ACTTest1163

1. Answer:C.JoiningandSeparatingSentences:CommaThestartofanewindependentclause(thatis,anideathatcontainsbothsubjectandpredicatewithoutneedofanotherideaonwhichto“depend”)signalstheneedofaperiod.Dincludestheunnecessary“While,”whichwouldimplyanothersimultaneousactioninthefollowingsentence,andthusisnotcorrect.

2. Answer:H.IsitRelevant:Inserting

Theanswermustbea“no”becausetheideapresentedisnotconsistentwiththepassage,whichmakesnoreferencetodancers’careers.WecaneliminateJbecausetheinformationdoesnotcontradictthepassage.

3. Answer:B.AdditionalCommaUsesand

MisusesTheclausesinthissentenceare“GrowingupinMexicointhe1920s”and“Hernandezbelievedshewasborntodance.”Identifyingthesewithoutanycommasmakesclearwheretheyareseparated.Imagineamovienarratorsayingthesentenceandemphasizingthepause.Wheredoyouhearit?

4. Answer:G.Non-EssentialTransitions,

Words,andPhrasesThephrases“despite,”“infact,”and“ontheotherhand”arealltransitionswhichintroduceanewthoughtwhichisbynaturecontrarytotheprecedingpoint.Herfather’sacquiescenceisnotcounterintuitive,however;itsimplyshowsthenaturalresultofherpersistence.

5. Answer:D.IsitRelevant:Deleting&

ShorterisBetter:RedundancyandWordinessTheunderlinedportionandallotheroptionsareunnecessaryandredundant.Wearealreadytoldthatheacquiesced,sotostatethathegaveinisalreadystatedandneednotberepeated.Omissionisgrammaticallycorrectandconcise.

6. Answer:H.ColonsAsinnumber3,readtheoptionswithcommasaloud.Wheredoesapauseoccurnaturally?Ordoesit?Inthiscase,theunderlinedportiondoesnotincludeachangeofclauseatall.Nopunctuationisnecessary,asitissimplycontinuingtheexplanationofAmalia’stutelage.

7. Answer:A.Non-EssentialTransitions,

Words,andPhrasesSimilarlytoquestion4,someanswershereusetransitionwordswhicharenotcorrectinthiscontext.AnswersCandDwouldservetointroducenewideas;however,thisisnotthecaseattheendofthisparagraph.OptionBissimplynotrelevanttothepassage,asonecandeterminefromreading.A,however,bothtiesupthisparagraphandhintsatthestartofthenext.Readingaheadbyasentenceortwoisagreatwaytogainsomecontextforthesetransitionquestions.

8. Answer:H.Apostrophes

Possessive.There’snotricktothis;youjusthavetoknowwheretheapostrophesgo.Asingularpossessivewillalwayshaveanapostrophebetweenthewordandthes(savethefewirregularexceptions).

9. Answer:A.WordPairsandComparison

Thesequestionsareahybridofvocabandinference.Ifoneknowsthemeaningsofall5(4answers+underlined)words,thereisonlytodeterminewhichisdifferentandwhy.Inthiscase,Aistheoutlierbecause“grouping”doesnotimplythehomogenizationtheotheroptionsdo.Intheother4,thepartsarechangedtocreateawhole.InA,theyarepreserved.

10. Answer:G.ParallelStructure:Lists

Listscanbetricky.It’simportanttoknowthatinlistsalllistedarticlesmustbeofthesamepartofspeech.Inthiscase,“life”and“death”arenouns.“Tohavearebirth,”aswellasoptionsHandJ,areactuallyverbsphrasesusing“Tohave”and“Tobe.”Theoption“Rebirth”isconsistentwiththeotherarticleslisted.

ACTTest1163

11. Answer:D.TransitionsOften,omissionsarethecorrectchoice.Youshouldstillchecktheotheroptions,though,toconfirm.Inthiscase,“However,”“Nevertheless,”and“Instead,”allimplyacontradiction.Readingthesentence,however,weseethatinfactthesetransitionsarenotonlyunnecessarybutincorrect.

