The correct answer is 1.02.
The initial deposit earns 2 percent
interest compounded annually. Thus at the end of 1 year, the new
YDOXHRIWKHDFFRXQWLVWKHLQLWLDOGHSRVLWRISOXVSHUFHQWRI
_
WKHLQLWLDOGHSRVLW
2
6LQFHWKHLQWHUHVW
is compounded annually, the value at the end of each succeeding
year is the sum of the previous year’s value plus 2 percent of the
previous year’s value. This is again equivalent to multiplying the
SUHYLRXV\HDUŞVYDOXHE\7KXVDIWHU\HDUVWKHYDOXHZLOO
EH
2
DIWHU\HDUVWKHYDOXHZLOOEH
; and after
t
\HDUVWKHYDOXHZLOOEH
t
. Therefore,
in the formula for the value for Jessica’s account after
t
\HDUV
[
)
t
,
the value of
[PXVWEH
QUESTION 38
The correct answer is 6.11.
-HVVLFDPDGHDQLQLWLDOGHSRVLWRI
into her account. The interest on her account is 2 percent compounded
DQQXDOO\VRDIWHU\HDUVWKHYDOXHRIKHULQLWLDOGHSRVLWKDVEHHQ
PXOWLSOLHGWLPHVE\WKHIDFWRU +HQFHDIWHU\HDUV
-HVVLFDŞVGHSRVLWLVZRUWK
= $121.899 to the nearest tenth
RIDFHQW7\VKDXQPDGHDQLQLWLDOGHSRVLWRILQWRKLVDFFRXQW
The interest on his account is 2.5 percent compounded annually, so
DIWHU\HDUVWKHYDOXHRIKLVLQLWLDOGHSRVLWKDVEHHQPXOWLSOLHG
WLPHVE\WKHIDFWRU +HQFHDIWHU\HDUV
7\VKDXQŞVGHSRVLWLVZRUWK
WRWKHQHDUHVW
tenth of a cent. Hence, Jessica’s initial deposit earned $21.899 and
7\VKDXQŞVLQLWLDOGHSRVLWHDUQHG7KHUHIRUHWRWKHQHDUHVW
cent, Tyshaun’s initial deposit earned $6.11 more than Jessica’s
initial deposit.
Document Outline - Structure Bookmarks
- Answer Explanations
- Answer Explanations
-
- Section 1: Reading Test QUESTION 1
- Section 1: Reading Test QUESTION 1
- Choice B is the best answer. In the passage, a young man (Akira) asks a mother (Chie) for permission to marry her daughter (Naomi). The request was certainly surprising to the mother, as can be seen from line 47, which states that prior to Akira’s question Chie “had no idea” the request was coming.
- Choice A is incorrect because the passage depicts two characters engaged in a civil conversation, with Chie being impressed with
-
- is incorrect because the passage is focused on the idea of Akira’s and Naomi’s present lives and possible futures. Choice D is incorrect because the interactions between Chie and Akira are polite, not critical; for example, Chie views Akira with “amusement,” not animosity.
- QUESTION 2
- QUESTION 2
- Choice B is the best answer. The passage centers on a night when a young man tries to get approval to marry a woman’s daughter. The passage includes detailed descriptions of setting (a “winter’s eve” and
-
- silent. She stood a full half minute looking straight into Chie’s eyes. Finally, she spoke,” lines 88-89).
- Choice A is incorrect because the passage focuses on a nontraditional marriage proposal. Choice C is incorrect because the passage concludes without resolution to the question of whether Akira and Naomi will receive permission to marry. Choice D is incorrect because the passage repeatedly makes clear that for Chie, her encounter with Akira is momentous and unsettling, as when Akira acknowledges in
-
- © 2018 The College Board. College Board and SAT are registered trademarks of the College Board.
- QUESTION 3
- QUESTION 3
- QUESTION 3
- Choice C is the best answer. Akira “came directly, breaking all tradition,” (line 1) when he approached Chie and asked to marry her daughter, and he “ask[ed] directly,” without “a go-between” (line 65) or “mediation,” because doing otherwise would have taken too much time.
- Choices A, B, and D are incorrect because in these contexts, “directly”
-
-
-
- Choice A is the best answer.
- marriage proposal inappropriate because he did not follow traditional
-
- when Akira says to Chie “Please don’t judge my candidacy by the unseemliness of this proposal.”
- Choice B is incorrect because there is no evidence in the passage that Akira worries that Chie will mistake his earnestness for immaturity. Choice C is incorrect because while Akira recognizes that his unscheduled visit is a nuisance, his larger concern is that Chie will reject him due to the inappropriateness of his proposal. Choice D is incorrect because there is no evidence in the passage that Akira worries Chie will underestimate the sincerity of his emotions.
- QUESTION 5
- QUESTION 5
- QUESTION 5
- Choice C is the best answer.
- “Please don’t judge my candidacy by the unseemliness of this proposal.” This reveals Akira’s concern that Chie may say no to the proposal simply because Akira did not follow traditional practices.
- Choices A, B, and D do not provide the best evidence for the answer
-
- because lines 71-72 indicate only that Akira was speaking in an eager and forthright matter.
- QUESTION 6
- Choice D is the best answer because Akira clearly treats Chie with respect, including “bow[ing]” (line 26) to her, calling her “Madame”
- after he concedes that he is not following protocol and admits to being
- Choice A is incorrect because while Akira conveys respect to Chie, there
-
- incorrect because neither objectivity nor impartiality accurately describes how Akira addresses Chie. Choice C is incorrect because Akira conveys respect to Chie and takes the conversation seriously.
- QUESTION 7
- Choice D is the best answer.
- how Akira approached Chie to ask for her daughter’s hand in marriage. In these lines, the narrator is wondering whether Chie would have been more likely to say yes to Akira’s proposal if Akira had followed tradition: “Akira came directly, breaking all tradition. Was that it? Had he followed form — had he asked his mother to speak to his father to approach a go-between — would Chie have been more receptive?”
-
- reacted a certain way to Akira’s proposal.
-
- aspect of Japanese culture (marriage proposals) but not the culture
-
- a criticism of Akira’s individual marriage proposal but not the entire tradition of Japanese marriage proposals. Choice C is incorrect because the narrator does not question a suggestion.
- QUESTION 8
- Choice B is the best answer. In line 1, the narrator suggests that Akira’s direct approach broke “all tradition.” The narrator then wonders if Akira had “followed form,” or the tradition expected of him, would Chie have been more receptive to his proposal. In this context, following “form” thus means following a certain tradition or custom.
- Choices A, C, and D are incorrect because in this context “form” does not mean the way something looks (appearance), the way it is built (structure), or its essence (nature).
- QUESTION 9
- Choice C is the best answer. Akira states that his unexpected meeting with Chie occurred only because of a “matter of urgency,” which he explains as “an opportunity to go to America, as dentist for Seattle’s Japanese community” (lines 41-42). Akira decides to directly speak to
-
- Choice A is incorrect because there is no evidence in the passage that Akira is worried his parents will not approve of Naomi. Choice B is
-
- Choice D is incorrect; while Akira may know that Chie is unaware of his feelings for Naomi, this is not what he is referring to when he mentions “a matter of urgency.”
- QUESTION 10
- Choice B is the best answer.
- of urgency” is that he has “an opportunity to go to America, as dentist for Seattle’s Japanese community.” Akira needs Chie’s answer to his marriage proposal so he can decide whether to accept the job in Seattle.
- Choices A, C, and D do not provide the best evidence for the answer to
- Choices A, C, and D do not provide the best evidence for the answer to
-
- apologizes for interrupting Chie’s quiet evening. Choice C is incorrect because lines 58-59 address the seriousness of Akira’s request, not its
-
- proposal has “startled” Chie and does not explain why his request is time-sensitive.
- QUESTION 11
- Choice A is the best answer. Lines 1-9 include examples of how many people shop (“millions of shoppers”), how much money they spend
- and the many occasions that lead to shopping for gifts (“including weddings, birthdays, anniversaries, graduations, and baby showers.”). Combined, these examples show how frequently people in the US shop for gifts.
- Choice B is incorrect because even though the authors mention that
-
- is never discussed as an increase (or a decrease). Choice C is incorrect because lines 1-9 provide a context for the amount of shopping that occurs in the US, but the anxiety (or “dread”) it might cause is not introduced until later in the passage. Choice D is incorrect because
-
- lead to gift-giving.
- QUESTION 12
- Choice B is the best answer.
- of gift-giving can engender ambivalent feelings in gift-givers.” In the subsequent sentences, those “ambivalent” feelings are further
-
- Choices A, C, and D are incorrect because in this context, “ambivalent” does not mean feelings that are unrealistic, apprehensive, or supportive.
- QUESTION 13
- Choice D is the best answer.
- a powerful means to build stronger bonds with one’s closest peers.”
