Section 3: Math Test Answers (No Calculator)

1. D 6. D 11. D 16. 502. B 7. B 12. D 17. 3.813. D 8. D 13. A 18. 44. B 9. B 14. C 19. 205. A 10. D 15. B 20. 14

Section 4: Math Test Answers (with Calculator)

1. D 11. A 21. B 31. 242. D 12. C 22. D 32. 123. C 13. A 23. D 33. 114. D 14. D 24. C 34. 815. A 15. B 25. E 35. 256. C 16. A 26. C 36. 36.27. C 17. A 27. A 37. 188. C 18. B 28. B 38. 10.99. D 19. C 29. A

10. B 20. B 30. D

Section 1: Reading Test Answers

1. B 14. A 27. A 40. C2. A 15. C 28. D 41. C3. A 16. B 29. C 42. A4. D 17. D 30. C 43. D5. C 18. D 31. A 44. D6. A 19. C 32. B 45. D7. B 20. D 33. D 46. B8. C 21. D 34. D 47. C9. C 22. B 35. C 48. D

10. A 23. C 36. B 49. D11. D 24. D 37. C 50. C12. D 25. A 38. C 51. B13. B 26. B 39. D 52. A

Section 2: Writing and Language Test Answers

1. D 12. B 23. C 34. B2. A 13. A 24. D 35. B3. B 14. D 25. A 36. A4. B 15. D 26. B 37. D5. D 16. B 27. B 38. B6. C 17. C 28. D 39. C7. A 18. A 29. D 40. A8. A 19. D 30. B 41. A9. B 20. B 31. A 42. C

10. C 21. C 32. D 43. B11. D 22. C 33. B 44. D

ANSWER KEY

5. Choice C is correct. The visit to the hospital wasawkward, but Dearing’s wife could not reduce the“stuffy discomfort.” To alleviate means to make abad situation better.

6. Choice A is correct. Bowles ridicules Smetana’sEnglish (“He has experience in . . .”) and doesn’tappear to care that he may have gotten the waiterin trouble and cost him his job. He clearly looksdown on Smetana, which is to say that he has acondescending attitude.

7. Choice B is correct. The situation is alreadysomewhat tense, since Alton is uneasy talking toSmetana about the position of valet, especially inthe presence of Bowles. The headwaiter watch-ing closely and then approaching the scene makesthe situation more tense; he may not approve ofSmetana talking to the members.

8. Choice C is correct. The passage makes clear thatAlton is moving to a smaller home, in the words ofBowles—“Just a cozy cottage for two in the coun-try?” This may be an exaggeration, since Alton isstill going to have a valet, a cook, etc., but Altonalso thinks that “He did not want a house full ofservants.” He wants to drive his own car—even,ashesays,learntofixit.Clearly,hewishestolivewith fewer luxuries than he had growing up.

9. Choice C is correct. The explanation to question 8includes a reference to this line.

10. Choice A is correct. Alton wishes to appear lessconcerned with social status than others at theclub.Thisisclearfromhisbehaviorinthefirstparagraphandfromthewaythatheatfirstjokeswith Smetana. This is also made clear from hisattitude regarding the terms used to refer to a

The Sussex Place Answers

1. Choice B is correct. The description shows thatAlton perceived that the other boy felt “resent-ment” because of his father’s status working forAlton’s father. In his memory, Alton believes thevalet’s son must have hated him as a result (conse-quence) of their difference in status.

2. Choice A is correct. Alton enjoys believing thatothers at the club thought that he was behavinginappropriately. He, in fact “relished the idea thathe was attracting attention in the hushed room,was encouraging the viewpoint that he was insuf-ficientlyappreciativeofhisstandingattheBrook-shire.” Behaving as he did (making noises, forinstance) was not the custom at the club.

3. Choice A is correct. The explanation to question 2includes a reference to this line.

4. ChoiceDiscorrect.Altonatfirstjokesinafriendly manner with Smetana about whether heshould have another drink. However, Smetana’smanner, including whispering and squatting downby the chair, clearly makes Alton uncomfortable.HeinterruptsSmetanabeforehefinishesasentenceand, at the end of the story, asks for his drink withsome annoyance.

EXPLANATORY ANSWERS

Section 1: Reading

frequently points out the contradictions, irrational-ity, and coercive tactics exhibited by advanced technological institutions.

19. Choice C is correct. See paragraph 6: “Salary andwage increases . . . lose their . . . importance . . .once . . . an ample supply of luxuries are assured.”

20. Choice D is correct. We link “technical specialists”with “such retraining only for a managing elite.”Therefore Choice D is correct. See also ReadingComprehension Strategy 5 (page 139).

21. Choice D is correct. See paragraph 5: “. . . techno-logical progress requires a continuous increase inthe skill levels of its workforce, skill levels whichfrequentlyembodyafairlyrichscientificandtech-nical training. . . . [T]hose skills will be less andless fully used.”

22. Choice B is correct. See paragraph 6: “. . . amongyoung people one can already observe a radicalweakening in the power of such incentives asmoney, status, and authority.”

Large Hadron Collider Answers23. ChoiceCiscorrect.Inthefirstparagraph,the

author states, “These purposes can seem quitespecific,eventrivial.”Inotherwords,somepeoplemight say that the reasons for the LHC are precise(specific)butnotsignificant(theyaretrivial).

24. Choice D is correct. The author states that in stringtheory, “the traditional idea of point-like particlesis replaced by one-dimensional objects known astrings.” Furthermore, string theory “depends onthe existence of more dimensions than the four weknow of.” Later in the same paragraph, the authorstates that the ATLAS detector “could provideobservationaldataconfirmingthevalidityofextradimensions,” therefore supporting a key idea instring theory.

25. Choice A is correct. It has been suggested that darkmatter consists of WIMPs, which barely affectmatter at all. The LHC could indirectly support thetheory, not through directly observing a WIMP butthrough the detection of “large amounts of energy[that] go missing.”

valet, such as “manservant.” Despite this, he is uncomfortable being too familiar with Smetana and he tells him that he would not be able to do the job of valet because he’s a waiter, he’s foreign-born, and he doesn’t know the same people that Alton knows.

11. Choice D is correct.Alton responds to Smetana’sbending down to whisper in his ear by smiling,but he withdraws a few inches. This implies thatthoughheappearstobefinewiththewaiter’sbehavior, he feels uncomfortable enough to pullback a few inches from the man’s face.

Advanced Technological Institutions Answers12. Choice D is correct. See paragraph 2: “Formerly,

technical rationality had been employed only toorganize the production of rather simple physicalobjects. . . . Now technical rationality is increas-ingly employed to organize all of the processesnecessary to the utilization of physical objects. . . .”

13. Choice B is correct. See paragraph 1: “The absenceof direct controls or of coercion should not serveto obscure from our view the . . . social controlswhich are employed (such as . . . advertising, selec-tive service channeling, and so on).”

14. Choice A is correct. It can be seen from the con-text of the sentence: “. . . there would be frequenterrors. . . .” Choice A is correct. See also ReadingComprehension Strategy 5 (page 139).

15. Choice C is correct. See paragraph 5: “. . . theworkforce must be relatively over-trained. . . .”

16. Choice B is correct. See paragraph 4: “The assem-bly line also introduced standardization in workskills and thus makes for a high degree of inter-changeability among the workforce. . . . If eachoperation taxed the workers still there would befrequent errors. . . .”

17. Choice D is correct. See paragraph 6: “. . . theworkforce within technologically advanced organi-zations is asked to work not less hard but more so.”

18. Choice D is correct. See paragraph 3: “. . . thereare very profound social antagonisms or contra-dictions. . . .” This article is one of skepticism. It

Double Passage Answers34. Choice D is correct. The author is stressing the

point that the true artist—the person with rarecreative ability and keen perception, or high intel-ligence—fails to communicate well with thoseabout him—“differs from the rest of us” (lines4–5). He is likely to be considered a “nut” by manywith whom he comes in contact. “Great wits” inthe Choice D quotation refers to the true artist. Thequotation states, in effect, that there is a thin linebetween the true artist and the “nut.” Choices A,B, and C are incorrect because they have little, ifanything, to do with the main idea of the passage.Note: Choices B and D were composed by JohnDryden (1631–1700), and Choices A and C byAlexander Pope (1688–1744).

35. Choice C is correct. See lines 9–10. The artistcreatesbecauseheis“lessfittedtoprosperandenjoy himself under the conditions of life whichhe and we must face alike.” Choice A is incor-rect. Although they may be true, they are nevermentioned in the passage. Choice B is incorrectbecause, although the artist may be a threat to thesocial order, he is by no means an unnecessaryone. The author, throughout the passage, is sidingwith the artist against the social order. Choice D isincorrect. See lines 10–12: “Therefore he takes . . .attempt to escape from life.” A person who isattempting to escape from life hardly knows howto enjoy life.

36. Choice B is correct. The author ridicules SamuelJohnson, saying that he is as much a true artistas a kazoo player is a musician. The author thensays that if Johnson were alive today, he wouldbe a senator or a university president. The authorthus implies that these positions do not merit highrespect. Choice A is the opposite of Choice B.Therefore, Choice A is incorrect. Choice C is incor-rect because, although the statement may be true,the author neither states nor implies that senatorsand university presidents are generally appreciativeof the great literary classics. Choice D is incorrect.The fact that the author lumps Johnson, senators,and university presidents together as nonartisticpeople indicates that the author believes that sena-tors and university presidents do not have nativewriting ability.