12. Answer:F.IsitRelevant:Inserting

OptionsG-Jareeasilyeliminatedbytheirreasoning.GandJbothmentiondescription,howevertheparagraphwasaninformativeonewhichdidnotdescribetheballets.HcanbeeliminatedbecausetheparagraphdidnotfocusontheMIFAinthefirstplace.Fistheonlyreasonableanswerbecauseitaccuratelyclassifiestheadditioninrelationtothetext.

13. Answer:C.Dashes

Thebiggesthinthereistheemdashimmediatelyfollowing.Emdashesalmostalwayscomeinpairs,especiallywheninthemiddleofasentence.Theotheroptionswouldimproperlyseparatetheportionfollowingtheexistingdashasanewclause,whenit’sreallybeinginterruptedbyanaside.

14. Answer:G.IsitRelevant:Replacing

Theanswerhereisinthequestion.Onlyoneanswershowsa“valuablecontribution.”

15. Answer:B.SupposetheWriter’sGoal

Wecaneliminate3answerseasilyinthisquestion.Aisincorrectbecausethepassagedoesnotfocusonawards,andC&Dtrytomakesemanticdistinctionsbutfailbecausetheyarenotactualevidence,seeingasthequestiondoesnotnecessitateartistsingeneralorspecificdanceforms.

16. Answer:E.Apostrophes:Possessivevs

PluralBecarefulnottomistakeageneralpronounforapluralone.“Someone”issingular,sothesingularpossessive“else’s”isalreadycorrect.

17. Answer:C.JoiningandSeparating

Sentences:Comma+FANBOYSHerearetwoindependentclauses,whichshouldbetheirownsentencesmoreoftenthannot.Theunderlined“which”isunnecessary,sosimplifyingthisinto2simplesentencesiseasy.Thisisanothertypeofquestionwhichisgoodtoreadaloudorimaginebeingreadbyanarrator.

18. Answer:F.WordPairsand

ComparisonsThisisavocabquestionindisguise!Whatdoallthesewordsmean?Whatdotheyaddtothetoneofthetext?Ifyoudon’tknowallthewords,usecontexttoestimatewhattheymean.Asthey’relistedtogether,youcanbettheyareverysimilar!

19. Answer:D.Verbs:Agreement

Amatterofredundancyoncemore.ReadingtheseoptionsaloudshouldquicklyeliminatetheunwieldyB&C,andDmakesaclearverb-nounagreement.

20. Answer:H.WordPairsand

ComparisonsThecluehereisintheword“of.”Allanswersmakesensefollowedbytheword“of”exceptH;hedoesn’tcarry“manyofpens.”

21. Answer:D.Verbs:Tense

Thisisatrickierquestion,whichcanbedeterminedbytense.“Ifeel”ispresent,sowecandetermineweneedanotherpresent-tenseverb.A&Barebothinfinitive,whileCisnoteventhecorrectpartofspeech.

22. Answer:G.Pronouns:Agreementand

TenseHandJcanbeeasilyeliminatedbecausetheyare,respectively,toovagueandblatantlyincorrectinnumbering.ThedistinctionbetweenFandGissubtlebutimportant:Greinforcesthepointtheauthorismaking.Whenthepenheisusingisrundryheneedsanother.“They”wouldmeanallofthepenshehaswith

ACTTest1163

him,inwhichcaseitwouldn’tmatterifhehadanotherasitmayalsobedry.

23. Answer:C.SentenceOrder&

Non-EssentialClause“,...,”Tryrearrangingthesentencetogetanideaoftheclauses.Itcanbewritteninsteadas“Smallpilesofuncappedballpointsgatheronmynighttableasifoftheirownaccord.”Herewecanseethat“asifoftheirownaccord”isaseparateclausefromtherestofthesentence,whichisplacedinthemiddleasastylisticchoice.Asitisnotdividingtheclauseinwhichitisplaced,acommaoneithersidedenotesitasaseparatethought.