- Choice A is incorrect because even though the authors state that some
-
- is no evidence in the passage that people view shopping as a form of self-expression. Choice B is incorrect because the passage implies that shopping is an expensive habit. Choice C is incorrect because the passage states that most people have purchased and received gifts, but it never implies that people are to reciprocate the gift-giving process.
-
-
- Choice A is the best answer.
- people value gift-giving because it may strengthen their relationships with others: “Many relish the opportunity to buy presents because
-
- closest peers.”
- Choices B, C, and D do not provide the best evidence for the answer
-
- discuss how people often buy gifts that the recipients would not
-
- givers often fail to consider the recipients’ preferences. Choice D is incorrect because lines 44-47 suggest that the cost of a gift may not correlate to a recipient’s appreciation of it.
- QUESTION 15
- Choice A is the best answer. The “deadweight loss” mentioned in the
-
- a gift-giver would pay for something and what a gift-recipient would
-
- psychologists, whose research “has found that people often struggle to take account of others’ perspectives — their insights are subject to egocentrism, social projection, and multiple attribution errors”
-
-
- that social psychologists would expect a disconnect between gift-givers and gift-recipients, not that they would question it, be disturbed
-
- QUESTION 16
- Choice C is the best answer. Lines 41-44 suggest that gift-givers assume a correlation between the cost of a gift and how well-received it will be: “. . . gift-givers equate how much they spend with how much recipients will appreciate the gift (the more expensive the gift, the stronger a gift-recipient’s feelings of appreciation).” However, the authors suggest this assumption may be incorrect or “unfounded” (line 47), as gift-recipients “may not construe smaller and larger gifts as representing smaller and
-
- Choices A, B, and D are all incorrect because the passage neither states nor implies that the gift-givers’ assumption is insincere, unreasonable, or substantiated.
- QUESTION 17
- Choice C is the best answer.
- made by gift-givers in lines 41-44 may be incorrect. The gift-givers assume that recipients will have a greater appreciation for costly gifts
- made by gift-givers in lines 41-44 may be incorrect. The gift-givers assume that recipients will have a greater appreciation for costly gifts
- than for less costly gifts, but the authors suggest this relationship may be incorrect, as gift-recipients “may not construe smaller and larger gifts as representing smaller and larger signals of thoughtfulness and
-
-
-
- than addressing the validity of these assumptions. Choice B is
-
- others.
- QUESTION 18
- Choice D is the best answer.
- believe that bigger (i.e., more expensive) gifts convey stronger signals of thoughtfulness and consideration.” In this context, saying that more expensive gifts “convey” stronger signals means the gifts send, or communicate, stronger signals to the recipients.
- Choices A, B, and C are incorrect because in this context, to “convey” something does not mean to transport it (physically move something), counteract it (act in opposition to something), or exchange it (trade one thing for another).
- QUESTION 19
- Choice A is the best answer. The paragraph examines how gift-givers believe expensive gifts are more thoughtful than less expensive gifts and will be more valued by recipients. The work of Camerer and
-
- attempt to signal their positive attitudes toward the intended recipient and their willingness to invest resources in a future relationship”
-
- Choices B, C, and D are incorrect because the theory articulated by Camerer and others is used to explain an idea put forward by the authors (“givers believe that bigger . . . gifts convey stronger signals”), not to introduce an argument, question a motive, or support a conclusion.
- QUESTION 20
- Choice B is the best answer. The graph clearly shows that gift-givers believe that a “more valuable” gift will be more appreciated than a “less valuable gift.” According to the graph, gift-givers believe the monetary value of a gift will determine whether that gift is well received or not.
- Choice A is incorrect because the graph does not suggest that gift-givers are aware of gift-recipients’ appreciation levels. Choices C and D are incorrect because neither the gift-givers’ desire for the gifts they purchase nor the gift-givers’ relationship with the gift-recipients is addressed in the graph.
- QUESTION 21
- Choice A is the best answer. Lines 69-75 explain that while people are often both gift-givers and gift-receivers, they struggle to apply information they learned as a gift-giver to a time when they were a gift-receiver: “Yet, despite the extensive experience that people have as both givers and receivers, they often struggle to transfer information gained from one role (e.g., as a giver) and apply it in another, complementary role (e.g., as a receiver).” The authors suggest that the disconnect between how mu
- Choices B and C are incorrect because neither the passage nor the graph addresses the idea that society has become more materialistic or that there is a growing opposition to gift-giving. Choice D is incorrect because the passage emphasizes that gift-givers and gift-recipients
-
- that the disconnect results only from a failure to understand the other’s intentions.
- QUESTION 22
- Choice B is the best answer. Lines 2-4 of the passage describe DNA as “a very long chain, the backbone of which consists of a regular alternation of sugar and phosphate groups.” The backbone of DNA, in other words, is the main structure of a chain made up of repeating units of sugar and phosphate.
- Choice A is incorrect because the passage describes DNA on the molecular level only and never mentions the spinal column of organisms. Choice C is incorrect because the passage describes the backbone of the molecule as having “a regular alternation” of sugar and phosphate, not one or the other. Choice D is incorrect because the nitrogenous bases are not the main structural unit of DNA; rather, they are attached only to the repeating units of sugar.
- QUESTION 23
- Choice D is the best answer. The authors explain that hydrogen bonds join together pairs of nitrogenous bases, and that these bases have a
-
- be a purine and the other a pyrimidine in order to bridge between the
-
- nitrogenous base, it would be inaccurate to call the process random.
- Choice A is incorrect because lines 5-6 describe how nitrogenous bases attach to sugar but not how those bases pair with one another.
-
- nitrogenous bases is.
-
-
-
- Choice D is the best answer.
- feature of our structure which is of biological interest is that it consists not of one chain, but of two.”
- Choices A and B are incorrect because lines 12-14 explicitly state that it is the two chains of DNA that are of “biological interest,” not the
-
- are wrapped around. Choice C is incorrect because, while the X-ray evidence did help Watson and Crick to discover that DNA consists of two chains, it was not claimed to be the feature of biological interest.
- QUESTION 25
- Choice C is the best answer. In lines 12-14 the authors claim that DNA molecules appear to be comprised of two chains, even though “it has often been assumed . . . there would be only one” (lines 15-17). The authors support this claim with evidence compiled from an X-ray: “the density, taken with the X-ray evidence, suggests very strongly that there are two [chains]” (lines 18-19).
- Choices A, B, and D are incorrect because the authors mention density and X-ray evidence to support a claim, not to establish that DNA carries genetic information, present a hypothesis about the
-
- density and chemical formula of DNA.
- QUESTION 26
- Choice B is the best answer. The authors explain that “only certain pairs
-
- These pairs must contain “a purine and the other a pyrimidine in order to bridge between the two chains” (lines 27-29), which implies that any
-
- Therefore, a pair of purines would be larger than the required purine/
-
- Choice A is incorrect because this section is not discussing the distance between a sugar and phosphate group. Choice C is incorrect because the passage never makes clear the size of the pyrimidines or purines in relation to each other, only in relation to the space needed to bond the chains of the DNA molecule. Choice D is incorrect because the lines do not make an implication about the size of a pair of pyrimidines in relation to the size of a pair consisting of a purine and a pyrimidine.
- QUESTION 27
- Choice D is the best answer. The authors explain how the DNA
-
- the authors can use the order of bases on one chain to determine the order of bases on the other chain: “If the actual order of the bases on one of the pair of chains were given, one could write down the exact
-
- Thus one chain is, as it were, the complement of the other, and it is this feature which suggests how the deoxyribonucleic acid molecule might duplicate itself” (lines 45-51). The authors use the words
-
- base pairings along a DNA chain is understood and predictable, and may explain how DNA “duplicate[s] itself” (line 51).
- Choice A is incorrect because the passage does not suggest that most nucleotide sequences are known. Choice B is incorrect because these lines are not discussing the random nature of the base sequence along one chain of DNA. Choice C is incorrect because the authors are describing the bases attached only to the sugar, not to the sugar-phosphate backbone.
- QUESTION 28
- Choice C is the best answer. Lines 6-7 state that “Two of the possible bases — adenine and guanine — are purines,” and on the table the
-
- Choices A, B, and D are incorrect because they do not state the percentages of both purines, adenine and guanine, in yeast DNA.
- QUESTION 29
- Choice A is the best answer. The authors state: “We believe that the bases will be present almost entirely in their most probable forms. If this is true, the conditions for forming hydrogen bonds are more restrictive, and the only pairs of bases possible are: adenine with
-
- that the pairs adenine/thymine and guanine/cytosine have notably similar percentages in DNA for all organisms listed.
- Choice B is incorrect. Although the choice of “Yes” is correct, the explanation for that choice misrepresents the data in the table. Choices C and D are incorrect because the table does support the authors’ proposed pairing of nitrogenous bases in DNA molecules.
