Princeton Review SAT Premium Prep ANSWERS, 2022 by The Princeton Review (z-lib.org)

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16. D Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. Look for a word with a definition that is consistent with the other ideas in the sentence.
The sentence says Without even realizing it, which is an introductory phrase. Therefore, the
correct answer must include a subject and a verb to make the sentence complete; eliminate
(A) and (B), as they each contain a verb but no subject. Choice (C) contains a subject but no
verb. Eliminate (C). Choice (D) contains the subject humans and the verb rely, so it makes the
sentence complete. The correct answer is (D).

17. D Note the question! The question asks whether a sentence should be added, so it’s testing con-
sistency. If the content of the new sentence is consistent with the ideas surrounding it, then it
should be added. The paragraph discusses the great tit and its calls and makes no mention of
any other birds. The new sentence discusses the chickadee and its genus, so it is not consistent
with the ideas in the text; the sentence should not be added. Eliminate (A) and (B). Eliminate
(C) because the passage has not discussed chickadees. Keep (D) because it accurately states that
the new sentence is irrelevant. The correct answer is (D).

18. C Transitions are changing in the answer choices, so this question is testing consistency of ideas.
A transition must be consistent with the relationship between the ideas it connects. The sen-
tence before the transition states that the birds would reliably respond to ABC-D calls, and the
sentence with the transition states that The birds would not respond to…an atypical combination
of the call, D-ABC. These are contrasting ideas, so eliminate (A), (B), and (D), which do not
contain disagreeing transitions. Choice (C) appropriately uses the opposite-direction transi-
tion however. The correct answer is (C).

19. A Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. Look for a word with a definition that is consistent with the other ideas in the sentence.
The previous sentences say that the birds respond to ABC-D calls but would not respond to D-
ABC calls, so the answer should mean that order “is important.” Matters means “is important,”
so keep (A). Maintains and preserves both mean to “keep” or “sustain,” so eliminate (B) and
(D). Aligns means to “be the same as,” so eliminate (C). The correct answer is (A).

20. A Note the question! The question asks which choice would reinforce the paragraph’s claim about
the importance of syntax in bird calls, so it’s testing consistency. Eliminate answers that are
inconsistent with the purpose stated in the question. The paragraph states that the birds
respond to ABC-D calls but would not respond to D-ABC calls. Look for an answer choice that
is consistent with this idea. Choice (A) suggests that birds, like humans, don’t respond to out-
of-order or garbled communication. This is consistent with the idea that word order, or syntax,
is important, so keep (A). Eliminate (B) because, while it does mention word order, it doesn’t
mention its importance. Eliminate (C) and (D) because they do not mention that the order of
words is important. The correct answer is (A).

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21. B Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. All four choices mean the same thing in this context, but (B) is the most concise.
Eliminate (A), (C), and (D) because they are overly wordy. The correct answer is (B).

22. C Apostrophes are changing in the answer choices, so this question is testing apostrophe usage. When
used with a pronoun, an apostrophe indicates a contraction. In this sentence, the intended
meaning is figure out whether “there are” other animals. Choice (A) means there is other ani-
mals. Eliminate (A) because the singular verb is is not consistent with the plural noun animals.
Choice (B) means they are is other animals, so eliminate it. Choice (C) correctly means there
are other animals, so keep it. Choice (D) means they are are other animals, so eliminate it. The
correct answer is (C).

23. A Note the question! The question asks which choice will convey an attitude of genuine interest
and avoid the appearance of sarcasm, so it’s testing consistency. Eliminate answers that are in-
consistent with the purpose stated in the question. Look for an answer choice that is consistent
with a formal tone and indicates a genuine interest. Choice (A) means “important” and conveys
a formal tone, so keep it. Eliminate (B) because it conveys an informal tone that isn’t genuine.
Eliminate (C) because it means “really big” and conveys an informal tone that isn’t genuine.
Eliminate (D) because it means “generous” or “noble,” which is not consistent with the mean-
ing of the sentence. The correct answer is (A).

24. B Conjunctions are changing in the answer choices, so this question is testing STOP, HALF-
STOP, and GO punctuation. Use the Vertical Line Test, and identify the ideas as complete or
incomplete. Draw lines around the FANBOYS word and, since it is connecting the two parts
of the sentence. The first part of the sentence, Countless pollsters check in with likely voters every
day in the time before an election, is a complete idea. In (A), also predict which way the elector-
ate will tend on decision day, is an incomplete idea, so GO punctuation is needed. However,
the comma plus and is STOP punctuation, so eliminate (A). In (B), predicting which way the
electorate will tend on decision day, is an incomplete idea, so GO punctuation is needed. The
comma without the FANBOYS word is a type of GO punctuation, so keep (B). In (C), they
also predict which way the electorate will tend on decision day, is a complete idea, so STOP punc-
tuation is needed. However, the comma alone is GO punctuation, so eliminate (C). In (D),
predict which way the electorate will tend on decision day, is an incomplete idea, so GO punc-
tuation is needed. However, the comma plus but is STOP punctuation, so eliminate (D). The
correct answer is (B).

25. D Prepositions are changing in the answer choices, so this question is testing idioms. Look at the
word before the preposition to determine the correct idiom. Use process of elimination, and
guess if there is more than one answer left. The correct idiom is “planned to.” Eliminate (A)
and (C) because they do not use the correct idiom. Between the remaining answers, to chose in
(B) is an incorrect phrasing, so eliminate (B). The correct answer is (D).

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26. C Note the question! The question asks which choice continues the idea in this sentence, so it’s test-
ing consistency. Eliminate answers that are inconsistent with the purpose stated in the ques-
tion. The first paragraph states that citizens have a sense of the likely outcome of that election and
that this knowledge comes from the opinion poll. This sentence says that the results predicted the
outcome correctly. Look for an answer choice that is consistent with these ideas. Eliminate (A)
because the polls will provide the people with knowledge but not tell the people what to think.
Eliminate (B) because the poll was correct and did not mislead anyone. To keep the public in-
formed is consistent with giving the public knowledge, so keep (C). Eliminate (D) because to
sell newspapers is new information and is not consistent with the information in the surround-
ing paragraphs. The correct answer is (C).

27. B Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. Choices (C) and (D) both include 1948 twice, so both answers can be eliminated
because they are repetitive. The first part of the sentence introduces a famous instance, and
the second part of the sentence describes the instance, so the connecting phrase should indi-
cate a same-direction transition. Eliminate (A) because yet is an opposite-direction transition.
Choice (B) appropriately uses the same-direction transition when. The correct answer is (B).

28. B The punctuation is changing in the answer choices, so this question is testing STOP, HALF-
STOP, and GO punctuation. Use the Vertical Line Test, and identify the ideas as complete
or incomplete. Draw the vertical line between the words election and by. The first part of the
sentence, Once all the ballots were cast, it had become clear that in fact Truman had won the elec-
tion, is a complete idea, and the second part, By that time polling had earned a statistical sophisti-
cation that had been unrivalled in earlier eras, is also a complete idea. To connect two complete
ideas, STOP or HALF-STOP punctuation is needed. The period is STOP punctuation and
the dash is HALF-STOP punctuation, so keep (A), (B), and (C). Eliminate (D) because no
punctuation is GO. Next, the punctuation between time and polling is changing, so use the
Vertical Line Test again. The first part of the sentence, By that time, is an incomplete idea, and
the second part, polling had earned a statistical sophistication that had been unrivalled in earlier
eras, is a complete idea. To connect an incomplete idea to a complete idea, GO punctuation
is needed. Eliminate (A) because a colon is HALF-STOP punctuation. Keep (B) because a
comma is GO punctuation. Eliminate (C) because a semicolon is STOP punctuation. The
correct answer is (B).