24. Answer:F.IsitRelevant:Inserting

Thesequestionsarealmostalwayseasiertosolvebyelimination.G-Jcanbeeliminatedbecauseoftheirreasoning.Itdoesnotexplainastatementordistractfromthefocus,norisitvague.Itisaspecific,relevantdetail,soFiscorrect.

25. Answer:D.Apostrophes:It’s/Its

It’svs.Its.Thewaytorememberthedifferenceistorememberthat“It’s”isacontractionof“Itis.”Inacontractiontheapostropheholdstheplaceoftheomittedletter(s).Asonecannotignorethemissingi,insteadthepossessivedropstheapostropheasitservesonlytodenotethatitisinfactpossessive,whichisredundantseeingasthereisnopreexistingwordwithwhichtoconfuseit(thepluralof“it”isnot“its”).

26. Answer:J.Transitions

“Still,”“consequently,”and“instead”allsuggestacontradictionoraconcession.Inthiscasethereisneither;theideasbeingconnectedaresimplybeingtiedtogether,soasimple“also”iscorrectanddoesnotmakeirrelevantimplications.

27. Answer:D.Verbs:Agreement

Subject-verbagreement!Theclothesarethesubject,andtheyaren’tcapableofdecorating.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.OptionsHandJjustdon’tmatter;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:It’s/Its

Possessive,notacontraction.“Itis”wouldnotfit,andtheotheroptionsareentirelyincorrect.

33. Answer:C.IsitRelevant:Inserting

Because“work”and“live”areusedspecificallyabove,itshouldbeanimmediateindicatorthatanswerCisredundant.Onceyoucheckthattheothersareindeednotbetteroptions,Ccanbedeterminedastheanswer.

ACTTest1163

34. Answer:F.ParallelStructure:PrepositionsThechangesprovided,whilenotglaringlywrong,areallunnecessaryandonlyaddconfusion.Aswritten,“outside”isspecificandconciseenoughandshouldbeleft.

35. Answer:B.AdjectivesandAdverbs

Readitoutloud!Wheredoesitmakesense?“Greatly”isanadverb,andthusmustmodifyaverb.Thetrickinesshereisthattheyaskwhatitcomesafter,whichisnotactuallybeingmodified.Theverb“extends”isbeingmodifiedby“greatly,”andtocomebefore“extends”itmustbeafter“ability.”

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.Theverbatthestartis“Bolted,”sowhatisbolted?Theresearchoutpost.A,C&Dwouldallbesayingthescientistsareboltedtotheseafloor.

40. Answer:F.IsitRelevant:InsertingGdoesnotofferacompleteanswer,Haddsthe“atodds”portionfornoreason,andJisfartoovague.Foffersallthenecessaryspecifications.

41. Answer:A.WordPairsand

ComparisonsOneofthesethingsisnotliketheother!Aclassificationisnotsimilartotheotheranswerswhichalldescribeanumberofobjects.

42. Answer:F.SentencesandFragments

“Aspecialairpocketthatkeepstheoceanoutside,”isnotacompletesentence.Itisadependentclause,soitmustbeattachedtoanindependentclausebyacommaasinthetext.

43. Answer:C.AdjectivesandAdverbs

Wemusthaveanadverb(endingin-ly)todescribetheverb“returned,”because“gradual”mustbedescribingsomesortofchange.Pressurecannotbegradual,butareturncan.Ciscorrectbecausethe“and”issuperfluousinoptionB.

44. Answer:H.ParagraphOrder

Animportantclueistheword“this”insentence1.Itmustbereferringtosomethingbeforeit,sowhichsentencehasadecompressiontowhichitmaybereferring?Sentence2.Similarly,sentence3impliesanotherobjectasthepricetopay,soitmustcomeaftersomething.Thisgivesusthefinalorderof2,1,3.

