ACTTest1572

1. Answer:A.AdditionalCommaUsesandMisusesTheonlynecessarycommaintheunderlinedportionistheonealreadythere,whichservestoseparatetheleadingindependentclausefromtherestofthesentence.

2. Answer:J.Non-EssentialTransitionWordsandPhrasesTheword“similarly”isincorrectherebecausetheusualsix-sidedsnowflakesareunderstoodwell,whilethetriangularonesarenot.Weneedatransitionwordtoshowthecontrarinessoftheseideas.Thebestoptionis“however.”

3. Answer:D.Verbs:Agreement

Theopeningclauseofthissentenceistellingusthatsomething“suggests.”Weneedtodeterminehowtoaccuratelysaywhattheysuggest,whilealsoagreeingwiththenon-underlinedportionthatfollows.Cdoesagreewiththerest;however,itdoesnotagreewith“suggests.”Bhastheoppositeproblem.OnlyDagreeswithbothsidesofthesentence.

4. Answer:H.Verbs:Agreement

Theopeningclauseoffersusaverbinneedofasubject.So,whatorwhore-createdthesnowflakeformation?Notthediscoveryitself,butthescientists.TheonlyanswerwiththemasthesubjectisH.

5. Answer:B.JoiningandSeparating

Sentences:Comma+FANBOYSAnswersC&Dbothofferasecondindependentclauseafterthecomma,whileAdoesthiswithoutevenacomma.Asthereisnoconjunction,wemusthaveadependentclausefollowingthecomma.OnlyBprovidesone.

6. Answer:J.Verbs:AgreementandTenseWemusthaveapluralverbtomatchtheplural“molecules,”aswellasapresent-tenseverbtomatchtherestofthepassage.AnswerJprovidesaplural,presentformof“bump.”

7. Answer:B.IsitRelevant:DeletingHopefullyanswersC&Dimmediatelystandoutasirrelevanttothetext,astheyclearlydonothavetodowiththeunderlinedportion.Aisincorrectbecauseitisnotactuallyanexplanation,butmerelythementionofastep,asinB.

8. Answer:J.Verbs:Agreement

Thesubjectfortheunderlinedverbis“snowflakes,”soweneedapluralconjugation.Italsomustretainthepresenttense.ThereisnoneedforthewordinessinoptionsG&H,soJiscorrect.

9. Answer:C.ColonsAcoloniscorrectherebecauseitthesentence,anindependentclauseuntilthelastword,isleadingtopresentanexample.Asemicolonisincorrectbecause“dust”isnotanindependentclause.“Is”wouldincorrectlycreateanewclausebycreatingapredicate.

10. Answer:J.SentencesandFragments

Theunderlinedportionshouldonlybecontinuingthesubjectofthesentencehere,notcreatingadependentclause.Thesubjectshouldbe“Thegreaterpressurefromthewind,”anddoesn’tneedacommabecausethepredicateimmediatelyfollows.

11. Answer:B.AdjectivesandAdverbs

Because“form”isaverb,itmustbedescribedbyanadverb.Theword“than”followingsoonafterindicatescomparisonwhilealsorulingout“most.”Thus,“morequickly”iscorrect.

12. Answer:G.Non-EssentialTransition

WordsandPhrasesHereweneedonlyincludeacomma.The“although”atthestartcreatesadependentclause,rulingoutalloptionsotherthanthecomma,whichcancombineadependenttoanindependentclause.

13. Answer:A.IsitRelevant:Replacing

Notethatthequestionasksforthemosteffectivewaytoconcludethesentence

ACTTest1572

andtheessay.Itisbestleftas-is,becausetheotheroptionsareeithertoospecific,toovague,orirrelevant.

14. Answer:H.SentenceOrder

Theword“this”inoursentenceisourclue.Wemustfindoutwhichoptionhasthe“growth”referredtoby“this.”TheonlyoptionwhichmakessensehereisH.

15. Answer:D.SupposetheWriter’sGoal

Recallthatwhatisimportanthereisnottheyes/noanswer,butthereasoning.TheonlyanswerwithsupportingevidencethatisbothrelevanttothetextandtrueisD.