26. Choice B is correct. The author emphasizes thehuge amount of data that must be analyzed. It is afiniteamount(notunlimited),notthrilling(notthedata itself) or incomprehensible (Why bother if itcan’t be understood?). Daunting can mean “almostoverwhelming” or “highly challenging.” Some-thing of this nature can be seen as intimidating.

27. Choice A is correct. The author states that the Stan-dard Model does not “resolve questions regardinggravity and general relativity.” Later in the pas-sage, the author describes gravity as “by far theweakest” of the forces.

28. Choice D is correct. The author states that theLHC’s ATLAS detector “could provide observa-tionaldataconfirmingthevalidityofextradimen-sions.” Earlier the author states that string theory“depends on the existence of more dimensions thanthe four we know of.”

29. Choice C is correct. The author states that “if thesymmetry is ‘broken,’ the sparticles may havemasses thousands of times greater than their part-ners, and producing them, even in an energy pow-erhouseliketheLHC,willprovedifficult.”

30. Choice C is correct. The explanation to question 7includes this line.

31. Choice A is correct. The author states that the Stan-dard Model “predicts that the decay width of theHiggs particle depends on the value of its mass.”This is clearly what the graph shows. As one valuechanges, so does the other.

32. Choice B is correct. The higher the line in thegraph rises, the greater is its decay width. Betweenthe approximate mass values (along the horizontalaxis) of 140 and 180, the line rises at its fastestrate, showing a large increase in decay width.

33. Choice D is correct. A value of 1,500 is beyond thegraph, but a clear trend can be seen. At a mass of500, the decay width is about 100, and at a massof 1,000, the decay width is close to 1,000. Inother words, an increase in mass of 500 (from 500to 1,000) yielded a decay width 10 times greater(from 100 to 1,000). If the mass is 1,500, againan increase of 500, the decay width would againincrease by a factor of (about) 10. It would increasefrom 1,000 to about 10,000.

respectively. The statements in III can be seen to be associated with the artist in Passage 2 from lines 57–59 and 49–57, respectively.

How Brilliant People Think Answers44. Choice D is correct. See lines 22–23: “All human

beings have at least four types of intelligence.”Choice A is incorrect. The passage simply states:“The idea for a self-starting electric motor cameto Nikola Tesla one evening as he was reciting apoem by Goethe and watching a sunset” (lines32–35). Choice B is incorrect. The author indicatesa span of time when he states: “The discoveriesmadebyscientificgeniuses,fromArchimedesthrough Einstein. . . .” (lines 1–2). Archimedes wasan ancient Greek mathematician, physicist, andinventor (287–212 BC), whereas Einstein was, ofcourse, a modern scientist (1879–1955). Choice Cis incorrect. The passage states: “. . . while an IQabove a certain point—about 120—is very helpfulfor a scientist, . . . [it] is not crucial for producinga work of genius” (lines 19–22). The passage doesnotspecificallysaythatmostscientistshaveIQscores above 120.

45. Choice D is correct. See lines 45–47: “The scientistsolves a problem by shifting from one intelligenceto another, although the logical-mathematical intel-ligence is dominant.” Accordingly, Choices A, B,and C are incorrect.

46. Choice B is correct. When the author describes thework experiences of Einstein and Tesla, he refersto their use of one or more of the four types ofintelligence. Moreover, lines 28–30 state: “Somecorroboration of these [four intelligence] categoriescomes from the reports of scientists who describethought processes centered on images, sensations,or words.” Choices A, C, and D are incorrectbecause the author does not refer to these choicesin the passage.

47. Choice C is correct. The author indicates that greatscientists use to advantage four intelligences—log-ical-mathematical, spatial, linguistic, and bodily- kinesthetic. See lines 23–27: “The great scientistpossesses the ability to move back and forth amongthem—the logical-mathematical, the spatial, which

37. Choice C is correct. Although a love of beauty is a quality we usually associate with artists, that idea about artists is never mentioned in the passage. All of the other characteristics are expressly mentioned inthefirsttwoparagraphsofthepassage.

38. Choice C is correct. From the context in Passage 2, we see that “world’s eye” and “world’s heart” refer to culture and wisdom, respectively. See lines 61–65: “. . . public and illustrious thoughts . . . resist the vulgar prosperity . . . by preserving and communicating . . . noble biographies . . . melodi-ous verse . . .” This is all about culture and wisdom.

39. ChoiceDiscorrect.SeethefirstsentenceinPas-sage 2: “. . . the self-accusation, the faint heart, the frequent uncertainty and loss of time, which are the nettles and tangling vines . . .” Here “nettles and tangling vines” refers to “self-accusation” and “uncertainty.” Nettles are plants covered with stinging hairs. Tangling vines give the impression of weaving all around in no particular or certain direction. So nettles can be thought of as “self-accusation”—something “stinging.” And “tangling vines” can be thought of as “uncertainty.”

40. Choice C is correct. See Passage 2: The most appro-priate groups are the hardships of the scholar, the scholar’sfunctions,andthescholar’sjustifications for disregarding the world’s business, as can be seen from the structure and content of the passage.

41. Choice C is correct. So far the tone of the passage issympathetictowardthedifficultiesoftheartist, so by placing “seems to be” in the context of the “virtual hostility” the artist feels from society, it is clear that the author is contrasting what the artist is and what he is perceived to be. The words “false impression”inChoiceCfitbest.

42. Choice A is correct. See lines 100–107 and 59–61 in Passage 2 and lines 14–18 and 27–37 in Passage 1.

43. Choice D is correct. The statements in I can be seen to be associated with the artist in Passage 2 from lines 92–94 and 62–63, respectively. The statements in II can be seen to be associated with the artist in Passage 1 from lines 29–35 and 5–6,

See lines 32–35 and lines 62–65. The author would agree with the statement in Choice B. See lines 45–50 in the context of the rest of the passage. The author would probably not disagree with the state-ment in Choice C since the author does not appear to distinguish artists from scientists in their think-ing process even though the passage is primarily about the scientists: See lines 10–15.

50. Choice C is correct. See lines 57–59. Note that although persistence is mentioned in lines 51–57, thepassagestatesthatfluidthinkingmaybecon-nectedtopersistence,notdefinedaspersistence. Thus Choice A is incorrect.

51. Choice B is correct. Given the context in lines 45–50, the word paradoxically means “seemingly contradictorily.”

52. Choice A is correct. It can be seen in the passage that the author is intrigued by and interested in the way the scientist thinks but at the same time feels thatthescientistreportsthefindingsveryobjec-tively.

includes visual perception, the linguistic, and the bodily kinesthetic.” Choices B and D are brought out in the passage but not at any length. Therefore, Choices B and D are incorrect. Choice A is incor-rect because the author nowhere compares the thinking of the average individual and that of the great scientist.

48. Choice D is correct. As a football star, he wouldcertainly have to have a high level of (a) spatialintelligence [II], which involves space sensitiv-ity as well as visual perception, and (b) bodilykinesthetic intelligence [IV], which involves themovement of muscles, tendons, and joints. As aliterature major, he would certainly have to havea high level of linguistic intelligence [III], whichinvolves the ability to read, write, speak, and listen.Whether he would have logical-mathematical intel-ligence to a high degree is questionable. It followsthat Choices A, B, and C are incorrect.

49. Choice D is correct. According to what is stated inlines 51–57, persistence is an important character-istic of the scientist. Thus the author would prob-ably not agree with the statement in Choice D. Theauthor would agree with the statement in Choice A.

4. Choice B is correct. This choice clearly describesa “creation to be consumed by elitists.” Choice Aincorrectly uses a contraction for “that is” withoutusing an apostrophe (that’s). Choice C incorrectlyuses the plural form “are,” though “creation” is sin-gular. Choice D confusingly uses the conjunction“and” though there are no two things to connect.

5. Choice D is correct. This sentence leads logicallyto the quote at the end of the paragraph. ChoiceA makes unclear who the “they” of the followingsentence refers to. Choices B and D place the sen-tence in locations that make the “therefore” in thesentence illogical. Also, the sentence should leadinto the quote at the end of the paragraph.

6. Choice C is correct. To “rail against” is to speakout (or write) forcefully against something. ChoiceA redundantly states that the artists created papersand manifestoes that “protested against.” To protestalready implies “against,” so the word “against” isnot needed. “Choice B states that the artists wrotematerials that “dictated against,” which has noclear meaning. Choice D illogically implies thatthe contents of the papers and manifestoes some-how “demonstrated against,” as if what was writtencould perform this action.

7. Choice A is correct. This choice makes clear thatthe theater-goers were scandalized by certain kindsof plays. Choice B makes it sound as though peo-ple went to the theater “with plays.” Choice C con-fusingly uses the pronoun “them” without makingclear what “them” refers to. Choice D confusinglystates that “Plays . . . made people scandalized.”

