathers made it?” It canbe inferred from this question that Douglas believes that since thisdivision is long-standing, the provisions for it in the US Constitution
have provided a good basic structure that doesn’t need to be changed.
Choice A is incorrect because in Passage 1, Douglas doesn’t observethat the US Constitution’s provisions for slavery lack a means forreconciling differences between slave states and free states. Choice B
is incorrect because although Douglas stresses that the provisions
for slavery are long-standing, he doesn’t characterize them as having
somehow anticipated the Union’s expansion to the west. Choice D
is correct because although it can be inferred from Passage 1 that
Douglas believes the provisions for slavery have had a positive
economic impact, he nowhere implies that the founders based them onan assumption that slavery was economically necessary.

QUESTION 34

Choice B is the best answer. The previous question asks about how
Douglas, in Passage 1, characterizes the Constitution’s provisions forslavery. The answer, that Douglas believes they provided a good basic
structure and don’t need to be changed, is best supported in the first
sentence of the second paragraph of Passage 1: “I now come back to
the question, why cannot this Union exist forever, divided into Freeand Slave States, as our fathers made it?”
Choices A, C, and D are incorrect because the cited lines don’t support
the answer to the previous question. Instead, they describe the various
ways in which the nation has expanded since its founding (choice A),
stress the likelihood that the nation will only continue to expand(choice C), and assert the importance of the sovereignty of individualstates to the future expansion of the nation (choice D).

Answer Explanations | SAT Practice Test #8

QUESTION 35

Choice C is the best answer. In the first sentence of the second
paragraph of Passage 2, Lincoln raises a question about how theconsequences of the division of the United States into slave states andfree states compare with the consequences of the other ways in whichstates differ from each other: “But has it been so with this element ofslavery?” In this context, the word “element” most nearly means factor.
Choices A, B, and D are incorrect because in the context of Lincoln’s
discussion of the “element of slavery,” the word “element” most nearlymeans factor, not ingredient (choice A), environment (choice B), or
quality (choice D).

QUESTION 36

Choice B is the best answer. In the second paragraph of Passage 2,
Lincoln asserts that the controversy surrounding slavery in the
United States has died down whenever the institution of slavery has
been restricted geographically: “Whenever it has been limited toits present bounds, and there has been no effort to spread it, there
has been peace.” Since Lincoln associates peace on this issue withgeographical limits on the institution of slavery itself, it can be inferredthat he would agree that the controversy would abate if all attempts toestablish slavery in new regions ceased.
Choice A is incorrect because Lincoln neither urges Northern states toattempt to abolish slavery unilaterally nor implies that such an attempt
would extinguish the controversy over slavery. Choice C is incorrect
because Lincoln neither suggests that the laws regulating slavery
are ambiguous nor that such ambiguity exacerbates controversy overslavery. Choice D is incorrect because Lincoln never attributes thecontroversy over slavery to differences in religion or social values fromone state to another.

QUESTION 37

Choice C is the best answer. The previous question asks which claim
about the controversy over slavery would Lincoln agree with. The
answer, that the controversy would abate if attempts to spread slavery
to regions where it isn’t practiced were abandoned, is best supported
in the second paragraph of Passage 2: “Whenever [slavery] has been
limited to its present bounds, and there has been no effort to spread it,
there has been peace.”
Choices A, B, and D are incorrect because the cited lines don’t
support the answer to the previous question. Instead, they discussstate-to-state differences in laws regulating issues other than slavery(choice A), assert that the differences among the various states
generally benefit the nation (choice B), and ask a philosophicalquestion that doesn’t directly address the issue of slavery (choice D).

QUESTION 38

Choice D is the best answer. In the last sentence of Passage 2, Lincoln
asks about the likelihood that people will fundamentally change: “Do
you think that the nature of man will be changed?” In this context, theword “nature” most nearly means character.
Choices A, B, and C are incorrect because in the context of a
discussion of the “nature of man,” the word “nature” most nearlymeans character, not force (choice A), simplicity (choice B), or world(choice C).

QUESTION 39

Choice C is the best answer. In the first paragraph of Passage 1,
Douglas claims that Lincoln considers the Constitution to be “a house
divided against itself,” due to its provisions for the division of thenation into slave states and free states, and to be “in violation of thelaw of God.” In Passage 2, Lincoln objects to this characterization ofhis position and devotes the majority of the passage to clarifying that
it isn’t the Constitution he finds fault with, or even its provisions forslavery, but rather with attempts to spread slavery to regions where it
isn’t currently practiced. Therefore it can be said that a central tension
between the two passages arises from, on the one hand, Douglas’s
criticism of Lincoln for finding fault with the Constitution and, on
the other, Lincoln’s insistence that Douglas has misrepresented
his position.
Choice A is incorrect because Douglas (Passage 1) proposes nochanges to federal policies on slavery and because Lincoln (Passage 2)
doesn’t consider whether changes to such policies would enjoy
popular support. Choice B is incorrect because Douglas (Passage 1)
never expresses concern about the potential impact of abolition on
the US economy and because Lincoln (Passage 2) neither discusses
such an impact nor dismisses concerns about it. Choice D is incorrect
because neither passage offers any interpretation of federal law.

QUESTION 40

Choice A is the best answer. In the first paragraph of Passage 1,
Douglas discusses the issue of slavery in the context of the divisionof free states and slave states throughout the period when the UnitedStates “extended our territory from the Mississippi to the Pacific
Ocean” and “acquired the Floridas and Texas, and other territory
sufficient to double our geographical extent.” In the second paragraphof Passage 2, Lincoln asserts that the controversy over slavery hashistorically been “excited by the effort to spread [slavery] into new
territory,” as in the case of Missouri, Texas, and “the territory acquiredby the Mexican War.” Therefore, it can be said that, notwithstanding
their differences of opinion, both Douglas and Lincoln discuss theissue of slavery in relationship to the expansion of the Union.

Answer Explanations | SAT Practice Test #8

Choices B, C, and D are incorrect because it is in relationship to thenation’s expansion that both passages discuss the issue of slavery, notin relationship to questions of morality (choice B), religious toleration(choice C), or laws regulating commerce (choice D).

QUESTION 41

Choice D is the best answer. In the second paragraph of Passage 1,
Douglas asks the rhetorical question: “why cannot this Union exist
forever, divided into Free and Slave States, as our fathers madeit?” The remainder of the paragraph amounts to an answer to thisrhetorical question and a refutation of Lincoln’s viewpoint on slavery,
as represented by Douglas. In the second paragraph of Passage 2,
Lincoln asks a series of rhetorical questions: “But has it been sowith this element of slavery? Have we not always had quarrels anddifficulties over it? And when will we cease to have quarrels over it?”
These questions imply that there are flaws in Douglas’s equating thedivision into slave states and free states with other, more unambiguously
beneficial differences from state to state. The remainder of the second
paragraph expands on these flaws. Therefore, it can be said thatin context, the rhetorical questions asked by each speaker serve toundermine the argument of the other speaker.
Choice A is incorrect because in asking rhetorical questions, neither
Douglas nor Lincoln casts doubt on the sincerity of his opponent.
Choices B and C are incorrect because although Douglas and Lincoln
find fault with each other’s ideas, they don’t criticize each other’s
methods (choice B) or reproach each other’s actions (choice C).

QUESTION 42

Choice A is the best answer. The first two paragraphs of the passage
describe the physical process by which the Venus flytrap closes its trap
but also note certain long-standing questions about that process: “Howdoes the plant encode and store the information from the unassuming
bug’s encounter with the first hair? How does it remember the first
touch in order to react upon the second?” The passage then answers
those questions by discussing, in the third and fourth paragraphs, astudy conducted by Dieter Hodick and Andreas Sievers that identified
the physiological means behind the closing of the Venus flytrap’s trap
and, in the last paragraph, a study conducted by Alexander Volkov that
confirmed and built on Hodick and Sievers’s findings. The primary
purpose of the passage can therefore be seen as discussing scientificfindings that explain how the Venus flytrap closes its trap.
Choice B is incorrect because the passage doesn’t discuss the Venus
flytrap’s ability to close its trap in the context of the abilities of otherplants. Choice C is incorrect because the passage discusses how
the closing action operates but not how it has evolved. Choice D isincorrect because the passage doesn’t provide an overview of theVenus flytrap and its predatory behavior; it merely notes in passingthat the closing action has a predatory function.

QUESTION 43

Choice C is the best answer. The first paragraph discusses thechallenge posed to the Venus flytrap by the opening and closing of
its trap: “Closing its trap requires a huge expense of energy, andreopening the trap can take several hours, so Dionaea only wants
to spring closed when it’s sure that the dawdling insect visiting its
surface is large enough to be worth its time.” Since closing andreopening the trap requires the expense of precious energy, it canbe inferred that by guarding against unnecessary closing, multiple
triggers safeguard the plant’s energy supply.
Choice A is incorrect because the passage never indicates that multiple
triggers allow the Venus flytrap to identify which species its preybelongs to, only that they allow it to gauge the prey’s size. Choice B isincorrect because although the passage implies that the plant needs
to conserve energy and indicates that calcium is involved in the trapclosing mechanism, there is no indication that the plant’s calcium
reserves themselves require conservation. Choice D is incorrect
because it can be inferred from the passage that the advantage ofmultiple triggers is that they prevent the Venus flytrap from closing on
the improper prey rather than from prematurely closing on the proper
prey; the passage never implies that when touched by its proper prey,
the Venus flytrap is at risk of closing too soon to capture it.

QUESTION 44

Choice A is the best answer. The previous question asks what the Venus
flytrap gains from requiring multiple triggers before closing. The answer,
that multiple triggers allow the plant to conserve energy, is best supported
near the beginning of the first paragraph: “Closing its trap requires ahuge expense of energy, and reopening the trap can take several hours,
so Dionaea only wants to spring closed when it’s sure that the dawdlinginsect visiting its surface is large enough to be worth its time.”
Choices B, C, and D are incorrect because the cited lines don’t support
the answer to the previous question. Instead, they describe how the hairson the Venus flytrap function and how the system of multiple triggers
works (choices B and C) and explain how the plant preserves a memory,
as it were, that something has touched the trigger hairs (choice D).