45. Answer:D.SupposetheWriter’sGoal

Thekeywordhereis“generally.”AandBreferencedescription,whichisnotrelevant.CincorrectlystatesthattheessayfocusesontheroleofUNC.Dcorrectlypointsoutthegeneralityoftheessay.

46. Answer:F.RelativePronouns:Who(se),

Whom,Which,Where,andThatTheword“in”makesnosensehere.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

Thewordbeingverb’dinthisquestionis“problem,”sowhichismostappropriate?Wouldhecorrect,alleviate,fix,orrescueaproblem?Evenifyoudon’tknowallthewordsused,ifyouknow“rescue”youknowitdoesn’tfit.

51. Answer:B.IsitRelevant:Inserting

Readtheparagraph!Thisgivesyouthecontexttofigureoutwhatneedstointroducethem.OnceyouidentifythesubjectoftheparagraphtobeGrant’sdentalachievements,Bistheclearchoice.

52. Answer:G.Apostrophes:It’s/Its

Thisquestiontestsyouonbothapostrophesandcommas.BecausethedesignispossessedbyGrant,wemusthaveanapostrophebeforethes.Thecommaisunnecessarybecause“ThoseconstructedaccordingtoGrant’sdesign,”isonlyasubjectwithnopredicateandthusmayleadstraightintothepredicate.

53. Answer:B.Verbs:Agreement

Findingthesubjectfortheverbiskeyhere.Whatisthesubject?“Thegeneralhealthofhispatients,”morespecifically“health.”Thisissingular,andtheplural“patients”aftermaythrowyouoff.Asour

subjectissingularandweareinthepasttense,“was”isthecorrectoption.

54. Answer:F.AdditionalCommaUsesand

MisusesInthiscase,thetemptationtoputacommaattheendcomesfromthemistakethat2articlesmakealist;theydonot.Jisnotcorrect,andthecommaafter“invention”inG&Hisalsounnecessary.Althoughit’samouthful,thetextiscorrectasis.

55. Answer:A.ShorterisBetter:

RedundancyandWordinessAnswersB-Dareredundant.Eachissimplyanother,moreconfusingwayofsaying“aneed.”Theneedisofcourseoutthere,inexistence,andbydefinitionthelackofsomething.Itcanbeleftasisforconcisenessandclarity.

56. Answer:H.ParallelStructure:

PrepositionsThekeyhereistorecognizetheword“focus”afewwordsbefore.Onedoesnotfocusatsomething,norforsomething,nortosomething.“On”isthecorrectprepositiontoaccompanytheword“focus.”

57. Answer:D.Non-EssentialTransitions,

Words,andPhrasesRemembertoalwayspayspecialattentiontoomissions.Inthiscase,thereisnoneedtoincludeoneofthesetransitionwordsbecausenoneofthemmakesensefollowingtheconclusionoftheparagraphprior.

58. Answer:H.Non-EssentialTransitions,

Words,andPhrases“Abrilliantprofessorofdentistry”isnotanindependentclause,andsocannotsupportmuchofthepunctuation.Acomma,however,simplymakesitastatementdescribingthesubject“he,”withtheantecedent“Dr.GeorgeFranklinGrant.”

ACTTest1163

59. Answer:D.Verbs:TenseInthiscase,aninfinitiveverbmustfollowtheconjugated“makingitpossible.”Thisisnecessarytoprevent2separatepredicatesfromformingoutofone.“Toconcentrate”doesjustthat.

60. Answer:H.SupposetheWriter’sGoal

Thisquestionistricky.Thefirsttwooptionsaretemptingbecausethedescriptionsaretruetotheessay,howevertheydonotaddressthequestionproperly.Thequestionrefersto“keyinnovations,”plural.Thismeanstheremustbemultiple.Hmentionsthis,andwhileJisthecorrectinitsconclusionthereasoningiscompletelyirrelevant.