29. A Note the question! The question asks which choice will correspond as closely as possible with the
information in the map, so it’s testing consistency. Eliminate answers that are inconsistent with
the map and its legend. The sentence states that Truman carried these states. Look for an answer
choice in which all of the states listed are dark gray. CA to NV to OH is the only list in which
all the states listed were won by Truman. The correct answer is (A).

30. D Apostrophes are changing in the answer choices, so this question is testing apostrophe usage.
When used with a pronoun, an apostrophe indicates a contraction. The intended meaning of
the first part of the phrase is it is only as good as…, so an apostrophe is needed. Eliminate (A)

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and (C). Next, look at the words after the underlined portion. Choice (B) would say “it is”
sample size, but the intended meaning is the possessive its, meaning “belonging to the poll.”
Eliminate (B) because it is the wrong form of the possessive pronoun. The correct answer is
(D).

31. B Note the question! The question asks where the new sentence should be placed, so it’s testing
consistency of ideas. The sentence must be consistent with the ideas that come both before and
after it. Determine the subject matter of the sentence, and find the other sentence(s) that also
discuss that information. The new sentence mentions those 100 people, so because of the word
those, it should come after a previous reference to 100 people. This is mentioned in sentence
2, so eliminate (A). The new sentence also mentions another one, so it needs to come after a
mention of something that another one could refer back to. Sentence 3 states that you’ d get one
answer, so the new sentence would correctly follow this idea by referencing another answer that
you’ d get. Therefore, the new sentence should follow sentence 3. The correct answer is (B).

32. C Verbs are changing in the choices, so this question is testing consistency of verbs. A verb must
be consistent with its subject and with the other verbs in the sentence. The subject of the verb
is voters, which is plural. To be consistent, the underlined verb must also be plural. Eliminate
(B) and (D) because their verbs are singular. The sentence says even today, so the verb must be
in present tense. Eliminate (A) because it is not in present tense. The correct answer is (C).

33. A Note the question! The question asks which choice concludes the sentence and paragraph, so it’s
testing consistency of ideas. Eliminate answers that are inconsistent with the purpose stated
in the question. The passage discusses how polls are used to predict public opinion. Look for
an answer choice that is consistent with polls predicting public opinions. Keep (A) because
it responds to the previous questions by asking for an opinion and a poll, so it is consistent.
Eliminate (B) because it describes the polls as harmful, which is not consistent. Eliminate (C)
because it says Who cares…?, which is inconsistent with the author’s tone. Eliminate (D) be-
cause it says it’s time to get rid of them, which is also inconsistent with the author’s tone. The
correct answer is (A).

34. D Pronouns are changing in the answer choices, so this question is testing consistency of
pronouns. A pronoun must be consistent in number with the noun or pronoun it refers to.
The underlined pronoun refers to someone, which is singular. To be consistent, the underlined
pronoun must also be singular. Eliminate (A), (B), and (C) because they contain the plural
pronouns they, we, and their. The correct answer is (D).

35. A Verbs are changing in the answer choices, so this question is testing consistency of verbs. A
verb must be consistent with its subject and with the other verbs in the sentence. The other
verb in the sentence is is, which is in the present tense. To be consistent, the underlined verb
must also be in the present tense. Eliminate (B) and (C) because they are not in the present
tense. The subject of the verb is public eye, which is singular. To be consistent, the underlined
verb must also be singular. Eliminate (D) because it is plural. The correct answer is (A).

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36. C Transitions are changing in the answer choices, so this question is testing consistency of ideas.
A transition must be consistent with the relationship between the ideas it connects. The first
part of the sentence says this may sound like a joke, and the second part of the sentence says
it’s not at all. These are contrasting ideas, so eliminate (B) and (D), which both contain same-
direction transitions. Although but does indicate a contrast, it makes the sentence incomplete,
so eliminate (A). Choice (C) appropriately uses the opposite-direction transition while and
makes the sentence complete. The correct answer is (C).

37. C Punctuation is changing in the answer choices, so this question is testing STOP, HALF-
STOP, and GO punctuation. Use the Vertical Line Test, and identify the ideas as complete or
incomplete. Draw the vertical line between the words restaurant and for. The first part of the
sentence, Imagine a new business opens in your city, a restaurant, is a complete idea. The second
part, for instance, food-critic reviews can be difficult to come by, and after all, how powerful can
a food critic’s review actually be in most places, is a complete idea. To connect two complete
ideas, STOP or HALF-STOP punctuation is needed, so (A) may seem to work. However, the
meaning is not precise in this construction: it implies that the second part of the sentence is
an example of the first, which isn’t correct. Eliminate (A). Next, (C) has a period after instance,
so do the Vertical Line Test again, in that location. In this case, the first part of the sentence
is Imagine a new business opens in your city, a restaurant, for instance, which is complete. The
second part of the sentence is Food-critic reviews can be difficult to come by, and after all, how
powerful can a food critic’s review actually be in most places, which is also complete. Therefore,
STOP or HALF-STOP is needed, so eliminate (B) and (D). Choice (C) correctly punctuates
the ideas and creates a precise meaning, as for instance should go with the first idea—a restau-
rant is an example of a business that could open. The correct answer is (C).

38. A Punctuation is changing in the answer choices, so this question is testing STOP, HALF-STOP,
and GO punctuation. The answer choices have combinations of multiple punctuation marks,
so consider each one individually. Choice (A) uses two dashes to separate a list of positive feed-
back types. Without the phrase, the sentence reads They might generate positive feedback on that
restaurant’s Facebook page. This is a complete and precise sentence, so it implies that the infor-
mation set off in dashes is unnecessary, which implies that (A) works, so keep it. Choice (B)
uses two semicolons, but semicolons only link complete ideas. The sentence does not contain
three complete ideas, so eliminate (B). Choices (C) and (D) both use a colon, but that can’t
work because the part after the comma contains both an unnecessary list and the completion
of the main idea of the sentence. A colon is used when the part after it provides a related expla-
nation or definition and nothing else. Eliminate (C) and (D). The correct answer is (A).

39. B Note the question! The question asks where sentence 2 should be placed, so it’s testing consis-
tency of ideas. The sentence must be consistent with the ideas that come both before and after
it. Sentence 2 introduces the Fake Facebookers, so it must come before more information about
this group. Sentence 3 says that the owner will create a powerful social-media presence instead

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of relying on the food critic. Sentence 4 says They might generate positive feedback and must be
referring to the Fake Facebookers, as there is no plural noun in the previous sentence that they
could refer back to. Therefore, sentence 2 should follow sentence 3. The correct answer is (B).

40. A Note the question! The question asks whether a sentence should be added, so it’s testing con-
sistency. If the content of the new sentence is consistent with the ideas surrounding it, then it
should be added. The paragraph states that One option is to post pictures of you and a new part-
ner having a great time and mentions this style of jealousy-inducing revenge. The new sentence
discusses a breakup and how to make him or her jealous, so it is consistent with the ideas in the
text; the sentence should be added, since it introduces the idea that the paragraph elaborates
on. Eliminate (C) and (D). The information in the new sentence is discussed further in the para-
graph, so keep (A). Eliminate (B) because the breakup is not discussed throughout the passage.
The correct answer is (A).

41. C Note the question! The question asks which choice best supports the point developed in this
paragraph, so it’s testing consistency. Eliminate answers that are inconsistent with the purpose
stated in the question. The paragraph discusses using Fake Facebookers to show any social aspect
of your personality. Look for an answer choice that is consistent with the idea that the Fake
Facebookers help one show something. Eliminate (A) because to provide solace is not to show.
Eliminate (B) because to provide harmful effects is not to show. Keep (C) because to provide
evidence matches to show. Eliminate (D) because to provide a profitable enterprise is not to show.
The correct answer is (C).