QUESTION 45

Choice C is the best answer. The phrases “dawdling insect,” “happily
meanders,” and “unassuming bug’s encounter” are less typical of word
choices made in formal, scientific writing than of those made in lessformal writing modes. Therefore, the tone that these phrases establish
is best described as informal.
Choices A, B, and D are incorrect because the phrases establish a tonethat is informal, not academic (choice A), melodramatic (choice B), or
mocking (choice D).

Answer Explanations | SAT Practice Test #8

QUESTION 46

Choice A is the best answer. The first paragraph describes themechanism that prompts the Venus flytrap to close its trap. The second
paragraph makes an analogy of each step of that mechanism to an
aspect of short-term memory formation in humans and then poses
questions about the precise physiological terms in which those steps
are carried out. It can therefore be said that the discussion of shortterm memory serves to clarify the first paragraph’s explanation of what
prompts the trap of the Venus flytrap to close.
Choice B is incorrect because it is the third paragraph, not the second,that discusses the function of electric charges in the Venus flytrap;
moreover, the passage presents this function as a fact, not as acontroversial hypothesis. Choice C is incorrect because rather thanstressing the differences between Venus flytraps and humans, theanalogy in the second paragraph stresses their superficial similarities.
Choice D is incorrect because the second paragraph implies that the
Venus flytrap’s capacity for retaining information is far from detailed:“something (it doesn’t know what) has touched one of its hairs.”

QUESTION 47

Choice D is the best answer. The third paragraph explains thattouching a single trigger hair results in “a rapid increase in theconcentration of calcium ions” in the plant. The fourth paragraphfurther explains that the calcium concentration produced by this initial
touch isn’t enough to cause the trap to close, but that a second hair
touch will bring the total concentration to the level necessary to close
the trap: “a second hair needs to be stimulated to push the calcium
concentration over this threshold and spring the trap.”
Choices A and B are incorrect because the fourth paragraph explainsthat the second trigger supplements the action of the first trigger, notthat it reverses it (choice A) or stabilizes its effect (choice B). Choice C
is incorrect because the third paragraph clearly states that the calcium
channels open after the first trigger hair is touched, not the second.

QUESTION 48

Choice B is the best answer. The fourth paragraph explains that
the Venus flytrap will close only if a second hair is stimulated to“push the calcium concentration over this threshold and spring the
trap.” But the last sentence of the paragraph notes that the calcium
concentrations “dissipate over time,” and if enough time elapses after
the first trigger, “the final concentration after the second trigger won’t
be high enough to close the trap.” It can be inferred, then, that if alarge insect didn’t touch a second trigger hair until after the calcium
ion concentrations had diminished appreciably, the Venus flytrap
would fail to close.

Choice A is incorrect because the fourth paragraph makes clear that
if the calcium concentration goes above the trap’s threshold, the plant
will close, not remain open. Choice C is incorrect because as the thirdparagraph explains, the touching of the trigger hair and opening of thecalcium ion channels don’t act to keep the trap open but are insteada precondition for the closing of the trap (though closing will occur
only if a second trigger hair is touched). Choice D is incorrect because
the last sentence of the fifth paragraph explains that the thresholdfor the time that can elapse between the touching of the first andsecond trigger hairs is twenty seconds, meaning that a large insect
touching two hairs within ten seconds would almost certainly make theplant close.

QUESTION 49

Choice B is the best answer. The second sentence of the lastparagraph says that Alexander Volkov and his colleagues “first
demonstrated that it is indeed electricity that causes the Venus flytrap
to close.” In this context, the word “demonstrated” most nearly means
established.
Choices A, C, and D are incorrect because in the context ofscientists showing what causes the Venus flytrap to close, theword “demonstrated” most nearly means established, not protested(choice A), performed (choice C), or argued (choice D).

QUESTION 50

Choice B is the best answer. As described in the third paragraph,
Hodick and Sievers’s model emphasizes that the Venus flytrap closes
by means of an electrical charge triggered when the plant’s hairs aretouched. But as explained in the last paragraph, when Alexander
Volkov tested this model, the design of his experiment involved the
direct application of an electrical charge, which “made the trap close
without any direct touch to its trigger hairs.” Therefore, Volkov’s
work could be criticized because his design omitted, rather thancorroborated, a central element of Hodick and Sievers’s model—
namely, the physical stimulation of the hairs.
Choice A is incorrect because although the last paragraph explainsthat Volkov omitted an element of Hodick and Sievers’s model when
designing his own experiment, there is no suggestion that he did soout of a faulty understanding of their model. Choice C is incorrect
because it is impossible to know from the passage if Hodick andSievers would have objected to Volkov’s methods. Choice D is incorrect
because the passage doesn’t indicate whether the technology Volkov
used had been available to Hodick and Sievers when they formulated
their model.

Answer Explanations | SAT Practice Test #8

QUESTION 51

Choice C is the best answer. The previous question asks what
potential criticism might be made of Volkov’s testing of Hodick andSievers’s model. The answer, that a central element of that model
wasn’t corroborated by Volkov’s measurements, is best supported
in the last paragraph: “This made the trap close without any direct
touch to its trigger hairs (while they didn’t measure calcium levels,the current likely led to increases).” Because the physical touch to thehairs figured in Hodick and Sievers’s model, it can be said that Volkov’s
decision to apply an electrical current directly to the plant means that
he failed to corroborate a central element of their model.
Choices A, B, and D are incorrect because the cited lines don’t support
the answer to the previous question. Instead, they summarize thebasic agreement of Volkov’s work with Hodick and Sievers’s model(choice A) and describe steps in Volkov’s experimental design thatare related to the application of an electrical current but don’t directly
address the omission of the central element of the physical touch to thehairs (choices B and D).

QUESTION 52

Choice C is the best answer. The second sentence of the lastparagraph says that the focus of Volkov’s work was the role ofelectricity in the Venus flytrap’s closing mechanism. The paragraphgoes on to explain that by applying electricity directly to the plantand “altering the amount of electrical current, Volkov could determine
the exact electrical charge needed for the trap to close.” It is therefore
accurate to say that Volkov and his colleagues made the most extensive
use of information obtained from measuring the plant’s response tovarying amounts of electrical current.
Choice A is incorrect because although the last paragraph explainsthat Volkov’s work was based on Hodick and Sievers’s mathematicalmodel in which an electrical charge is required to close the Venus
flytrap, that model isn’t described as predicting the precise amount ofcharge required; moreover, although Volkov made use of this earlier
model, it served as a starting point, and his work made greater useof the findings generated by his experiment. Choice B is incorrect
because the passage doesn’t describe Volkov’s work as having
involved analysis of data from earlier studies on the plant’s response toelectricity. Choice D is incorrect because although the last paragraphexplains that Volkov based his work on Hodick and Sievers’s earlier
model, this was the sole model that Volkov relied on, and there isno suggestion that he made use of multiple “published theories”
or “earlier models”; moreover, he made more extensive use of data
generated by his own experiment than of Hodick and Sievers’s model.

Section 2: Writing and Language Test
QUESTION 1

Choice D is the best answer. The prepositional phrase “for example”
logically connects the two sentences and correctly indicates that what
follows in the second sentence will be examples of household waste
products: paper, glass, aluminum, and garbage.
Choices A, B, and C are incorrect because they don’t indicate thetrue relationship between the two sentences. “Regardless” (choice A)means in spite of something, “however” (choice B) indicates a contrast,and “furthermore” (choice C) means in addition. None of thesetransitions indicates that an example will follow.

QUESTION 2

Choice B is the best answer. The verb “eliminate” means to remove,and it makes the most sense in the sentence because the object of theverb is “need.” “Eliminating the need” is an idiomatic expression for“removing the need.”
Choices A, C, and D are incorrect. Although all the choices mean “toget rid of,” their connotations are different. “Annihilating” (choice A)
is usually used to refer to the act of completely destroying, which is
too intense in this context. “Ousting” (choice C) is generally used
when referring to the act of forcibly removing a person from a position.
“Closing the door on” (choice D) is a colloquial expression that usuallymeans shutting out the possibility of something happening or not
being willing to consider an idea. This expression doesn’t fit the toneof the passage and is not idiomatic when used with “need.”

QUESTION 3

Choice C is the best answer. The singular present tense verb
“increases” agrees in number with the singular noun “compost” andmaintains the parallel structure of the other two compound verbs in thesentence, “minimizes” and “helps.”
Choices A and D are incorrect because the use of the pronoun “it”
(choice A) and “also it” (choice D) to begin new independent clauses
creates comma splices. Choice B is incorrect because “savings
increase” doesn’t maintain the parallel structure of the verbs in thesentence: “minimizes water waste and storm runoff” and “helps
reduce erosion.”

QUESTION 4

Choice B is the best answer. When setting off nonessential
information, a pair of parentheses needs to be used. This
choice provides the initial parenthesis that the parenthesis after“municipality” requires.

Answer Explanations | SAT Practice Test #8

Choice A is incorrect because the initial parenthesis is missing andno comma is needed between the noun “quantities” and the modifying
information. Choice C is incorrect because the initial parenthesis is
missing. Choice D is incorrect because no semicolon is needed before
the parenthetical information.

QUESTION 5

Choice D is the best answer. According to the information from the graph,
33 million tons of food waste were discarded in US landfills in 2009,
which is consistent with the discussion of food waste in the passage.
Choices A, B, and C are incorrect because the passage thus far has
focused on compost. Metal, rubber, leather, and textiles are notmaterials that are composted.

QUESTION 6

Choice C is the best answer. According to the graph, this is the only
choice that makes the sentence true. More food waste was discarded inlandfills in 2009 “than any other substance, including plastics or paper.”
Choices A, B, and D are incorrect because they are not true, according
to the graph. The graph indicates that less glass, metal, and yard waste
were discarded in the landfills than plastics and paper.

QUESTION 7

Choice B is the best answer. No comma is needed between thecomparative adjective “worse” and the comparative conjunction “than.”Choices A, C, and D are incorrect because the word “then” indicates“when” and is not used in comparisons (choices A and C), and nocomma is needed after worse (choice D).