- QUESTION 30
- Choice A is the best answer because it gives the percentage of
-
- authors’ proposal that possible pairings of nitrogenous bases are
-
- Choices B, C, and D do not provide the best evidence for the answer to the previous question. Choice B (cytosine and thymine), Choice C (cytosine and adenine), and Choice D (guanine and adenine) are incorrect because they show pairings of nitrogenous bases that do not compose a similar percentage of the bases in sea urchin DNA.
- QUESTION 31
- QUESTION 31
- Choice D is the best answer. The table clearly shows that the
-
- Choices A and B are incorrect because the table shows that the
-
- pairs with thymine but does not mention the variability of the base composition of DNA.
- QUESTION 32
- Choice B is the best answer. In this passage, Woolf asks women a series of questions. Woolf wants women to consider joining “the procession of educated men” (lines 56-57) by becoming members of the workforce. Woolf stresses that this issue is urgent, as women “have very little time in which to answer [these questions]” (lines 48-49).
- Choice A is incorrect because Woolf argues against the tradition of
-
- Choice C is incorrect because Woolf is not highlighting the severity of social divisions as much as she is explaining how those divisions might be reduced (with women joining the workforce). Choice D is incorrect because Woolf does not question the feasibility of changing the workforce dynamic.
- QUESTION 33
- Choice A is the best answer. Throughout the passage, Woolf advocates for more women to engage with existing institutions by joining the workforce: “We too can leave the house, can mount those
-
- they are at a “moment of transition” (line 51) where they must consider their future role in the workforce.
- Choice B is incorrect because even though Woolf mentions women’s traditional roles (lines 68-69: “while they stirred the pot, while they rocked the cradle”), she does not suggest that women will have to give up these traditional roles to gain positions of influence. Choice C is incorrect because though Woolf wonders how “the procession of the sons of educated men” impacts women’s roles, she does not argue that this male-dominated society has had grave and continuing effects. Choice D is incorrect because wh
-
-
- Choice C is the best answer. Woolf uses the word “we” to refer to herself and educated women in English society, the “daughters of educated men” (line 64). Woolf wants these women to consider participating in a changing workforce: “For there, trapesing along at the tail end of the procession [to and from work], we go ourselves”
-
- establishes a sense of solidarity among educated women.
-
- whether people in a group are friendly to one another; she is concerned with generating solidarity among women. Choice B is incorrect because though Woolf admits women have predominantly “done their thinking” within traditional female roles (lines 64-69), she does not use “we” to advocate for more candor among women. Choice D is incorrect because Woolf does not use “we” to emphasize a need for people in a group to respect one other; rather, she wants to establish a sense of solidarity among women.
- QUESTION 35
- Choice B is the best answer. Woolf argues that the “bridge over the River Thames, [has] an admirable vantage ground for us to make a
-
- [their] eyes upon the procession — the procession of the sons of educated men” (lines 9-11) walking to work.
- Choice A is incorrect because while Woolf states the bridge “is a place to stand on by the hour dreaming,” she states that she is using the bridge “to consider the facts” (lines 6-9). Woolf is not using the bridge for fanciful
-
- bridge to historic episodes. Choice D is incorrect because Woolf does not suggest that the bridge is a symbol of a male-dominated past, but rather that it serves as a good place to watch men proceed to work.
- QUESTION 36
- Choice D is the best answer. Woolf writes that the men who conduct
-
- preaching, teaching, administering justice, practising medicine, transacting business, making money”) are the same men who go to
-
- joining this procession, an act that suggests the workforce has become less exclusionary: “For there, trapesing along at the tail end of the
-
- Choice A is incorrect because the procession is described as “a solemn sight always” (lines 17-18), which indicates that it has always been influential. Choice B is incorrect because the passage
- Choice A is incorrect because the procession is described as “a solemn sight always” (lines 17-18), which indicates that it has always been influential. Choice B is incorrect because the passage
- does not indicate that this procession has become a celebrated feature of English life. Choice C is incorrect because the passage states only that the procession is made up of “the sons of educated
-
-
- QUESTION 37
- Choice C is the best answer,
- has become less exclusionary. In these lines Woolf describes how women are joining the male-dominated procession that travels to and from the work place: “For there, trapesing along at the tail end of the procession, we go ourselves.”
- Choices A, B, and D are incorrect because they do not provide the best evidence for the answer to the previous question. Choice A is incorrect because lines 12-17 describe the positions predominantly held by men. Choice B is incorrect because lines 17-19 use a metaphor to describe how the procession physically looks.
-
- jobs for women.
- QUESTION 38
- Choice C is the best answer. Woolf characterizes the questions she
-
- urgent (“we have very little time in which to answer them,” lines 48-49).
-
- Choice A is incorrect because Woolf characterizes the questions as urgent and important, not as something that would cause controversy or fear. Choice B is incorrect because though Woolf considers the questions to be weighty (or “important”), she implies that they can be answered. Choice D is incorrect because Woolf does not imply that the questions are mysterious.
- QUESTION 39
- Choice B is the best answer. The answer to the previous question
-
- as momentous and pressing. In lines 48-49, Woolf describes these questions as “important,” or momentous, and states that women “have very little time in which to answer them,” which shows their urgency.
- Choices A, C, and D do not provide the best evidence for the answer to the previous question. Choices A and D are incorrect because lines 46-47 and line 62 suggest that women need to think about these
-
- because line 57 characterizes only the need for urgency and does not
-
-
-
- Choice C is the best answer. Woolf writes that women “have thought” while performing traditional roles such as cooking and caring for children (lines 67-69). Woolf argues that this “thought” has shifted women’s roles in society and earned them a “brand-new
-
- “sixpence” mentioned in these lines is not a literal coin. Woolf is using the “sixpence” as a metaphor, as she is suggesting women take advantage of the opportunity to join the male-dominated workforce.
- Choices A, B, and D are incorrect because in this context, “sixpence” does not refer to tolerance, knowledge, or perspective.
-
-
- Choice B is the best answer. In lines 72-76, Woolf repeats the phrase “let us think” to emphasize how important it is for women to critically reflect on their role in society. Woolf states this reflection can occur at any time: “Let us think in offices; in omnibuses; while we are standing in the crowd watching Coronations and Lord Mayor’s Shows; let us think . . . in the gallery of the House of Commons; in the Law Courts; let us think at baptisms and marriages and funerals.”
- Choices A, C, and D are incorrect because in lines 72-76 Woolf is not emphasizing the novelty of the challenge faced by women, the complexity of social and political issues, or the enjoyable aspect of women’s career possibilities.
-
-
- Choice B is the best answer.
- “Deep Space Industries of Virginia,” and “Golden Spike of Colorado” to support his earlier assertion that there are many interested groups “working to make space mining a reality” (line 8).
- Choices A, C, and D are incorrect because the author of Passage 1 does
-
- approaches to space mining.
- approaches to space mining.
-
- Choice A is the best answer. The author of Passage 1 explicitly states
-
- earth elements: “within a few decades, [space mining] may be meeting earthly demands for precious metals, such as platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum” (lines 18-22).
- Choice B is incorrect because Passage 1 does not suggest that precious metals extracted from space may make metals more valuable on Earth. Choice C and Choice D are incorrect because Passage 1 never mentions how space mining could create unanticipated technological innovations or change scientists’ understanding of space resources.
- Choice B is incorrect because Passage 1 does not suggest that precious metals extracted from space may make metals more valuable on Earth. Choice C and Choice D are incorrect because Passage 1 never mentions how space mining could create unanticipated technological innovations or change scientists’ understanding of space resources.
-
-
-
- Choice A is the best answer. Lines 18-22 suggest that space mining may help meet “earthly demands for precious metals . . . and the rare earth elements vital for personal electronics.” In this statement, the author is stating materials (“metals,” “earth elements”) that may be gathered as a result of space mining, and that these materials may be important to Earth’s economy.
- Choices B, C, and D do not provide the best evidence for the answer to the previous question. Choice B is incorrect because lines 24-28 focus
-
- value of water found in space. Choice D is incorrect because lines 41-44
-
- lunar soil and asteroids but do not address how these resources are important to Earth’s economy.
-
-
-
- Choice D is the best answer. The author suggests in lines 19-22 that space mining may meet “earthly demands for precious metals, such as platinum and gold, and the rare earth elements vital for personal electronics.” In this sentence, “earthly demands” suggests that people want, or desire, these precious metals and rare earth elements.
- Choices A, B, and C are incorrect because in this context “demands”
-
-
- Choice C is the best answer.
- mined in space may be very valuable: “water mined from other worlds
-
- assertion by suggesting how mined space water could be used “for
-
- Choice A is incorrect because the comparison in the previous paragraph (the relative value of gold and water to someone in the
-
- because the question asked in the previous paragraph is also answered
-
- are made in the previous paragraph; rather, an assertion is made and a question is posed.