42. B Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. Look for a word with a definition that is consistent with the other ideas in the sentence.
The sentence says that the ethics are irrelevant, so the correct word should mean “to judge.”
Adore means “to love,” so eliminate (A). Assess means “to determine,” which can mean to judge,
so keep (B). Obsess means “to dwell on,” so eliminate (C). Philosophize means “to theorize,” so
eliminate (D). The correct answer is (B).

43. B The length of the phrase after because is changing in the answer choices, so this question is
testing precision and concision. Choice (A) misplaces the word culture. The avatars are not of
culture, so eliminate (A). Choice (B) correctly places culture to modify internet avatars, so keep
(B). Choice (C) says the strong culture…has so much power, which is redundant, so eliminate
(C). Choice (D) says the powerful culture…is full of strength, which is also redundant. Elimi-
nate (D). The correct answer is (B).

44. C Vocabulary is changing in the answer choices, so this question is testing precision of word
choice. The sentence starts with the verb phrase shuddering or not, so the subject of the verb
shuddering must immediately follow the comma. The previous sentence states We may shudder,
so the subject is we. Choices (A), (B), and (D) do not begin with we, so eliminate them. The
correct answer is (C).

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Section 3: Math (No Calculator)

1. B The question asks for the value of a function at a specific x-value. First, find the value of

the constant c. The question states that g(15) = 2, so plug 15 in for x in the function and set
bionefcftoohmrexeestqou2ga=teito25ng(s1(−5to5) +)g=ect.52cT(h=−i5–s)4s−i.m4Tp,hlweifrhieefiscohtroes,i2mg=(pxli3)5f0i=es+52gc(x–o−5r)42=.
the result equal to 2. The equation
=6 + c. Subtract 6 from both sides
The question asks for g(–5). Plug –5

–2 – 4 = –6. The correct answer is (B).

2. B The question asks for the value of x in a system of equations. Since the question asks for a

specific value and the answers contain numbers in increasing order, plug in the answers. Begin

by labeling the answers as “x” and start with (B), 3. Plug x = 3 into the first equation to get

9(3 + 4) = y. This becomes 9(7) = y or 63 = y. Now check to see whether these values of x and y

satisfy the second equation. If y = 21 , then 63 = 21 , which is true, so stop here. The correct
x 3

answer is (B).

3. D The question asks which equation is true for some value of a. Taking the absolute value of an
expression will yield a positive result. Isolate the absolute value in each choice, and eliminate
any that result in a negative value for the absolute value. Subtract 1 from both sides of (A) to
get |a – 1| = –1. This cannot be true, so eliminate (A). Subtract 1 from both sides of (B) to get
|1 – a| = –1. Eliminate (B). Subtract 1 from both sides of (C) to get |a + 1| = –1. Eliminate (C).
Add 1 to both sides of (D) to get |a – 1| = 1. Since the absolute value is set equal to a positive
number, there is a value of a that could make this true. Choice (D) is true if a = 0 or a = 2. The
correct answer is (D).

4. A The question asks which equation must be true given an initial equation. There are variables

in the answers, so plug in. Start by setting the denominators equal by making y = 5. Then set

the numerators equal to get x – y = 2. Plug in y = 5 to get x – 5 = 2. Add 5 to both sides of the

equation to get x = 7. Therefore, x = 7 and y = 5 satisfy the equation. Plug these values into each

of the choices and eliminate any that are not true. Choice (A) becomes 7 = 7 . This is true, so
5 5
7 3
keep (A), but check the remaining answers just in case. Choice (B) becomes 5 = − 5 . Elimi-

nate (B). Choice (C) becomes 7 − 2(5) = − 8 , which simplifies to 7 − 10 = − 8 or − 3 = − 8 .
5 5 5 5 5 5
7 5 7 12 7
Eliminate (C). Choice (D) is + = 5 or 5 = 5 . Eliminate (D). The correct answer is (A).
5

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5. C The question asks for the result when plugging an expression into an equation. Because there
are variables in the answer choices, plug in. Make x = 3. If x = 3, then –2x = –2(3) = –6. There-
fore, h(–2x) = h(–6) = –5(–6) + 3 = 30 + 3 = 33. This is the target value; circle it. Now plug
x = 3 into the answer choices to see which one matches the target value. Choice (A) becomes
–10(3) – 3 = –30 – 3 = –33. This does not match the target, so eliminate (A). Choice (B)
becomes 10(3) – 3 = 30 – 3 = 27. Eliminate (B). Choice (C) becomes 10(3) + 3 = 30 + 3 = 33.
Keep (C), but check (D) just in case. Choice (D) becomes 10(3)2 – 6(3) = 10(9) – 18 = 90 – 18
= 72. Eliminate (D). The correct answer is (C).

6. D The question asks for an equivalent form of an expression. One approach to this question is to
use Bite-Sized Pieces. First determine the x2 term. Multiply the two terms with x to get (9x)
(3x) = 27x2. Multiply this by the coefficient in front to get 2(27x) = 54x2. Eliminate (A) and (B)
because they do not have 54x2. Now look at the remaining choices. Choice (D) includes 24x
while (C) has no x term. Determine whether the x term could cancel. Terms could only cancel
if they subtract out. Since all terms are positive, this cannot happen, so eliminate (C). Only
one choice remains. Because there are variables in the choices, another approach is to plug in
for x. Make x = 2. If x = 2, then 2(9x + 1)(3x + 1) = 2[9(2) + 1][3(2) + 1] = 2(19)(7) = 38(7) =
266. This is the target value; circle it. Now plug x = 2 into the answer choices to see which one
matches the target value. Choice (A) becomes 80(2) = 160. This does not match the target, so
eliminate (A). Choice (B) becomes 12(2)2 + 4 = 12(4) + 4 = 48 + 4 = 52. Eliminate (B). Choice
(C) becomes 54(2)2 + 2 = 54(4) + 2 = 216 + 2 = 218. Eliminate (C). Choice (D) becomes
54(2)2 + 24(2) + 2 = 216 + 48 + 2 = 266, so keep (D). The correct answer is (D).

7. C The question asks for the solution set of an equation. First, plug k = 3 into the equation to

get x − 3 = x − 9 . Since the answers contain numbers, plug in the answers. Two of the solu-

tion sets involve 7 and 12, so pick one of these values and plug in. Plug in x = 7. The equation
becomes 7 − 3 = 7 − 9 or 4 = −2 , which is not true. Eliminate (B) and (D) because they

both contain 7. Plug in one of the two remaining choices. Try (C), 12. The equation becomes
12 − 3 = 12 − 9 or 9 = 3 . Since this is true, x = 12 is a solution. The correct answer is (C).

