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ACTTest1163
1. Answer:C.JoiningandSeparatingSentences:CommaThestartofanewindependentclause(thatis,anideathatcontainsbothsubjectandpredicatewithoutneedofanotherideaonwhichtoโdependโ)signalstheneedofaperiod.DincludestheunnecessaryโWhile,โwhichwouldimplyanothersimultaneousactioninthefollowingsentence,andthusisnotcorrect.
2. Answer:H.IsitRelevant:Inserting
Theanswermustbeaโnoโbecausetheideapresentedisnotconsistentwiththepassage,whichmakesnoreferencetodancersโcareers.WecaneliminateJbecausetheinformationdoesnotcontradictthepassage.
3. Answer:B.AdditionalCommaUsesand
MisusesTheclausesinthissentenceareโGrowingupinMexicointhe1920sโandโHernandezbelievedshewasborntodance.โIdentifyingthesewithoutanycommasmakesclearwheretheyareseparated.Imagineamovienarratorsayingthesentenceandemphasizingthepause.Wheredoyouhearit?
4. Answer:G.Non-EssentialTransitions,
Words,andPhrasesThephrasesโdespite,โโinfact,โandโontheotherhandโarealltransitionswhichintroduceanewthoughtwhichisbynaturecontrarytotheprecedingpoint.Herfatherโsacquiescenceisnotcounterintuitive,however;itsimplyshowsthenaturalresultofherpersistence.
5. Answer:D.IsitRelevant:Deleting&
ShorterisBetter:RedundancyandWordinessTheunderlinedportionandallotheroptionsareunnecessaryandredundant.Wearealreadytoldthatheacquiesced,sotostatethathegaveinisalreadystatedandneednotberepeated.Omissionisgrammaticallycorrectandconcise.
6. Answer:H.ColonsAsinnumber3,readtheoptionswithcommasaloud.Wheredoesapauseoccurnaturally?Ordoesit?Inthiscase,theunderlinedportiondoesnotincludeachangeofclauseatall.Nopunctuationisnecessary,asitissimplycontinuingtheexplanationofAmaliaโstutelage.
7. Answer:A.Non-EssentialTransitions,
Words,andPhrasesSimilarlytoquestion4,someanswershereusetransitionwordswhicharenotcorrectinthiscontext.AnswersCandDwouldservetointroducenewideas;however,thisisnotthecaseattheendofthisparagraph.OptionBissimplynotrelevanttothepassage,asonecandeterminefromreading.A,however,bothtiesupthisparagraphandhintsatthestartofthenext.Readingaheadbyasentenceortwoisagreatwaytogainsomecontextforthesetransitionquestions.
8. Answer:H.Apostrophes
Possessive.Thereโsnotricktothis;youjusthavetoknowwheretheapostrophesgo.Asingularpossessivewillalwayshaveanapostrophebetweenthewordandthes(savethefewirregularexceptions).
9. Answer:A.WordPairsandComparison
Thesequestionsareahybridofvocabandinference.Ifoneknowsthemeaningsofall5(4answers+underlined)words,thereisonlytodeterminewhichisdifferentandwhy.Inthiscase,Aistheoutlierbecauseโgroupingโdoesnotimplythehomogenizationtheotheroptionsdo.Intheother4,thepartsarechangedtocreateawhole.InA,theyarepreserved.
10. Answer:G.ParallelStructure:Lists
Listscanbetricky.Itโsimportanttoknowthatinlistsalllistedarticlesmustbeofthesamepartofspeech.Inthiscase,โlifeโandโdeathโarenouns.โTohavearebirth,โaswellasoptionsHandJ,areactuallyverbsphrasesusingโTohaveโandโTobe.โTheoptionโRebirthโisconsistentwiththeotherarticleslisted.
ACTTest1163
11. Answer:D.TransitionsOften,omissionsarethecorrectchoice.Youshouldstillchecktheotheroptions,though,toconfirm.Inthiscase,โHowever,โโNevertheless,โandโInstead,โallimplyacontradiction.Readingthesentence,however,weseethatinfactthesetransitionsarenotonlyunnecessarybutincorrect.
12. Answer:F.IsitRelevant:Inserting
OptionsG-Jareeasilyeliminatedbytheirreasoning.GandJbothmentiondescription,howevertheparagraphwasaninformativeonewhichdidnotdescribetheballets.HcanbeeliminatedbecausetheparagraphdidnotfocusontheMIFAinthefirstplace.Fistheonlyreasonableanswerbecauseitaccuratelyclassifiestheadditioninrelationtothetext.