8. Choice A is correct. The semicolon correctly joinstwo independent clauses. Choice B incorrectly usesa comma to join two independent clauses. Choice

Art as Destruction Answers

1. Choice D is correct. There is no reason for makingthis comparison at this point in the passage. Thesentence does not provide information that followsthe previous sentence or that leads into the follow-ing paragraph. Choice A is incorrect because thecomparison is not relevant to the surrounding text.Choice B is wrong because the comparison to thepost-modern movement is not expanded on in thefollowing paragraph. Choice C is wrong becausethe issue is not whether the statement needs evi-dence but whether it is relevant.

2. Choice A is correct. The choice correctly places thephrase“especiallythosewhofirstgatheredattheCabaret Voltaire in Switzerland in 1916” betweena pair of commas. Choice B incorrectly says thatthe artists “were gathered” as if they were gatheredby someone or something. Choice C uses a dashand the a comma, rather than a pair of dashes or apair of commas. Choice D, by placing the secondcomma after “Switzerland,” makes it sound asthough “in 1916 French artist Marcel Duchampand others were engaged in something very simi-lar a year or so earlier in New York.” The commabelongs after “1916.”

3. Choice B is correct. The correct phrase to use inthis context is to say that x is opposed to y. The art-ists were opposed to the traditional process. ChoiceA incorrectly implies that the artists were opposedby tradition. Choice C uses the meaningless phrase“in opposition from.” Choice D uses the phrase“opposite from,” which has no clear meaning inthis context.

EXPLANATORY ANSWERS

Section 2: Writing and Language

13. Choice A is correct. This idiom (expression) is cor-rectly linked to “resentment.” Choice B incorrectlyuses the phrase “amounts of resentment.” Choice Cincorrectly forms the phrase “much of resentment.”Choice D incorrectly forms the phrase “a big dealof resentment.”

14. Choice D is correct. This choice correctly uses“where” after a location. Choice A incorrectly uses“when” after a location and awkwardly places theword “there” at the end of the phrase. Choices Band C are awkwardly lengthy; the phrases “in theplace” and “in the location” are not needed.

15. Choice D is correct. This sentence merely restatesinformation found in the preceding sentence. To“hamper communication between different areas”is to “keep the other parts of the city from know-ing what was going on.” Choices A, B, and C areincorrect because they inaccurately describe thesentence.

16. Choice B is correct. The statement after “Usually”describes what would have happened “usually.”Choice A implies that whatever follows “As usual”actually did take place. Choice C implies thatcalling in the “state militia” was more typical thansomething preceding this phrase. Choice D incor-rectly implies a frequent or common occurrence.

17. Choice C is correct. This choice makes clearthat “Kennedy . . . was recognized” despite notbeing in uniform. Choice A unnecessarily uses acomma after “though.” Choice B incorrectly omitsa comma after “uniform.” Choice D incorrectlyomits a comma after “Kennedy.”

18. Choice A is correct. The two sentences are inde-pendent clauses that do not need to be joined.Choices B and C incorrectly use a semicolon toconnect an independent clause to a dependentclause. Choice D uses the word “also,” which hasno clear meaning here.

19. Choice C is correct. “New York governor” correctlyandrestrictivelymodifiesHoratioSeymour.ChoiceD is incorrect because it places a comma after“GovernorofNewYork”—arestrictivemodifier.

C incorrectly uses a comma to join two indepen-dent clauses and also incorrectly uses a colon after a dependent clause. Choice D would be somewhat better if a comma were used after “meaning,” though the word “while” serves no clear purpose in the sentence.

9. Choice B is correct. This choice clearly statesthat surrealism and social realism were notableart forms that Dadaism “blurred into.” The word“notably” means something like “most famously.”Choice A needlessly uses “including” so that itsounds as if “notably surrealism and social real-ism” were included. A pair of commas to sepa-rate “notably” from the surrounding text wouldimprove this choice. Choices C and D use the word“of,” which has no clear meaning in this context.

10. Choice C is correct. The preceding sentence claimsthat “the spirit of Dada lives on,” and this choicegives an example of that. Choice A describes punkrock as a rejection of the impulse to questionauthority, the opposite of the anti-authoritariannature of Dada (and punk rock). Choice B empha-sizes that punk rockers established their owntraditions, a claim that does not follow from thepreceding sentence. Choice D describes the inter-national origins of punk rock, a statement thatdoes not follow from the preceding sentence.

11. Choice D is correct. This idiom (expression) makesitclearthat“thebelief...will...findvoice...many times more.” It is another way to express“many more times.” Choices A and B make it soundas though “the belief” will happen “more times”than something else will happen. Choice C uses aphrase—“many times again”—that is not used instandard English.

Racial Tension in New York Answers12. Choice B is correct. This choice correctly uses the

subjective form “who,” because it precedes theverb phrase “would be drafted.” Choice A incor-rectly uses the objective form “whom.” ChoiceC incorrectly uses the phrase “for determining.”Choice D incorrectly uses “which” instead of“who.”

Choice B confusingly uses “or even,” to set off “perform many other important functions” from the other items in this list. Choice C does not con-nectthefinaliteminthelisttotheprevioustwo.

25. Choice A is correct. The phrase “an individualgoingintonursingwillfirstpursue...”isclear.Nothing else is needed to link “an individual” to“going into nursing.” Choice B incorrectly usesthe possessive form of “who.” (The contraction“who’s” would have been acceptable.) Choice Cincorrectly forms the phrase “an individual goesintonursingwillfirstpursue.”ChoiceDconfus-ingly uses “will go,” which implies that the indi-vidual has not yet gone into nursing.

26. Choice B is correct. The introductory phrase“While pursuing an ADN” clearly refers to theword “students,” which comes immediately afterthe comma. Choice A follows the introductoryphrase “While pursuing an ADN” with anatomy,as if “anatomy” were (impossibly) pursuing thedegree. Choice C needlessly states that “studentsstudy” subjects that “are studied.” Choice D incon-sistently uses the pronoun “one” and then “you.”Both pronouns should be the same.

27. Choice B is correct. This choice makes the com-parison clear: the four-year BSN program placesmore emphasis on research and theory than theADN does. Choice A compares the BSN programto “taking the ADN program.” This is not thecorrect comparison. Choice C confuses the com-parison. It seems to compare the ADN program to“some people.” Choice D says that the BSN degree“is opted,” a phrase with no clear meaning.

28. Choice D is correct. The shortage of nurses is notdiscussed elsewhere in the paragraph. Choices A,B, and C are incorrect because they inaccuratelydescribe the sentence.

29. Choice D is correct. The meaning is clear: a nursecan perform a procedure. Choice A incorrectlystates that a nurse can perform material. Choice Bstates that a nurse performs a decision, but deci-sions are not performed. Choice C states that anurse can perform an advanced action, but onedoes not perform actions.

Choice A incorrectly uses “spoke” instead of the participle “speaking,” which is necessary to connect to the clause that begins with “claimed.”

20. Choice B is correct. This choice correctly usesthe parallel phrases “Troops were brought in” and“militia forces ordered.” Choice A incorrectlystates that “Troops brought in” as if the troopsbrought (something) in. Choice C uses the pronoun“them” without making clear who this would be.Choice D needlessly puts a pair of commas around“from surrounding areas” and after “forces.”

21. Choice C is correct. A “turn of events” implies achange in events, as is the case here: The draftwas delayed. Choice A uses a word that is moreproperly used to describe a physical altering.There is no “experience,” as implied by ChoiceB. There is no clear “condition,” as implied byChoice D.

22. Choice C is correct. Though the Draft Riots tookplace because of the Civil War, this sentence doesnot connect the war to the riots, and the wordingabout “still feeling the effects” goes beyond thescope of the passage. Choice A is wrong becausethe sentence does not summarize the main events,which are all about the riots. Choice B is incorrectbecausethesentence,thoughitdoes,likethefirstsentence, refer to the Civil War, does not functionas a conclusion to the passage, which focuses onthe riots. Choice D is incorrect because the tone isnot more personal than the tone of the rest of thepassage.

Modern Nursing Answers23. Choice C is correct. The plural “patients” matches

the plural pronoun “their.” Choices A and B incor-rectly use the singular “patient,” which does notmatch the pronoun “their.” Choice D incorrectlyuses “The patients,” as if a particular group ofpatients is being discussed.

24. Choice D is correct. The conjunction “and” isneededtoaddthefinalitemtoalist.ChoiceAconfusingly uses “still” as if nurses perform manyother important functions even though they alsodiagnose health problems and prescribe medicine.

by sailboat long ago as a venture. Choice A con-fusingly refers to travel itself as an investigation. Choice B calls travel a chance, and choice C calls it a plan. Travel involves chances and plans (and investigations, perhaps), but travel itself is not any of these things.

35. Choice B is correct. There is no reason that thetwo sentences have to be joined. Choice A uses“yet,” though this word is not used to connecttwo contrasting statements. Choice C uses “andalso” but does not clearly connect two parts thatrequire connecting. This choice also creates theconfusingphrase“floodedareasandalsoasearlyas 1987. . . .” Choice D creates a comma splice—two independent clauses joined by a comma.