16. Answer:H.SentencesandFragments

Becausethebeginningofthissentenceisadependentclause,itdoesnotneedaconjunctionwiththecomma.Ifitwasrearrangedsotheclausebeforethecommacameattheend,itwouldmakesense.Thus,noconjunctionisneeded:onlyacomma.

17. Answer:B.Verbs:AgreementandTense

It’snecessarytohavetheappropriateformoftheverb“need”inthissentence.“Willneed,”isimproperlyfuturetense.“Wouldhaveneeded”impliesthattheydidnotinfactneedthem.“Need”ispresenttense.Theonlypast-tenseandappropriateoptionis“wouldneed,”whichshowsthatitwasinthepast,butcameafterthecurrently-narratedportion.

18. Answer:J.ShorterisBetter:

RedundancyandWordinessItisredundanttorestatetheinformationgivenatthestartofthissentence:“Wetriedtosteadyourselveswithourwalkingsticks.”

19. Answer:C.Verbs:AgreementandTense

ThepasttenseofthestoryimmediatelyeliminatesoptionsB&Dfortheirpresent-tenseverbs.ThedifferencebetweenAandCisthepreposition.“With”isappropriate,because“on”wouldimplytheroofwasliterallyatopthefallenrocks.

20. Answer:H.AdditionalCommaUsesand

MisusesGisquicklyruledoutbecauseitcreatesanewindependentclausewithoutconjunction.WhileJisdependent,itdoesnothaveacomma.OnlyHprovidesadependentclauseproperlypunctuatedwithacomma.

21. Answer:A.Modification

“Mostof”isthecorrectmodifierfor“theroute.”Bisimproperbecause“most”iscomparative,and“part”isnotinthiscase.Clacksa“the”tomakeitcorrect,because“majority”needstobespecifiedas“themajority”vs“theminority,”asthereisonlyonepossiblemajority.Disincorrectbecause“more”isdirectlycomparative,butthereisnootheroptiontowhichitiscompared.

22. Answer:F.Verbs:AgreementandTense

Don’tbethrownoffbytheclausebetweentheemdashes;itdoesnotimpacttherestofthesentence.Becausewehaveacommaandnoconjunction,weknowweneedadependentclausetomatchtheindependentclausebefore.Only“forming,”whichdoesnotaddapronountocreateanewsubject,iscorrect.

23. Answer:B.DictionandRegister

Theuseof“only”and“able”givesasenseoftheauthorbeingpreventedfromdoingmore.Theotheroptionsmerelystatehisprogress,withoutansweringthequestion’srequesttoemphasize“theslownessoftheascent”andhowthey“didnotsettheirownpace.”

24. Answer:H.AdditionalCommaUsesand

MisusesAgainherewehaveaninvertedsentencestructurewithadependentclauseleadingintoanindependent.Asalwaysinthesesituations,asimplecommaisthebestandcorrectwaytopunctuate.Theotheroptionsprovidedallrequirebeginningwithanindependentclause,regardlessofwhatfollows.

ACTTest1572

25. Answer:C.Apostrophes:PossessivevsPluralAlthoughwedon’tknowfromthecontextwhetherthereareoneormorecraters,wecandetermineouranswerfromjustthefirstword.“Cliffs”shouldbepluralandnotpossessive,sothereisnoneedforanapostrophe.BetweenCandD,onlyChasapossessiveformof“crater,”soitistheonlycorrectoption.

26. Answer:F.IsitRelevant:Deleting

Wecanruleoutanumberofanswers.Gbecausetheideaofwaitingwasintroducedjustbefore.Hbecause,necessaryornot,itdoesnotcontradictanything.Jbecauseitisnotanimageatall.

27. Answer:D.WordPairsand

ComparisonsThewordwhichismostappropriatehereis“finally,”becausetheauthorhasjustdescribedtheirwaiting.Theotheroptionsdonotrelatetothisstatementoftime.

28. Answer:G.WordPairsand

ComparisonsWecaneasilydisqualify“wentover,”becauseitdoesn’treallydescribeanything.“Smothered”and“squelched”arenotvery“rugged”words,asthequestionrequests.Only“shattered”bearsthisviolentconnotation.