13. Answer:C.Dashes
Thebiggesthinthereistheemdashimmediatelyfollowing.Emdashesalmostalwayscomeinpairs,especiallywheninthemiddleofasentence.Theotheroptionswouldimproperlyseparatetheportionfollowingtheexistingdashasanewclause,whenitโsreallybeinginterruptedbyanaside.
14. Answer:G.IsitRelevant:Replacing
Theanswerhereisinthequestion.Onlyoneanswershowsaโvaluablecontribution.โ
15. Answer:B.SupposetheWriterโsGoal
Wecaneliminate3answerseasilyinthisquestion.Aisincorrectbecausethepassagedoesnotfocusonawards,andC&Dtrytomakesemanticdistinctionsbutfailbecausetheyarenotactualevidence,seeingasthequestiondoesnotnecessitateartistsingeneralorspecificdanceforms.
16. Answer:E.Apostrophes:Possessivevs
PluralBecarefulnottomistakeageneralpronounforapluralone.โSomeoneโissingular,sothesingularpossessiveโelseโsโisalreadycorrect.
17. Answer:C.JoiningandSeparating
Sentences:Comma+FANBOYSHerearetwoindependentclauses,whichshouldbetheirownsentencesmoreoftenthannot.Theunderlinedโwhichโisunnecessary,sosimplifyingthisinto2simplesentencesiseasy.Thisisanothertypeofquestionwhichisgoodtoreadaloudorimaginebeingreadbyanarrator.
18. Answer:F.WordPairsand
ComparisonsThisisavocabquestionindisguise!Whatdoallthesewordsmean?Whatdotheyaddtothetoneofthetext?Ifyoudonโtknowallthewords,usecontexttoestimatewhattheymean.Astheyโrelistedtogether,youcanbettheyareverysimilar!
19. Answer:D.Verbs:Agreement
Amatterofredundancyoncemore.ReadingtheseoptionsaloudshouldquicklyeliminatetheunwieldyB&C,andDmakesaclearverb-nounagreement.
20. Answer:H.WordPairsand
ComparisonsThecluehereisinthewordโof.โAllanswersmakesensefollowedbythewordโofโexceptH;hedoesnโtcarryโmanyofpens.โ
21. Answer:D.Verbs:Tense
Thisisatrickierquestion,whichcanbedeterminedbytense.โIfeelโispresent,sowecandetermineweneedanotherpresent-tenseverb.A&Barebothinfinitive,whileCisnoteventhecorrectpartofspeech.
22. Answer:G.Pronouns:Agreementand
TenseHandJcanbeeasilyeliminatedbecausetheyare,respectively,toovagueandblatantlyincorrectinnumbering.ThedistinctionbetweenFandGissubtlebutimportant:Greinforcesthepointtheauthorismaking.Whenthepenheisusingisrundryheneedsanother.โTheyโwouldmeanallofthepenshehaswith
ACTTest1163
him,inwhichcaseitwouldnโtmatterifhehadanotherasitmayalsobedry.
23. Answer:C.SentenceOrder&
Non-EssentialClauseโ,...,โTryrearrangingthesentencetogetanideaoftheclauses.ItcanbewritteninsteadasโSmallpilesofuncappedballpointsgatheronmynighttableasifoftheirownaccord.โHerewecanseethatโasifoftheirownaccordโisaseparateclausefromtherestofthesentence,whichisplacedinthemiddleasastylisticchoice.Asitisnotdividingtheclauseinwhichitisplaced,acommaoneithersidedenotesitasaseparatethought.
24. Answer:F.IsitRelevant:Inserting
Thesequestionsarealmostalwayseasiertosolvebyelimination.G-Jcanbeeliminatedbecauseoftheirreasoning.Itdoesnotexplainastatementordistractfromthefocus,norisitvague.Itisaspecific,relevantdetail,soFiscorrect.
25. Answer:D.Apostrophes:Itโs/Its
Itโsvs.Its.ThewaytorememberthedifferenceistorememberthatโItโsโisacontractionofโItis.โInacontractiontheapostropheholdstheplaceoftheomittedletter(s).Asonecannotignorethemissingi,insteadthepossessivedropstheapostropheasitservesonlytodenotethatitisinfactpossessive,whichisredundantseeingasthereisnopreexistingwordwithwhichtoconfuseit(thepluralofโitโisnotโitsโ).