61. Answer:C.Non-EssentialClause“,...,”

Aperiodcannotbecorrectbecausetheleadingsentencewouldbeafragment.Itmusthaveacomma,however,todenotethephrase“theyearourhousewasbuilt”doesnotbeginthepredicate.

62. Answer:J.ParallelStructure:

PrepositionsGandHcanbereadilyeliminatedbecausetheydonotfitwiththesurroundingsentence,howeverdeterminingbetweenFandJcanbedifficultbecauseit’slessreadilydeterminable.Itcanbededuced,however,becausethe“scheme”wasoneforthecollectionofgarbage.Althoughitisaboutitaswell,forismorespecific.

63. Answer:A.RelativePronouns:Who(se),

Whom,Which,Where,andThatThisisnotsuggestingareasoning,soB-Darenotcorrect.“Beingthat,”“sothat,”and“since,”allimplyanexplanation,whichisunnecessaryandincorrect.

64. Answer:H.DictionandRegister

It’simportanttogetsomecontextbeforeansweringthisquestion,soreadaheadtounderstandhowthesidewalksarebeingportrayed.Astheauthoristryingtocontrastwiththeimageofuncleantrashcans,optionHisthemostappropriatetoshowcasehowthetrashcanshurttheimage.

65. Answer:B.ParallelStructure:PrepositionsNoneoftheoptionsherearefantastic,andindeedthecorrectoneevensoundsalittleoff.TryreadingthemaloudtoeliminatethemoreobviouslyincorrectoptionslikeAandD.

66. Answer:J.ShorterisBetter:

RedundancyandWordinessThe“werehave”and“wouldhave”inFandGarenotcorrectbecausetheydidworkthatway.Itispasttenseandfact,sothereisnocatch.Hisincorrectbecausethe“that”isunnecessary,andJisbothdefiniteandconcise.

67. Answer:A.WordPairsand

ComparisonsThequestionspecificallyreferences“thewriter’sdescription,”sothefirstthingyoushoulddoisgoandfindit.Thewords“narrow”and“slender”areusedtodescribethealleys,soitmakessensethatthelargetruckshadto“squeezethrough.”Theotheroptionsdonotmakereferencetothescarcedescriptionprovided,soareincorrect.

68. Answer:H.IsitRelevant:Replacing

There’snotricktoaquestionlikethis.F,G,&Jsimplydon’thaveanythingtodowiththetext,whereasHisanaturalinclusionwiththedescriptionsoflargetruckstraversingnarrowalleys.

69. Answer:C.JoiningandSeparating

Sentences:Periods,Semicolons&Comma+FANBOYSBecareful!The“NOT”inthequestioniseasytomiss.Colonsandsemicolonscanbeconfusing,soifyouaren’tsureaboutthemmakesureyouuseallyourcommaknowledgefirst.Ifyoudothis,recognizingthatCisdefinitelywrong(evenifBandDaremaybes)getsyoutheanswer.Asanew,independentthoughtisstarted,acommaisindeedincorrect.

ACTTest1163

70. Answer:G.Verbs:TenseThisisanothertrickyone.Thesubjectisunclearly“what,”sowehavetodetermineitbylookingattheverbs.Since“whatwas,”inthepasttense,itmakessensethatinthepresenttense“whatis.”Theword“now”cluesyouintothatchangeoftense,andifyou’recarefulwiththesubjectyoushouldfindtheanswerreadily.

71. Answer:B.WordPairsand

Comparisons“Attraction”hasaconnotationunliketheother4words.While“display,”“exhibition,”“spectacle,”and“showing,”allmerelydenotethetrashcans’beingputoutforalltosee,“attraction”hasaconnotationwhichwouldimplytheyareputoutwiththeintentionofdrawingpeopletoseethem.Thisisasubtledifference;however,theothersaresosimilarthateventhissmalldiscretioniskey.

72. Answer:F.RelativePronouns:Who(se),

Whom,Which,Where,andThatInthiscase,eliminatingtheanswersprovidedisthebestbet.“Whom”isusedwithprepositions,“which”wouldnotbeusedforpeople,and“whose”ispossessive.Noneoftheseapplytothechildren,whothusremain“who.”

