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°