26. Answer:J.Transitions
โStill,โโconsequently,โandโinsteadโallsuggestacontradictionoraconcession.Inthiscasethereisneither;theideasbeingconnectedaresimplybeingtiedtogether,soasimpleโalsoโiscorrectanddoesnotmakeirrelevantimplications.
27. Answer:D.Verbs:Agreement
Subject-verbagreement!Theclothesarethesubject,andtheyarenโtcapableofdecorating.Theycanonlybedecorated,andBisinthewrongtense.ThisonlyleavesD.
28. Answer:F.SentenceOrderRearrangingthesentencetofindtheclausesisveryuseful.Inthiscase,byswappingtheclausespresentedwecanseetheyareinfactalreadycorrect.Theotheroptionscannotbemovedinthesameway,andaregrammaticallyincorrect.
29. Answer:B.ParagraphOrder
Usecluesinthesentencestoconnectthedots.Sentence4naturallyleadsintosentence2,andinthesameway1and3areconnected.Withthesetwopartsweonlyhavetofindwhichgoesinfront.Assentence2doesnotleadintosentence1,wecandeterminethat1,3,4,2isthecorrectorder.
30. Answer:F.IsitRelevant:Deleting
Gisobviouslyincorrectbecausethefriendisnotonlyirrelevantbutalsonotevenidentified.OptionsHandJjustdonโtmatter;neitherisareasontonotincludetheopeningparagraph,astheyreferencenorulesofwriting.F,however,correctlyidentifiesthepurposeoftheintrotoestablishsubjectandtonewithananecdote.
31. Answer:D.Non-EssentialandEssential
ClausesOptionsA&B,despitepunctuation,areinthewrongtense.Thesentenceshouldbeinthepasttensetomatchthetext,aswithC&D.C,however,isnotpunctuatedcorrectly,soonlyDiscorrect,eventhoughitomitsthedetail.
32. Answer:H.Apostrophes:Itโs/Its
Possessive,notacontraction.โItisโwouldnotfit,andtheotheroptionsareentirelyincorrect.
33. Answer:C.IsitRelevant:Inserting
Becauseโworkโandโliveโareusedspecificallyabove,itshouldbeanimmediateindicatorthatanswerCisredundant.Onceyoucheckthattheothersareindeednotbetteroptions,Ccanbedeterminedastheanswer.
ACTTest1163
34. Answer:F.ParallelStructure:PrepositionsThechangesprovided,whilenotglaringlywrong,areallunnecessaryandonlyaddconfusion.Aswritten,โoutsideโisspecificandconciseenoughandshouldbeleft.
35. Answer:B.AdjectivesandAdverbs
Readitoutloud!Wheredoesitmakesense?โGreatlyโisanadverb,andthusmustmodifyaverb.Thetrickinesshereisthattheyaskwhatitcomesafter,whichisnotactuallybeingmodified.Theverbโextendsโisbeingmodifiedbyโgreatly,โandtocomebeforeโextendsโitmustbeafterโability.โ
36. Answer:H.IsitRelevant:Inserting
Thereasoninginthefirsttooptionsisnotrelevant;neithercamaraderienorcomfortpertainstothepassage.Jisalsoincorrectbecausethelackofdescriptionshasnothingtodowithwhetheritshouldbeincludedinrelationtotherestofthepassage.
37. Answer:D.Non-EssentialandEssential
ClausesTheextraspecificationofdepthshouldnotinfluencetheexistingclauses,sobynestingitbetweencommasitbecomesanasidethatdoesnotchangethestructureofthesentencewhilestilladdingthedetailinacorrectandrelevantplace.
38. Answer:J.JoiningandSeparating
Sentences:Comma+FANBOYSThismarksthestartofanewideainnowaydependentonthepriorsentence.Thus,aperiodandastartofanewsentenceisappropriate.ThesemicoloninoptionCwouldonlybenecessaryifthefollowingindependentclauseneededtobetiedtotheprecedingsentence.
39. Answer:B.Verbs:Agreement
Subjectandverb.TheverbatthestartisโBolted,โsowhatisbolted?Theresearchoutpost.A,C&Dwouldallbesayingthescientistsareboltedtotheseafloor.
40. Answer:F.IsitRelevant:InsertingGdoesnotofferacompleteanswer,Haddstheโatoddsโportionfornoreason,andJisfartoovague.Foffersallthenecessaryspecifications.