36. Choice A is correct. The paragraph discusses theadvantages of placing wind farms offshore. Theparenthetical comment brings to the reader’sattention, through the use of the phrase “It shouldbe noted,” one drawback of the offshore farms.Choice B illogically implies that the higher cost ofoffshore wind farms is because of the advantagesof locating then offshore. Choice C implies thesame thing. Choice D uses “Additionally” but doesnot give the sense that the parenthetical comment,which mentions a disadvantage to offshore farms,is in contrast to the earlier part of the paragraph,which discusses advantages to offshore windfarms.

37. Choice D is correct. A colon can be used after anindependent clause that introduces a list, and thatis the case here. Choice A incorrectly implies thatthe advantages of using wind power are obviousbecause wind is easily available, etc. Choice Buses a semicolon, but the second part of the sen-tence is not an independent clause.

38. Choice B is correct. The phrase between the com-mas could be taken out of the sentence and thegrammar and basic meaning would be intact.Choice A incorrectly states that “the strengthand frequency of wind . . . is.” The plural subject(strength and frequency) does not agree with thesingular form of the verb (is). Choice C incorrectlyconnects the plural subject (strength and frequency)to “varies” instead of “vary.” Choice D confusinglyuses the singular pronouns “this” and “it.”

30. Choice B is correct. The semicolon correctly joinstwo independent clauses. In Choice A an indepen-dent clause is incorrectly connected to a dependentclause with a semicolon rather than a comma. InChoice C, the word “yet” indicates a contrast orsurprising situation where none exists. Choice Dincorrectly joins two independent clauses with acomma.

31. Choice A is correct. The list of workplaces is rel-evant to the statement that nurses can work outsideof a hospital setting. Choice B is incorrect becausethe sentence does not explain anything. Choice Cis incorrect because the information in the sentenceis not unnecessary—it does help the reader under-stand the kind of work that nurses do outside of ahospital. Choice D is incorrect because the infor-mationisspecificandrelevanttotheparagraph.

32. Choice D is correct. No connecting word or phraseis needed at this point. Choice A incorrectlyimplies that the sentence describes something thatneeds to be joined to the previous sentence, as if itwere part of a list or series. Choice B incorrectlyimpliesthatthesentenceisthefinaliteminalist.Choice C incorrectly implies that the sentence issomehow surprising or in contrast to the previoussentence.

33. Choice B is correct. This sentence summarizes thewide range of job possibilities within nursing, asdescribed throughout the passage. It also empha-sizes the positive aspects of nursing that are foundin the previous sentence. Choice A brings in thesubject of personal growth, never mentioned inthe passage. Choice C emphasizes the number ofpeople helped by nurses; this is not the main topicof the passage. Choice D emphasizes the relation-ship between training and the practice of nursing;this is not the main topic of the passage. Educationisnotmentionedinthefirstparagraphorthefinaltwo.

The Power of the Wind Answers34. Choice B is correct. A venture is an activity, fre-

quently a risky one, that is done for gain of somesort. A new business can be described as a venture.In this context, it makes sense to describe traveling

42. Choice C is correct. The sentence begins with“For example,” so it must introduce an example ofsomething mentioned in the previous sentence. Thefirstsentencerefersto“Otherchallenges,”andsen-tence 3 refers to the challenge of carrying the windpower over great distances. Choices A, B, and Ddo not place sentence 3, which begins with “Forexample,” so that it clearly introduces an exampleof something mentioned in the previous sentence.

43. Choice B is correct. The graph increases exponen-tially, meaning that it does not rise in a straightline but instead rises at a faster and faster rate.The difference in cumulative capacity betweenconsecutive years keeps increasing. This meansthat the cumulative capacity during the later span,2006–2010, increased more rapidly than it did dur-ing the earlier span, 2000–2005. Choice A is wrongbecause the increase was continuous but not steady(straight line). Choice C is wrong because the morelikely value for 2015 would be greater than 400.Choice D goes beyond the scope of the given infor-mation since we have no way of knowing whathappened before 1996.

44. Choice D is correct. None of the other choices canbe concluded. Choices A and B refer to hydroelec-tricity, but the graph does not provide any informa-tion about this type of energy. Choice C refers tothe number of windy days, but that goes beyondthe scope of the graph.

39. Choice C is correct. This choice clearly states thata day without strong winds is likely to be a sunnyday. Choice A says that a day without strong windsis more likely than a sunny day, but the contextdoes not support this comparison. The point theauthor is making is that the sun is more likely tobe shining on a day without wind. Choice B redun-dantly uses “most likely” and “probably.” ChoiceD redundantly uses “could” and “potentially.”

40. Choice A is correct. This choice makes clear thatforecasting (predicting) wind strength is helpfulbut hard to do (success is low). This then leads intothe next sentence, which says that consequentlyhere is what can be done to compensate for anyunexpected loss of power. Choices B and D do notlead into the next sentence, which says that con-sequently here is what can be done to compensatefor any unexpected loss of power. The idea thatthere is a problem with forecasting wind conditionsneedstobeinthefirstsentence.ChoiceCconfusesthe meaning of the sentence by stating that theunpredictability of wind conditions is avoidable.

41. Choice A is correct. This choice correctly statesthat“thebenefits...aresoexcitingthat....”ChoiceBincorrectlystatesthat“thebenefits...are going to excite so much,” implying that thebenefitswillexcite(who?).ChoiceCmisplaces“eventually.” It would be somewhat better to statethat“thebenefits...willeventuallybeexciting.”Choice D incorrectly uses the singular “is,” whichdoesnotagreewith“benefits.”

Canceling each of these from each side, we get,A/ 1 8 1 A/ 1 1/ 1 A/ 1 2/

5 A/ 1 A/ 1 1/ 1 A/ 1 2/ 1 A 1 3Thus, 8 5 A 1 3

5 5 A

3. Choice D is correct.Given: 500w 5 3 3 700 1(Use Strategy 13: Find an unknown by dividing.)Divide 1 by 500, giving

500w _____ 500 5

3 3 700 _______ 500

(Use Strategy 19: Factor and reduce first. Then multiply.)

w 5 3 3 7 3 100 / __________ 5 3 100 / w 5 21__5

4. Choice B is correct.(Use Strategy 17: Use the given informationeffectively.)The circle graph tells you that 19% of this mix-ture is carbon. Since the total mixture weighs 24pounds, 19% of that will be the amount of carbonin the mixture (in pounds). We would multiply 24lbs 3 0.19. But since the choices are not that closeand since we are looking for the closest number ofpounds, make the problem simpler by multiplying24 3 0.20 5 4.8, which is close to 4.6.

1. Choice D is correct.

Given: 3__4x 5 9 1

(Use Strategy 13: Find unknowns by multiplying.)

Multiplying 1 by 4, we get

4/ (3x__4/ ) 5 (9)43x 5 36 2

Multiply 2 by 2. We have 2(3x) 5 2(36)

6x 5 72

2. Choice B is correct.(Use Strategy 2: Translate from words into algebra.)We are told:

A 1 8 1 A 1 1 1 A 1 2 5 A 1 A 1 1 1 A 1 2 1 A 1 3 1

(Use Strategy 1: Cancel expressions that appear on both sides of an equation.) Each side contains an A, A 1 1, and A 1 2.

EXPLANATORY ANSWERS

Section 3: Mathematics, No Calculator

After 18 hours, 1_2(1_2)(x_2) grams remain.After 24 hours, 1_2(1_2)(1_2)(x_2) 5 x __16 grams remain.

8. Choice D is correct.

I. Slopeisdefinedasy2 2 y1 ______ x2 2 x1

where (x1,y1) and

(x2,y2) are points on the line. Thus here 0 5 x1,a 5 y1, a 5 x2, and 0 5 y2.

(Use Strategy 18: Know and use facts about triangles.) II. The triangle created is an isosceles right tri-

angle with sides a, a, a√_2. Thus II is true.

III. In an isosceles right triangle, the interiorangles of the triangle are 90-45-45 degrees.Thus III is true.

9. Choice B is correct.(Use Strategy 3: Know how to find unknownquantities from known quantities.)Tofindthemidpointoftwopoints,allyouneedtodoisfindtheaverageofthex-coordinates andthe average of the y-coordinates. In this case,

the average of the x-coordinates is 21 1 5 ______ 2 5 2.

This is the x-coordinate of the midpoint. For the

y-coordinates, the average is 21 1 1 ______ 2 5 0. This is

the y-coordinate of the midpoint. The midpoint’s coordinates are therefore (2, 0).

10. Choice D is correct.(Use Strategy 8: When all choices must be tested,start with the last choice and work backward.)Choice A is false because if b , 22, the absolutevalue of b (denoted as |b|) must be greater than 2.Choice B is false: c is positive (c . 13 . 0) soc 5/ 2|c|, since 2|c| is negative. Choice C is false:Since a and b are negative numbers and sincea , b, |a| . |b|. Choice D is correct and Choice Cis correct.