QUESTION 8

Choice C is the best answer. The present tense singular verb “contributes”
agrees in number with the singular noun “material,” and the present tenseverb is consistent with the other present tense verbs in the passage.
Choices A and B are incorrect because “contribute” (choice A) and “arecontributing” (choice B) are plural present tense verbs. Choice D isincorrect because “have contributed” is a plural past tense verb.

QUESTION 9

Choice A is the best answer. “Potent” means strong or powerful,which makes sense in the context of discussing greenhouse gas.
Choice B is incorrect because “sturdy” is usually used to refer tothe physical strength or solidity of something. Choice C is incorrect
because “influential” refers to the power of a person to affect or swayothers or events without any apparent effort. Choice D is incorrect
because “commanding” indicates that the inanimate greenhouse gas is
actually commanding something.

QUESTION 10

Choice C is the best answer. “Armed with these facts” is the mosteffective transition from the previous paragraph, which discusses
the amounts of various substances that end up in landfills and theresulting methane gas that is released from the organic matter. The
paragraph that this transition introduces goes on to discuss lawsthat some cities have instituted to control the handling of compost in
landfills to reduce the release of methane gas.
Choices A, B, and D are incorrect because they do not offer transitions
that indicate a connection between the problem identified in theprevious paragraph—the release of dangerous methane gas from thecompost in landfills—and the concluding paragraph that identifies
what some cities have done to help alleviate the problem.

QUESTION 11

Choice A is the best answer. No change is needed because thecorrelative conjunctions “either” and “or” are used together to indicatethat one choice or another should be considered. In this sentence,residents are encouraged to choose the option to create their own
compost piles or to dispose of compostable materials in bins forcollection.
Choices B, C, and D are incorrect because they do not provide thecorrelating conjunction for “either” used earlier in the sentence.

QUESTION 12

Choice A is the best answer. The sentences are effectively combinedby placing a comma after “red” and making the second sentence anappositive that explains the significance of the color red.
Choices B, C, and D are incorrect because they all contain excessive
words that add no meaning to the resulting sentence.

QUESTION 13

Choice D is the best answer. Punctuation is not necessary in theunderlined portion of the sentence.
Choice A is incorrect because no commas are needed after “festive”
and “red” because the adjectives don’t equally modify “banners.” Nocomma is needed after “banners” because there is no reason to put
one between “banners” and “and garlands,” the two objects of the
preposition “with.” Choice B is incorrect because placing commas
around the prepositional phrase “with festive red banners” wrongly
indicates that the information is nonessential and could be eliminatedwithout changing the meaning of the sentence. Choice C is incorrect
because there should not be a dash or any other kind of punctuation
between “banners” and “and garlands.”

Answer Explanations | SAT Practice Test #8

QUESTION 14

Choice C is the best answer. This choice expands on the idea thatthe lion dance may have originated to ward off an evil spirit and thatdressing in a lion costume was part of the effort to scare the spirit away.
Choice A is incorrect because it doesn’t make a connection between
the fierce quality of a lion and scaring away spirits. Choices B and
D are incorrect because the name of the spirit (choice B) and thelocation of the village where the dance originated (choice D) are not asimportant as why a lion was incorporated into the dance.

QUESTION 15

Choice C is the best answer. It ties the information about the possible
origins and historical purpose of the lion dance to its present purpose
as a New Year’s celebration of hope.
Choices A, B, and D are incorrect because they don’t effectively bring
the paragraph to a conclusion. Each of these options is vague and callsfor elaboration: choice A lacks specific information, choice B lacks
proof for the idea of irrelevance, and choice D lacks a connection to thesubject of the paragraph.

QUESTION 16

Choice A is the best answer. The pronoun “both” and prepositional
phrase “of whom” refer to “dancers” and are used correctly tointroduce a clause that describes how the dancers are hidden by
the lion costume. “Whom” is used correctly as the object of the
preposition “of.”Choice B is incorrect because the word order doesn’t make grammaticalsense and the pronoun “which” can’t be used to refer to people.
Choices C and D are incorrect because they create comma splices.

QUESTION 17

Choice D is the best answer. The pronoun “those” correctly indicatesthat the moves in dance are being compared to the moves in martial
arts. “Those” takes the place of the noun “moves” in the comparison.
Choices A, B, and C are incorrect because they do not compare similar
things. “Moves” can’t be compared to “martial arts,” “acrobatics,”“disciplines,” “martial artists,” or “acrobats.”

QUESTION 18

Choice B is the best answer. This choice indicates that the phoenix
represents new beginnings, which is consistent in content with
the information explaining that the tortoise represents longevity.
Additionally, this choice is presented as a parenthetical prepositional
phrase beginning with the preposition “for,” which is consistent in
structure with the parenthetical prepositional phrase “for longevity.”Choice A is incorrect because the parenthetical information indicateswhat a phoenix is, not what it represents. Furthermore, the information
is not presented in a prepositional phrase. Choice C is incorrect
because this choice indicates the source of the phoenix, not what
it represents. Choice D is incorrect because it is vague and doesn’t
identify what the phoenix symbolizes.

QUESTION 19

Choice D is the best answer. Sentence 5 most logically should follow
sentence 7. The pronoun “their” in sentence 5 refers to the “blacklions” (which are the youngest lions and dance quickly) in sentence 7.
Sentence 5 indicates that the “older counterparts” to the young lions
don’t move as quickly.
Choices A, B, and C are incorrect because placing sentence 5 after
any other sentence in the paragraph would not be logical and wouldinterrupt the flow of the passage.

QUESTION 20

Choice B is the best answer. The singular possessive pronoun “its”
agrees in number with the singular antecedent “dance” and correctly
indicates that the “climax” belongs to the dance.
Choice A is incorrect because “it’s” is the contraction for “it is” anddoesn’t make sense in the sentence. Choice C is incorrect because“there” is not a possessive pronoun. Choice D is incorrect because“their” is a plural possessive pronoun that doesn’t agree with thesingular antecedent “dance.”

QUESTION 21

Choice B is the best answer. This choice correctly indicates that thelion is doing the approaching and the snaring, not the teeth.
Choices A and D are incorrect because the teeth don’t do theapproaching or the snaring; only an animate object can do either.
Choice C is incorrect because it is written in the passive voice,which changes the subject of the sentence from “lion” to “envelope.”
Furthermore, an “envelope” cannot approach a doorway.

QUESTION 22

Choice D is the best answer. The single word “envelope” is concise
and clearly refers to the envelope that has been described earlier in theparagraph.
Choices A, B, and C are incorrect because they are wordy andcontain information that has been given previously in the paragraph.
Additionally, choice A contains inaccurate information because
once the money has been chewed up, the envelope is no longer“money-filled.”

Answer Explanations | SAT Practice Test #8

QUESTION 23

Choice A is the best answer. No change is needed because“scrupulous” fits the formal tone of the passage. “Scrupulous” means
exact and conscientious, and it is appropriate when discussing notes
taken during a court proceeding.
Choices B and C are incorrect because they are too informal andtherefore do not fit the tone of the passage. Choice D is incorrect
because “intense” is an adjective that is used to describe somethingthat is done to an extreme degree, such as putting forth effort or
performing a physical act.

QUESTION 24

Choice C is the best answer. Commas after “hearings” and“depositions” are correct because they separate the first two items in aseries of three.
Choices A, B, and D are incorrect because they all contain semicolons
either after “hearings,” “depositions,” or both of the words. Semicolons
can be used to separate items in a series that already contains
commas, but not to separate individual items in a simple series ofwords or phrases.

QUESTION 25

Choice C is the best answer. The graph should not be added because
it doesn’t support the information in the paragraph. The paragraphdescribes what a court reporter does. The graph provides informationthat compares the median salary of court reporters to that of other jobs.
Choices A and B are incorrect because the graph should not be added.
It neither supports the claim that court reporting is an important partof a trial nor offers a relevant counterpoint to the argument that theuse of digital recorders is on the rise. Choice D is incorrect because it
doesn’t matter that there is no information provided in the graph about
the pay scale for more experienced court reporters. The paragraphdoesn't deal with the subject of pay, so therefore the graph doesn’t
support the paragraph.

QUESTION 26

Choice A is the best answer. No change needs to be made because
the word “to” is the idiomatic preposition to connect “subject” withthe phrase “human errors” to show that technology such as a digitalrecorder doesn’t make the same mistakes that people make, such as“mishearing or mistyping.”
Choices B and C are incorrect because the verb “subjected” is atransitive verb that requires a direct object, which is not present in thesentence. Furthermore, “subjected from” is not idiomatic. Choice D isincorrect because “subject for human errors” doesn’t make sense.

QUESTION 27

Choice C is the best answer. The preposition “as” means “functioning
in the same way” or “in the capacity of.” The plural noun “record
keepers” agrees in number with the plural noun “court reporters.”
The sentence indicates that court reporters are functioning as record
keepers.
Choices A and D are incorrect because the singular “record keeper”
can’t be used to refer to plural “court reporters.” Additionally, inchoice D the infinitive verb phrase “to be” can’t be used in placeof a preposition. Choice B is incorrect because the word “each” isunnecessary and makes the sentence confusing.

QUESTION 28

Choice C is the best answer. To make the paragraph most logical,
sentence 6 should be placed after sentence 3. Sentence 3 explainsthat the words the recorder types are “instantaneously” available to a
judge to view on a computer screen. Sentence 6 explains, by using thetransition “however,” that even though words are available instantly,
recording technology continues to improve and therefore the need forcourt reporters is decreasing.
Choices A, B, and D are incorrect because placing sentence 6 after any
other sentence would not be logical and would interrupt the flow of theparagraph.

QUESTION 29

Choice B is the best answer. The dash most effectively combines thetwo sentences. It correctly indicates that what follows is explanatory
information. In this case, the information after the dash could be
inferred from what has already been stated because the opposite ofmaking fewer mistakes is making more mistakes. The information after
the dash in this sentence makes the conclusion overt.
Choice A is incorrect because the word “such” indicates incorrectlythat an example of something will follow it. Choices C and D areincorrect because they are wordy and not as succinct as using a dash.