29. Answer:A.ParagraphOrder

Thefirstparagraphmentions“theotherhikers”justastheproposedadditiondoes.Italsofitsintothechronologyofthenarrative,astheyuseflashlightsonceitisdark.

30. Answer:F.SupposetheAuthor’sGoal

Ifyoureadthepassage(whichhopefullyyouhavebynow),shouldnotbedifficulttodeterminewhichoptionaccuratelydescribesthestory.Itdoesnotfocusontheirtools,therewardingnature,orthebeauty—itjustmentionsthem.Theyareallpartofthestorywhich,overall,describesthechallengesinvolvedintheirjourney.

31. Answer:B.AdditionalCommaUsesandMisusesThereisnoneedforacommahere.Theunderlinedportiondoesnotseparateclauses,listarticles,oranythingelse.Themodifier“namedJuanQuezada”canimmediatelyfollowthemodified“boy,”andsimilarlyleaddirectlyintothepredicate.

32. Answer:H.Non-EssentialandEssential

ClausesThefactthattwoanswersuseparenthesesshouldbeanimmediatesignalthatoneofthemisusingthemincorrectly.Inthiscase,theextracommaafter“pots”makesitincorrectbecauseitisredundant.

33. Answer:B.SentencesandFragments

Theactiveverbhereis“wondered.”Becausetherootofthesentence,“Quezadawondered,”isnotaquestion,wecannotendthesentenceinaquestionmark.ThecommainCisalsoincorrectbecause,again,nothingisbeingseparated;itismerelystatingwhatisbeingwondered.

34. Answer:H.Transitions

Toformagoodtransition,wewantasentencewhichincludesanideafromthelastparagraphandtheupcomingparagraph.TocombineQuezada’sdesiretoemulatethepotswithhisexperimentingwiththeclay,optionHistheonlypossibility.

35. Answer:A.Verbs:AgreementandTense

OptionsB&CimplyQuezadawassellingadedicationtoteachingandateacher.Ashewasnot,infact,sellingthese,weneedanewverbintheunderlinedsentence,notasubject.“Hastaught”isincorrectlypresenttense,sothepast-tense“hadtaught”iscorrect.

36. Answer:F.IsitRelevant:Deleting

Treatthislikeadeletionquestion.Whatwouldbelostwithoutthisdetail?Well,itshowsthathispotsweresoauthentictheyevenfooledananthropologist.This

ACTTest1572

isanimportantsupportingdetail,andisonlyreflectedinanswerF.

37. Answer:A.Verbs:AgreementandTense

&9,Pronouns:AgreementandCaseTheverbforthissentencemustmatchthesubject,“hissearch.”“Himself”isareflexivepronoun,whichmeanssomethingacteduponitself.As“hissearch”didtheacting,itshouldnotbereflexive.“Ledhim”agreeswiththesubjectandtheantecedent.

38. Answer:F.WordPairsand

ComparisonsTheonlyoptionwhichimpliesdelayis“eventual.”Theothershavedifferentmeanings,noneofwhichrespondtothequestionaccurately.

39. Answer:C.RelativePronouns:Who(se),

Whom,Which,Where,andThatAlthoughomissionisoftencorrect,hereitisnot.ThefactthatCismuchshorterandsimpler,though,isagoodhintthatit’sabetteroption.“Where”isnecessarytocreateadependentclause,asthereisnoconjunction.

40. Answer:J.ShorterisBetter:

RedundancyandWordinessTheshortestanswerisoftencorrect.Alsonotethat“morethen”isnevercorrect,asitshouldbe“morethan.”ThestrangepronouninoptionHmakesthisaconfusingmess.Whatistheantecedent?Village,money,pottery?Jissimpleandcorrect.

41. Answer:C.IsitRelevant:Inserting,

Deleting,andReplacingWeneedaspecificanswerhere.Ofcoursetherearemorethan400potters;therearethousands,millions.ItisonlyrelevanttothetextifitistellinghowmanypottersareinMataOrtiz.

42. Answer:G.RelativePronouns:Who(se),

Whom,Which,Where,andThat“Which”isnotusedforpeople.“Them”wouldcreateanindependentclause,whichisincorrectasthereisno

conjunction.“Who”doesnotfollow“of.”Thecorrectpronounhereis“whom.