41. Answer:A.WordPairsand
ComparisonsOneofthesethingsisnotliketheother!Aclassificationisnotsimilartotheotheranswerswhichalldescribeanumberofobjects.
42. Answer:F.SentencesandFragments
โAspecialairpocketthatkeepstheoceanoutside,โisnotacompletesentence.Itisadependentclause,soitmustbeattachedtoanindependentclausebyacommaasinthetext.
43. Answer:C.AdjectivesandAdverbs
Wemusthaveanadverb(endingin-ly)todescribetheverbโreturned,โbecauseโgradualโmustbedescribingsomesortofchange.Pressurecannotbegradual,butareturncan.CiscorrectbecausetheโandโissuperfluousinoptionB.
44. Answer:H.ParagraphOrder
Animportantclueisthewordโthisโinsentence1.Itmustbereferringtosomethingbeforeit,sowhichsentencehasadecompressiontowhichitmaybereferring?Sentence2.Similarly,sentence3impliesanotherobjectasthepricetopay,soitmustcomeaftersomething.Thisgivesusthefinalorderof2,1,3.
45. Answer:D.SupposetheWriterโsGoal
Thekeywordhereisโgenerally.โAandBreferencedescription,whichisnotrelevant.CincorrectlystatesthattheessayfocusesontheroleofUNC.Dcorrectlypointsoutthegeneralityoftheessay.
46. Answer:F.RelativePronouns:Who(se),
Whom,Which,Where,andThatThewordโinโmakesnosensehere.Grantwasnotinsidehisownaccomplishments!Theothersaresimplyrewordingsmeanttoconfuseyou.
ACTTest1163
47. Answer:D.ShorterisBetter:RedundancyandWordinessTheotheroptionsareexceedinglyredundant.Whendiscussinghisinvention,itisalreadyimpliedthathecreatedit.
48. Answer:F.Apostrophes:Possessivevs.
PluralGimpliesthegolfersinventedthem.Hisnotevenusable.Jisacontractionandwouldnotmakesense.AttributingtheinventiontoGrant,asisintheoriginaltext,isthemostcorrectoption.
49. Answer:A.Verbs:Tense
Inthiscasethetensemustbeinitsinfinitiveform,asitalreadyis.Theotheroptionsincorrectlyconjugateitandaddextraneouswordstomixyouup.
50. Answer:J.WordPairsandComparisons
Thewordbeingverbโdinthisquestionisโproblem,โsowhichismostappropriate?Wouldhecorrect,alleviate,fix,orrescueaproblem?Evenifyoudonโtknowallthewordsused,ifyouknowโrescueโyouknowitdoesnโtfit.
51. Answer:B.IsitRelevant:Inserting
Readtheparagraph!Thisgivesyouthecontexttofigureoutwhatneedstointroducethem.OnceyouidentifythesubjectoftheparagraphtobeGrantโsdentalachievements,Bistheclearchoice.
52. Answer:G.Apostrophes:Itโs/Its
Thisquestiontestsyouonbothapostrophesandcommas.BecausethedesignispossessedbyGrant,wemusthaveanapostrophebeforethes.ThecommaisunnecessarybecauseโThoseconstructedaccordingtoGrantโsdesign,โisonlyasubjectwithnopredicateandthusmayleadstraightintothepredicate.
53. Answer:B.Verbs:Agreement
Findingthesubjectfortheverbiskeyhere.Whatisthesubject?โThegeneralhealthofhispatients,โmorespecificallyโhealth.โThisissingular,andthepluralโpatientsโaftermaythrowyouoff.Asour
subjectissingularandweareinthepasttense,โwasโisthecorrectoption.
54. Answer:F.AdditionalCommaUsesand
MisusesInthiscase,thetemptationtoputacommaattheendcomesfromthemistakethat2articlesmakealist;theydonot.Jisnotcorrect,andthecommaafterโinventionโinG&Hisalsounnecessary.Althoughitโsamouthful,thetextiscorrectasis.
55. Answer:A.ShorterisBetter:
RedundancyandWordinessAnswersB-Dareredundant.Eachissimplyanother,moreconfusingwayofsayingโaneed.โTheneedisofcourseoutthere,inexistence,andbydefinitionthelackofsomething.Itcanbeleftasisforconcisenessandclarity.