-
-
- Choice B is the best answer. The author of Passage 2 recognizes
-
- space mining should be carefully considered before it is implemented:
-
- here on Earth and in space — merit careful consideration” (lines 57-59).
- Choice A is incorrect because the author of Passage 2 concedes that “space mining seems to sidestep most environmental concerns” (lines 55-56) but does not imply that space mining will recklessly harm the environment, either on Earth or in space. Choice C is incorrect because the author of Passage 2 does not address any key resources that may be disappearing on Earth. Choice D is incorrect because the author of Passage 2 admits that “resources that are valuable in
-
- (lines 74-76) but does not mention any disagreement about the commercial viabilities of space mining discoveries.
-
-
- Choice A is the best answer.
- environmental arguments against space mining: “[space] is not ours to despoil” and we should not “[glut] ourselves on space’s riches.” The author then suggests that these environmental arguments will be hard to “hold,” or maintain, when faced with the possible monetary rewards of space mining: “History suggests that those will be hard lines to hold . . .” (line 68).
- Choices B, C, and D are incorrect because in this context, “hold” does not mean grip, restrain, or withstand.
-
-
- Choice D is the best answer. The author of Passage 1 is excited about the possibilities of space mining and how it can yield valuable
-
- also states that space mining should be thoughtfully considered before being implemented. Therefore, the author of Passage 2 expresses some concerns about a concept discussed in Passage 1.
- Choice A is incorrect because the author of Passage 2 does not refute the central claim of Passage 1; both authors agree there are possible
-
- Passage 1 does not describe space mining in more general terms than does the author of Passage 2. Choice C is incorrect because the author of Passage 2 is not suggesting that the space mining proposals stated in Passage 1 are impractical.
- QUESTION 50
- QUESTION 50
- Choice B is the best answer. In lines 18-28, the author of Passage 1
-
- without regulation: “But miners have much to gain from a broad
-
- claims will be disputed, investments risky, and the gains made
-
-
- regulation procedures.
- QUESTION 51
- Choice D is the best answer. In lines 85-87, the author of Passage 2
-
- regulations because “claims will be disputed, investments risky, and the gains made insecure.”
- Choices A, B, and C are incorrect because they do not provide the best evidence for the answer to the previous question. Choice A is incorrect
-
- space mining. Choice B is incorrect because lines 74-76 focus on how
-
- simply describe one person’s objections to the regulation of the space mining industry.
- QUESTION 52
- Choice A is the best answer because both Passage 1 and Passage 2
-
- from those most valued on our planet. Passage 2 says this explicitly in lines 74-76: “The resources that are valuable in orbit and beyond may
-
- suggests that water mined from space may be more valuable than
-
- Choice B is incorrect because neither passage discusses, either implicitly or explicitly, the need for space mining to be inexpensive.
-
- identify precious metals or rare earth elements but instead focuses on theoretical problems with space mining. Choice D is incorrect because diminishing resources on Earth is not discussed in Passage 2.
-
-
- QUESTION 1
- Choice D is the best answer because “outweigh” is the only choice
-
- between “advantages” and “drawbacks.”
- Choices A, B, and C are incorrect because each implies a competitive relationship that is inappropriate in this context.
- QUESTION 2
- QUESTION 2
- Choice B is the best answer
- farmers can undertake to address the problem of acid whey disposal, thus supporting the claim made in the previous sentence (“To address the problem of disposal, farmers have found a for acid whey”).
-
- of how farmers could make use of acid whey.
- QUESTION 3
- QUESTION 3
- Choice A is the best answer because it results in a sentence that is grammatically correct and coherent. In choice A, “waterways,” the correct plural form of “waterway,” conveys the idea that acid whey could impact multiple bodies of water. Additionally, the compound verb “can pollute” suggests that acid whey presents an ongoing, potential problem.
- Choices B and D are incorrect because both use the possessive form of “waterway.” Choice C is incorrect because it creates an unnecessary shift in verb tense. The present tense verb “can pollute” should be used instead, as it is consistent with the other verbs in the paragraph.
-
-
- Choice C is the best answer because it utilizes proper punctuation for items listed in a series. In this case those items are nouns: “Yogurt
-
- Choices A and B are incorrect because both fail to recognize that the items are a part of a series. Since a comma is used after “manufacturers,” a semicolon or colon should not be used after “scientists.” Choice D is incorrect because the comma after “and” is unnecessary and deviates from grammatical conventions for presenting items in a series.
- QUESTION 5
- QUESTION 5
- Choice C is the best answer because sentence 5 logically links sentence 2, which explains why Greek yogurt production yields large
-
- dispose of acid whey properly.
- dispose of acid whey properly.
- Choices A, B, and D are incorrect because each would result in an illogical progression of sentences for this paragraph. If sentence 5 were
-
- after the discussion of “the problem of disposal.” If sentence 5 were
-
- QUESTION 6
- Choice D is the best answer because the paragraph includes several
-
- and satisfying hunger, to support the sentence’s claim that the
-
- the passage’s earlier claim that “the advantages of Greek yogurt outweigh the potential drawbacks of its production.”
- Choices A, B, and C are incorrect because they inaccurately describe the sentence in question.
- QUESTION 7
- Choice B is the best answer because it provides a grammatically standard preposition that connects the verb “serves” and noun “digestive aid” and accurately depicts their relationship.
-
- grammatically incorrect verb construction: “serves to be.” Choices C and D are incorrect because both present options that deviate from standard English usage.
- QUESTION 8
- Choice C is the best answer because it presents a verb tense that is consistent in the context of the sentence. The choice is also free of the redundant “it.”
- Choice A is incorrect because the subject “it” creates a redundancy. Choices B and D are incorrect because they present verb tenses that are inconsistent in the context of the sentence.
- QUESTION 9
- Choice A is the best answer because it properly introduces an
-
- “Also” is the logical and coherent choice to communicate an addition.
- Choices B, C, and D are incorrect because none of the transitions they
-
- choice.
- QUESTION 10
- Choice A is the best answer because “satiated” is the only choice that
-
- longer period of time.
- Choices B, C, and D are incorrect because each is improper usage in
-
- but a person who has eaten until he or she is no longer hungry cannot
-
- QUESTION 11
- Choice B is the best answer because it provides a syntactically coherent and grammatically correct sentence.
- Choices A and C are incorrect because the adverbial conjunctions “therefore” and “so,” respectively, are unnecessary following “Because.” Choice D is incorrect because it results in a grammatically incomplete sentence (the part of the sentence before the colon must be an independent clause).
- QUESTION 12
- Choice B is the best answer because the graph clearly indicates that, on March 5, average low temperatures are at their lowest point: 12 degrees Fahrenheit.
- Choice A is incorrect because the phrase “as low as” suggests that
-
- chart shows that in January, February, and March, the temperature frequently falls below that point. Choices C and D are incorrect because the information each provides is inconsistent with the information on the chart.
- QUESTION 13
- Choice A is the best answer because it concisely combines the two sentences while maintaining the original meaning.
- Choices B, C, and D are incorrect because each is unnecessarily wordy, thus undermining one purpose of combining two sentences: to make the phrasing more concise.
-
-
- Choice B is the best answer because it provides a conjunctive adverb that accurately represents the relationship between the two sentences. “However” signals an exception to a case stated in the preceding sentence.
- Choices A, C, and D are incorrect because each provides a transition that does not accurately represent the relationship between the two sentences, and as a result each compromises the logical coherence of these sentences.
- QUESTION 15
- Choice C is the best answer
- nonrestrictive modifying clause “an associate professor of geology at
-
-
- Choices A, B, and D are incorrect because each provides punctuation that does not adequately separate the nonrestrictive modifying clause about Jason Box from the main clause.
- QUESTION 16
- Choice C is the best answer because the colon signals that the other factor that contributed to the early thaw is about to be provided.
- Choice A is incorrect because it results in a sentence that deviates from grammatical standards: a semicolon should be used to separate two independent clauses, but in choice A the second clause only has a subject, not a verb. Choice B is incorrect because it is unnecessarily wordy. Choice D is incorrect because “being” is unnecessary and creates an incoherent clause.
- QUESTION 17
- Choice C is the best answer because it provides the correct preposition (“of”) and relative pronoun (“which”) that together create a dependent clause following the comma.
- Choices A, B, and D are incorrect because each results in a comma splice. Two independent clauses cannot be joined with only a comma.
- QUESTION 18
- Choice A is the best answer because the verb tense is consistent with
-
- and “drifted.”
- Choices B, C, and D are incorrect because each utilizes a verb tense that is not consistent with the preceding past tense verbs in the sentence.
- QUESTION 19
- Choice D is the best answer because “their” is the possessive form of a plural noun. In this case, the noun is plural: “snow and ice.”
- Choices A and B are incorrect because the possessive pronoun must refer to a plural noun, “snow and ice,” rather than a singular noun. Choice C is incorrect because “there” would result in an incoherent sentence.