8. B The question asks which statement best describe Kyung’s deposits. Kyung had a balance of

$5,000 after 5 months and $5,800 after 21 months. First, subtract to find the number of

months between 5 and 21 months to get 21 – 5 = 16 months. Next, find the total amount

deposited over these 16 months by subtracting the balance at 5 months from the balance at 21

months to get $5,800 – $5,000 = $800 deposited. Finally, divide $800 by 16 months to get

the amount deposited each month, or $800 = $50 . The correct answer is (B).
16

9. D The question asks for the equation of a line that is parallel to another line. When two lines are

parallel, they have equal slopes. To determine the slope of a line given the equation, put the

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equation into slope-intercept form: y = mx + b, where m is the slope. The equation in the ques-

tion is already in y = mx + b form, so the slope of the line represented by y = –5x + 9 is –5. Put

the equations in the answer choices in y = mx + b form, and find a choice that has a slope equal

to –5. In (A), subtract x from both sides of the equation to get 5y = –x + 1. Divide both sides

by 5 to get y = − 1 x + 1 . The slope is − 1 . This does not equal –5, so eliminate (A). In (B),
5 5 5

subtract 3x from both sides of the equation to get –5y = –3x + 15. Divide both sides by –5 to

get y = 3 x − 3 . The slope is 3 . Eliminate (B). In (C), subtract 5x from both sides of the equa-
5 5

tion to get –y = –5x + 3. Divide both sides by –1 to get y = 5x – 3. The slope is 5. Eliminate (C).

In (D), subtract 15x from both sides of the equation to get 3y = –15x + 12. Divide both sides by

3 to get y = –5x + 4. The slope is –5. The correct answer is (D).

10. B The question asks for the number of solutions to a set of equations. Questions about the num-

ber of solutions to a system of equations are asking for the number of points of intersection.

Since the first equation is a quadratic, which represents a parabola, and the second equation is

a line, there can be at most two points of intersection. Eliminate (A). Solving this system by

substitution would be difficult, so sketch the equations. Rearrange the second equation into 

y = mx + b form. Subtract 7 from both sides of the equation to get x – 7 = 3y, and flip the equa-

tion to get 3y = x – 7. Divide both sides by 3 to get y = 1 x − 7 . The line will have a y-intercept
of − , which is between –2 and 3 3
7
3 –3, and a shallow slope, looking like this:

y = 1 x 7
3 3

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Now sketch the parabola. Set y = 0 to find the x-intercepts. If 0 = (3x – 2)(x + 4), then x = 2
3
or –4. Now, to find the y-intercept, plug in x = 0. The equation becomes y = [3(0) – 2](0 + 4) =

(–2)(4) = –8. Add these intercepts to the sketch. The vertex of the parabola will be between the

two x-intercepts, somewhere to the left of and below the y-intercept. Sketch the parabola by

connecting the dots.

y = 1 x 7
3 3

y = (3x – 2)(x + 4)

The line and the parabola intersect twice; therefore, there are two solutions. The correct answer
is (B).

11. B The question asks for an expression representing the amount paid by each of Gary and Ron

for the radio. There are variables in the answer choices, so plug in. Make d = 20. The price of

Gary’s radio becomes $20, and the price of Ron’s radio becomes $20 + $10 = $30. Therefore,

the radios together cost $20 + $30 = $50. The taxes and shipping fees are 25% of the cost

of the radios alone. This is 25 × 50 = 1 × 50 = 50 = $12.50 . Add this to the total cost to
100 4 4
get $50 + $12.50 = $62.50. The question asks what each of them paid. They agree to equally

divide the total cost, so they each pay $62.50 ÷ 2 = $31.25. This is the target value; circle it.

Now plug d = 20 into the answer choices to see which one matches the target value. Choice (A)

becomes 0.25(20) + 2.5 = 5 + 2.5 = $7.50. This does not match the target value, so eliminate

2 8   |   Practice Test 9: Answers and Explanations

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(A). Choice (B) becomes 1.25(20) + 6.25 = 25 + 6.25 = $31.25. Keep (B), but check the rest
of the choices just in case. Choice (C) becomes 1.75(20) + 10 = 35 + 10 = $45. Eliminate (C).
Choice (D) becomes 2.5(20) + 12.5 = 50 + 12.5 = $62.50. Eliminate (D). The correct answer
is (B).

12. A The question asks for the value of y in an equation. Although there are numbers in the choices,

the numbers are complicated and this is the no-calculator section, so do not plug in the an-

swers. Instead solve algebraically. First, get rid of the denominator by multiplying each side of

the equation by (y – 3) to get y + 3 = 6(y – 3). Distribute the 6 on the right side to get y + 3 =

6y – 18. Add 18 to both sides of the equation to get y + 21 = 6y. Subtract y from both sides to

get 21 = 5y. Divide both sides by 5 to get 21 = y . The correct answer is (A).
5

13. A The question asks for the values for x in an equation. The answer choices are in the form of the

quadratic equation, which is x = −b ± b2 − 4ac for quadratics in the form ax2 + bx + c = 0.
2a

Put the equation in the question into ax2 + bx + c = 0 form by subtracting 3n from both sides

of the equation to get x 2 + m x − 3n = 0 . To avoid plugging a fraction into the quadratic for-
3

mula, multiply everything in the equation by 3 to get 3x2 + mx – 9n = 0. In this form, a = 3,

b = m, and c = –9n. Plug these into the quadratic formula to get x = −m ± m2 − 4(3)(−9n)
2(3)

or x = −m ± m2 + 108n . The choices break this into two fractions, so do the same to get
6

x = − m ± m2 +108n . The correct answer is (A).
6 6

14. C The question asks for the value of c, which, according to the figure, is the x-coordinate of the

point of intersection on the positive x-axis. One way to find the point of intersection is to set

the two equations equal and solve for x. However, in this case, that is unnecessary since the

y-coordinate is known to be 0. Set either one of the two equations equal to 0. If p(x) = 0, then

27x2 – 3 = 0. Add 3 to both sides of the equation to get 27x2 = 3. Divide both sides by 27 to

get x2 = 3 . Reduce the fraction by 3 to get x2 = 1 . Take the square root of both sides of the
27 9
1 1 1
equation to get x = ± 9 = ± 9 = ± 3 . The question asks for the value of c, which is positive,

so c = 1 . The correct answer is (C).
3

|Practice Test 9: Answers and Explanations    2 9

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15. C The question asks for a coefficient of an imaginary number given as a fraction with imaginary

parts. To simplify such a fraction, multiply the numerator and denominator by the conjugate of

the base. The conjugate is the same expression but with the sign of the imaginary part changed.

The conjugate of 4 – 3i is 4 + 3i. Multiply the numerator and denominator by this expression

to get 10 + 5i × 4 + 3i . Multiply the fractions by multiplying the numerators and denomina-
4 − 3i 4 + 3i
10(4) +10(3i) + 5i(4) + 5i(3i)
tors separately. In both cases, use FOIL to get 4(4) + 4(3i) + (−3i)(4) + (−3i)(3i) . Simplify to

get 40 + 30i + 20i +15i2 . Combine like terms to get 40 + 50i +15i2 . Since i2 = –1, the expres-
16 +12i −12i − 9i2 16 − 9i2

sion equals 40 + 50i +15(−1) , which becomes 40 + 50i −15 or 25 + 50i . Factor out 25 in the
16 − 9(−1) 16 + 9 25

numerator to get 25(1+ 2i) , then cancel the 25 in the numerator and the 25 in the denominator
25

to get 1 + 2i. The question says that this expression is written in the form a + bi. Since 1 + 2i =

a + bi, a = 1 and b = 2. The question asks for the value of b, which is 2. The correct answer is (C).

16. 8 , 4 , or 0.8
10 5

The question asks for the value of the sine of angle a. There are trigonometric expressions involved,

so write out SOHCAHTOA to remember the trig functions. The value 0.8 is equivalent to the frac-

tion 8 . The CAH part defines the cosine as adjacent , so co=sb ha=ydpj 8 . Plug in 8 for the
10 hypotenuse 10

adjacent side (the base of the triangle) and 10 for the hypotenuse. This is a 6-8-10 right triangle,
opposite
making the opposite side 6. The question asks for sin a. The SOH part defines the sine as hypotenuse .
oh=pypp 8
The side opposite angle a is 8, and the hypotenuse is 10, so si=n a 10 . The correct answer

can be expressed as 8 , 4 , or 0.8.
10 5

17. 30 The question asks for the value of c, which is the constant decrease in restoring force for each

additional 20 centimeters of stretching. When the rubber band is stretched from 30 centime-

ters to 90 centimeters, the restoring force decreases from –35 Newtons to –125 Newtons. Find

the distance stretched and the difference between the restoring force at each stretched distance.