56. Answer:H.ParallelStructure:
PrepositionsThekeyhereistorecognizethewordโfocusโafewwordsbefore.Onedoesnotfocusatsomething,norforsomething,nortosomething.โOnโisthecorrectprepositiontoaccompanythewordโfocus.โ
57. Answer:D.Non-EssentialTransitions,
Words,andPhrasesRemembertoalwayspayspecialattentiontoomissions.Inthiscase,thereisnoneedtoincludeoneofthesetransitionwordsbecausenoneofthemmakesensefollowingtheconclusionoftheparagraphprior.
58. Answer:H.Non-EssentialTransitions,
Words,andPhrasesโAbrilliantprofessorofdentistryโisnotanindependentclause,andsocannotsupportmuchofthepunctuation.Acomma,however,simplymakesitastatementdescribingthesubjectโhe,โwiththeantecedentโDr.GeorgeFranklinGrant.โ
ACTTest1163
59. Answer:D.Verbs:TenseInthiscase,aninfinitiveverbmustfollowtheconjugatedโmakingitpossible.โThisisnecessarytoprevent2separatepredicatesfromformingoutofone.โToconcentrateโdoesjustthat.
60. Answer:H.SupposetheWriterโsGoal
Thisquestionistricky.Thefirsttwooptionsaretemptingbecausethedescriptionsaretruetotheessay,howevertheydonotaddressthequestionproperly.Thequestionreferstoโkeyinnovations,โplural.Thismeanstheremustbemultiple.Hmentionsthis,andwhileJisthecorrectinitsconclusionthereasoningiscompletelyirrelevant.
61. Answer:C.Non-EssentialClauseโ,...,โ
Aperiodcannotbecorrectbecausetheleadingsentencewouldbeafragment.Itmusthaveacomma,however,todenotethephraseโtheyearourhousewasbuiltโdoesnotbeginthepredicate.
62. Answer:J.ParallelStructure:
PrepositionsGandHcanbereadilyeliminatedbecausetheydonotfitwiththesurroundingsentence,howeverdeterminingbetweenFandJcanbedifficultbecauseitโslessreadilydeterminable.Itcanbededuced,however,becausetheโschemeโwasoneforthecollectionofgarbage.Althoughitisaboutitaswell,forismorespecific.
63. Answer:A.RelativePronouns:Who(se),
Whom,Which,Where,andThatThisisnotsuggestingareasoning,soB-Darenotcorrect.โBeingthat,โโsothat,โandโsince,โallimplyanexplanation,whichisunnecessaryandincorrect.
64. Answer:H.DictionandRegister
Itโsimportanttogetsomecontextbeforeansweringthisquestion,soreadaheadtounderstandhowthesidewalksarebeingportrayed.Astheauthoristryingtocontrastwiththeimageofuncleantrashcans,optionHisthemostappropriatetoshowcasehowthetrashcanshurttheimage.
65. Answer:B.ParallelStructure:PrepositionsNoneoftheoptionsherearefantastic,andindeedthecorrectoneevensoundsalittleoff.TryreadingthemaloudtoeliminatethemoreobviouslyincorrectoptionslikeAandD.
66. Answer:J.ShorterisBetter:
RedundancyandWordinessTheโwerehaveโandโwouldhaveโinFandGarenotcorrectbecausetheydidworkthatway.Itispasttenseandfact,sothereisnocatch.Hisincorrectbecausetheโthatโisunnecessary,andJisbothdefiniteandconcise.
67. Answer:A.WordPairsand
ComparisonsThequestionspecificallyreferencesโthewriterโsdescription,โsothefirstthingyoushoulddoisgoandfindit.Thewordsโnarrowโandโslenderโareusedtodescribethealleys,soitmakessensethatthelargetruckshadtoโsqueezethrough.โTheotheroptionsdonotmakereferencetothescarcedescriptionprovided,soareincorrect.
68. Answer:H.IsitRelevant:Replacing
Thereโsnotricktoaquestionlikethis.F,G,&Jsimplydonโthaveanythingtodowiththetext,whereasHisanaturalinclusionwiththedescriptionsoflargetruckstraversingnarrowalleys.
69. Answer:C.JoiningandSeparating
Sentences:Periods,Semicolons&Comma+FANBOYSBecareful!TheโNOTโinthequestioniseasytomiss.Colonsandsemicolonscanbeconfusing,soifyouarenโtsureaboutthemmakesureyouuseallyourcommaknowledgefirst.Ifyoudothis,recognizingthatCisdefinitelywrong(evenifBandDaremaybes)getsyoutheanswer.Asanew,independentthoughtisstarted,acommaisindeedincorrect.