QUESTION 30

Choice B is the best answer. The comma is used correctly to separate
the introductory dependent clause from the main independent clausethat follows it.
Choice A is incorrect because a semicolon can’t be used to separate adependent and an independent clause. Choice C is incorrect because
a period can’t be used at the end of a dependent clause. Choice D isincorrect because the adverb “therefore” doesn’t make sense in thiscontext; what follows does not result from something said earlier in thesentence.

Answer Explanations | SAT Practice Test #8

QUESTION 31

Choice B is the best answer. “In other words” indicates correctly thatwhat follows will be an elaboration of the idea that digital recorders
can’t distinguish “important parts of the proceedings from other noises
in the courtroom,” “such as a book dropping.”
Choices A, C, and D are incorrect because they don’t show the true
relationship between the two sentences. “Despite this” means thatin spite of something already said, what follows will be the case.
“Therefore” and “consequently” indicate that what follows will be
the result of something said earlier. None of these offers a further
explanation of what was previously said.

QUESTION 32

Choice D is the best answer. The prepositional phrase “between thewords and the extrinsic noises” clearly and concisely identifies what a
court reporter is able to distinguish. It is also the only parallel option,using two noun phrases after “between,” which are joined by “and.”
Choice A is incorrect because it needlessly repeats “distinguishbetween.” Choice B is incorrect because it is not parallel orgrammatical. Choice C is incorrect because it is wordy and wrongly
suggests that court reporters distinguish between words and a time
period (when).

QUESTION 33

Choice D is the best answer. The main idea of the paragraph is thatcourt reporters can distinguish between words and extraneous noises
in the courtroom, which digital recorders can’t always do. This choiceoffers an example of what can go wrong in a courtroom because digitalrecorders can’t always pick up “indistinct testimony”: the need for
retrial because of indistinct testimony from witnesses.
Choices A, B, and C are incorrect because they don’t support themain idea of the paragraph. Making additional announcements atthe beginning of a trial (choice A), monitoring to ensure equipment
is functioning properly (choice B), and changing roles and duties ofseveral members of the courtroom staff (choice C) are not examplesof what can happen as a result of using digital recorders that can’t
distinguish words from other courtroom noises.

QUESTION 34

Choice B is the best answer. The adverb “however” indicates thatregardless of the conditions that affect “combustion and the resultingfire” on Earth, their behavior in space is different.
Choices A, C, and D are incorrect because they do not show the true
relationship between the information that comes before and what follows
the linking adverb. “Moreover” means that additional information
will follow; “accordingly” means that what follows corresponds towhat has already been said or that what follows is a consequence;and “subsequently” means that what follows happens after what
was previously stated. None of these choices indicates the difference
between the behaviors of combustion and fire on Earth and in space.

QUESTION 35

Choice D is the best answer. The past tense verb “sought” clearlyand concisely conveys the idea that the students were trying to finda method to study combustion of biofuels. Additionally, the word
“biofuels” is correctly placed immediately in front of the parentheticalinformation that defines it to prevent confusion.
Choices A and B are incorrect because they are wordy and the word
“biofuel” is not placed immediately in front of the parentheticalinformation that defines it. Choice C is incorrect because it uses the verb
“looked,” which is not preferable to “sought” in this science context.

QUESTION 36

Choice A is the best answer. No change needs to be made because
the word “deformation” provides the most precise description of what
results when fuel droplets lose their symmetrical form while burning.
A droplet that is deformed loses some good attribute due to the
influence of some external condition.
Choices B and D are incorrect because “alteration” and “modification”
imply that something is changed on purpose. Choice C is incorrect
because “transformation” means that one thing is changed intoanother. None of these choices is accurate when discussing the effectof “gravitational influence” and the “movement of molecules” ondroplets of fuel.

QUESTION 37

Choice B is the best answer. The plural verbs “cause” and “limit”
agree in number with the plural pronoun “both,” which refers to theplural noun “variations.”
Choices A and C are incorrect because “causes” and “limits” aresingular verbs that don’t agree in number with the plural pronoun“both.” Choice D is incorrect because “has caused” and “has limited”
are also singular verbs. Additionally, they are present perfect tenseverbs that are used to describe a past event that has an influence on
the present, which is not the case in this context.

QUESTION 38

Choice D is the best answer. The underlined portion should be deleted
because “built for this purpose” repeats the idea of being “speciallydesigned” used previously in the sentence.
Choices A, B, and C are incorrect because they are redundant. There is
no reason to repeat the idea of “specially designed.”Answer Explanations | SAT Practice Test #8

QUESTION 39

Choice B is the best answer. This choice offers the most effective
transition because it links the previously mentioned problems of
conducting the biofuel experiment to the UCSD students’ solution:
participating in NASA’s Microgravity University program.
Choices A, C, and D are incorrect because they don’t link thepreviously identified problems with the specific solution: a programthat could help the students overcome too little microgravity time andtoo small droplets.

QUESTION 40

Choice D is the best answer. The commas after “weightlessness”
and “space” are used correctly to set off the nonessential information
between them. The information between the commas could be removed
and the sentence would still make sense.
Choice A is incorrect because it is missing the comma after“weightlessness.” In this context, choices B and C are incorrect
because the commas are misplaced. In each of these choices, if theinformation between the commas were removed, the sentence would
not make sense.

QUESTION 41

Choice A is the best answer. The addition should be made because
the information specifically identifies an advantage the students
gained by working with NASA’s Microgravity University program: nottraveling to space.
Choice B is incorrect because it isn’t accurate. The previous paragraphdoes suggest that the students didn’t actually go into space by statingthat researchers fly their experiments aboard aircraft that simulate themicrogravity environment. Choices C and D are incorrect because theaddition should be made. The addition neither shifts focus away fromthe students’ experiences while on the flight nor restates what has
already been said in the sentence.

QUESTION 42

Choice D is the best answer. This choice, “were able to investigate,”
focuses on what the flights enabled the UCSD students to do that they
were not able to do previously using the drop towers. It is consistent
with the previous sentence, which states what the flights allowed thestudents to do.
Choices A, B, and C are incorrect because their focus is on“investigating” and not on allowing or enabling the students toinvestigate combustion in an environment that provided larger dropletsand microgravity similar to that experienced in space.

QUESTION 43

Choice A is the best answer. No change is needed because the larger“spherically symmetric” droplets indicate that the flights remedied the
problem of smaller deformed droplets mentioned earlier in the passage.
Choices B, C, and D are incorrect because none of these choices refers
to the size or shape of the biofuel droplets, which is what made theinvestigation of combustion and fire on Earth problematic.

QUESTION 44

Choice C is the best answer. No comma is needed in the underlined
phrase, which clearly and concisely expresses the improved techniques
for fighting fires in space or at future outposts on the Moon and Mars
that may result from better combustion-rate models.
Choices A and B are incorrect because the commas are incorrectly
separating the prepositional phrases from the noun “techniques.”
Choice D is incorrect because the pair of commas indicate thatthe information contained between them is nonessential, which
isn’t accurate.

Section 3: Math Test – No Calculator
QUESTION 1

Choice D is correct. Combining like terms on each side of thegiven equation yields 6x − 5 = 7 + 2x. Adding 5 to both sides of
6x − 5 = 7 + 2x and subtracting 2x from both sides yields 4x = 12.
Dividing both sides of 4x = 12 by 4 yields x = 3.
Choices A, B, and C are incorrect because substituting those values
into the equation 3x + x + x + x − 3 − 2 = 7 + x + x will result in a
false statement. For example, in choice B, substituting 1 for x in theequation would give 3(1) + 1 + 1 + 1 – 3 – 2 = 7 + 1 + 1, which yields thefalse statement 1 = 9; therefore, x cannot equal 1.

QUESTION 2

Choice A is correct. The line passes through the origin. Therefore, thisis a relationship of the form d = km, where k is a constant representing
the slope of the graph. To find the value of k, choose a point (m, d) on
the graph of the line other than the origin and substitute the valuesof m and d into the equation. For example, if the point (2, 4) is chosen,
then 4 = k(2), and k = 2. Therefore, the equation of the line is d = 2m.
Choice B is incorrect and may result from calculating the slope of theline as the change in time over the change in distance traveled insteadof the change in distance traveled over the change in time. Choices
C and D are incorrect because each of these equations represents aline with a d-intercept of 2. However, the graph shows a line with ad-intercept of 0.

Answer Explanations | SAT Practice Test #8

QUESTION 3

Choice A is correct. Multiplying both sides of the equation by 6
results in 6E = O + 4M + P. Then, subtracting O + 4M from both sides of
6E = O + 4M + P gives P = 6E − O – 4M.
Choice B is incorrect. This choice may result from solving for −P
instead of for P. Choice C is incorrect and may result from transposing
P with E in the given equation rather than solving for P. Choice D isincorrect and may result from transposing P with E and changing thesign of E rather than solving for P.

QUESTION 4

Choice C is correct. Since RT = TU, it follows that ∆RTU is an
isosceles triangle with base RU. Therefore, ∠TRU and ∠TUR are
the base angles of an isosceles triangle and are congruent. Let themeasures of both ∠TRU and ∠TUR be t °. According to the triangle sum
theorem, the sum of the measures of the three angles of a triangle is
180°. Therefore, 114° + 2t ° = 180°, so t = 33.
Note that ∠TUR is the same angle as ∠SUV. Thus, the measure of∠SUV is 33°. According to the triangle exterior angle theorem, an
external angle of a triangle is equal to the sum of the opposite interior
angles. Therefore, x° is equal to the sum of the measures of ∠VSU and∠SUV; that is, 31° + 33° = 64°. Thus, the value of x is 64.
Choice B is incorrect. This is the measure of ∠STR, but ∠STR is notcongruent to ∠SVR. Choices A and D are incorrect and may result froma calculation error.

QUESTION 5

Choice B is correct. It is given that the width of the dance floor isw feet. The length is 6 feet longer than the width; therefore, the lengthof the dance floor is w + 6. So the perimeter is w + w + (w + 6) + (w + 6) =4w + 12.
Choice A is incorrect because it is the sum of one length and one
width, which is only half the perimeter. Choice C is incorrect and may
result from using the formula for the area instead of the formula forthe perimeter and making a calculation error. Choice D is incorrect
because this is the area, not the perimeter, of the dance floor.