There is a change in stretched distance of 90 – 30 = 60 centimeters, and there is a decrease in

3 0   |   Practice Test 9: Answers and Explanations

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the restoring force of –35 – (–125) = 90 Newtons. The question asks for the decrease in restor-

ing force when the rubber band is stretched an additional 20 centimeters, so set up the propor-

tion c Newtons = 90 Newtons . Cross-multiply to get 60c = 1,800. Divide both sides of the
20 centimeters 60 centimeters

equation by 60 to get c = 30. The correct answer is 30.

18. 12 The question asks for the maximum height of a book on the bottom shelf. The question states that
the shelves are all parallel. All the smaller triangles within the big triangle contain the same angle
at the top. Because the shelves are all parallel, these smaller triangles and the big triangle also con-
tain the same angle on the right side. Therefore, the shelves form four similar triangles. Use the
fact that similar triangles have proportional sides. As a result, the heights of the four shelves are in
the same proportion as the slant height of the four shelves. On the right side of the figure, the slant
heights of the four shelves are listed as x, 2x, 3x, and 2x. Therefore, the proportion of the heights is
also 1:2:3:2. Since the height of the entire bookcase is 48 inches, set up the equation y + 2y + 3y +
2y = 48. Combine like terms to get 8y = 48. Divide both sides of the equation by 8 to get y = 6. The
question asks for the maximum height of a book on the bottom shelf, which is 2y = 2(6) = 12. The
correct answer is 12.

19. 2 The question asks for the real value of x in an equation. To solve this, factor by grouping. Fac-
tor the first two terms and the last two terms separately. The first two terms, x3 – 2x2, factor to
x2(x – 2). The last two terms, 3x – 6, factor to 3(x – 2). The equation can be rewritten as x2(x – 2) +
3(x – 2) = 0. Since both of the new terms have a factor of (x – 2), factor this term out to get (x – 2)
(x2 + 3) = 0. To find the solutions, set both of the factors equal to 0. Set the second factor equal to
0 to get x2 + 3 = 0. Subtract 3 from both sides to get x2 = –3. Since the square of a real number can-
not be negative, this has no real solutions. Set the other factor equal to 0 to get x – 2 = 0. Add 2 to
both sides of the equation to get x = 2. The correct answer is 2.

20. 5 The question asks for the value of b, the y-coordinate of a solution to a system of equations. To
solve a system of equations, stack and then add or subtract. First, though, it is necessary to mul-
tiply both sides of both equations by a constant in order to cancel one of the variables. The ques-
tion asks for the value of b, so cancel out the a’s. Make the coefficients of a the same number with
opposite signs in the equations by multiplying the first equation by 6 and the second by –5. The
two equations become 30a – 12b = –60 and –30a – 20b = –100, respectively. Now stack and add
the equations.

30a – 12b = –60

–30a – 20b = –100

–32b = –160

Divide both sides of the equation by –32 to get b = 5. The correct answer is 5.

|Practice Test 9: Answers and Explanations    3 1

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Section 4: Math (Calculator)

1. A The question asks for an expression that models a specific situation. Translate English to math us-
ing bite-sized pieces. The question states that Yoonhee’s longest run was 23 kilometers. The number 23
represents the initial value. Eliminate (C) and (D) since the initial value is not 23. The question also
states that Yoonhee’s training plan increases...her longest run by 2 kilometers per week. This indicates
that the value 2w should be added to the run, not subtracted. Eliminate (B). The correct answer is (A).

2. A The question asks for a measurement and gives conflicting units. The question states that the baker

separates a 6-pound batch of dough in half. Divide by 2 to get the weight of half the dough, or 6 ÷ 2

= 3 pounds. When dealing with scale maps or models, make a proportion, being sure to match up
1 pound 3 pounds
units. The proportion is 16 ounces = x ounces . Cross-multiply to get x = 48 ounces. Each half

batch of dough makes 12 donuts. Divide the number of ounces to find the weight per donuts, or

48 ÷ 12 = 4 ounces per raw donut. The correct answer is (A).

3. C The question asks for the number of tournaments Kitty participated in during a specific month.
Since the question asks for a specific value and the answers contain numbers in increasing order,

plug in the answers. Begin by labeling the answers as “# of tournaments” and start with (B), 3. The
question states that the cost of participating in tournaments is an additional $2.50 per tournament.
Multiply the number of tournaments by the cost per tournament to get 3 × $2.50 = $7.50. To get
the total cost, add the monthly subscription fee to the cost of participating in tournaments to get
$14.95 + $7.50 = $22.45. Since this does not match Kitty’s cost of participating, eliminate (B). Try
(C), 4. Multiply the number of tournaments by the cost per tournament to get 4 × $2.50 = $10.00.
To get the total cost, add the monthly subscription fee to the cost of participating in tournaments
to get $14.95 + $10.00 = $24.95. This matches the value given in the question, so stop here. The
correct answer is (C).

4. C The question asks for the number of necklaces Nathalie made last month. Since the ques-
tion asks for a specific amount and the answers contain numbers in increasing order, plug
in the answers. Begin by labeling the answers as “necklaces made by Nathalie” and start
with (B), 37. The question states that Aaron made 14 fewer necklaces than Nathalie. If
Nathalie made 37 necklaces, then Aaron made 37 – 14 = 23 necklaces. Add the number of
necklaces Nathalie made and the number of necklaces Aaron made to get 37 + 23 = 60 neck-
laces. This does not match the total number of necklaces made, so eliminate (B). Try (C), 44. If
Nathalie made 44 necklaces, then Aaron made 44 – 14 = 30 necklaces. Add the number of necklaces
Nathalie made and the number of necklaces Aaron made to get 44 + 30 = 74 necklaces. This
matches the value given in the question, so stop here. The correct answer is (C).

3 2   |   Practice Test 9: Answers and Explanations

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5. B The question asks about population based on information about a study of a sample from that

population. Since the members were randomly selected, the number of members who prefer

attending the Montreal event found in the study should match that of the larger population. To

extrapolate the study results, multiply the given percent by the total number of people in the club
39.3
to get 100 × 80 = 31.44 . The correct answer is (B).

6. C The question asks for the value of the force when given other information. Translate the infor-

mation in bite-sized pieces. One piece of information says that the distance traveled is equal to

the work expended divided by the force. Make the distance traveled D, work expended W, and

force F. The equation becomes D = W . Next, plug in the given information. The work (W ) is
F Multi-
36
36 Newton-meters, and the distance (D) is 9 meters, so the equation becomes 9 = F .

ply both sides of the equation by F to get 9F = 36. Divide both sides of the equation by 9 to get

F = 4. The correct answer is (C).

7. D The question asks for a probability, which is defined as # of outcomes that fit requirements .
total # of outcomes

Read the table carefully to find the numbers to make each probability. In 2010, there were

1,298,300 total employees, so that is the total # of outcomes. Of those employees, 150,890

employees are in the Service category and 623,320 employees in the Office category. Add

both numbers together to get a total of 150,890 + 623,320 = 774,210 employees in both cat-

egories, so that is the # of outcomes that fit requirements. Therefore, the probability of

choosing an employee in either the Service category or the Office category is 774, 210 < 0.60 .
1, 298, 300

The correct answer is (D).