ACTTest1163
70. Answer:G.Verbs:TenseThisisanothertrickyone.Thesubjectisunclearlyโwhat,โsowehavetodetermineitbylookingattheverbs.Sinceโwhatwas,โinthepasttense,itmakessensethatinthepresenttenseโwhatis.โThewordโnowโcluesyouintothatchangeoftense,andifyouโrecarefulwiththesubjectyoushouldfindtheanswerreadily.
71. Answer:B.WordPairsand
ComparisonsโAttractionโhasaconnotationunliketheother4words.Whileโdisplay,โโexhibition,โโspectacle,โandโshowing,โallmerelydenotethetrashcansโbeingputoutforalltosee,โattractionโhasaconnotationwhichwouldimplytheyareputoutwiththeintentionofdrawingpeopletoseethem.Thisisasubtledifference;however,theothersaresosimilarthateventhissmalldiscretioniskey.
72. Answer:F.RelativePronouns:Who(se),
Whom,Which,Where,andThatInthiscase,eliminatingtheanswersprovidedisthebestbet.โWhomโisusedwithprepositions,โwhichโwouldnotbeusedforpeople,andโwhoseโispossessive.Noneoftheseapplytothechildren,whothusremainโwho.โ
73. Answer:B.Apostrophes:Itโs/Its
WatchtheโNOTโinthequestion!Itshouldbeclearthatsomethingisneededtojointheseideas,andthescarcityofoptionBisasglaringasitappears.Theothersallprovidesomemeansofconjunctionortransition(and,comma,thatis)whichallowthetwoideastoremaintogether.Simplysquishingthemintoonesentenceisnotallowed.
74. Answer:G.Colons
Colonsareusedmostcommonlytopresentanexampleorlist.Inthiscase,alistoffeaturesimmediatelyfollows,soacolonisappropriatetoleadthelist.
75. Answer:C.ParagraphOrder
Theclueforthisquestionisthewordโthemโinsentence4.Towhomisitreferring?Asgarbagetrucksarealsomentioned,โthemโmustbereferringtothechildrenmentionedinsentence2,soitwouldbestfitimmediatelyfollowingit.
ACTTest1163
1.C.Mean,Average1998 1,417=3.59 394
C.3.62.H.MultipleFigures
20+10+5+4+5+6=60
H.60
3.B.Inequalities
B.-2ยฃx<3
4.J.Exponents3ร2$%& = 3ร2()*3ร8 = 24
J.245.D.PropertiesofIntegers๐๐ = 8If๐ = โ6๐ = )2
3
NOTaninteger.D.-6
6.J.Solids44 = 64
J.64
7.B.AlgebraicOperations$40forlarge$25forsmall40๐ฟ + 25โข50.
B.๐๐๐ณ + ๐๐๐๐8.B.Angles
10๐ฅ = 180๐ฅ = 187โข๐ฅ = 7โข18 = 126 G.1269.E.Probability
E.3431
Probabilitycannotbegreaterthan100%10.K.LinearFunction:Rate
K.
11.E.Rate&Proportion60ร80 = 4800(2LLMN
= 19.2
E.๐๐๐๐๐๐
ACTTest1163
12.F.Rate&Proportion12ร1414" = 1๐๐ก
124ร144= 3ร3
12
F:๐ร๐ ๐
๐
13.E.Percent20+40+20=8020%tomato(.2)x=250x=250/.2x=1250