QUESTION 6

Choice B is correct. Subtracting the same number from each side of
an inequality gives an equivalent inequality. Hence, subtracting 1 fromeach side of the inequality 2x > 5 gives 2x − 1 > 4. So the given system
of inequalities is equivalent to the system of inequalities y > 2x − 1 and2x − 1 > 4, which can be rewritten as y > 2x − 1 > 4. Using the transitive
property of inequalities, it follows that y > 4.

Choice A is incorrect because there are points with a y-coordinate
less than 6 that satisfy the given system of inequalities. For example,(3, 5.5) satisfies both inequalities. Choice C is incorrect. This may
result from solving the inequality 2x > 5 for x, then replacing x with y.
Choice D is incorrect because this inequality allows y-values that are
not the y-coordinate of any point that satisfies both inequalities. For
3example, y = 2 is contained in the set y > ​ __ ​ ; however, if 2 is substituted
2
3
into the first inequality for y, the result is x < ​ __ ​ . This cannot be true
2
5
because the second inequality gives x > ​ __ ​ .
2

QUESTION 7_

Choice B is correct. Subtracting 4 from both sides of √​ 2x + 6 ​+ 4 = x + 3
isolates theradicalexpression
on
the
left
side
of
the
equationas__follows: ​√ 2x + 6 ​= x – 1. Squaring both sides of ​√ 2x + 6 ​= x – 1 yields
2x + 6 = x 2 − 2x + 1. This equation can be rewritten as a quadratic
equation in standard form: x 2 – 4x – 5 = 0. One way to solve thisquadratic equation is to factor the expression x 2 − 4x – 5 by identifying
two numbers with a sum of –4 and a product of –5. These numbers are–5 and 1. So the quadratic equation can be factored as (x – 5)(x + 1) = 0.
It follows that 5 and –1 are the solutions to the quadratic equation.
However, the solutions must be verified
by checking whether 5 and_–1 satisfy the original equation,​√ 2x + 6 ​+ 4 = x + 3. When x = –1, the_original equation gives ​√ 2(−1) + 6 ​+ 4 = (−1) + 3, or 6 = 2, which isfalse. Therefore, –1 does not _satisfy the original equation. When x = 5,
the original equation gives ​√ 2(5) + 6 ​+ 4 = 5 + 3, or 8 = 8, which is true.
Therefore, x = 5 is the only solution to the original equation, and so
the solution set is {5}.
Choices A, C, and D are incorrect because each of these sets contains
at least one value that results in a false statement when substituted
into the given equation. For instance, in choice
D, when 0 is substituted_
for x_into the given equation, the result is ​√ 2(0) + 6 ​+ 4 = (0) + 3,
or ​√6 ​+ 4 = 3. This is not a true statement, so 0 is not a solution to thegiven equation.

QUESTION 8

Choice D is correct. Since x 3 – 9x = x (x + 3)(x − 3) andf(x)x 2 – 2x – 3 = (x + 1)(x – 3), the fraction _​  ​can be written asg(x)x(x + 3)(x − 3)_____________​       ​ . It is given that x > 3, so the common factor x – 3 is not(x + 1)(x − 3)x(x + 3)equal to 0. Therefore, the fraction can be further simplified to ​  _x + 1 ​.

Answer Explanations | SAT Practice Test #8

f(x)
1
_
Choice A is incorrect. The expression ​ _x + 1 ​is not equivalent to ​  g(x) ​f(x)
1_because at x = 0, ​ _x + 1 ​as a value of 1 and ​  g(x) ​has a value of 0.
Choice B is incorrect and results from omitting the factor x in thefactorization of f (x). Choice C is incorrect and may result fromincorrectly factoring g (x) as (x + 1)(x + 3) instead of (x +1)(x – 3).

QUESTION 9

Choice A is correct. The standard form for the equation of a circle is(x – h)2 + (y – k)2 = r 2, where (h, k) are the coordinates of the centerand r is the length of the radius. According to the given equation, thecenter of the circle is (6, –5). Let (x1, y1) represent the coordinates ofpoint Q. Since point P (10, –5) and point Q (x1, y1) are the endpointsof a diameter of the circle, the center (6, –5) lies on the diameter,
halfway between P and Q. Therefore, the following relationships hold:x1 + 10y1 + (−5)​  _ ​= 6 and ​  _ ​= −5. Solving the equations for x1 and y1,
22
respectively, yields x1 = 2 and y1 = −5. Therefore, the coordinates ofpoint Q are (2, –5).
Alternate approach: Since point P (10, −5) on the circle and the centerof the circle (6, −5) have the same y-coordinate, it follows that theradius of _the circle is 10 – 6 = 4. In addition, the opposite end of thediameter PQ​ ​ must have the same y-coordinate as P and be 4 units awayfrom the center. Hence, the coordinates of point Q must be (2, –5).
Choices B and D are incorrect because the points given in these_choices lie on a diameter that is perpendicular
to the diameter PQ​​ . If_either of these points were point Q, then PQ​​ would not be the diameterof the circle. Choice C is incorrect because (6, −5) is the center of thecircle and does not lie on the circle.

QUESTION 10

Choice C is correct. Let x represent the number of 2-person tents
and let y represent the number of 4-person tents. It is given that the
total number of tents was 60 and the total number of people in thegroup was 202. This situation can be expressed as a system of two
equations, x + y = 60 and 2x + 4y = 202. The first equation can be
rewritten as y = −x + 60. Substituting −x + 60 for y in the equation
2x + 4y = 202 yields 2x + 4(−x + 60) = 202. Distributing and combining
like terms gives −2x + 240 = 202. Subtracting 240 from both sidesof −2x + 240 = 202 and then dividing both sides by −2 gives x = 19.
Therefore, the number of 2-person tents is 19.
Alternate approach: If each of the 60 tents held 4 people, the total
number of people that could be accommodated in tents would be 240.
However, the actual number of people who slept in tents was 202. The
difference of 38 accounts for the 2-person tents. Since each of these38
tents holds 2 people fewer than a 4-person tent, ​ _ ​= 19 gives the2number of 2-person tents.

Choice A is incorrect. This choice may result from assuming exactly
half of the tents hold 2 people. If that were true, then the total numberof people who slept in tents would be 2(30) + 4(30) = 180; however,
the total number of people who slept in tents was 202, not 180.
Choice B is incorrect. If 20 tents were 2-person tents, then theremaining 40 tents would be 4-person tents. Since all the tents werefilled to capacity, the total number of people who slept in tents would be2(20) + 4(40) = 40 + 160 = 200; however, the total number of people who
slept in tents was 202, not 200. Choice D is incorrect. If 18 tents were
2-person tents, then the remaining 42 tents would be 4-person tents.
Since all the tents were filled to capacity, the total number of people
who slept in tents would be 2(18) + 4(42) = 36 + 168 = 204; however,
the total number of people who slept in tents was 202, not 204.

QUESTION 11

Choice B is correct. The x-coordinates of the x-intercepts of thegraph are –3, 0, and 2. This means that if y = f (x) is the equation of
the graph, where f is a polynomial function, then (x + 3), x, and (x − 2)are factors of f. Of the choices given, A and B have the correct factors.
However, in choice A, x is raised to the first power, and in choice B,
x is raised to the second power. At x = 0, the graph touches the x-axis
but doesn’t cross it. This means that x, as a factor of f, is raised
to an even power. If x were raised to an odd power, then the graphwould cross the x-axis. Alternatively, in choice A, f is a third-degree
polynomial, and in choice B, f is a fourth-degree polynomial. The
y-coordinates of points on the graph become large and positive as x
becomes large and negative; this is consistent with a fourth-degree
polynomial, but not with a third-degree polynomial. Therefore, of the
choices given, only choice B could be the equation of the graph.
Choice A is incorrect. The graph of the equation in this answer choice
has the correct factors. However, at x = 0 the graph of the equation inthis choice crosses the x-axis; the graph shown touches the x-axis but
doesn’t cross it. Choices C and D are incorrect and are likely the resultof misinterpreting the relationship between the x-intercepts of a graphof a polynomial function and the factors of the polynomial expression.

QUESTION 12

2a 1
Choice D is correct. Dividing both sides of equation ​ _ ​= ​ _ ​by 2
b 2
b
a _
1
_
gives ​   ​ = ​   ​. Taking the reciprocal of both sides yields a​  _ ​ = 4.
b 4baChoice A is incorrect. This is the value of ​  _ ​  , not a​  _ ​. Choice B is
2bba
incorrect. This is the value of ​  _ ​ , not a​  _ ​. Choice C is incorrect. This isbbb
the value of ​  _ ​ , not a​  _ ​.
2a

Answer Explanations | SAT Practice Test #8

QUESTION 13

Choice C is correct. It is assumed that the oil and gas production
decreased at a constant rate. Therefore, the function f that best models
the production t years after the year 2000 can be written as a linear
function, f (t) = mt + b, where m is the rate of change of the oil andgas production and b is the oil and gas production, in millions ofbarrels, in the year 2000. Since there were 4 million barrels of oil andgas produced in 2000, b = 4. The rate of change, m, can be calculated
2.1
21
4 − 1.9as ​  _ ​ = − ​ _ ​ , which is equivalent to − ​ _ ​ , the rate of change in
0 − 13
13
130
choice C.
Choices A and B are incorrect because each of these functions has apositive rate of change. Since the oil and gas production decreased
over time, the rate of change must be negative. Choice D is incorrect.
This model may result from misinterpreting 1.9 million barrels as theamount by which the production decreased.