5. Choice A is correct.(Use Strategy 14: Label unknown quantities tohelp solve the problem.)

l

mn

x°

a°y°

Know the properties of parallel lines. If 2 parallel lines are crossed by a transversal, the pairs of cor-responding angles are equal. Thus,

x 5 a 1From the diagram, a 1 y 5 180 2Substituting 1 into 2 , we get

x 1 y 5 180

6. Choice D is correct.(Use Strategy 11: Use new definitions carefully.)

A

6

9 3

12

B

6

9 3

12

Bythedefinitionofamove,every4movesbringseach hand back to 12.Thus, after 4, 8, 12, and 16 moves, respectively, each hand is at 12.Hand A, moving counterclockwise, moves to 9 on its 17th move.Hand B, moving clockwise, moves to 3 on its 17th move.

7. Choice B is correct.(Use Strategy 11: Use new definitions carefully.)

After 6 hours x_2 grams remain.

After 12 hours, 1_2(x_2) grams remain.

14. Choice C is correct.(Use Strategy 2: Translate English words intomathematical expressions.)

6

4

2

02 4 6

22

The given equation describes a parabola, one that opens upward, has a minimum value (vertex) at 3 and has been shifted 3 units over to the right from (0, 0). The line y 5 2 is parallel to the x-axis.Iftheparabolaisreflectedovertheline,thenewparabola will face downward and will be as far from the line as the original parabola was, as seen inthefigureabove.The new parabola can be described by the equation y 5 2(x 2 3)2 11.Tofindthezeros,substitutezero for y. This will give you the x-values of the pointsatwhichthereflectedparabolacrossesthex-axis (and therefore has a y-value of zero).

0 5 2(x 2 3)2 1 1To solve, you could try out the choices, or work it outalgebraically.Todosoefficiently,youcouldrealize that the equation will work out only if (x 2 3)2 equals 1. This means that x must equal 4 or 2.

15. Choice B is correct.(Use Strategy 17: Use the given informationeffectively.)Any circle with radius r in the xy plane whosecenter is (a,b) can be represented as

(x 2 a)2 1 (y 2 b)2 5 r2

x2 1 y2 2 8y 1 4 5 0 can be factored:

(x 2 0)2 1 (y 2 4)2 5 12

11. Choice D is correct.(Use Strategy 17: Use the given informationeffectively.)

Given: w 5 7r 1 6r 1 5r 1 4r 1 3rThen, w 5 25r 1

We are told we must add something to w so that the resulting sum will be divisible by 7 for every posi-tive integer r.Check the choices.(Use Strategy 8: Start with the last choice.) Add 3r to 1

25r 1 3r 5 28r 5 7(4r)will always be divisible by 7. Thus, Choice D is correct.

12. Choice D is correct.(Use Strategy 17: Use the given informationeffectively.)

8 feet

5 feet

xo

Since you’ve been given the lengths of the adjacent sideandthehypotenuse,firstcheckthefunctionsthat involve those two values.

cos x° 5 adjacent _________ hypotenuse 5 5_8

sec x° 5 1 _____ cos x° 5 8_5

13. Choice A is correct.(3 1 4i)(6i 2 1) 5 3(6i) 1 4i(6i) 1 3(21) 1 4i(21)5 18i 1 24i2 2 3 2 4i5 24i2 1 14i 2 3Since i2 5 21:(3 1 4i)(6i 2 1) 5 24(21) 1 14i 2 3 5 14i 2 27.

This value, 3,810,000 can be expressed as 3.81 3 106, which means that a 5 3.81.

18. 4(Use Strategy 17: Use the given informationeffectively.)By trial and error, it can be seen that 4 is theanswer. A second way of approaching this problemis as follows:Let o 5 x. Then we have

x 16 xx 9

15 xWe get 1 1 x 1 9 5 10 1 x. So we carry the 1 and get 1 1 x 1 6 1 x 5 15. So 7 1 2x 5 15; 2x 5 8; x 5 4.A third way to approach this problem (and the most sophisticated way) is: Let o 5 x. Then o1 is x 1, which is 10x 1 1 since o is in the tens column. (Any number XY is 10X 1 Y; any number XYZ is 100X 1 10Y 1 Z.) 6 o 5 6 x 5 60 1 x. o9 5 x 9 5 10x 1 9. So adding, we get10x 1 1 1 60 1 x 1 10x 1 9 5 21x 1 70.This must equal 15o 5 15 x

5 100 1 50 1 x 5 150 1 x.So 21x 1 70 5 150 1 x and 20x 5 80; x 5 4.

19. 20(Use Strategy 17: Use the given informationeffectively.)You can begin this problem by squaring both sidesofthefirstequation.Thisgivesyou:

( x_y )220 5 (w_z )5A negative exponent inverts the base, so that

( x_y )220 5 ( y_x )20You now have ( y_x )20 5 (w_z )5, which means that p 5 20.

Thus a 5 0, b 5 4, and r2 5 12

r 5 √__12 5 √

_____ 4 3 3 5 2√

_3

16. 50(Use Strategy 2: Translate English words intomathematical expressions.)The estimated ratio of people who came into the

officetoclientsisp_c . This estimate would have been

accurate if 30 fewer people had become clients, and since 240 did become clients, we can say that:

p_c 5

350 ________ 240 2 30 5

350 ___ 210 5

5_3

The estimated ratio was therefore 5 : 3. If we keep the number of clients the same (as it actually was) and change the number of people who came into theofficebyx, we get:

5_3 5

350 1 x _______ 240

You could solve this by cross-multiplying or by realizing the following: Since 3 times 80 equals 240, if you multiply 5 by 80, you’ll get the correct numerator. Since 5 3 80 = 400, we can say that 350 1 x 5 400 and that x 5 50.

17. 3.81(Use Strategy 13: Know how to find unknownexpressions by adding, subtracting, multiplying,or dividing equations or expressions.)Since the company charges $2,535,000 for lessthan 15,000 square feet, we can plug this informa-tionintothefirstequationtofindx, the number ofsquare feet:

2,535,000 5 200x 1 135,000If you subtract 135,000 from each side and then divide by 200, you’ll get:

x 5 12,000If the footage had been two times greater, it would have been 24,000 square feet, which means that we should use the other equation to determine the charge:

g(x) 5 150(24,000) 1 210,000 5 3,810,000

This means that a could be 0 or a2 1 a 5 0. We are told that a 5/ 0, so it must be that a2 1 a 5 0. If we factor this, we get:

a(a 1 1) 5 0This means that a 5 21. If we plug this informa-tion into the question, we get:

f [22(21)],whichsimplifiestof (2)Using the original function equation, we get:

f (2) 2 23 1 22 1 2 5 14

20. 14(Use Strategy 13: Know how to find unknownexpressions by adding, subtracting, multiplying,or dividing equations or expressions.)Since f (a) 5 a, we can plug a in for x in the func-tion equation and get:

f (a) 5 a3 1 a2 1 a 5 aWe can take the “non-function notation” part of the equation and solve:

a3 1 a2 1 a 5 aa3 1 a2 5 0

a(a2 1 a) 5 0

To change 3 to a percent we multiply by 100.

100(1_4) 5 100 ___4 5 25%

3. Choice C is correct.(Use Strategy 10: Know how to use units.)

We are given his rate is 90 laps ______ 6 hours 90 laps ______ 6 hours 3

1 hour _________ 60 minutes 5

90 laps __________ 360 minutes

1_4 lap per minute

4. Choice D is correct.(Use Strategy 15: Know how to eliminate certainchoices.)The graph y 5 2x 2 4 is a straight line such thatwhen x 5 0, y 5 24 and when y 5 0, 2x 2 4 5 0and thus x 5 2. So we look for a line that cuts they-axis (vertical axis where x 5 0) at y 5 24, andcuts the x-axis (horizontal axis where y 5 0) atx 5 2.

5. Choice A is correct.(Use Strategy 11: Use new definitions carefully.) Given: x o• y 5 3 1 xy 1

y 5/ 0 2x o• y 5 3 3

Substituting 3 into 1 , we get3 5 3 1 xy0 5 xy 4

Noting 2 , we divide 4 by y0_y 5

xy__y

0 5 x

1. Choice D is correct.

Given: 3 1 y _____ y 5 7 1

(Use Strategy 13: Know how to find unknown expressions by multiplying.)Multiply 1 by y, to get

y/ (3 1 y _____ y/ ) 5 (7)y3 1 y 5 7y

3 5 6y3_6 5 y

1_2 5 y

2. Choice D is correct.Given: 8 people divide a cash prize equally 1(Use Strategy 2: Translate from words into algebra.)From 1 we get:

Each person receives 1_8 of the total prize 2

2 people receive 2_8 51_4 of the prize 3

EXPLANATORY ANSWERS

Section 4: Mathematics, with Calculator

Area of a circle 5 p r2 3Substituting 2 into 3 , we have

Area of circle 5 p52Area of circle 5 25p

9. Choice D is correct.(Use Strategy 8: When all choices must be tested,start with the last choice and work backward.)

Choice D is x2 1 x 1 2(Use Strategy 7: Use specific numerical examples.)Let x 5 3 (an odd positive integer)

Then x2 1 x 1 25 32 1 3 1 25 9 1 3 1 25 14 (an even result)

Now let x 5 2 (an even positive integer)Then x2 1 x 1 2

5 22 1 2 1 25 4 1 2 1 25 8 (an even result)

Whether x is odd or even, Choice D is even.