E.125014.H.CirclesC=50โ300(12)50
= 72
H:๐๐15.A.AlgebraicOperations4๐ฅM โ 3๐ฅ + 7 โ โ1 + 5๐ฅ + 2๐ฅM 4๐ฅM โ 3๐ฅ + 7 + 1 โ 5๐ฅ โ 2๐ฅM2๐ฅ๐ โ 8๐ฅ + 8
A.๐๐๐ โ ๐๐ + ๐16.H.Fractions$5.00=ticket12๐ฅ โ $1.00 = $5.00
12๐ฅ = 6
๐ฅ = 12
H:1217.B.PercentOnlyonegivesawholenumber.. 85 20 = 17
B.85%
18.F.SequenceGeometricsequencemeansmultiplyordivide.375-1.56-2496Multiplier=)M(
3=-4
96 โ4 = โ384
F:-38419.A.Factoring&FOIL2๐ฅ โ 3๐ฆ M4๐ฅM โ 12๐ฅ๐ฆ + 9๐ฆM
A.๐๐๐ โ ๐๐๐๐ + ๐๐๐
20.J.Triangles
64=
๐ฅ14๐ฅ = 21
J.21
21.C.SolvingEquations7๐ฅ โ ๐ฅ โ 3 = 67๐ฅ โ ๐ฅ + 3 = 66๐ฅ = 3
๐ฅ =12
C.๐/๐
Trap:Beverycarefuldistributingnegativesigns.Thisproblemdoesnottakelongtodo,sogetitrightbybeingmindfulandexecuting.22.G.Triangles,301GeometryVocabulary๐ด =
12๐โ
32 =12ร8รโ
G:8
ACTTest1163
23.D.Functionsf(x)๐ ๐ฅ = 2๐ฅM โ 5๐ฅ + 7๐ โ10 = 2 โ10 M โ 5 โ10 + 7= 200 + 50 + 7
D.25724.J.Rate&Proportion. 4 200 + . 5 300 + . 6 ๐ฅ = 35080 + 150 + .6๐ฅ = 350. 6๐ฅ = 120๐ฅ = 200200 + 300 + 200 = 700
J.70025.E.PercentAtleast16meanseveryone16,17,and18.26+31+9=66%
E.66%26.H.Percent๐ฅ100
23
=13
x=50%
H.๐๐%27.B.Fractions84 โ . 75 4 = 21
B.$21.00
28.K.Ratio
K.๐: ๐
29.A.Variation:Direct,Inverseyvariesdirectlytoproductofw2andx๐ฆ = ๐๐คM๐ฅyvariesinverselyasz3
๐ฆ =๐๐ง4A.y=kw2x
z3
30.K.Triangles
๐ = 2๐ฃ๐ฃ + ๐ + ๐ = 180๐ฃ + 2๐ฃ + 2๐ฃ = 1805๐ฃ = 180๐ฃ = 36๐ = 2๐ฃ = 2โข36 = 72
K.7231.E.Factoring&FOIL๐ = ๐M โ 300๐ โ 100,000๐ = ๐ โ 500 ๐ + 200
E.๐๐๐32.F.LinearFunctions:y=mx+b
โBreakevenโiswherelinescross.Cost=Revenue
F.10,00033.H.LinearFunctions:y=mx+b
H.$30,00034.H.LinearFunctions:y=mx+b
(L(= $10๐๐๐โ
H.$10.00
ACTTest1163
35.E.Factoring&FOIL2๐ฅ + 2๐ฅ๐ฆ + 6๐ฅM๐ฆ2๐ฅ 1 + ๐ฆ + 3๐ฅ๐ฆ
E.๐๐ ๐ + ๐ + ๐๐๐ 36.G.LinearFunctions:y=mx+bPluginpoints4(1)โ3=14(-3)โ(-13)=1-12+13=1
G.๐๐ โ ๐ = ๐
37.B.MultipleFiguresArea=ะป r2 36 ะป = ะป r2 r = 6 perimeter square = 4s 4ร6 = 24 Biggest mistake is to solve for area of a square and get (c) = 36
B.๐๐38.G.SystemsofEquations3๐ฅ + 6๐ฆ = 52๐ฅ + 6๐ฆ = 24EliminationSubtractbottomfromtop 3๐ฅ + 6๐ฆ = 52โ๐ฅ โ 6๐ฆ = โ242๐ฅ = 28๐ฅ = 14
G.1439.C.Quadrilaterals
3L%*LL
M80 = 6,400
C.6400
40.J.Triangles
40M + 80M = ๐ต๐ถM8000 = ๐ต๐ถM๐ต๐ถ = 8000
J. ๐๐๐๐41.A.MultipleFigures
Fitthecircleinside!Radius=2L
M
=40
A.4042.J.Trigonometry
๐ ๐๐ 15 =
?35
. 259 35 =?9.065 =?