QUESTION 14

Choice C is correct. The second equation of the system can be
rewritten as y = 5x − 8. Substituting 5x − 8 for y in the first equation
gives 5x − 8 = x 2 + 3x − 7. This equation can be solved as shown
below:
x 2 + 3x − 7 − 5x + 8 = 0
x 2 − 2x + 1 = 0(x − 1)2 = 0
x=1
Substituting 1 for x in the equation y = 5x − 8 gives y = −3. Therefore,(1, −3) is the only solution to the system of equations.
Choice A is incorrect. In the xy-plane, a parabola and a line canintersect at no more than two points. Since the graph of the firstequation is a parabola and the graph of the second equation is a line,
the system cannot have more than 2 solutions. Choice B is incorrect.
There is a single ordered pair (x, y) that satisfies both equations of thesystem. Choice D is incorrect because the ordered pair (1, −3) satisfies
both equations of the system.

QUESTION 15

Choice D is correct. Since h (x) = 1 − g (x), substituting 0 for x yields
h (0) = 1 − g (0). Evaluating g (0) gives g (0) = 2(0) − 1 = −1. Therefore,h (0) = 1 − (−1) = 2.
Choice A is incorrect. This choice may result from an arithmetic
error. Choice B is incorrect. This choice may result from incorrectly
evaluating g(0) to be 1. Choice C is incorrect. This choice may result
from evaluating 1 − 0 instead of 1 − g(0).

QUESTION 16

The correct answer is 3. The solution to the given equation canbe found by factoring the quadratic expression. The factors can be
determined by finding two numbers with a sum of 1 and a productof −12. The two numbers that meet these constraints are 4 and –3.
Therefore, the given equation can be rewritten as (x + 4)(x − 3) = 0. It
follows that the solutions to the equation are x = −4 or x = 3. Since it
is given that a > 0, a must equal 3.

QUESTION 17

The correct answer is 32. The sum of the given expressions is(−2x 2 + x + 31) + (3x 2 + 7x − 8). Combining like terms yields x 2 + 8x + 23.
Based on the form of the given equation, a = 1, b = 8, and c = 23.
Therefore, a + b + c = 32.
Alternate approach: Because a + b + c is the value of ax 2 + bx + c whenx = 1, it is possible to first make that substitution into each polynomial
before adding them. When x = 1, the first polynomial is equal to−2 + 1 + 31 = 30 and the second polynomial is equal to 3 + 7 − 8 = 2.
The sum of 30 and 2 is 32.

QUESTION 18

3
The correct answer is ​ _​. One method for solving the system of2
equations for y is to add corresponding sides of the two equations.
Adding the left-hand sides gives (−x + y) + (x + 3y), or 4y. Adding theright-hand sides yields −3.5 + 9.5 = 6. It follows that 4y = 6. Finally,
6
3—
dividing both sides of 4y = 6 by 4 yields y = ​ —4 ​or ​ 2 ​ . Any of 3/2, 6/4, 9/6,
12/8 or the decimal equivalent 1.5 will be scored as correct.

QUESTION 19

The correct answer is 8. The number of employees, y, expected tobe employed by the company x quarters after the company opened
can be modeled by the equation y = ax + b, where a represents theconstant rate of change in the number of employees each quarterand b represents the number of employees with which the company
opened. The company’s growth plan assumes that 2 employees will be
hired each quarter, so a = 2. The number of employees the company
opened with was 8, so b = 8.

QUESTION 20

The correct answer is 144. In a circle, the ratio of the length of a givenarc to the circle’s circumference is equal to the ratio of the measure of
the arc, in degrees, to 360°. The ratio between the arc length and the
x
2
2 _
—
circle’s circumference is given as ​ —5 ​. It follows that ​ 5 ​= ​  360 ​. Solving
this proportion for x gives x = 144.

Answer Explanations | SAT Practice Test #8

Section 4: Math Test – Calculator
QUESTION 1

Choice A is correct. If one pound of grapes costs $2, two pounds ofgrapes will cost 2 times $2, three pounds of grapes will cost 3 times $2,
and so on. Therefore, c pounds of grapes will cost c times $2, which is
2c dollars.
Choice B is incorrect and may result from incorrectly adding insteadof multiplying. Choice C is incorrect and may result from assumingthat c pounds cost $2, and then finding the cost per pound. Choice D
is incorrect and could result from incorrectly assuming that 2 pounds
cost $c, and then finding the cost per pound.

QUESTION 2

Choice C is correct. According to the graph, the number of figurines
decreased between 1 and 2 months and between 3 and 4 months.
Because the line segment between 3 and 4 months is steeper than theline segment between 1 and 2 months, it follows that the number of
figurines decreased the fastest between 3 and 4 months.
Choice A is incorrect. Between 1 and 2 months, the number of
figurines decreased. However, the number of figurines decreased
faster during the interval between 3 and 4 months. Choices B and D
are incorrect. The number of figurines during these intervals wasincreasing, not decreasing.

QUESTION 3

Choice A is correct. The fraction of the cars in the random sample
3
that have a manufacturing defect is _  ​= 0.015. At this rate, out
200
of 10,000 cars there would be 0.015 × 10,000 = 150 cars that have amanufacturing defect.
Choices B, C, and D are incorrect because the fractions of cars in200
the population that have a defect, ​ _  ​= 0.02 in choice B,
10,000250
300​  _  ​= 0.025 in choice C, and ​ _  ​= 0.03 in choice D, are all
10,00010,000different from the fraction of cars in the sample with a manufacturing
defect, which is 0.015.

QUESTION 4

Choice C is correct. The given line of best fit can be used to predictthe length when the width is known. The equation of the line of best
fit is given as y = 1.67x + 21.1, where x is the width in millimeters andy is the predicted length in millimeters. If the width of the petal is
19 millimeters, then x = 19 and y = 1.67(19) + 21.1 = 52.83.

Choice A is incorrect and may result from incorrectly using x = 0 in theequation. Choice B is incorrect and may result from neglecting to add
21.1 in the computation. Choice D is incorrect and may result from anarithmetic error.

QUESTION 5

Choice B is correct. Let the measure of the third angle in the smaller
triangle be a°. Since lines ℓ and m are parallel and cut by transversals,
it follows that the corresponding angles formed are congruent.
So a° = y° = 20°. The sum of the measures of the interior angles of atriangle is 180°, which for the interior angles in the smaller triangle
yields a + x + z = 180. Given that z = 60 and a = 20, it follows that
20 + x + 60 = 180. Solving for x gives x = 180 − 60 − 20, or x = 100.
Choice A is incorrect and may result from incorrectly assumingthat angles x + z = 180. Choice C is incorrect and may result fromincorrectly assuming that the smaller triangle is a right triangle,
with x as the right angle. Choice D is incorrect and may result froma misunderstanding of the exterior angle theorem and incorrectly
assuming that x = y + z.

QUESTION 6

Choice D is correct. Since only two types of tickets were sold and a
total of 350 tickets were sold, the sum of the numbers of both types ofticket sold must be 350. Therefore, B + L = 350. Since the bench tickets
were $75 each, the income from B bench tickets was 75B. Similarly,
since the lawn tickets were $40 each, the income from L lawn tickets
sold was 40L. The total income from all tickets was $19,250. So thesum of the income from bench tickets and lawn tickets sold must equal
19,250. Therefore, 75B + 40L = 19,250. Only choice D has both correct
equations.
Choice A is incorrect and may result from incorrectly multiplying
the income from each type of ticket instead of adding them. It also
incorrectly uses 1,950 instead of 19,250. Choice B is incorrect and may
result from confusing the cost of bench tickets with the cost of lawntickets. Choice C is incorrect and may result from confusing the total
number of tickets sold with the total amount raised.

QUESTION 7

Choice C is correct. The graph of an equation given in the formy = mx + b has slope m. The equation in choice C is y = 3x + 2, so theslope of its graph is 3.
Choices A, B, and D are incorrect. They are all given in the formy = mx + b, where m is the slope. Therefore, choice A has a graph with1
a slope of ​ _ ​, choice B has a graph with a slope of 1 (because x = 1 ∙ x),3
and choice D has a graph with a slope of 6.

Answer Explanations | SAT Practice Test #8

QUESTION 8

Choice B is correct. Multiplying both sides of the equation by x + 1
gives (x + 1)2 = 2._This meansx + 1 is a_number whose square is 2, so_(x + 1) is either ​√2 ​or −​√2 ​. Therefore, ​√2 ​is a possible value for x + 1.
Choice A is incorrect and may result from trying to find the value of x
instead of x + 1 and making a sign error. Choice C is incorrect and may
result from solving for (x + 1)2 instead of x + 1. Choice D is incorrect
and may result from squaring instead of taking the square root to findthe value of x + 1.

QUESTION 9

7πk 3
Choice D is correct. Using the volume formula V = _ and the given
48
information that the volume of the glass is 473 cubic centimeters, thevalue of k can be found as follows:
7πk 3
473 = _
48
473(48)k3 = _
7π_k=√​  7π ​ ≈ 10.10690

3

473(48)_Therefore, the value of k is approximately 10.11 centimeters.
Choices A, B, and C are incorrect. Substituting the values of k fromthese choices in the formula results in volumes of approximately
7 cubic centimeters, 207 cubic centimeters, and 217 cubic centimeters,
respectively, all of which contradict the given information that thevolume of the glass is 473 cubic centimeters.

QUESTION 10

Choice C is correct. Due to the shape of the glass, if the water ispoured at a constant rate, the height of the water level will increase
faster initially, where the diameter of the glass is smaller, and increase
more slowly later, as the diameter of the glass increases. Choice C is
the only graph that shows this behavior: it is steeper initially and thengets less steep.
Choice A is incorrect since it shows the height of the water level
increasing at a constant rate over time. Choice B is incorrect since itshows the height of the water level increasing slowly at first and faster
later. Choice D is incorrect since it shows the height of the water levelstaying constant even as water is being poured into the glass.

QUESTION 11

Choice B is correct. It is given that the volume of the glass isapproximately 16 fluid ounces. If Jenny has 1 gallon of water, which is
128
128 fluid ounces, she could fill the glass ​ _ ​ = 8 times.
16

Choice A is incorrect because Jenny would need 16 × 16 fluid
ounces = 256 fluid ounces, or 2 gallons, of water to fill the glass
16 times. Choice C is incorrect because Jenny would need only
4 × 16 fluid ounces = 64 fluid ounces of water to fill the glass
4 times. Choice D is incorrect because Jenny would need only
3 × 16 fluid ounces = 48 fluid ounces to fill the glass 3 times.