10. Choice B is correct.(Use Strategy 11: Use new definitions carefully.)

Bydefinition 20 5 10

11. Choice A is correct.(Use Strategy 14: Draw lines to help solve theproblem.)Before the rotation, we have

A B

D C

y

x

(5,3)53

6. Choice C is correct.(Use Strategy 13: Know how to find unknownexpressions by adding, subtracting, multiplying,or dividing equations or expressions.)This problem can be simply solved by adding thegiven equations.

r 2 3s 5 91 2r 1 4s 5 22

3r 1 s 5 7

7. Choice C is correct.(Use Strategy 2: Translate from words into algebra.)

In 1_2 year, 600 pounds of feed were used at a rate of

$1.25 per pound. Thus (600 pounds) 3 ($1.25 perpound), or $750, was spent. Hence,

Feed cost per egg 5 total cost for feed ______________ number of eggs

5 $750 _________ 5,000 eggs (Use Strategy 19: Factor and reduce.)

5 $75 3 10 ____________ 500 3 10 eggs

5 $25 3 3 ___________ 25 3 20 eggs

5$3__20 per egg

5 $0.15 per egg

8. Choice C is correct.(Use Strategy 2: Translate from words into algebra.)(Use Strategy 17: Use the given informationeffectively.)

Diameter Side

Given the perimeter of the square 5 40Thus, 4(side) 5 40

side 5 10 1A side of the square 5 length of diameter of circle.

Thus, diameter 5 10 from 1Since diameter 5 2(radius)

10 5 2(radius)5 5 radius 2

14. Choice D is correct.(Use Strategy 17: Use the given informationeffectively.)Two-fifths,or40%,oftheapplicantsfailontheexamination. Of the 60% remaining, three-fourths

fail to get into the program. 3_4 3 60% 5 45%.

Thus, the total number of failures is equal to 40%1 45%, or 85%.Or, to solve it algebraically:Let x be the number of applicants.3_5x 5 applicants who passed the exam

3_5x__4 5

3__20x 5 applicants who passed the exam and

were accepted 3__20x ___

x 5 3__20 5 % of all applicants who gain admission

1 2 3__20 5 17__20 5 85% 5 % who fail to gain admission

15. Choice B is correct.

Method I (shortest method):a 1 b 1 c 5 180 1

g 1 d 5 180 2e 1 i 5 180 3f 1 h 5 180 4

(Use Strategy 13: Find unknowns by adding equations.)Adding 1 1 2 1 3 1 4 , we get

a 1 b 1 c 1 g 1 d 1 e 1 i 1 f 1 h 5 720

ad

hfc

g ib e

After the rotation, we have

A

B

D

C

y

x

5

3

Note that the new y-coordinate of B is negative because B is below the x-axis. Since B is to the right of the y-axis, its x-coordinate is positive. By looking at the second diagram, we see that the coordinates of B are:

(3,25)

12. Choice C is correct.(Use Strategy 17: Use the given informationeffectively and ignore irrelevant information.)Tofindthetotalcostofalluniformsinchild sizesat School B, we would multiply the number of uni-forms at School B of Type A with the Child’s TypeA cost, multiply the number of uniforms at SchoolB of Type B with the Child’s Type B cost, and mul-tiply the number of uniforms at School B of TypeC with the Child’s Type C cost, and add those threequantities. That is:

30 3 $9 1 60 3 $10 1 50 3 $11 5 $1,420

13. Choice A is correct.(Use Strategy 2: Translate English words intomathematical expressions.)Wecantranslatethefirstsentenceinto

d 5 5c 2 8The second sentence becomes:

b 5 (d 1 c) 1 20The question asks for b in terms of c, so we can combine the equations, substituting 5c 2 8 in for d in the second equation.

b 5 [(5c 2 8) 1 c] 1 20Thissimplifiestob 5 4c 1 12, which is the same as Choice A.

By adding equations 12 , 13 , and 14 together, we get:j 1 k 1 l 1 a 1 b 1 c 5 3(180) 15

And since the angles of a triangle 5 180°a 1 b 1 c 5 180 16

Substituting 16 into 15 , we get:j 1 k 1 l 1 180 5 3(180)

j 1 k 1 l 5 3(180) 2 180 5 2(180) 5 360 17Substituting 17 into 11, we get:

X 1 360 5 3(360)X 5 3(360) 2 360 5 2(360) 5 720

16. Choice A is correct.(Use Strategy 12: Try not to make tedious calcula-tions, since there is usually an easier way.)To determine how many ways there are of combin-ing 8 waiters with 3 hosts, you simply multiplythese numbers, giving you 24 possible waiter/hostcombinations.16 more combinations would give us 40 possibili-ties. Only A is correct because that would give us10 waiters and 4 hosts, yielding 40 (10 3 4) pos-sibilities.

17. Choice A is correct.(Use Strategy 5: Average 5 sum of values ___________________ total number of values.)

p 5 x 1 y _____ 2 1

q 5 y 1 z _____ 2 2

r 5 x 1 z _____ 2 3

(Use Strategy 13: Find unknown expressions by adding equations.)Adding 1 , 2 , and 3 , we get

p 1 q 1 r 5 x 1 y _____ 2 1 y 1 z _____

2 1 x 1 z _____

2

5 2x 1 2y 1 2z ___________ 2p 1 q 1 r 5 x 1 y 1 z 4

The average of x, y, and z 5 x 1 y 1 z ________ 3 5

Substitute 4 into 5 . We have

The average of x, y, and z 5 p 1 q 1 r ________ 3

Method II: From the diagram, we get

a 1 d 5 180 1b 1 e 5 180 2c 1 f 5 180 3

(Use Strategy 13: Find unknowns by adding equations.)Adding 1 1 2 1 3 , we get

a 1 b 1 c 1 d 1 e 1 f 5 540 4(Use Strategy 3: The whole equals the sum of its parts.)Thesumoftheanglesofa∆5 180

Thus, a 1 b 1 c 5 180 5From the diagram (vertical angles), we have

a 5 g, b 5 i, c 5 h 6Substituting 6 into 5 , we get

g 1 i 1 h 5 180 7Adding 4 1 7 , we get

a 1 b 1 c 1 d 1 e 1 f 1 g 1 i 1 h 5 720

Method III: Let X be the value of a 1 b 1 c 1 d 1 e 1 f 1 g 1 h 1 i.

ad

hfc

g ib e

l

jk

Label the unmarked angles j, k, and l.We know that the sum of the angles in a circle is 360°. So we get:

a 1 d 1 g 1 j 5 360 8b 1 e 1 i 1 k 5 360 9c 1 f 1 h 1 l 5 360 10

(Use Strategy 13: Add equations.)X 1 j 1 k 1 l 5 3(360) 11

We know that the sum of angles in a straight line is 180°. So we get:

j 1 a 5 180 12 k 1 b 5 180 13 l 1 c 5 180 14

20. Choice B is correct.(Use Strategy 2: Translate from words into algebra.)Let the capacity of container B be x. Then thecapacity of container A will be 2x, and that of con-tainer C will be 3x. The amount poured into con-tainer C is equal to half of 2x plus one-third of x, or2x__2 1

x_3 5 x 1

x_3 5

4x__3 . Dividing this amount by the

totalcapacityofcontainerC,wefindthefractionthatwasfilled:

(4x__3 ) ____ 3x 5

4_9

21. Choice B is correct.(Use Strategy 17: Use the given informationeffectively.)By looking at the diagram, we have

P1 5 22P2 5 21

We can approximate the other numbers by looking at their positions on the number line:

P3 ≈ 1_3

P4 ≈ 2_3

P5 ≈ 3_2

Thus,

P1 P2 P3 P4 P5 ≈ (22)(21)(1_3)(2/_3/)(3/_2/)P1 P2 P3 P4 P5 ≈

2_3

22. Choice D is correct.Since vertical angles are equal, then

m AOC 5 m DOB 5 108 1Thus, from 1 , we get length of minor AC 5 length of minor DB 2From geometry we know length of

minor AC 5 108 ___ 360 3 circumference of circle

5 108 ___ 360 3 p (diameter)

5 108 ___ 360 3 p (20)

18. Choice B is correct.(Use Strategy 14: Label unknown quantities.)

AD

E

BCc

a b

Label angles as above with a, b, c.You are given that

a 1 b 1 c 5 90 1b 1 c 5 62 2a 1 b 5 37 3

Youwanttofind DCE 5 b(Use Strategy 13: Find unknown expressions by adding or subtracting.)First add 2 and 2 :We get:

a 1 2b 1 c 5 62 1 37 5 99 4Now subtract 1 from 4 :

a 1 2b 1 c 5 99a 1 b 1 c 5 90

b 5 9

19. Choice C is correct.(Use Strategy 2: Translate from words into algebra.)Let the 3 consecutive even integers be

x, x 1 2, x 1 4 1where x is even. We are told that

x 1 x 1 2 1 x 1 4 5 Kor 3x 1 6 5 K 2

From 1 , we know thatx 2 5, x 2 3, x 2 1

must be the 3 consecutive odd integers immedi-ately preceding x. We are told that

x 2 5 1 x 2 3 1 x 2 1 5 yor 3x 2 9 5 y 3

(Use Strategy 13: Find unknown expressions by subtraction.)Subtracting 3 from 2 , we get

15 5 K 2 yor y 5 K 2 15

25. Choice E is correct.

ℓ

ℓ

m

m

n

n

p

p

q

q

5

5

12

12

{{

{

{Since we know only that m is not parallel to either ℓ or n, both of the following situations could be true. (Use Strategy 17: Use the given information effectively.)Note: p 1 q 5 13 is still true in both cases in the drawings above.