- QUESTION 20
- Choice D is the best answer. The preceding sentences in the paragraph have established that a darker surface of soot-covered snow leads to more melting because this darker surface absorbs heat, whereas a
-
- that the preceding sentences already imply.
- Choices A, B, and C are incorrect because the information each provides fails to support the previous claim that the “result” of the soot “is a self-reinforcing cycle.”
- QUESTION 21
- Choice B is the best answer because it is free of redundancies.
- Choices A, C, and D are incorrect because each of the three presents a redundancy: Choice A uses “repeat” and “again”; Choice C uses
-
- “possibly.”
- Choice D is the best answer because sentence 5 describes the information Box seeks: “to determine just how much the soot is contributing to the melting of the ice sheet.” Unless sentence 4 comes after sentence 5, readers will not know what the phrase “this crucial information” in sentence 4 refers to.
- Choices A, B, and C are incorrect because each results in an illogical sentence progression. None of the sentences that would precede sentence 4 provides details that could be referred to as “this crucial information.”
- QUESTION 23
- Choice D is the best answer because it is free of redundancies and
-
- Choices A, B, and C are incorrect because all three contain a
-
- choice A’s “soon” and choice B and C’s “promptly” all result in redundancies. Choices A and B are also incorrect because each uses an incorrect form of the verb.
-
-
- Choice D is the best answer because it is the only choice that provides a grammatically standard and coherent sentence. The participial phrase “Having become frustrated. . .” functions as an adjective modifying “I,” the writer.
- Choices A, B, and C are incorrect because each results in a dangling
-
- not refer to choice A’s “no colleagues,” choice B’s “colleagues,” or choice C’s “ideas.” As such, all three choices yield incoherent and grammatically incorrect sentences.
- QUESTION 25
- Choice B is the best answer because it provides the correct preposition in this context, “about.”
- Choices A, C, and D are incorrect because each provides a preposition
- Choices A, C, and D are incorrect because each provides a preposition
-
- coworking spaces but not an article “into,” “upon,” or “for” coworking spaces.
- QUESTION 26
- Choice A is the best answer because it provides the correct punctuation for the dependent clause that begins with the phrase “such as.”
- Choices B, C, and D are incorrect because each presents punctuation that deviates from the standard way of punctuating the phrase “such as.” When “such as” is a part of a nonrestrictive clause, as it is here, only one comma is needed to separate it from the main independent clause.
- QUESTION 27
- Choice B is the best answer because it provides a transitional phrase, “In addition to equipment,” that accurately represents the relationship between the two sentences connected by the transitional phrase. Together, the sentences describe the key features of coworking spaces,
-
- Choices A, C, and D are incorrect because each provides a transition that does not accurately represent the relationship between the two sentences.
- QUESTION 28
- Choice C is the best answer because the sentence is a distraction from the paragraph’s focus. Nothing in the paragraph suggests that the cost of setting up a coworking business is relevant here.
- Choices A and D are incorrect because neither accurately represents the information in the paragraph. Choice B is incorrect because it does not accurately represent the information in the next paragraph.
- QUESTION 29
- Choice B is the best answer because it logically follows the writer’s preceding statement about creativity and accurately represents the information in the graph.
- Choices A, C, and D are incorrect because they present inaccurate and unsupported interpretations of the information in the graph. In addition, none of these choices provides directly relevant support for the main topic of the paragraph.
- QUESTION 30
- Choice D is the best answer because it provides a relative pronoun and verb that create a standard and coherent sentence. The relative pronoun “who” refers to the subject “the people,” and the plural verb “use” corresponds grammatically with the plural noun “people.”
- Choices A and B are incorrect because “whom” is the relative pronoun used to represent an object. The noun “people” is a subject performing an action (using the coworking space). Choices B and C are also incorrect because they display a form of the verb “to use” that does not correspond to the plural noun “people.”
- QUESTION 31
- Choice C is the best answer
- necessary and logical transition between sentence 2, which introduces
-
- happened at the facility “Throughout the morning.”
- Choices A, B, and D are incorrect because each would result in an illogical progression of sentences.
- QUESTION 32
- Choice A is the best answer because the punctuation it provides results in a grammatically standard and coherent sentence. When an independent clause is followed by a list, a colon is used to link the two.
- Choice B is incorrect because the punctuation creates a fragment (a semicolon should be used to link two independent clauses). Choice C is incorrect because its use of the comma creates a series in which “several of my coworking colleagues” are distinguished from the “website developer” and others, although the logic of the sentence would suggest that they are the same. Choice D is incorrect because it lacks the punctuation necessary to link the independent clause and the list.
- QUESTION 33
- Choice A is the best answer because it provides a phrase that is consistent with standard English usage and also maintains the tone and style of the passage.
- Choice B is incorrect because “give some wisdom” deviates from standard English usage and presents a somewhat colloquial phrase in a text that is generally free of colloquialisms. Choices C and D are incorrect because both are inconsistent with the tone of the passage as well as its purpose. The focus of the paragraph is on sharing, not on proclaiming opinions.
-
-
- Choice A is the best answer
-
- does not suit the purpose of the sentence.
- QUESTION 35
- QUESTION 35
- Choice A is the best answer
- philosophy. There is no need to include the participle “speaking” in
-
- Choices B, C, and D are incorrect because they provide options that are unnecessarily wordy.
- QUESTION 36
- Choice B is the best answer because it provides a verb that creates a grammatically complete, standard, and coherent sentence.
- Choices A, C, and D are incorrect because each results in a grammatically incomplete and incoherent sentence.
- QUESTION 37
- Choice D is the best answer
- information in the following sentences, which state that (according
-
- independent philosophy departments were eliminated” from colleges. These details are most logically linked to the claim that “colleges have not always supported the study of philosophy.”
-
- sets up the information that follows, which is about colleges’ failure to support the study of philosophy.
- QUESTION 38
- Choice C is the best answer because it provides a transition that logically connects the information in the previous sentence to the information in this one. Both sentences provide evidence of colleges’ lack of support of philosophy programs, so the adverb “Moreover,” which means “In addition,” accurately captures the relationship between the two sentences.
- Choices A, B, and D are incorrect because each presents a transition that does not accurately depict or support the relationship between
-
- (“Therefore,” “Thus”), and the sentences do not provide a contrast (“However”).
- QUESTION 39
- Choice A is the best answer because it succinctly expresses the idea that “students who major in philosophy often do better . . . as measured by standardized test scores.”
- Choices B and D are incorrect because they introduce a redundancy
-
- “results,” so it is confusing to refer to “these results” and indicate that they “can be” or “are measured by standardized test scores.” The best way to express the idea is simply to say that some students “often do better” than some other students “in both verbal reasoning and analytical writing as measured by standardized test scores.” Choice C is incorrect because there is no indication that multiple criteria are used to evaluate students’ “verbal reasoning and analytical writing”:
-
-
-
- Choice B is the best answer because it provides subject-verb agreement and thus creates a grammatically correct and coherent sentence.
- Choice A is incorrect because the verb “has scored” does not correspond with the plural subject “students.” Similarly, Choice C is incorrect because the verb “scores” would correspond with a singular subject, but not the plural subject present in this sentence. Choice D is incorrect because it results in a grammatically incomplete and incoherent sentence.
-
-
- Choice B is the best answer because it provides a coherent and grammatically standard sentence.
- Choices A and D are incorrect because both present “students” in the possessive form, whereas the sentence establishes “students” as the subject (“many students . . . have”). Choice C is incorrect because the verb form it proposes results in an incomplete and incoherent sentence.
-
- Choice C is the best answer because it accurately depicts how
-
- that Plato used the dialogue form has little relevance to the preceding claim about the usefulness of a philosophy background.
- Choices A and B are incorrect because the proposed sentence interrupts the progression of reasoning in the paragraph. Choice D is incorrect because, as with Choice A, Plato’s works have nothing to do with “the employability of philosophy majors.”
-
-
- Choice D is the best answer because it creates a complete and coherent sentence.
- Choices A, B, and C are incorrect because each inserts an unnecessary relative pronoun or conjunction, resulting in a sentence without a main verb.
-
-
- Choice D is the best answer because it provides a possessive pronoun that is consistent with the sentence’s plural subject “students,” thus creating a grammatically sound sentence.
- Choices A, B, and C are incorrect because each proposes a possessive pronoun that is inconsistent with the plural noun “students,” the established subject of the sentence.
-
-
-
- QUESTION 1
- Choice D is correct. Since kk in the
- equation = k, which gives
-
- _
-
- =
- Choices A, B, and C are incorrect because the result of subtracting 1
- k
- QUESTION 2
- QUESTION 2
- Choice A is correct.i i), add the real parts i + 9i = 12ii.
- Choices B, C, and D are incorrect and likely result from common errors that arise when adding complex numbers. For example, choice B is ii, and choice C is the result of adding 7 and 8.