73. Answer:B.Apostrophes:It’s/Its

Watchthe“NOT”inthequestion!Itshouldbeclearthatsomethingisneededtojointheseideas,andthescarcityofoptionBisasglaringasitappears.Theothersallprovidesomemeansofconjunctionortransition(and,comma,thatis)whichallowthetwoideastoremaintogether.Simplysquishingthemintoonesentenceisnotallowed.

74. Answer:G.Colons

Colonsareusedmostcommonlytopresentanexampleorlist.Inthiscase,alistoffeaturesimmediatelyfollows,soacolonisappropriatetoleadthelist.

75. Answer:C.ParagraphOrder

Theclueforthisquestionistheword“them”insentence4.Towhomisitreferring?Asgarbagetrucksarealsomentioned,“them”mustbereferringtothechildrenmentionedinsentence2,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.-2£x<3

4.J.Exponents3×2$%& = 3×2()*3×8 = 24

J.245.D.PropertiesofIntegers𝑎𝑏 = 8If𝑎 = −6𝑏 = )2

3

NOTaninteger.D.-6

6.J.Solids44 = 64

J.64

7.B.AlgebraicOperations$40forlarge$25forsmall40𝐿 + 25•50.

B.𝟒𝟎𝑳 + 𝟏𝟐𝟓𝟎8.B.Angles

10𝑥 = 180𝑥 = 187•𝑥 = 7•18 = 126 G.1269.E.Probability

E.3431

Probabilitycannotbegreaterthan100%10.K.LinearFunction:Rate

K.

11.E.Rate&Proportion60×80 = 4800(2LLMN

= 19.2

E.𝟐𝟎𝒄𝒂𝒏𝒔

ACTTest1163

12.F.Rate&Proportion12×1414" = 1𝑓𝑡

124×144= 3×3

12

F:𝟑×𝟑 𝟏

𝟐

13.E.Percent20+40+20=8020%tomato(.2)x=250x=250/.2x=1250

E.125014.H.CirclesC=50”300(12)50

= 72

H:𝟕𝟐15.A.AlgebraicOperations4𝑥M − 3𝑥 + 7 − −1 + 5𝑥 + 2𝑥M 4𝑥M − 3𝑥 + 7 + 1 − 5𝑥 − 2𝑥M2𝑥𝟐 − 8𝑥 + 8

A.𝟐𝒙𝟐 − 𝟖𝒙 + 𝟖16.H.Fractions$5.00=ticket12𝑥 − $1.00 = $5.00

12𝑥 = 6

𝑥 = 12

H:1217.B.PercentOnlyonegivesawholenumber.. 85 20 = 17

B.85%

18.F.SequenceGeometricsequencemeansmultiplyordivide.375-1.56-2496Multiplier=)M(

3=-4

96 −4 = −384

F:-38419.A.Factoring&FOIL2𝑥 − 3𝑦 M4𝑥M − 12𝑥𝑦 + 9𝑦M

A.𝟒𝒙𝟐 − 𝟏𝟐𝒙𝒚 + 𝟗𝒚𝟐

20.J.Triangles

64=

𝑥14𝑥 = 21

J.21

21.C.SolvingEquations7𝑥 − 𝑥 − 3 = 67𝑥 − 𝑥 + 3 = 66𝑥 = 3

𝑥 =12

C.𝟏/𝟐

Trap:Beverycarefuldistributingnegativesigns.Thisproblemdoesnottakelongtodo,sogetitrightbybeingmindfulandexecuting.22.G.Triangles,301GeometryVocabulary𝐴 =

12𝑏ℎ

32 =12×8×ℎ

G:8

ACTTest1163

23.D.Functionsf(x)𝑓 𝑥 = 2𝑥M − 5𝑥 + 7𝑓 −10 = 2 −10 M − 5 −10 + 7= 200 + 50 + 7

D.25724.J.Rate&Proportion. 4 200 + . 5 300 + . 6 𝑥 = 35080 + 150 + .6𝑥 = 350. 6𝑥 = 120𝑥 = 200200 + 300 + 200 = 700