8. D The question asks for a proportion of the number of novels published by a certain publisher dur-

ing a specific range. To find the proportion, set up a ratio of the novels published by Doubleday

divided by the total number of books published. Asimov had 2 novels published by Doubleday in

the years 1960-1979, and he had 40 novels published in total, so the ratio becomes 2 = 1 . The
40 20
correct answer is (D).

|Practice Test 9: Answers and Explanations    3 3

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9. C The question asks for a statement that must be true if a line has a positive slope in the xy–plane.
Use process of elimination to eliminate answer choices that are either false or could be true some of
the time, but not all the time. First, draw the xy-plane with the quadrants labeled.
y

II I

x

III IV

A line with a positive slope passes through Quadrants I and III since lines in the xy-plane go to in-
finity in both directions. Eliminate (A) and (B) because they do not contain both Roman numer-
als I and III. Next determine if Roman numeral II must be true. A line with a negative y-intercept
will not intersect Quadrant II. For example:

y

II I
x

III IV

Therefore, Roman numeral II is not necessarily true since a line with a positive slope will not
include points in Quadrant II when the line has a negative y-intercept. Eliminate (D) since it con-
tains Roman numeral II. The correct answer is (C).

10. D The question asks for the equation of a function given the x-intercepts. If h(x) has x-intercepts at
−2, 2, and 4, then the function will have factors of (x – 2), (x + 2), and (x – 4). Eliminate answer
choices (A), (B), and (C) since the equations do not have all three factors. The correct answer is (D).

3 4   |   Practice Test 9: Answers and Explanations

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11. B The question asks for a value based on data from a graph. Start by finding the point that represents
the rodent with the fewest litters per year. Since the variable along the x-axis is Litters per Year, the
fewest litters per year is the point closest to the left-hand side, at around 1.2 litters per year. Since
the average litter size is the variable along the y-axis, find the corresponding average litter size when
the litters per year is 1.2 The average litter size is 4. The correct answer is (B).

12. D The question asks which point has the smallest ratio of average litter size to litters per year. Set up

a ratio as average litter size . Fill in the ratio with data from the graph to find the smallest ratio.
litters per year

Points A and B both have 2 litters per year, but point A has a higher average litter size, giving a

ratio of 5 . Point B has a ratio of 2 = 1 . Eliminate (A) since the ratio is larger than the ratio in (B).
2 2
11.5
Point C has a ratio of about 3.5 < 3.3 . This is much higher than the ratio in point B. Eliminate

(C). Point D has a ratio of about 4 = 0.8 . This is lower than the ratio in point B. Eliminate (B).
5

The correct answer is (D).

13. A The question asks for a scatterplot based on given information. Since b is positive, the y-intercept
must be positive; eliminate (B) and (C) because they have y-intercepts that are not positive. The x
in the equation is squared, meaning the graph will be a parabola. The a coefficient on the x2 term
is negative, which means that the parabola would open down toward the negative y-axis and not
up toward the positive y-axis. Eliminate (D) because it has a parabola that opens up. The correct
answer is (A).

14. B The question is asking for a type of function that is represented by data. Look at the answer choices
to determine the possible options. All answer choices refer to either exponential or linear changes,
and those changes could be increases/growth or decreases/decay. As the time increases in the chart,
the population also increases. Eliminate (A) and (C) which indicate a decreasing population over
time. Now determine if the increase is linear or exponential. A population with linear growth will
increase by the same amount for each unit of time. From a time of 0 minutes to a time of 17 min-
utes, the population increases from 1 to 2, for an increase of 1. From 17 minutes to 34 minutes,
another 17 minutes of time passes, but the population increases from 2 to 4 for an increase of 2.
Since the population is not increasing by the same amount every 17 minutes, the growth is not lin-
ear. Eliminate (D). Choice (A) indicates exponential growth, which means that the population is
growing by a multiplier each unit of time. From 0 minutes to 17 minutes, the population doubles,
and it doubles again over the next 17 minutes to the time of 34 minutes. If the population doubles
every 17 minutes, then the population is showing exponential growth. The correct answer is (B).

15. C The question asks for an expression for a specific scenario based on given information. The ques-

tion states that y is the number of years after 2010. The question also gives that there are 15,000

people on January 1, the initial day, in City X, and the population increases by 1.2% per year.

|Practice Test 9: Answers and Explanations    3 5

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Therefore, to estimate the population of the city 10 years after 2010, plug y = 10 into the expres-

sion to get 15, 000 1 + 1.2 10 . Follow the same steps to find the estimated population of the city
100 

5 years after 2010 by plugging in y = 5 to get 15,000 1+ 1.2 5 . To find the difference, subtract
100 
10 5
these two expressions to get 15,000 1 + 1.2  − 15, 000 1 + 1.2  . The correct answer is (C).
100 100

16. A The question asks for the meaning of a part of a given equation. At the y-intercept of an equation,

x = 0. Plug x = 0 into the equation to get y = C + (I + S)(0) = C + 0 = C . This represents the cost of

the computer. The correct answer is (A).

17. C The question asks for the number of months that the total cost will be less using the data for one
business vs. another. Use the equation given to set up an inequality. The cost for Cat’s Computers
will be 990 + (50 + 65)x, and the cost for Bobby’s Bounty will be 1,100 + (60 + 45)x . Because the
cost of Cat’s Computers is less than or equal to the cost of Bobby’s Bounty, make the first expres-
sion less than or equal to the second: 990 + (50 + 65)x ≤ 1,100 + (60 + 45)x. Solve for x. Start by
adding like terms in the parentheses to get 990 + 115x ≤ 1,100 + 105x. Subtract 990 from both
sides of the inequality to get 115x ≤ 110 + 105x. Subtract 105x from both sides of the inequality to
get 10x ≤ 110. Divide both sides by 10 to get x ≤ 11. The correct answer is (C).

18. D The question asks for a representative graph based on a specific scenario. If Norepinephrine loses
half of its pharmacological activity every 2 minutes, then pharmacological activity must be
decreasing as time increases. Eliminate (B). Losing 50% pharmacological activity every 2 minutes
is exponential decay, because the actual amount lost each time period is not constant. Eliminate
(A) and (C) since they do not represent exponential decay. The correct answer is (D).

19. A The question asks for the number of glasses that can be filled from a full bottle of grape juice. Start by

finding the volume of the glass. The volume of a cone is given by the equation V = 1 pr 2h . Because
3

the diameter is 5 inches, the radius is 2.5 inches. The height is 4 inches. The volume of each glass

is V = 1 p (2.5)2 ( 4) ≈ 26.18 cubic inches. One bottle contains approximately 46 cubic inches, so
3

divide the number of cubic inches in a bottle of grape juice by the number of cubic inches per glass

to get 46 ÷ 26.18 = 1.76. Because the question wants the glasses to be completely filled, round

down to 1. The correct answer is (A).

20. D The question asks for the greatest possible value of an expression. It is possible to solve the given
inequality for x and then put that into the expression in the question. To save time, though, make
sure to read the final question, which ask about the value of 2x – 3. Solve the inequality to get the
2x term by itself. Subtract 3 from both sides of the inequality to get 2x ≤ 1. Now, to find 2x – 3,

3 6   |   Practice Test 9: Answers and Explanations

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subtract 3 from both side of the inequality to get 2x – 3 ≤ 1 – 3. This simplifies to 2x – 3 ≤ –2.
Therefore, the greatest possible value of the expression is –2. The correct answer is (D).
21. D The question asks for the length of an arc in a circle. Because XZ is a diameter, arc XYZ will be

half of the circumference. The radius is 2, so the diameter is double the radius, or 4. Circumfer-

ence has the formula C = πd, so the circumference is 4π. Divide the circumference in half to get
the length of arc XYZ , so 4π ÷ 2 = 2π. The correct answer is (D).