- QUESTION 3
- QUESTION 3
- QUESTION 3
- Choice C is correct. The total number of text messages sent by Armand can be found by multiplying his rate of texting, in number of text messages sent per hour, by the total number of hours he spent sending them; that is texts/hour × 5 hours = 5 texts. Similarly, the total number of text messages sent by Tyrone is his hourly rate of texting multiplied by the 4 hours he spent texting: texts/hour × 4 hours = 4 texts. The total number of text messages sent by Armand and Tyrone is the sum of the total number
- Choice A is incorrect and arises from adding the coefficients and multiplying the variables of 5 and 4. Choice B is incorrect and is the result of multiplying 5 and 4. The total number of messages sent by Armand and Tyrone should be the sum of 5 and 4, not the product of these terms. Choice D is incorrect because it multiplies Armand’s number of hours spent texting by Tyrone’s hourly rate of
- Choice A is incorrect and arises from adding the coefficients and multiplying the variables of 5 and 4. Choice B is incorrect and is the result of multiplying 5 and 4. The total number of messages sent by Armand and Tyrone should be the sum of 5 and 4, not the product of these terms. Choice D is incorrect because it multiplies Armand’s number of hours spent texting by Tyrone’s hourly rate of
- texting, and vice versa. This mix-up results in an expression that does not equal the total number of messages sent by Armand and Tyrone.
-
-
- Choice B is correct. in when
- or when
- _
- = , not when
- does indicates that the number of phones left will decrease
- QUESTION 5
- QUESTION 5
- Choice C is correct.
- exponents, can be combined to determine the answer as shown here: 2 2
- yy + 5yy
- = (y yy)) + (5)
- = 2y
- Choices A, B, and D are incorrect and are the result of common calculation errors or of incorrectly combining like and unlike terms.
- QUESTION 6
- Choice A is correct. In the equation h + 28.6, if , the age of the boy, increases by 1, then h becomes h
-
- Alternatively: The height, h, is a linear function of the age, , of
-
- Choices B, C, and D are incorrect and are likely the result of dividing
-
- 2 has no meaning in the context of this question.
- QUESTION 7
- QUESTION 7
- Choice B is correct. Since the right-hand side of the equation is _ _
- 1 +
- ( )( )
- times the expression , multiplying both
- _
- 1 +
-
- sides of the equation by the reciprocal of this expression results _
- 1 +
- ( )
- in = .
- _ _
- 1 +
- ( )( )
- Choice A is incorrect and is the result of multiplying both sides of the _ _ N
- 1 +
- ( )( )
- equation by the rational expression rather than
- _
- 1 +
-
- _
- 1 +
- P
- by the reciprocal of this expression . Choices C
- _ _
- 1 +
- ( )( ) and D are incorrect and are likely the result of errors while trying to solve for .
- QUESTION 8
- QUESTION 8
- QUESTION 8
- _ _ _1
- Choice C is correct. Since = 2, it follows that = . Multiplying both
- StyleSpan
-
- StyleSpan
- StyleSpan
- 2
- _ _1 _4
- sides of the equation by 4 gives 4 = 4 , or = 2.
- ( ) () Choice A is incorrect because if
- 2
- 4
- StyleSpan
-
- StyleSpan
- StyleSpan
- Choice B is incorrect because if = 1, then = 4. Choice D is
- 4
- StyleSpan
- StyleSpan
- StyleSpan
- StyleSpan
- incorrect because if = 4, then = 1.
- 4
- StyleSpan
- StyleSpan
- StyleSpan
- StyleSpan
- QUESTION 9
- Choice B is correct. Adding and 19 to both sides of 2y gives = 2y + 19. Then, substituting 2y + 19 for + 4y y + 19) + 4yy yyy in 2y , y)
- Choices A, C, and D are incorrect because when the given values of and y are substituted in 2y
- QUESTION 10
- Choice A is correct. Since g is an even function, g g(4) = 8.
- Alternatively: First find the value of , and then find g Since g(4) = 8, substituting 4 for and 8 for g() gives 8 = (4) + 24 = 16 + 24. Solving this last equation gives Thus g( + 24, from which it follows that g + 24; g g
- Alternatively: First find the value of , and then find g Since g(4) = 8, substituting 4 for and 8 for g() gives 8 = (4) + 24 = 16 + 24. Solving this last equation gives Thus g( + 24, from which it follows that g + 24; g g
- Choices B, C, and D are incorrect because g is a function and there can only be one value of g
- QUESTION 11
- Choice D is correct. To determine the price per pound of beef when it was equal to the price per pound of chicken, determine the value of (the number of weeks after July 1) when the two prices were equal. The prices were equal when = ; that is, when . This last equation is equivalent to
- Sect
- , and so = = 4. Then to determine , the price per
- pound of beef, substitute 4 for in , which gives
- Choice A is incorrect. It results from substituting the value 1, not 4, for in . Choice B is incorrect. It results from substituting the value 2, not 4, for in . Choice C is incorrect. It in .
- QUESTION 12
- Choice D is correct. In the -plane, all lines that pass through the origin are of the form y = , where is the slope of the line.
- _1
- Therefore, the equation of this line is y = , or = 7y. A point
- 7 with coordinates (, ) will lie on the line if and only if = 7
- y-axis.
- _
- The slope of the y _
- does not lie on the line that passes the origin and has slope . Choices B and C are incorrect because neither of the ordered pairs has
- _
- a y-coordinate that is the value of the corresponding -coordinate.
- QUESTION 13
- QUESTION 13
- Choice B is correct. To rewrite —, multiply
- 11
- ( + 2)( ( + 2)(
- by—. This results in the expression , which
- ( + 2)( ( + 2) + ( is equivalent to the expression in choice B.
- Choices A, C, and D are incorrect and could be the result of common algebraic errors that arise while manipulating a complex fraction.
-
- Choice A is correct. so that the
- 2y
- numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 2 for 8 in the numerator
- numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 2 for 8 in the numerator
- (2)
- (2)
- of gives , which can be rewritten as . Since the numerator
- 2y 2y 2y _
- and denominator of have a common base, this expression can be
- 2y rewritten as 2y = 12, so one can substitute 12
- _
- for y, given that the expression is equal to 2.
- 2y
- Choice B is incorrect. The expression can be rewritten as y , or
- 2y
- 2. If the value of 2 is 4, which can be rewritten as 28, then
- StyleSpan
- StyleSpan
- 4
- 2
- = 2
- 8
- , y = 8, not 12. Choice C is incorrect. If _
- the value of is 8, then 2 = 8y = 6, not 12.
- 2y _
- Choice D is incorrect because the value of y can be determined.
- QUESTION 15
- Choice D is correct. and in ( + 2) ( + 7) by using the given equation + = 8 and and . Since ( + 2)( + 7) = 15 + + 14, one can expand the left side of the equation to obtain + 7 + 2 + 14 = 15 + + 14. Since is the of on the right side of the equation, it must be true that = 15. Since + = 8, it follows that . Thus, = 15 can be rewritten as ) = 15, which in turn can be rewritten as gives ( = 5, or = 5 and = 5, then ( + 2)( + 2)(5 + 7) = 15 + 14. Thus, one of the possible values of = 5 and
-
- and , but not possible values for . Choice B is incorrect; if = 5 and when the expression (5 + 7) is expanded as 15 + 6 + 14. However, when is 41 and not 6 and + 2)(5 + 7) is expanded as 15 + 21 21, the value of
- QUESTION 16
- The correct answer is 2. To solve for t, factor the left side of t giving (t ttt tt = 2, and if tt tt must be 2.
- Another way to solve for t is to add 4 to both sides of t t = 4. Then, taking the square root of the left and the right side of the equation
- _
- gives t = ±4 = ± 2. Since it is given that tt must be 2.
- QUESTION 17
- The correct answer is 1600. It is given that ∠ and ∠ have the same measure. Since ∠ and ∠ are vertical angles, they have the same measure. Therefore, triangle is similar to triangle because the triangles have two pairs of congruent corresponding angles (angle-angle criterion for similarity of triangles). Since the triangles are similar, the corresponding sides are in the same
- __
- proportion; thus = CD,
-
- __ __
- for in = gives = . Therefore,
-
- Sect
- The correct answer is 7. Subtracting the left and right sides of + y + 2y ( + 2y + y y y in + y equivalent to
- QUESTION 19
- QUESTION 19
- The correct answer is or 0.8. By the complementary angle relationship for sine and cosine, sin(°). Therefore, _
- °) = may be gridded as the correct answer. Alternatively, one can construct a right triangle that has an angle of
- _
- mea sure ° such that sin(°) = sin(°) is equal to the ratio of the length of the side opposite the angle _
- measuring ° to the length of the hypotenuse, or .
- 90° – x°
- 5
- x° 90°
- Since two of the angles of the triangle are of measure °. From °), which is equal to the ratio of the length of
- the side ° to the hypotenuse, _
- is also .