J.70025.E.PercentAtleast16meanseveryone16,17,and18.26+31+9=66%

E.66%26.H.Percent𝑥100

23

=13

x=50%

H.𝟓𝟎%27.B.Fractions84 − . 75 4 = 21

B.$21.00

28.K.Ratio

K.𝟒: 𝟑

29.A.Variation:Direct,Inverseyvariesdirectlytoproductofw2andx𝑦 = 𝑘𝑤M𝑥yvariesinverselyasz3

𝑦 =𝑘𝑧4A.y=kw2x

z3

30.K.Triangles

𝑏 = 2𝑣𝑣 + 𝑏 + 𝑏 = 180𝑣 + 2𝑣 + 2𝑣 = 1805𝑣 = 180𝑣 = 36𝑏 = 2𝑣 = 2•36 = 72

K.7231.E.Factoring&FOIL𝑝 = 𝑛M − 300𝑛 − 100,000𝑝 = 𝑛 − 500 𝑛 + 200

E.𝟓𝟎𝟎32.F.LinearFunctions:y=mx+b

“Breakeven”iswherelinescross.Cost=Revenue

F.10,00033.H.LinearFunctions:y=mx+b

H.$30,00034.H.LinearFunctions:y=mx+b

(L(= $10𝑒𝑎𝑐ℎ

H.$10.00

ACTTest1163

35.E.Factoring&FOIL2𝑥 + 2𝑥𝑦 + 6𝑥M𝑦2𝑥 1 + 𝑦 + 3𝑥𝑦

E.𝟐𝒙 𝟏 + 𝒚 + 𝟑𝒙𝒚 36.G.LinearFunctions:y=mx+bPluginpoints4(1)–3=14(-3)–(-13)=1-12+13=1

G.𝟒𝒙 − 𝟕 = 𝟏

37.B.MultipleFiguresArea=л r2 36 л = л r2 r = 6 perimeter square = 4s 4×6 = 24 Biggest mistake is to solve for area of a square and get (c) = 36

B.𝟐𝟒38.G.SystemsofEquations3𝑥 + 6𝑦 = 52𝑥 + 6𝑦 = 24EliminationSubtractbottomfromtop 3𝑥 + 6𝑦 = 52−𝑥 − 6𝑦 = −242𝑥 = 28𝑥 = 14

G.1439.C.Quadrilaterals

3L%*LL

M80 = 6,400

C.6400

40.J.Triangles

40M + 80M = 𝐵𝐶M8000 = 𝐵𝐶M𝐵𝐶 = 8000

J. 𝟖𝟎𝟎𝟎41.A.MultipleFigures

Fitthecircleinside!Radius=2L

M

=40

A.4042.J.Trigonometry

𝑠𝑖𝑛 15 =

?35

. 259 35 =?9.065 =?

J.𝟗. 𝟏

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 (𝑥M − 𝑥*)M + (𝑦M − 𝑦*)M(−2 − 1)M + (−1 − 3)M(−3)M(−4)M9 + 1625

5

ordrawit

D.546.F.LinearFunctions:y=mx+bSula Jean2𝑚𝑒𝑡𝑒𝑟𝑠𝑠𝑒𝑐𝑜𝑛𝑑

𝑡 + 10𝑚𝑒𝑡𝑒𝑟𝑠𝑎ℎ𝑒𝑎𝑑 = (2.4𝑚𝑠

)(𝑡)

F.2t+10=2.4t47.D.Inequalitiesx≤64+2x≥0-solve2x≥-4x≥-2-switch-2≤x≤6

D.-2≤x≤6

48.K.Counting,Permutations,&Combinations

55+40–20=75120–7s=45

K.45

49.C.LinearFunctions:y=mx+bm=3perpendicularslopeis“oppositereciprocal”