J.๐. ๐
ACTTest1163
43.B.PropertiesofIntegers
Drawcircle,labelit,count.2-skipsalltheodds3-rightanswerultimatelyhitseverymark4-ultimatelyonlyhitsevens5-onlyhitsbyfives6-onlyevens,neverodds
B.344.H.Exponents&Rootsy=catSincetheexponenttisapositiverealnumber,theonlywayforytodecreaseisforatobeadecimalorfraction.0<a<1Ex:*
M *
M
M= *
( *
M
4= *
2
H.0<a<1
45.D.CoordinateGeometry&XY-PlaneDistanceformula (๐ฅM โ ๐ฅ*)M + (๐ฆM โ ๐ฆ*)M(โ2 โ 1)M + (โ1 โ 3)M(โ3)M(โ4)M9 + 1625
5
ordrawit
D.546.F.LinearFunctions:y=mx+bSula Jean2๐๐๐ก๐๐๐ ๐ ๐๐๐๐๐
๐ก + 10๐๐๐ก๐๐๐ ๐โ๐๐๐ = (2.4๐๐
)(๐ก)
F.2t+10=2.4t47.D.Inequalitiesxโค64+2xโฅ0-solve2xโฅ-4xโฅ-2-switch-2โคxโค6
D.-2โคxโค6
48.K.Counting,Permutations,&Combinations
55+40โ20=75120โ7s=45
K.45
49.C.LinearFunctions:y=mx+bm=3perpendicularslopeisโoppositereciprocalโ
๐๐ =โ13
C.-๐
๐
ACTTest1163
50.J.CoordinateGeometry&XY-Plane๐ฅM + ๐ฅ*2
,๐ฆM + ๐ฆ*2
2๐ + 4๐
2= 12
6๐2= 12
3๐ = 12๐ = 4
J.451.D.Counting,Permutations,&CombinationsNOTREPEATED5 ร 4 ร 3 ร 2 ร 1 = 120
D.12052.H.CoordinateGeometry&XY-Plane
๐ป๐ทhaslengthof1
H.(๐, ๐, ๐)
53.B.Logarithms2๐๐๐4
$ยฃ
ยค+ ๐๐๐3 ๐ฆ
Firstpart:combineliketerms(samebase)2๐๐๐4๐ฅ โ ๐๐๐4๐งCoefficientofalogisanexponent2๐๐๐4๐ฅ = ๐๐๐4๐ฅM๐๐๐4๐ฅM โ ๐๐๐4๐งSubtractioninlogarithmisdivision๐๐๐4
$ยฃ
ยค
Nextpart:*M๐๐๐3๐ฆ = ๐๐๐3 ๐ฆ Putitalltogether:๐๐๐4
$ยฃ
ยค+ ๐๐๐3( ๐ฆ)
๐ฉ. ๐๐๐๐
๐๐
๐+ ๐๐๐๐( ๐)
54.G.Inequalities,ABSAbsoluteValue*Note:TheACTlovestoputinequalitiesandabsolutevaluestogetherTip:MaximumValueforanabsolutevalealmostalwaysmeansthemostnegative.|-4-2(5)|=|-14|
G.1455.D.Polygons
Totaldegreesofapentagon:540 Individualangleofaregularpentagon:108360โ108=252
D.252ยฐ56.F.Trigonometry๐ ๐ฅ = ๐ ๐๐ ๐ฅ โ ๐๐๐๐๐๐ก๐๐ข๐๐๐ก๐๐๐๐ ๐ฅ = ๐ด๐ ๐๐ ๐ต๐ฅ + ๐ + ๐ท-Amplitude=A-Period=Mยฐ
ยฑ
-Phaseshift=)ยฒยฑ
-Verticalshift=DTip:ACTfocusesonAmplitude,A,andVerticalShift,D-Foranamplitudeof2,๐ ๐ฅ = ๐ด๐ ๐๐ ๐ฅ ๐ด = 2๐ ๐ฅ = 2๐ ๐๐(๐ฅ)
F.f(x)=2sin(x)57.A.AlgebraicOperationsSolveforr
๐ =๐๐ก โ 3๐ โ ๐ก
๐ ๐ โ ๐ก = ๐๐ก โ 3 ๐๐ โ ๐๐ก = ๐๐ก โ 3๐๐ โ ๐๐ก = ๐๐ก โ 3๐ ๐ โ ๐ก = ๐๐ก โ 3
๐ =๐ ๐ก โ 3๐ โ ๐ก
A.๐๐)๐๐)๐
ACTTest1163
58.G.Angles,Triangles
180โ(100+35)=45
G.45ยฐ59.E.Trigonometry
bisadjacentto20,butoppositeto703isoppositeto20,butadjacentto70
๐ก๐๐ 70 =๐3
๐ = 3๐ก๐๐(70)
E.๐๐๐๐(๐๐)60.K.Trigonometry,Angles1573รท3604Remainder133
A. โ227-360=-587TRUEB. 133โ260=-227TRUEC. 133=133TRUED. 133+360=493TRUEE. 573โ360=213FALSE
K.573ยฐ