- is also .
- QUESTION 20
- The correct answer is 100. Since = 52, one can substitute 52 for
- in 2 = 22 = 22 = 2 gives 2) = (2) (2) = (2), or
- _ . This gives and 52 for
- _ in the equation 2 = 2, which yields 2(52) =
- _ since 2(52)2 and 22.
-
-
-
- QUESTION 1
- Choice B is correct.
- slope represents an interval over which the target heart rate is strictly increasing as time passes. A horizontal line segment represents an interval over which there is no change in the target heart rate as time passes, and a line segment with a negative slope represents an interval over which the target heart rate is strictly decreasing as
-
- consists of a line segment with a positive slope followed by a line segment with a negative slope, with no horizontal line segment in between, indicating that the target heart rate is strictly increasing then strictly decreasing.
- Choice A is incorrect because the graph over the interval between
-
- period in which there was no change in the target heart rate. Choice C
-
- 65 minutes consists of a line segment with a negative slope followed by a line segment with a positive slope, indicating that the target heart rate is strictly decreasing then strictly increasing. Choice D is incorrect
-
- contains horizontal line segments and no segment with a negative slope.
- QUESTION 2
- QUESTION 2
- QUESTION 2
- Choice C is correct. Substituting 6 for and 24 for y in y = gives 24 = (k)(6), which gives k = 4. Hence, y = 4. Therefore, when = 5, the value of yy is correct because y is a function of , and so there is only one y-value for a given -value.
- Choices A, B, and D are incorrect. Choice A is the result of substituting 6 for y and substituting 5 for in the equation y = , when solving for kk and 5 for in the equation y = , when solving for y. Choice D results from using y = k + instead of y = .
- QUESTION 3
- QUESTION 3
- Choice D is correct. Consider the measures of ∠∠ below.
- m 1 2 4 3 s t .
- The measure of ∠∠1 because they are corresponding angles for the parallel lines and intersected by the transversal line t. Similarly, the measure of ∠ of ∠4 because they are corresponding angles for the parallel lines and t intersected by the transversal line . Since the measure of ∠1 ∠∠∠4 and ∠2 are supplementary angles, the sum of the measures of these two angles is
- ∠
- ∠1, and ∠1 is not congruent to ∠2. Choice B is incorrect because it is the measure of the complementary angle of ∠1, and ∠1 and ∠2 are not complementary angles. Choice C is incorrect because it is double the measure of ∠1, which cannot be inferred from the information given.
-
-
- Choice C is correct. The description “16 + 4 be written as the equation 16 + 4 16 + 4 = 24. Subtracting 16 from each side of 16 + 4 = 24 gives 4 = 8. Since 8 is 2 times 4, multiplying both sides of 4 = 8 by 2 gives 8 = 16. Therefore, the value of 8 is 16.
- Choice A is incorrect because it is the value of , not 8. Choices B and D are incorrect and may be the result of errors made when solving the equation 16 + 4. For example, choice D could be the result of subtracting 16 from the left side of the equation and adding 16 to the right side of the equation 16 + 4 and 8
- QUESTION 5
- QUESTION 5
- Choice D is correct. A graph with a strong negative association between and t would have the points on the graph closely aligned with a line that has a negative slope. The more closely the points on a graph are aligned with a line, the stronger the association between and t graphs, the points on graph D are most closely aligned with a line with a negative slope. Therefore, the graph in choice D has the strongest negative association between and t.
- Choice A is incorrect because the points are more scattered than the points in choice D, indicating a weaker negative association between and t. Choice B is incorrect because the points are aligned to either a curve or possibly a line with a small positive slope. Choice C is incorrect because the points are aligned to a line with a positive slope, indicating a positive association between and t.
- Choice A is incorrect because the points are more scattered than the points in choice D, indicating a weaker negative association between and t. Choice B is incorrect because the points are aligned to either a curve or possibly a line with a small positive slope. Choice C is incorrect because the points are aligned to a line with a positive slope, indicating a positive association between and t.
- QUESTION 6
- Choice D is correct.
- 2-decagram container.
-
- is the number of milligrams in 2 grams, not the number of milligrams in 2 decagrams.
- QUESTION 7
- Choice C is correct. Let represent the number of installations that each unit on the y-axis represents. Then 9, 5, 6, 4 are the number of rooftops with solar panel installations in cities A, B, C,
- it follows that 9 + 5 + 6 + 4 27.5 y-axis is “Number of installations (in thousands).”
- Choices A, B, and D are incorrect and may result from errors when setting up and calculating the units for the y-axis.
- QUESTION 8
- Choice D is correct. If the value of | | | absolute value of be negative. Thus | values for for which the value of |
-
- QUESTION 9
- Choice A is correct. t gives t. Then dividing both sides of
-
- _
- tt = .
-
- Choices B, C, and D are incorrect and could arise from errors in rewriting t is added to the left side of t and subtracted from the
- QUESTION 10
- Choice B is correct. The air temperature at which the speed of a sound
- and then solving for t in the given formula. Substituting in the equation tt. t
- _
- t =
- Choices A, C, and D are incorrect and might arise from errors made when or solving for t in the equation t or in rounding the result to the nearest integer. For example, choice C
-
- QUESTION 11
- Choice A is correct. . Therefore, if and only if .
- Choices B, C, and D are incorrect because each is a value of that is less
-
- QUESTION 12
- Choice C is correct. The average number of seeds per apple is the total number of seeds in the 12 apples divided by the number of apples, which
-
- and the height of each bar is the number of apples with the corresponding
-
- the third bar indicates that 1 apple has 6 seeds, the fourth bar indicates
-
- have 9 seeds each. Thus, the total number of seeds for the 12 apples is average number of _
- seeds per apple is
-
- Choice A is incorrect; it is the number of apples represented by the tallest bar but is not the average number of seeds for the 12 apples. Choice B is incorrect; it is the number of seeds per apple corresponding to the tallest bar, but is not the average number of seeds for the 12 apples. Choice D is incorrect; a student might choose this
-
- incorrectly rounding up to 7.
- incorrectly rounding up to 7.
- QUESTION 13
- Choice C is correct.
- _19
- to of males taking Geometry, is closest to 58.9 respondents.
- Choices A, B, and D are incorrect because the number of males taking
-
- respondents in each of these categories.
-
-
-
- Choice C is correct.
- the change in range, 8 inches, is much greater than the change in the mean or median.
- Choice A is incorrect. Let be the mean of the lengths, in inches,
- is 21
- _
- mean , which is a
- _
- change of inches. Since must be between the smallest
- and largest from which it can be seen that the change in the mean, in inches, is
- between = , and so must be less than the
- StyleSpan
- _
- StyleSpan
- StyleSpan
- _
- _
- 4
- 5
-
- change in the range, 8 inches. Choice B is incorrect because the median
-
- in the range (8). Choice D is incorrect because the changes in the mean,
-
- QUESTION 15
- Choice A is correct. The total cost C of renting a boat is the sum of the initial cost to rent the boat plus the product of the cost per hour and the number of hours, h, that the boat is rented. The C-intercept is the point on the C-axis where h, the number of hours the boat is rented, is C-intercept is the initial cost of renting the boat.
- Choice B is incorrect because the graph represents the cost of renting only one boat. Choice C is incorrect because the total number of hours of rental is represented by h-values, each of which corresponds to the C-intercept of the graph. Choice D is incorrect because the increase in cost for each additional hour is given by the slope of the line, not by the C-intercept.
- QUESTION 16
- Choice C is correct. If is the slope and is the C-intercept of the line, the relationship between h and C can be represented by C = + . The C
- (1, 8) lie on the line, the slope of the line is =
- the relationship between h and C can be represented by Ch + 5, the slope-intercept equation of the line.
- Choices A and D are incorrect because each of these equations
- C is not equal to zero when h from errors made when reading the scale on each axis as related to calculating the slope.
- QUESTION 17
- Choice B is correct. The minimum value of the function corresponds to the y-coordinate of the point on the graph that has the smallest y-coordinate on the graph. Since the smallest y-coordinate belongs to
- () is at
- -coordinate, not the y-coordinate, of a point on the graph of y = (). Choice C is incorrect; it is the minimum value of , not the value of that corresponds to the minimum of . Choice D is incorrect; it is the value of for which the value of () has its , not minimum.
- QUESTION 18
- Choice A is correct. y in the given system must result in two true inequalities. After this substitution, y + , and y > + . Hence, is positive and is negative. Therefore, > .