QUESTION 12

Choice C is correct. Since Roberto sells only two types of policies
and he didn’t meet his goal of selling at least 57 policies, the sum of x,
the number of $50,000 policies, and y, the number of $100,000 policies,
must be less than 57. Symbolically, that is x + y < 57. The total value,in dollars, from selling x number of $50,000 policies is 50,000x.
The total value, in dollars, from selling y number of $100,000 policies
is 100,000y. Since the total value of the policies he sold was over
$3,000,000, it follows that 50,000x + 100,000y > 3,000,000. Only
choice C has both correct inequalities.
Choice A is incorrect because the total value, in dollars, of the policies
Roberto sold was greater than, not less than, 3,000,000. Choice B isincorrect because Roberto didn’t meet his goal, so x + y should beless than, not greater than, 57. Choice D is incorrect because both
inequalities misrepresent the situation.

QUESTION 13

1
Choice C is correct. Since a has the exponent − ​ _ ​ , a can be isolated by2
raising both sides of the equation to the −2 power.
	​a ​(​−​ 2 ​  )​​ −2 ​​= ​x −2
​​
1 (
_

)

a = ​x −2​​
1
a = ​ _2 ​​x ​ ​
Alternate method:
1
_
1
1_
	​
a−​ ​ 2 ​ ​= ​ __1  ​= ​ _ ​​ a ​​a​ ​2 ​​ √
So,
1_
	​  _
 ​= x
​ a ​
√
Square both sides of the equation:
1
2
	​  _
a ​= ​x ​ ​Then take the reciprocal of both sides:1
a = ​ _2 ​​x​ ​Choice A is incorrect and may result from incorrectly taking the squareroot of both sides to eliminate the exponent of a. Choice B is incorrect
and may result from incorrectly taking the square root of both sides
to eliminate the exponent of a, and incorrectly multiplying by −1 tomake the exponent positive. Choice D is incorrect and may result fromincorrectly multiplying by −1 to make the exponent positive.

Answer Explanations | SAT Practice Test #8

QUESTION 14

Choice D is correct. A rational expression is undefined when the
denominator is 0. To determine the values of x that result in adenominator of 0, set the denominator equal to 0 and solve for x:
x 2 + 3x − 10 = 0(x + 5)(x − 2) = 0
x + 5 = 0 or x − 2 = 0
x = −5 or x = 2
Among the answer choices, only the value x = 2 is listed, so choice D
is correct.
Choice A is incorrect. When x = −3, the denominator is(−3)2 + 3(−3) − 10 = −10, so the given expression is not undefined.
Choice B is incorrect and may result from incorrectly factoring thedenominator or incorrectly assuming that if (x − 2) is a factor, thenx = −2 is a solution. Choice C is incorrect and may result fromgiving the value of the denominator that makes the given expression
undefined rather than the value of x that makes the denominator
equal to 0.

QUESTION 15

Choice D is correct. Since density is mass per unit volume, the massis the density times volume. The volume of a right rectangular prism isthe product of the lengths of the sides. Therefore:	mass = (2.8 grams per cubic centimeter) ×(30 centimeters × 40 centimeters × 50 centimeters)
mass = (2.8 grams per cubic centimeter) × (60,000 cubic centimeters)
mass = 168,000 grams
Choice A is incorrect and may result from adding, instead ofmultiplying, the lengths of the sides to find the volume. Choice B isincorrect and may result from the same error as in choice A, as well asa place value error. Choice C is incorrect and may result from a placevalue error when finding the volume.

QUESTION 16

Choice B is correct. A total of 150 adults received the sugar pill.
33
Of those, 33 reported contracting a cold. Therefore, ​ _  ​, or the150
11
equivalent ​ _ ​, is the proportion of adults receiving a sugar pill who
50
reported contracting a cold.

Choice A is incorrect. This is the proportion of adults receiving a( )33sugar pill and contracting a cold to all adults contracting a cold ​ ​  _ ​  ​.
54
Choice C is incorrect. This is the proportion of adults who reported
54
9contracting a cold to all the participants in the study ​ ​  _  ​= ​ _ ​  ​.
300 50
Choice D is incorrect. This is the proportion of adults who received a()

sugar pill and reported contracting a cold to all the participants in the33
11
study ​ ​  _  ​= ​ _  ​  ​.
300 100()

QUESTION 17

Choice A is correct. The mode is the data value with the highest
frequency. So for the data shown, the mode is 18. The median is the
middle data value when the data values are sorted from least to
greatest. Since there are 20 ages ordered, the median is the average ofthe two middle values, the 10th and 11th, which for these data are both
19. Therefore, the median is 19. The mean is the sum of the data values
divided by the number of the data values. So for these data, the mean is(18 × 6) ______+ (19 × 5) + (20 × 4) + (21 × 2) + (22 × 1) + (23 × 1) + (30 × 1)_​              ​= 20.

20
Since the mode is 18, the median is 19, and the mean is 20,
mode < median < mean.

Choice B and D are incorrect because the mean is greater than the
median. Choice C is incorrect because the median is greater thanthe mode.
Alternate approach: After determining the mode, 18, and the
median, 19, it remains to determine whether the mean is less than
19 or more than 19. Because the mean is a balancing point, there is
as much deviation below the mean as above the mean. It is possible
to compare the data to 19 to determine the balance of deviation aboveand below the mean. There is a total deviation of only 6 below 19(the 6 values of 18); however, the data value 30 alone deviates by 11
above 19. Thus the mean must be greater than 19.

QUESTION 18

Choice C is correct. Based on the line of best fit shown, the predictedpercent of leaf litter mass remaining for a forest with a mean annual
temperature of −2°C is about 70%.
Choice A is incorrect; it is the predicted percent of leaf litter mass
remaining at about 6.5°C. Choice B is incorrect; it is the predictedpercent of leaf litter mass remaining at 2°C instead of at −2°C.
Choice D is incorrect; it is the predicted percent of leaf litter mass
remaining at about −7°C.

Answer Explanations | SAT Practice Test #8

QUESTION 19

Choice A is correct. Since zeros of f correspond to the x-intercepts ofthe graph of f, and the range of f gives all the possible y-values on thegraph of the function, the correct graph of the function has only points
with y-values less than or equal to 4, and crosses the x-axis at only(−3, 0) and (1, 0). The graph in choice A satisfies both of these
conditions.
Choice B is incorrect. The graph of the function matches the range
given, but the zeros are at −1 and 3, not −3 and 1. Choice C is incorrect.
The graph has y-values greater than 4. Choice D is incorrect. Even
though the graph has zeros at −3 and 1, it has an additional zero at 0,
and the range of the graph is the set of all real numbers.

QUESTION 20

Choice B is correct. The savings each year from installing thegeothermal heating system will be the average annual energy cost for
the home before the geothermal heating system installation minus
the average annual energy cost after the geothermal heating systeminstallation, which is (4,334 − 2,712) dollars. In t years, the savings willbe (4,334 − 2,712)t dollars. Therefore, the inequality that can be solved
to find the number of years after installation at which the total amountof energy cost savings will exceed (be greater than) the installation
cost, $25,000, is 25,000 < (4,334 − 2,712)t.
Choice A is incorrect. It gives the number of years after installation
at which the total amount of energy cost savings will be less than the
installation cost. Choice C is incorrect and may result from subtracting
the average annual energy cost for the home from the onetime costof the geothermal heating system installation. To find the predicted
total savings, the predicted average cost should be subtracted fromthe average annual energy cost before the installation, and the result
should be multiplied by the number of years, t. Choice D is incorrect
4,332
and may result from misunderstanding the context. The ratio ​ _  ​2,712
compares the average energy cost before installation and the averageenergy cost after installation; it does not represent the savings.

QUESTION 21

Choice D is correct. The number 3.39 in the equation y = 3.39x + 46.89
is the slope, which is the change in y per unit change in x. Because
y represents the amount of plastic produced annually, in billions ofpounds, and x represents the number of years since 1985, the number
3.39 represents the rate of change of the amount of plastic producedwith respect to time, in units of billions of pounds per year. Thechange is an increase since 3.39 is positive, and it is described as anaverage change because the data show increases that are sometimes
more and sometimes less than 3.39.

Choice A is incorrect. It is the interpretation of the number 46.89 in
the line of best fit equation, y = 3.39x + 46.89. Choices B and C areincorrect because they are expressed in the wrong units. The number
3.39 has units of billions of pounds per year, but choice B has units ofyears and choice C has units of billions of pounds.

QUESTION 22

Choice A is correct. Since x is the number of years since 1985,
the year 2000 corresponds to x = 15 and the year 2003 corresponds
to x = 18. The corresponding points on the line of best fit areapproximately (15, 98) and (18, 107). This means that approximately
98 billion pounds of plastic were produced in 2000 and approximately
107 billion pounds of plastic were produced in 2003. To calculate thepercent increase, subtract the amount of plastic produced in 2000
from the amount of plastic produced in 2003 and then divide the result
by the amount of plastic produced in 2000 and multiply by 100. This107 − 98
yields ​ ​  _ ​  ​ ∙ 100 = 9.2, or approximately 10%.
98

(

)

Choices B and C are incorrect and may be the result of misreading thegraph or making an arithmetic error. Choice D is incorrect and may be
the result of approximating the amount of plastic produced, in billionsof pounds, in the year 2003 (x = 18).

QUESTION 23

Choice A is correct. In 1 year, there are 4 quarter years, so the numberof quarter years, q, is 4 times the number of years, t ; that is, q = 4t.
qThis is equivalent to t = _​   ​ , and substituting this into the expression for
4q_
M in terms of t gives M = 1​ ,800(1.02)​​  4 ​​.
Choices B and D are incorrect and may be the result of incorrectly
using t = 4q. In choice D, 1.024q = 1.024(q), which is approximately
1.082q. Choice C is incorrect and may be the result of incorrectly usingt = 4q and unnecessarily dividing 0.02 by 4.