22. D The question asks for a percent based on provided data. The words percent greater than or per-

cent less than indicate percent difference, which is defined as difference × 100 . Male deaths from
original

colorectal cancer are about 5,000, and female deaths are about 4,200. Because the question asks

for percent greater, the original is the smaller value. The difference is 5,000 – 4,200 = 800, so the

percent difference is 800 × 100 = 19% . The correct answer is (D).
4, 200

23. B The question asks for the number of points plotted below a specific line. To find the number of

points, draw the line y = x . Label the horizontal axis as “number of male deaths” and the vertical

axis as “number of female deaths.”

y y=x

number of female deaths 10

8

6

4

2

2 4 6 8 10 x
number of male deaths

|Practice Test 9: Answers and Explanations    3 7

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Points below the line will have an x-value (number of male deaths) that is greater than their y-value
(number of female deaths). Graph the points on the coordinate plane.
number of female deaths
y y=x

10 lung
8

6 breast colorectal
4
pancreas
2
prostate

2 4 6 8 10 x
number of male deaths

Lung, colorectal, and prostate cancers have more male deaths than female deaths, so there are 3
points that are below the line. The correct answer is (B).

24. A The question asks for a true statement regarding the results of a study that was conducted. Read
each answer carefully and use process of elimination. All the answer choices refer to standard de-
viation. Standard deviation is a measure of the spread of values in a data set. The more spread out
the numbers are from the mean value, the greater the standard deviation is. Ms. Minster’s class
has 16 students with 97%, and there is at least 1 student who scored in each of the different score
categories. This data largely falls into the 97% category, so it would be closely grouped around the
mean. Dr. Chiu’s class has several students with the same score for all scores except 96%, so the
data is more spread out and not clustered around one value as with Ms. Minster’s class. This would
give the scores in Dr. Chui’s class a higher standard deviation than the scores in Ms. Minster’s
class. The correct answer is (A).

25. B The question asks for a true statement based on an inequality. There are variables in the question,
so plug in. Make a = –2 and b = 1. It is unnecessary to consider Roman numeral III, as every an-
swer choice includes III. Test Roman numeral I. Roman numeral I is false because b can be posi-
tive; eliminate (C) and (D). Roman numeral II is true because a must be negative if a is less than
–a. Eliminate (A). The correct answer is (B).

26. B The question asks for the meaning of a coefficient in context. Start by reading the full question,

which asks for the meaning of the number 2.3788. Then label the parts of the equation with

the information given. In the equation, 2.3788 is multiplied by x. The x-axis is median annual

household income, so x can be labeled as “income.” The y-axis is median home price, so y can be

labeled as “home price.” The equation becomes “home price” = 2.3788(“income”) – 2,895.2. Now

3 8   |   Practice Test 9: Answers and Explanations

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eliminate answer choices that are not consistent with these labels. Choice (A) refers to the change

in home price based on income. The two variables are related by the equation, but it is difficult to

determine the relationship. Keep (A) and check the other answers. Choice (B) also has a relation-

ship between the variables; keep (B), too. Choice (C) refers to the ratio of income to home price,
income
which would be written as home price . The linear equation does not have this ratio, and rearrang-

ing the equation would not result in this ratio being equal to 2.3788. Eliminate (C). Choice (D)

say that the home price increased regardless of…income. Based on the graph and the labels of the

equation, different incomes will be associated with different home prices. Eliminate (D). To check

(A) and (B), plug in some numbers. It is easier to plug in an increase of $1 than of $2.3788, so

check (B) first. If the median annual household income is $10,000, then the median home price

is 2.3788(10,000) – 2,895.2 = $20,892.8. If the median annual income increases by $1 to $10,001,

the median home price is 2.3788(10,001) – 2,895.2 = $20,895.1788. Subtract the two amounts to

find the increase in median home price, or 20,895.1788 – 20,892.8 = $2.3788. Thus, an increase of

$1 in the income does increase the home price by 2.3788. The correct answer is (B).

27. C The question asks for a polynomial that is divisible by a specific factor. There are variables in the
answer choices, so plug in. There are a lot of 2’s in the answer choices, so don’t make x = 2; doing
so might make more than one answer choice work. Make x = 5. Find the values of the functions f
and g when x = 5. This becomes f(5) = 2(5)2 – 8(5) + 6 = 50 – 40 + 6 = 16 and g(5) = (5)3 – 4(5)2
+ 3(5) = 125 – 100 + 15 = 40. When x = 5, x + 4 = 9. Check each answer to see if it is divisible by
9. Choice (A) becomes h(5) = f(5) + g(5) = 16 + 40 = 56. This is not divisible by 9; eliminate (A).
Choice (B) becomes l(5) = f(5) + 2g(5) = 16 + 2(40) = 96. This is not divisible by 9; eliminate (B).
Choice (C) becomes m(5) = 2f(5) + g(5) = 2(16) + 40 = 72. This is divisible by 9; keep (C). Check
the remaining answer choice just in case. Choice (D) becomes n(5) = 2f(5) + 2g(5) = 2(16) + 2(40)
= 112. This is not divisible by 9; eliminate (D). The correct answer is (C).

28. C The question asks which value of c means f(x) = c has 3 real solutions. If f(x) = c has three real solu-
tions, then f(x) = c exactly three times. Use the graph provided and draw horizontal lines for each
answer choice. For (A), the value of c is −2. For f(x) = −2, draw the line y = −2 to see where it in-
tersects the curve. The graph of the two functions has only one point of intersection, so it only has
one solution. Eliminate (A). For (B), at y = 0 (the x-axis) the graph only intersects once. Eliminate
(B). For (C), at y = 1.25, the graph shows three points of intersection. There can be only one correct
answer, so if (C) works, there is no need to try (D). The correct answer is (C).

|Practice Test 9: Answers and Explanations    3 9

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29. A The question asks for the form of a quadratic which gives the solutions as constants or coefficients.
The correct form is the factored form. Eliminate choices that are not completely factored. Elimi-
nate (C), which is incompletely factored, and (D), which is in standard form y = ax2 + bx + c. To
choose between (A) and (B), plug in to find which one is equivalent to the given equation. Make

x = 2. The original equation becomes 3(2 +1)2 − 27 = 0. This is the target value; circle it. Make

x = 2 in (A) to get 3(2 – 2)(2 + 4) = 0; keep (A). Check the remaining answer choice just in case.
Choice (B) becomes 3(2 – 4)(2 + 2) = −24. Eliminate (B). The correct answer is (A).

30. A The question asks for the average in terms of a variable. There are variables in the answer choices,

so plug in. For averages, use the formula T = AN, in which T is the total, A is the average, and N is

the number of things. Make x = 3. This makes a = 3 + 7 = 10 = 5 , b = 5(3) + 4 = 15 + 4 = 19 = 9.5 ,
2 2 + 2 2 2
6(3) +1 18 + 1 19
and c = 2 = 2 = 2 = 9.5 . The Total of a, b, and c is 5 9.5 + 9.5 = 24, and there are 3

things, so the formula becomes 24 = A(3). Divide both sides of the formula by 3 to get 8 = A. This is

the target value; circle it. Make x = 3 in each answer choice and eliminate any answer which does

not equal 8. Choice (A) becomes 2(3) + 2 = 8. This matches the target, so keep (A) but check the

remaining choices just in case. Choice (B) becomes 3(3) + 1 = 9 1 . Eliminate (B). Choice (C) be-
2 2

comes 4(3) + 4 = 16. Eliminate (C). Choice (D) becomes 6(3) + 6 = 24. Eliminate (D). The correct

answer is (A).