Clearly, the value of p_q is different for each case.

Hence, p_q cannot be determined unless we know

more about m.

26. Choice C is correct.

First Second Third Place Place Place

(6 points) (4 points) (2 points)Game 1Game 2 ArisaGame 3 Arisa

(Use Strategy 17: Use the given information effectively.)Dylan can attain the minimum possible score by placing third in Game 1 and Game 2 and second in Game 3.From the chart he would have 2, 2, and 4 points for eachofthesefinishes.Thus, minimum score 5 2 1 2 1 4

minimum score 5 8 points

18 3 6 _______

(Use Strategy 19: Factor and reduce.)

length of minor AC 5 18 3 20 3 p (20 )

length of minor AC 5 6p 3length AC 1 length DB can be found using 2 and 3length AC 1 length DB 5 6p 1 6plength AC 1 length DB 5 12p

23. Choice D is correct.(Use Strategy 17: Use the given informationeffectively.)Of the N French students, P are in both programs,so only (N 2 P) are in the French program alone;similarly, (M 2 P) students are in the Spanishprogram alone. Thus, the number of students inonly one language program is equal to (N 2 P) 1(M 2 P), which equals N 1 M 2 2P.Note: The following diagram may help you tovisualize the answer better.

French (N ) Spanish (M)

Spanishonly

Frenchonly Both Frenchand Spanish

PN–P M–P

24. Choice C is correct.(Use Strategy 17: Use the given informationeffectively.)In 12 seconds, the wheel travels through 2 revolu-

tions (since 12 seconds is 1_5 of the minute it would

take for ten revolutions). Since this distance isequal to 16 feet, the wheel travels 8 feet per revolu-tion; thus, 8 feet must be the circumference of thewheel.Tofindthediameter,wedividethisfigureby p (because the circumference of a circle is

p times its diameter). Thus, the diameter is 8__p feet.

Note: This is the only solution because x . 0 and y . 0.

29. Choice A is correct.volume of cube 5 (side)3

Thus, volume of each small cube 5 r3 1volume of larger cube 5 s3 2

and sum of the volumes of the 27 cubes 5 27r3 3(Use Strategy 3: The whole equals the sum of its parts.) We are told that the sum of the volumes of the 27 cubes 5 the volume of the larger cube

5 81 4From 2 , 3 , and 4 together, we have

27r3 5 81 5s3 5 81 6

(Use Strategy 13: Know how to find unknown expressions by dividing.) Dividing 5 by 6 , we get

27r3 __

s3 5 1 7

Multiplying 7 by 1__27, we get

r3 __s3 5

1__27

or r_s 5 1_ 3

30. Choice D is correct.(Use Strategy 3: The whole equals the sum of itsparts.)The perimeter of the shaded region

5 PM 1 PN 1 length of MN 1From basic geometry, we know that if two tangents to a circle meet at a point, the lengths of the tan-gents from that point to where they touch the circle are equal. If a radius is drawn from the center of a circle to the point where the tangent touches the circle, the angle of the radius line is perpendicular to the tangent. Thus,

PM 5 PN m PMO 5 90 2and OP bisects MON.

27. Choice A is correct.(Use Strategy 3: The whole equals the sum of itsparts.)The area between the curved path and the dodeca-gon is simply the sum of the areas of the 12 semi-circles.Since area of circle 5 pr2

then area of semicircle 5 1_2pr2

where r is the radius of the circle.Thus, the area of the shaded region 5 12 (1_2pr2)

5 6pr2 1We are told that the diameter of a semicircle 5 the side of the dodecagon. 2Since each side of a regular dodecagon has the same length, then

length of a side of dodecagon

5 perimeter of dodecagon

125

24__12

5 2From 2 , we know that

diameter of semicircle 5 2Thus, radius of semicircle 5 1 3Substituting 3 into 1 ,

area of shaded region 5 6p

28. Choice D is correct.Given: x9 5 4 1

x7 5 9__y2 2

x . 0 and y . 0(Use Strategy 13: Know how to find unknown expressions by dividing equations.)Divide 1 by 2 . We get

x9 __x7 5

4___9__y2

x2 5 4 3 y2 __

9

x2 5 4_9y2

√__x2 5 √

___ 4_9y

2

x 5 2_3y

31. 24(Use Strategy 2: Translate from words into algebra.)Let n 5 the numberWe are given:

5_8n 5

3_4n 2 3 1

(Use Strategy 13: Find unknowns by multiplica-tion.)Multiply 1 by 8. We get

8/ (5_8/n) 5 8(3_4n 2 3)5n 5 24__4 n 2 24

5n 5 6n 2 2424 5 n

32. 12(Use Strategy 17: Use the given informationeffectively.)In order to use the least number of rooms, youmust use as many of the larger rooms as possible.Thesearetheroomsthatcanfit52people.Ifall9of these rooms are used, that would be enough toaccommodate 468 people (52 3 9 5 468).There are 510 people, so we still need rooms for 42people (510 2 468 5 42).There are no more of the larger rooms, so if we use3oftheroomsthatfit15people,wecanaccommo-date the remaining 42 people (15 3 3 5 45).That’s 9 of the big rooms and 3 of the smallerrooms, giving us a total of 12 rooms.

33. 11Sincelinesaredrawnevery10yardsafterthefirst

one, 100 ___ 10 lines, or 10 additional lines, are drawn.

(Use Strategy 2: Translate from words into algebra.)Thetotalnumberoflinesonthefield5 the origi-nal line 1 the number of additional lines

5 1 1 10 5 11

(Use Strategy 14: Draw additional lines.) Thus, we can redraw the diagram. (Use Strategy 18: Remember facts about right triangles.)

M N

560°60°

O

P

ΔPMO is similar to one of the standard triangles previously discussed.

60°1

23

Corresponding sides of similar triangles are in proportion, so that

√_3__1 5

PM ___5

or PM 5 5√_3 5 PN 3

It is always true that the length of MN

5 m MON ________

360 3 circumference of the circle

5 m MON ________

360 3 2p (5)

5120 ___ 360 3 2p (5)

(Use Strategy 19: Factor and reduce.)

5 12 3 10/ _______ 36 3 10/ 3 2p (5)

5 12/ ______ 12/ 3 3 3 2p (5)

5 10p ___3 4

Substituting 4 and 3 into 1 , we get the perimeter of shaded region

5 10√_3 1 10p ___3

and sum of the ages of the 20 students40 5 _____________________________20

Thus, the sum of the ages of the 60 students5 (60) (20) 5 1,200

and the sum of the ages of the 20 students5 (40) (20) 5 800

Hence, the sum of the ages of the 80 students5 sum of the ages of the 60 students

1 sum of the ages of the 20 students5 1,200 1 800 5 2,000 3

Substituting 3 into 2 , we get2,000 _____

80 5 25

Average age of all 80 students 5 25

36. 36.2(Use Strategy 2: Translate from words into algebra.)

Fraction mowed during evening 1 5 2_9 1

Fraction mowed during evening 2 5 2(2_9) 5 4_9 2Adding 1 and 2 , we getTotalfractionmowedduringfirsttwoevenings

5 2_9 1 4_9

5 6_9

5 2_3(Use Strategy 3: The whole equals the sum of its parts.)Amount left for evening 3

5 1 whole lawn 2 2_3 already mowed

5 1_3 3

Given: Lawn area 5 108.6 square feet 4Multiplying 3 by 4 , we getAmount left for evening 3

51_3 3 108.6 square feet

5 36.2 square feet

34. 81(Use Strategy 18: Know and use facts abouttriangles.)It’s important to realize that this problem presentsus with two similar triangles. We know that theyare similar because they both have a right angleand both share the angle at B. This means that theratio between each pair of corresponding sides isthe same.Sides DE and AC are corresponding sides, weknow that the ratio between them is 0.9 : 1, whichis the same as 9 : 10. If these are the heights of thetriangles, then the bases (sides EB and CB) havethe same ratio.It doesn’t matter what the actual lengths of thebasesandheightsarewhenfindingtheratiooftheareas. You could go ahead and choose to make boththe base and height of the smaller triangle 9, andmake the base and height of the larger triangle 10(thoughitdoesn’tlookthiswayinthefigure).Thiswayyoudefinitelyhavea9:10ratio.Theareaofthe triangle is one-half (base 3 height), so the area

of the smaller triangle is 9 3 9 _____ 2 5 81__2 and the area

of the larger triangle is 10 3 10 _______ 2 5 100 ___

2 .

The ratio of the areas is therefore 81 : 100, which

is the same as saying that the smaller area is 81 ___ 100

of the larger triangle, and this is the same as saying that it is 81% of the area of the larger one.Another approach is simply to realize that if the ratio of the sides is 9 : 10, the ratio of the areas is this ratio squared, which is 81 : 100.