QUESTION 24

Choice D is correct. It is given that Contestant 2 earned 70% of thevotes cast using social media and 40% of the votes cast using a text
message. Based on this information, viewers voting by social media
were more likely to prefer Contestant 2 than were viewers voting by
text message.
Choices A, B, and C are incorrect. There is not enough information
about the viewers to reach these conclusions.

Answer Explanations | SAT Practice Test #8

QUESTION 25

Choice A is correct. It is given that the relationship between
population and year is linear; therefore, the function that models
the population t years after 2000 is of the form P (t) = mt + b,
where m is the slope and b is the population when t = 0.
In the year 2000, t = 0. Therefore, b = 862. The slope is given by
P(10)− P(0) 846− 862 _
−16__m = ​    ​= ​ _ ​= ​   ​= −1.6. Therefore, P (t) = −1.6t + 862,
10 − 010 − 010which is equivalent to the equation in choice A.
Choice B is incorrect and may be the result of incorrectly calculating
the slope as just the change in the value of P. Choice C is incorrect
and may be the result of the same error as in choice B, in addition toincorrectly using t to represent the year, instead of the number of years
after 2000. Choice D is incorrect and may be the result of incorrectly
using t to represent the year instead of the number of years after 2000.

QUESTION 26

Choice C is correct. In order to use a sample mean to estimate
the mean for a population, the sample must be representative of
the population (for example, a simple random sample). In thiscase, Tabitha surveyed 20 families in a playground. Families in theplayground are more likely to have children than other households
in the community. Therefore, the sample isn’t representative of the
population. Hence, the sampling method is flawed and may produce
a biased estimate.
Choices A and D are incorrect because they incorrectly assume thesampling method is unbiased. Choice B is incorrect because a sampleof size 20 could be large enough to make an estimate if the sample had
been representative of all the families in the community.

QUESTION 27

Choice B is correct. Since the point (p, r) lies on the line with equationy = x + b, the point must satisfy the equation. Substituting p for x andr for y in the equation y = x + b gives r = p + b. Similarly, since thepoint (2p, 5r) lies on the line with the equation y = 2x + b, the point
must satisfy the equation. Substituting 2p for x and 5r for y in theequation y = 2x + b gives 5r = 2(2p) + b, or 5r = 4p + b. Solving eachequation for b gives b = r − p and b = 5r − 4p, respectively. Substitutingr − p for b in the equation b = 5r − 4p gives r − p = 5r − 4p. Subtractingr from each side of the equation and adding 4p to each side of theequation gives 3p = 4r. Dividing each side of the equation by p and3 r
dividing each side of the equation by 4 gives ​ _ ​= ​ _ ​.
4 p
Choices A, C, and D are incorrect. Choices A and D may be the resultof incorrectly forming the answer out of the coefficients in the point(2p, 5r). Choice C may be the result of confusing r and p.

QUESTION 28

Choice D is correct. The two data sets have the same range. The
first data set has a range of 88 − 56 = 32, and the second data set
has a range of 112 − 80 = 32. Alternatively, it can be seen visuallythat the ranges are the same because the two dot plots are aligned,
the scales of the graphs are the same, and the graphs have the same
width. The two data sets have different standard deviations. Bothdot plots show distributions that have a mean near the center valueof the dot plot. The first dot plot shows most values clustered near
the mean, while the second dot plot shows most values farther fromthe mean. Therefore, the standard deviations of the two data sets are
not equal—the data represented by the second dot plot has a greater
standard deviation.
Choices A, B, and C are incorrect because they incorrectly assert
either that the standard deviations are the same or that the ranges
are different.

QUESTION 29

Choice B is correct. Since the machine copies at a constant rate,
the relationship between p, the number of sheets of paper remaining,and m, the time in minutes since the machine started printing, ismodeled by a linear equation. The initial number of sheets of paper
is given as 5,000. It is also given that the machine used 30% of those
5,000 sheets in 20 minutes, so it used 0.30 × 5,000 = 1,500 sheets in
20 minutes. Therefore, the number of sheets used per minute is
1,500
​  _
 ​= 75. To determine the number of sheets of paper used
20
m minutes after the machine started printing, multiply 75 by m, which
gives 75m. Therefore, a linear equation modeling this relationship isthe number of sheets remaining equals the initial number of sheets ofpaper minus the number of sheets of paper used m minutes after themachine started printing, which is p = 5,000 − 75m.
Choice A is incorrect and may be the result of using the given numberof minutes, 20, as the rate at which the copy machine uses paper.
However, the rate is 75, not 20, sheets per minute. Choices C and D areincorrect because they aren’t linear equations; they assume that the
copy machine prints at a nonconstant rate.

QUESTION 30

Choice B is correct. The maximum value of the function f occurs at thehighest point on the graph of y = f (x); the highest point on the graphis (4, 3). For any point on the graph of f, the y-coordinate gives thevalue of the function at the x-coordinate; therefore, the maximum valueof the function f is 3. It is stated that k is the maximum value of f, so
k = 3. Thus, g (k) = g (3). From the table of values for g, it can be seenthat when x = 3, g (3) = 6.

Answer Explanations | SAT Practice Test #8

Choice A is incorrect and may result from using the x-coordinate of the
maximum point as the value of k. Choice C is incorrect; it is the valueof k, not of g (k). Choice D is incorrect and may be the result of giving
the value of x that makes g (x) = 3 instead of finding the value of g (x)when x = 3.

QUESTION 31

The correct answer is 102. Since each molecule of water has 2 atomsof hydrogen, 51 molecules of water have a total of (51)(2) = 102 atomsof hydrogen.

QUESTION 32

1
The correct answer is 2. Substituting x = 1 in the equation x − ​ _ ​a = 0
2
1
1
1
_
_
gives 1 − ​   ​a = 0. Adding ​   ​a to both sides of this equation gives 1 = ​ _ ​a.
2
22Multiplying both sides of this last equation by 2 gives 2 = a.

QUESTION 33

The correct answer is 30. Since the equations x + 2y = 10 and
3x + 6y = c represent the same line in the xy-plane, they must be
equivalent equations. The expression 3x + 6y on the left-hand side of
the second equation is equivalent to 3(x + 2y), which is 3 times the lefthand side of the first equation. Thus, to be equivalent, the right-handside of the second equation, c, must be 3 times the right-hand side of
the first equation, 10. Therefore, c = 30.

QUESTION 34

The correct answer is 25.4. The average speed is the total distancedivided by the total time. The total distance is 11 miles and the total
11
time is 26 minutes. Thus, the average speed is ​ _ ​miles per minute.
26
The question asks for the average speed in miles per hour, and there
are 60 minutes in an hour; converting miles per minute to miles perhour gives the following:
11 miles60
minutes__
Average speed = —​    ​× ​    ​
26 minutes
1 hour660= ​ _ ​miles per hour26
≈ 25.38 miles per hour
Therefore, to the nearest tenth of a mile per hour, the average speed ofPaul Revere’s ride would have been 25.4 miles per hour.

QUESTION 35

The correct answers are 2 and 8. Substituting x = a in the definitions
1
for f and g gives f (a) = −​ _ ​(a − 4)2 + 10 and g(a) = −a + 10, respectively.
2
1
If f (a) = g(a), then −​ _ ​(a − 4)2 + 10 = −a + 10. Subtracting 10 from both2
1sides of this equation gives −​ _ ​(a − 4)2 = −a. Multiplying both sides2
by −2 gives (a − 4)2 = 2a. Expanding (a − 4)2 gives a2 − 8a + 16 = 2a.
Combining the like terms on one side of the equation givesa 2 − 10a + 16 = 0. One way to solve this equation is to factor
a 2 − 10a + 16 by identifying two numbers with a sum of −10 anda product of 16. These numbers are −2 and −8, so the quadratic
equation can be factored as (a − 2)(a − 8) = 0. Therefore, thepossible values of a are either 2 or 8. Either 2 or 8 will be scored asa correct answer.
Alternate approach: Graphically, the condition f (a) = g(a) implies thegraphs of the functions y = f (x) and y = g(x) intersect at x = a. The
graph y = f (x) is given, and the graph of y = g(x) may be sketched asa line with y-intercept 10 and a slope of −1 (taking care to note thedifferent scales on each axis). These two graphs intersect at x = 2
and x = 8.

QUESTION 36

The_correct answer is 0. Note that no matter where point W is
on RT
​ ,​ the sum of the measures of ∠RSW and ∠WST is equal tothe measure of ∠RST, which is 90°. Thus, ∠RSW and ∠WST arecomplementary angles. Since the cosine of an angle is equal to thesine of its complementary angle, cos(∠RSW) = sin(∠WST ). Therefore,cos(∠RSW ) − sin(∠WST ) = 0.

QUESTION 37

The correct answer is 576. According to the table, 5 minutes after the
injection, the penicillin in the patient’s bloodstream is 152 micrograms
per milliliter. Thus, there are 10 × 152 = 1520 micrograms of penicillin
in 10 milliliters of blood drawn 5 minutes after the injection. Similarly,
10 minutes after the injection, the penicillin concentration is
118 micrograms per milliliter. Thus, there are 8 × 118 = 944 microgramsof penicillin in 8 milliliters of blood drawn 10 minutes after the
injection. Therefore, there are 1520 − 944 = 576 more micrograms of
penicillin in 10 milliliters of blood drawn 5 minutes after the injection
than in 8 milliliters of blood drawn 10 minutes after the injection.

Answer Explanations | SAT Practice Test #8

QUESTION 38t_

The correct answer is 0.8. The value of b in the equation P (t) = ​200b​​  5 ​​can be estimated using any row of the table other than the first one.
Substituting t = 5 and P (5) = 152 from the second row of the table5_
into the definition of P yields 152 = ​200b​​  5 ​​, or 152 = 200b. Dividing
152
both sides of this equation by 200 yields b = ​ _  ​. The fraction can be
200
76
rewritten as ​ _  ​, or its decimal equivalent .76. Rounded to the nearest
100
tenth, this value is .8. Other rows of the table also give a value of b thatrounds to .8. Therefore, the value of b, rounded to the nearest tenth,is .8. Either .8, or its fractional equivalents, 4/5 or 8/10, can be gridded
as the correct answer.