31. 5 , .555, or .556
9

The question asks for the increase in degrees Celsius when the temperature increases by one degree

Fahrenheit. There are variables in the question, so plug in. Choose two numbers for F which have

a difference of 1. If F = 32, the equation is simplified, so use F = 32 and F = 33. If F = 32, then

C = 5 (32 − 32) = 5 (0) = 0 . If F = 33, then iCnc=re59as(e3o3f−5932d) e=gr59e(e1s) C=e59lsi.uTs.hTehdeifcfoerrerenccteabnestwweereins
9 9 . This is an
5 5
the two values for C is 9 − 0 = 9

5 , 0.555, or 0.556.
9

32. 430 The question asks for the number of pages written at the end of a certain number of days. Mei

writes at a rate of 6 pages per day. If Mei writes 6 pages per day for 30 days, she will write 6 × 30

= 180 additional pages. She has already written 250 pages, so she will have 250 + 180 = 430 total

pages at the end of the 30-day period. The correct answer is 430.

4 0   |   Practice Test 9: Answers and Explanations

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33. 1 or .333
3
The question asks for a ratio, which can be expressed as a fraction or a decimal. The frequency us-

ing the heavier weight is 1 k , and the frequency of the harmonic oscillator using the lighter
2p 9m

weight is 1 k . The ratio of the frequency using the heavier weight to the frequency using the
2p m

1k

lighter weight is frequency using heavier weight or 2p 9m
frequency using lighter weight 1 k . Simplify this fraction by canceling

1 k 2p m
2p in the numerator and denominator to get
9m . Next, put everything under the same radical
k

km

to get 9m . To divide one fraction by another, flip the fraction in the denominator and multiply
k

m

it by the fraction in the numerator by it to get k × m = km . Cancel km in the numerator
9m k 9km

and the denominator to get =19 =19 1 . The correct answer is 1 .
3 3

34. 672 The question asks for a measurement and gives conflicting units. When dealing with scale maps or

models, make a proportion, being sure to match up units. The question states that a hobbit of oats

weighs 105 pounds. The proportion is 1 pound = 105 pounds . Cross-multiply to get x = 1,680
16 ounces x ounces
ounces. There are 2.5 imperial bushels of oats in a hobbit, so to find how many ounces are in one

imperial bushel, divide the number of ounces by 2.5 to get 1,680 ÷ 2.5 = 672 ounces per bushel of

oats. The correct answer is 672.

35. 5, 6, or 7

The question asks for one possible integer value of the radius of a circle. The arc of a cir-

cle relates to the circumference in the same proportion as the central angle relates to 360⁰, so

arc = central angle . To find a possible radius for the circle, make the arc 3, the central
circumference 360° 2πr Cross-multiply to get (3)(360) = (40)
3 40°
angle 40⁰, and the circumference to get 2pr = 360° .

|Practice Test 9: Answers and Explanations    4 1

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(2πr), or 1,080 = 80πr. Divide both sides of the equation by 80π to get 4.3 ≈ r. Because r must be
an integer and 3 was the smallest possible arc, round up to 5. Other possible answers are 6 and 7.
The correct answer is 5, 6, or 7.

36. 180 The question asks for an additional number of girls to be surveyed to make a certain fraction. Set

up a proportion. Ashley has surveyed 100 girls and 210 boys for a total of 310 students. She wants

girls to make up 4 of the eventual total. If x is the number of additional girls Ashley surveys, then
7

the total number of girls surveyed will be 100 + x and the total number of students surveyed will

be 310 + x. The proportion is 4 = 100 + x . Cross-multiply to get 4(310 + x) = 7(100 + x). Distrib-
7 310 + x

ute on both sides to get 1,240 + 4x = 700 + 7x. Subtract 700 from both sides of the equation to get

540 + 4x = 7x. Subtract 4x from both sides of the equation to get 540 = 3x. Divide by 3 on both

sides of the equation to get 180 = x. The correct answer is 180.

37. 28 The question asks for the population 20 years after 2015. This means that y, the number of
20
years after 2015, is 20. Plug this into the given equation to get P = 20(r )10 , which simplifies to
P = 20(r)2. To find the value of r, use the growth formula, which is final amount = original amount
(1 ± rate)number of .changes The rate is given as an 18% increase, but it must be expressed as a decimal.
Therefore, r = 1 + 0.18 = 1.18. Plug this into the formula to get P = 20(1.18)2 = 27.848. This is in
millions, and the question asks for the value to the nearest million. The correct answer is 28.

38. 1.18 The question asks for the value of a variable in the previous equation. The equation given is a
variation of the equation for exponential growth: final amount = original amount(1 ± rate)number
of ,changes where rate is expressed as a decimal. The population is expected to increase 18 percent
every ten years, so when y = 10, there is only one change. The rate per decade is 18%, which is
0.18 when expressed as a decimal. Because the population is growing, the rate is added to 1, so
r = 1 + 0.18 = 1.18. The correct answer is 1.18.

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RAW SCORE CONVERSION TABLE SECTION AND TEST SCORES

Raw Score Math Reading Writing Raw Score Math Reading Writing
Section Test Score and Section Test Score and
(# of correct Score Language (# of correct Score Language
answers) 10 Test Score answers) 28 Test Score
200 10 28
0 200 10 10 30 530 29 29 Please note that the
1 210 11 10 31 540 29 30 numbers in the table may
2 230 12 10 32 550 30 30 shift slightly depending
3 240 13 10 33 560 30 31 on the SAT’s scale from
4 260 14 11 34 560 31 32 test to test; however, you
5 280 15 12 35 570 31 32 can still use this table to
6 290 15 13 36 580 32 33 get an idea of how your
7 310 16 13 37 590 32 34 performance on the prac-
8 320 17 14 38 600 33 34 tice tests will translate to
9 330 17 15 39 600 33 35 the actual SAT.
10 340 18 16 40 610 34 36
11 360 19 16 41 620 35 37 TOTAL SAT
12 370 19 17 42 630 35 38 SCORE
13 380 20 18 43 640 36 39
14 390 20 19 44 650 37 40 (400–1600)
15 410 21 19 45 660 37
16 420 21 20 46 670 38
17 430 22 21 47 670 38
18 440 22 21 48 680 39
19 450 23 22 49 690 40
20 460 23 23 50 700 40
21 470 24 23 51 710
22 480 24 24 52 730
23 480 25 25 53 740
24 490 25 25 54 750
25 500 26 26 55 760
26 510 26 26 56 780
27 520 27 27 57 790
28 520 28 58 800
29 28

CONVERSION EQUATION SECTION AND TEST SCORES

Convert



READING TEST READING TEST
RAW SCORE SCORE
(10–40)
(0–52)

Convert + = x 10 =



WRITING AND WRITING AND READING TEST READING AND EVIDENCE-BASED READING
LANGUAGE TEST LANGUAGE TEST SCORE WRITING TEST AND WRITING
(10–40) SECTION SCORE
RAW SCORE SCORE SCORE (200–800)
(0–44) (10–40) (20–80)

+ = Convert +=

 EVIDENCE-BASED READING
AND WRITING
MATH TEST MATH TEST MATH SECTION MATH SECTION SECTION SCORE
NO CALCULATOR CALCULATOR RAW SCORE SCORE (200–800)
RAW SCORE (0–58) (200–800)
RAW SCORE
(0–20) (0–38)

|Practice Test 9: Answers and Explanations    4 3