35. 25(Use Strategy 5: Average 5 sum of values ___________________ total number of values.)Average age of students in a class

sum of the ages of students in the class5 _________________________________ 1number of students in the class

Thus,Average age of all 80 students

sum of the ages of the 80 students5 _____________________________ 280

Using 1 , we know that sum of the ages of the 60 students20 5 _____________________________60

38. 10.9(Use Strategy 18: Know and use facts abouttriangles.)(Use Strategy 3: Know how to find unknownquantities [areas, lengths, arc and angle measure-ments] from known quantities.)

Since the triangle is inscribed in the circle, weknow that ACB is a right angle. This is the anglethat “creates” arc AB, which is a semicircle. Asemicircle has 180°, and the angle that formsit along the circumference must be half of that,or 90°. Using this same principle, we know thatthe degree measure of CAB must be half of thedegree measure of arc BC, the thing we’re lookingfor. We”ll come back to that later.You are told that 126cos85° 5 x and that leg BCis equal to x. Knowing that the cosine of an angleto its adjacent side over the hypotenuse, we candivide each side of this equation by 126, giving us:

cos85° 3 x___ 126Since leg BC is equal to x, and this side is adjacent to CBA, it must be that this angle is 85°, and BA (the hypotenuse) is equal to 126. Note that this side is also the diameter of the circle.Since all triangles have angles that sum to 180, we can now say that CAB must equal 5°. Remember that we said that this is half of the degree measure of arc BC, which is therefore 10°. And since the entire circle is 360°, the length of minor arc BC

must equal 10 ___ 360 of the entire circumference. This

canbesimplifiedto 1__36 of the circumference.

We know that the diameter is 126, so the circum-

ference is 126p. The arc length we want is 1__36 of

this, so it’s equal to 126p ____ 36 . You can now use your

calculator, using 3.1 for p, as instructed or you

couldsimplifythefractionfirstto7p__2 . Either way,

youll get 10.85 which, to the nearest tenth, rounds up to 10.9.

37. 18

Method I:(Use Strategy 14: Draw lines to help solve theproblem.)

1

1112

102

38

6 7

5 9

4

Above is a rectangular solid with each of its edges numbered 1 through 12, respectively. There are 3 groups of 4 parallel edges each.

1, 2, 3, and 4 are parallel.5, 6, 7, and 8 are parallel.9, 10, 11, and 12 are parallel.

Within each group of 4 parallel edges, there are 6 pairs of parallel edges. For example, within the firstgrouplistedabove,1and2areparallel,1and3 are parallel, etc. Because there are 3 groups and each group has 6 pairs of parallel edges, there are 3 3 6 5 18 different pairs of parallel edges in all. Below is a listing of all the pairs:1–2 2–3 5–6 6–7 9–10 10–111–3 2–4 5–7 6–8 9–11 10–121–4 3–4 5–8 7–8 9–12 11–12

Method II:A rectangular solid exists in three dimensions; within each dimension, there are four edges that run parallel to each other. Therefore the combina-tions of parallel edges for one dimension, taken two at a time, is:

4C2 5 (4 3 3) ______ (2 3 1) 5 6

Since there are three dimensions, the total number of combinations is:

3(4C2) 5 3(6) 5 18

n Theresponsecontainsrelevant,sufficient,andstrategically chosen support for claim(s) or point(s)made.

n The response focuses consistently on those fea-tures of the text that are most relevant to address-ing the task.

Writingn The response is cohesive and demonstrates a

highly effective use and command of language.n The response includes a precise central claim.n The response includes a skillful introduction and

conclusion. The response demonstrates a deliber-ate and highly effective progression of ideas bothwithin paragraphs and throughout the esssay.

n The response has a wide variety in sentence struc-tures. The response demonstrates a consistent useof precise word choice. The response maintains aformal style and objective tone.

n The response shows a strong command of the con-ventions of standard written English and is free orvirtually free of errors.

Score Point 3: Proficient

Readingn The response demonstrates effective comprehen-

sion of the source text.n The response shows an understanding of the text’s

central idea(s) and important details.n The response is free of substantive errors of fact

and interpretation with regard to the text.n The response makes appropriate use of textual

evidence (quotations, paraphrases, or both), dem-onstrating an understanding of the source text.

SAT Essay responses are scored using a carefully designed process:

n Two different people will read and score youressay.

n Each scorer awards 1–4 points for each dimension:reading, analysis, and writing.

n The two scores for each dimension are added.n You’ll receive three scores for the SAT Essay—one

for each dimension—ranging from 2 to 8 points.

Essay Scoring Rubric

Score Point 4: Advanced

Readingn The response demonstrates thorough comprehen-

sion of the source text.n The response shows an understanding of the text’s

central idea(s) and of most important details andhow they interrelate, demonstrating a comprehen-sive understanding of the text.

n The response is free of errors of fact or interpreta-tion with regard to the text.

n The response makes skillful use of textual evidence(quotations, paraphrases, or both), demonstrating acomplete understanding of the source text.

Analysisn The response offers an insightful analysis of the

source text and demonstrates a sophisticatedunderstanding of the analytical task.

n The response offers a thorough, well-consideredevaluation of the author’s use of evidence, rea-soning, stylistic and persuasive elements, and/orfeature(s) of the student’s own choosing.

SECTION 5: TEST 2 ESSAY SCORING

n The response makes limited and/or haphazard useof textual evidence (quotations, paraphrases, orboth), demonstrating some understanding of thesource text.

Analysisn The response offers limited analysis of the source

text and demonstrates only partial understanding ofthe analytical task.

n Theresponseidentifiesandattemptstodescribethe author’s use of evidence, reasoning, and/orstylistic and persuasive elements, and/or feature(s)of the student’s own choosing, but merely assertsrather than explains their importance, or one ormore aspects of the response’s analysis are unwar-ranted based on the text.

n The response contains little or no support forclaim(s) or point(s) made.

n The response may lack a clear focus on those fea-tures of the text that are most relevant to address-ing the task.

Writingn The response demonstrates little or no cohesion

and limited skill in the use and control of language.n The response may lack a clear central claim or

controlling idea or may deviate from the claim oridea over the course of the response.

n The response may include an ineffective introduc-tion and/or conclusion. The response may demon-strate some progression of ideas within paragraphsbut not throughout the response.

n The response has limited variety in sentence struc-tures; sentence structures may be repetitive.

n The response demonstrates general or vagueword choice; word choice may be repetitive. Theresponse may deviate noticeably from a formalstyle and objective tone.

n The response shows a limited control of the con-ventions of standard written English and containserrors that detract from the quality of writing andmay impede understanding.

Analysisn The response offers an effective analysis of the

source text and demonstrates an understanding ofthe analytical task.

n The response competently evaluates the author’suse of evidence, reasoning, and/or stylistic andpersuasive elements, and/or feature(s) of the stu-dent’s own choosing.

n Theresponsecontainsrelevantandsufficientsup-port for claim(s) or point(s) made.

n The response focuses primarily on those featuresof the text that are most relevant to addressing thetask.

Writingn The response is mostly cohesive and demonstrates

effective use and control of language.n The response includes a central claim or implicit

controlling idea.n The response includes an effective introduction

and conclusion. The response demonstrates a clearprogression of ideas both within paragraphs andthroughout the essay.

n The response has variety in sentence structures.The response demonstrates some precise wordchoice. The response maintains a formal style andobjective tone.

n The response shows a good control of the conven-tions of standard written English and is free ofsignificanterrorsthatdetractfromthequalityofwriting.

Score Point 2: Partial

Readingn The response demonstrates some comprehension

of the source text.n The response shows an understanding of the text’s

central idea(s) but not of important details.n The response may contain errors of fact and/or

interpretation with regard to the text.

n The response may not focus on features of thetext that are relevant to addressing the task, or theresponse offers no discernible analysis (e.g., islargely or exclusively summary).

Writingn The response demonstrates little or no cohesion

and inadequate skill in the use and control of lan-guage.

n The response may lack a clear central claim orcontrolling idea.

n The response lacks a recognizable introduction andconclusion. The response does not have a discern-ible progression of ideas.

n The response lacks variety in sentence structures;sentence structures may be repetitive. The responsedemonstrates general and vague word choice; wordchoice may be poor or inaccurate. Th responsemay lack a formal style and objective tone.

n The response shows a weak control of the conven-tions of standard written English and may containnumerous errors that undermine the quality ofwriting.

Score Point 1: Inadequate

Readingn The response demonstrates little or no comprehen-

sion of the source text.n The response fails to show an understanding of the

text’s central idea(s), and may include only detailswithout reference to central idea(s).

n The response may contain numerous errors of factand/or interpretation with regard to the text.

n The response makes little or no use of textualevidence (quotations, paraphrases, or both), dem-onstrating little or no understanding of the sourcetext.

Analysisn The response offers little or no analysis or ineffec-

tive analysis of the source text and demonstrateslittle or no understanding of the analytic task.

n Theresponseidentifieswithoutexplanationsomeaspects of the author’s use of evidence, reasoning,and/or stylistic and persuasive elements, and/orfeature(s) of the student’s choosing, or numerousaspects of the response’s analysis are unwarrantedbased on the text.

n The response contains little or no support forclaim(s) or point(s) made, or support is largelyirrelevant.