- Choice B is incorrect because > cannot be true if is negative and |; for example, if = 6 and equation to the system of inequalities if = 1 and
- QUESTION 19
- Choice B is correct. To determine the number of salads sold, write and solve a system of two equations. Let equal the number of salads sold and let y equal the number of drinks sold. Since a total + y the total revenue from selling salads and y
- Choice B is correct. To determine the number of salads sold, write and solve a system of two equations. Let equal the number of salads sold and let y equal the number of drinks sold. Since a total + y the total revenue from selling salads and y
- y + y + 2y = 418, and subtracting (2 + 2y) from the left-hand side and subtracting 418 from the right-hand side
- y _
- y _
- salads sold, , was =
- Choices A, C, and D are incorrect and could result from errors in writing the equations and solving the system of equations. For example, choice C
-
- QUESTION 20
- Choice D is correct. Let be the original price of the computer, in
- is the discounted price, in dollars. The sales tax is ) represents the sales tax Alma paid. The price , in dollars, that Alma paid the cashiers is the sum of the discounted price and the tax: ) which can be rewritten as ). Therefore, the original price, , of
-
- _
- the computer, in dollars, can be written as in terms of .
-
- Choices A, B, and C are incorrect. The expression in choice A
-
- tax is over the discounted price, not the original one. The expression in choice B is the result of adding the factors associated with the discount
-
- in choice C results from assigning to represent the original price of the laptop, rather than to the amount Alma paid to the cashier.
- QUESTION 21
- Choice C is correct. The probability that a person from Group Y who recalled at least 1 dream was chosen at random from the group of all people who recalled at least 1 dream is equal to the number of people in Group Y who recalled at least 1 dream divided by the total number of people in the two groups who recalled at least 1 dream. The number of people in Group Y who recalled at least 1 dream is the sum of the 11 people in Group Y who recalled 1 to 4 dreams and the 68 people in Group Y who recalled 5 or mo
- _
- more dreams: 79 + 28 + 57 = 164. Therefore, the probability is
- 164
- Choice A is incorrect; it is the probability of choosing at random a person from Group Y who recalled 5 or more dreams. Choice B is incorrect; it is the probability of choosing at random a person from Group Y who recalled at least 1 dream. Choice D is incorrect; it is
- Choice A is incorrect; it is the probability of choosing at random a person from Group Y who recalled 5 or more dreams. Choice B is incorrect; it is the probability of choosing at random a person from Group Y who recalled at least 1 dream. Choice D is incorrect; it is
- the probability of choosing at random a person from the two groups combined who recalled at least 1 dream.
- QUESTION 22
- Choice B is correct. The amounts given in the table are in thousands of dollars. Therefore, the amount in the annual budget for
-
- change in the annual budget for agriculture/natural resources from
- Sect
-
- Choices A and C are incorrect and may result from errors in setting up or calculating the average rate of change. Choice D is incorrect;
-
- QUESTION 23
- Choice B is correct.
- = . Similar estimates
- 6
-
- _
- ; for education, a ratio of slightly _
- greater than ; for highways and transportation, a ratio of slightly
- less than ; and for public safety, a ratio of slightly greater than
- 9
-
-
- further from the corresponding ratio for human resources than the corresponding ratio for education.
-
-
- Choice A is correct. The equation of a circle can be written as (h) + (yk) = where (h, k) are the coordinates of the center of the circle and is the radius of the circle. Since the coordinates
- + (y = . The radius of the circle is the distance from the center,
- _4
- endpoint of a radius, , 5 . By the distance formula, 2 _4 _25
- (
- StyleSpan
- )
- StyleSpan
- 2
- = = . Therefore, an equation of the given circle is
- + (y = .
- + (y = .
- Choices B and D are incorrect. The equations given in these choices
-
- results from using instead of in the equation for the circle.
- QUESTION 25
- Choice D is correct. h in ht + 25tt + 25t, t t + 25). Thus, the possible values of
- _25
- t are tt = t time the ball is launched from the ground, and the time t
- Choice A, B, and C are incorrect and could arise from conceptual or t + 25t for t.
- QUESTION 26
- QUESTION 26
- QUESTION 26
- Choice B is correct. Let represent the number of pears produced by
- Type B trees, or , which can be represented as pears. Since Type A trees = 144. Thus
- _144
- = Therefore, the Type B trees
- Choice A is incorrect because while 144 is reduced by approximately
-
- produced by the Type A trees. Choice D is incorrect; it results from
-
- the number of pears produced by Type A trees.
- QUESTION 27
- Choice C is correct.
- 1-meter-by-1-meter square has an area of 1 square meter. Thus, on average, the earthworm counts to a depth of 5 centimeters for each of
- _1
- the regions investigated by the students should be about of the total number of earthworms to a depth of 5 centimeters in the entire
-
-
- QUESTION 28
- Choice C is correct. To determine which quadrant does not contain any solutions to the system of inequalities, graph the inequalities. Graph the inequality y + 1 by drawing a line through the y this inequality are all points contained on and above this line. Graph
- _1
- the inequality y > y
- this inequality are all points above this dashed line.
- x y II I IVIII y x – 1 y 2x + 1> > 2 1
- The solution to the system of inequalities is the intersection of the regions above the graphs of both lines. It can be seen that the solutions only include points in quadrants I, II, and III and do not include any points in quadrant IV.
- Choices A and B are incorrect because quadrants II and III contain
-
- Choice D is incorrect because there are no solutions in quadrant IV.
- QUESTION 29
- Choice D is correct. If the polynomial () is divided by ()
- __
- can be written as = () + , where () is a polynomial and is the remainder. Since is a real number. Hence, () can be written as () = ( () + , where is a real number. It is given that = . Therefore, the remainder when () is divided by
- Choice A is incorrect because imply that
- opposite, 2, need not be a root of ().
- QUESTION 30
- Choice D is correct. Any quadratic function can be written in the form () = (h) + k, where , h, and k are constants and (h, k) is the vertex of the parabola when is graphed in the coordinate plane. This form can be reached by completing the square in the . The equation of the graph is y =
- ( = + 1 as follows: y = (
- ( = + 1 as follows: y = (
- Choices A and C are incorrect because the coordinates of the vertex do not appear as constants in these equations. Choice B is incorrect because it is not equivalent to the given equation.
- QUESTION 31
- The correct answer is any number between 4 and 6, inclusive. Since Wyatt can husk at least 12 dozen ears of corn per hour, it will take him
- _
- no more than
- hand, since Wyatt can husk at most 18 dozen ears of corn per hour, _
- it will take him at least
- = 4 hours to husk 72 dozen ears of corn. Therefore, the possible times it could take Wyatt to husk 72 dozen ears of corn are 4 hours to 6 hours, inclusive. Any number between 4 and 6, inclusive, can be gridded as the correct answer.
- QUESTION 32
- QUESTION 32
- QUESTION 32
- The correct answer is 107. Since the weight of the empty truck and
- in pounds, of the delivery truck, its driver, and .
- and then dividing both sides by 14 yields or . Since
- 14 the number of packages must be an integer, the maximum possible value for that will keep the combined weight of the truck, its driver, and the
- QUESTION 33
- QUESTION 33
- QUESTION 33
- _
- The correct answer is or .625. Based on the line graph, the number
-
- _
- of
-
- _
- . Either 5/8 or its decimal equivalent, .625, may be gridded as the correct answer.
-
-
- The correct answer is 96. Since each day has a total of 24 hours of time slots available for the station to sell, there is a total of 48 hours of time slots available to sell on Tuesday and Wednesday. Each time slot
- _
- -hour interval. Therefore,
- 48 hours
- there are = 96 time slots of
- _1
- hours/time slot to sell on Tuesday and Wednesday.
- QUESTION 35
- The correct answer is 6. The volume of a cylinder is h, where is the radius of the base of the cylinder and h is the height of the cylinder. Since the storage silo is a cylinder with volume 72 cubic yards and height 8 yards, it follows that 72 = (8), where is the radius of the base of the cylinder, in yards. Dividing both sides of the equation 72 = (8) by 8 gives = 9, and so the radius of the base of the base of the cylinder is 6 yards.
- QUESTION 36
- The correct answer is 3. The function h( __1
- denominator of is equal to zero. The expression
- ( + 4( ( + 4( 4 is a perfect square: ( + 4((( , which can be rewritten as ( . The expression ( is equal to zero if and only if for which h(
- QUESTION 37
- The correct answer is 1.02. The initial deposit earns 2 percent interest compounded annually. Thus at the end of 1 year, the new
-
- _
- is compounded annually, the value at the end of each succeeding year is the sum of the previous year’s value plus 2 percent of the previous year’s value. This is again equivalent to multiplying the
- ; and after t . Therefore, in the formula for the value for Jessica’s account after t ), the value of
- QUESTION 38
- QUESTION 38
- The correct answer is 6.11.
- into her account. The interest on her account is 2 percent compounded
- = $121.899 to the nearest tenth
- The interest on his account is 2.5 percent compounded annually, so
-
- tenth of a cent. Hence, Jessica’s initial deposit earned $21.899 and
-
- cent, Tyshaun’s initial deposit earned $6.11 more than Jessica’s initial deposit.
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