𝑚𝑝 =−13

C.-𝟏

𝟑

ACTTest1163

50.J.CoordinateGeometry&XY-Plane𝑥M + 𝑥*2

,𝑦M + 𝑦*2

2𝑎 + 4𝑎

2= 12

6𝑎2= 12

3𝑎 = 12𝑎 = 4

J.451.D.Counting,Permutations,&CombinationsNOTREPEATED5 × 4 × 3 × 2 × 1 = 120

D.12052.H.CoordinateGeometry&XY-Plane

𝐻𝐷haslengthof1

H.(𝟎, 𝟐, 𝟏)

53.B.Logarithms2𝑙𝑜𝑔4

$£

¤+ 𝑙𝑜𝑔3 𝑦

Firstpart:combineliketerms(samebase)2𝑙𝑜𝑔4𝑥 − 𝑙𝑜𝑔4𝑧Coefficientofalogisanexponent2𝑙𝑜𝑔4𝑥 = 𝑙𝑜𝑔4𝑥M𝑙𝑜𝑔4𝑥M − 𝑙𝑜𝑔4𝑧Subtractioninlogarithmisdivision𝑙𝑜𝑔4

$£

¤

Nextpart:*M𝑙𝑜𝑔3𝑦 = 𝑙𝑜𝑔3 𝑦 Putitalltogether:𝑙𝑜𝑔4

$£

¤+ 𝑙𝑜𝑔3( 𝑦)

𝑩. 𝒍𝒐𝒈𝟑

𝒙𝟐

𝒛+ 𝒍𝒐𝒈𝟔( 𝒚)

54.G.Inequalities,ABSAbsoluteValue*Note:TheACTlovestoputinequalitiesandabsolutevaluestogetherTip:MaximumValueforanabsolutevalealmostalwaysmeansthemostnegative.|-4-2(5)|=|-14|

G.1455.D.Polygons

Totaldegreesofapentagon:540 Individualangleofaregularpentagon:108360–108=252

D.252°56.F.Trigonometry𝑓 𝑥 = 𝑠𝑖𝑛 𝑥 − 𝑝𝑎𝑟𝑒𝑛𝑡𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑓 𝑥 = 𝐴𝑠𝑖𝑛 𝐵𝑥 + 𝑐 + 𝐷-Amplitude=A-Period=M°

±

-Phaseshift=)²±

-Verticalshift=DTip:ACTfocusesonAmplitude,A,andVerticalShift,D-Foranamplitudeof2,𝑓 𝑥 = 𝐴𝑠𝑖𝑛 𝑥 𝐴 = 2𝑓 𝑥 = 2𝑠𝑖𝑛(𝑥)

F.f(x)=2sin(x)57.A.AlgebraicOperationsSolveforr

𝑆 =𝑟𝑡 − 3𝑟 − 𝑡

𝑆 𝑟 − 𝑡 = 𝑟𝑡 − 3 𝑆𝑟 − 𝑆𝑡 = 𝑟𝑡 − 3𝑆𝑟 − 𝑟𝑡 = 𝑆𝑡 − 3𝑟 𝑆 − 𝑡 = 𝑆𝑡 − 3

𝑟 =𝑠𝑡 − 3𝑠 − 𝑡

A.𝒔𝒕)𝟑𝒔)𝒕

ACTTest1163

58.G.Angles,Triangles

180–(100+35)=45

G.45°59.E.Trigonometry

bisadjacentto20,butoppositeto703isoppositeto20,butadjacentto70

𝑡𝑎𝑛 70 =𝑏3

𝑏 = 3𝑡𝑎𝑛(70)

E.𝟑𝒕𝒂𝒏(𝟕𝟎)60.K.Trigonometry,Angles1573÷3604Remainder133

A. –227-360=-587TRUEB. 133–260=-227TRUEC. 133=133TRUED. 133+360=493TRUEE. 573–360=213FALSE

K.573°