43. Answer:D.Pronouns:Agreementand

Case“They’re”isverywrong;itisthecontractionof“theyare.”Bincorrectlyusesareflexivepronoun,whenthepeopledescribedareactinguponaseparateentity.Theword“each”means“her”iscorrect,not“hers,”becauseitreferstomultiplesingularpeopleinsteadofagroup.Thus,“hisorher”isthecorrectwaytousepossessivepronounsinthissentence.

44. Answer:J.SentenceOrder

Thereferenceto“eachartist”shouldpointusinthedirectionofasentencediscussingtheartists.TheonlyoptionwhichdoesthisisJ.

45. Answer:C.SupposetheAuthor’sGoal

Thispieceisnotoneofhistoricalinformation,butabiographicalstoryofoneartistinparticular.Althoughitdoesmentionthingsintheotheroptions,noneofthemarethefocusoftheessay.

46. Answer:J.Apostrophes:It’s/Its

Thisisanimportantthingtolearnforthetest.Theapostrophestandsinforthemissingletter“I”in“Itis.”Thissentenceneedsapossessive,sothereshouldnotbeanapostrophe.

47. Answer:D.AdditionalCommaUsesand

Misuses&8,Verbs:AgreementandTenseThereshouldnotbeacommahere!Nothingneedstobeseparatedintheunderlinedportion.Thecorrectverbis“fill,”because“filling”wouldcreateamodificationinsteadofapredicate,leavingthesentenceasafragment.

48. Answer:H.Non-EssentialTransition

WordsandPhrasesBecausetheinformationbeingpresentedafterthetransitionwordiscontrastingfromthatbeforeit,“however”isthecorrectword.Theothersdonotimply

ACTTest1572

thiscontrast,butinsteadcausationorreinforcement.

49. Answer:B.ModificationWecannotcreateanewclausehere.Weinsteadmustmodifythe“architecturebuffs”bydescribingthemas“theretoadmire.”Thepronounsofferedareallincorrect,andtheclosest,D,createsanewindependentclausewithoutconjunction.

50. Answer:F.SeparatingSentences:

SemicolonWouldaperiodworkhere?Yes!OntheACTasemicolonisjustaperiod.Ifitiseveranoption,substituteaperiodandseeifitiscorrect.Herewehavetwoindependentclauses,separatedcorrectlybyasemicolon.

51. Answer:D.IsitRelevant:Inserting

OptionsA&Careeasilyeliminatedbecausetheyhavesuchweakreasoning,butBisatemptingchoice.Theevidenceistrue,becauseitdoesprovidethiscontext.Thisanswerisincorrectbecausethisdetailisnotrelevanttothefocusoftheessay,asoptionDpointsout.Byreadingthroughalltheanswers,youwillrealizethisonceyoureachD.

52. Answer:J.IsitRelevant:Deleting

Omissionisveryoftencorrect,andthefactthattheotheranswersherearesosimilarshouldclueyouin.Thecolorandmaterialcompositionofthebuildingareirrelevantdetailswhichdonotserveanypurposetothistext.

53. Answer:A.SentencesandFragments

Althoughthisisanoddwaytopunctuatethissentence,itismorecorrectthantheoptionspresented.B&Ccreatedependentclausesseparatedbyaperiod,whichisincorrect.Dcreatesanindependentclausewithacommaandnoconjunction,whichisjustaswrong.

54. Answer:F.Verbs:Agreement&

AdjectivesandAdverbsAs“chandeliers”arebeingdescribedby“elegant,”itshouldremainanadjective,notanadverb.As“chandeliers”isplural,wemusthavetheplural“illuminates.”

ACTTest1572

55. Answer:B.DictionandRegisterA&Daredullandwithoutanyimplications,whileCisaverynegativeportrayal.Bispositiveandaccuratelymimicsthestyleofthearchitecture.

56. Answer:G.IsitRelevant:Deleting

Theotheroptionsdonotsufficientlyjustifytheirclaims.Fisoutrightfalse,Hmisidentifiestheessay’sclaim,andJincorrectlyassumesthepurposeofthesentence.

57. Answer:C.ParagraphOrder

AtpointCtheparagraphshiftsfromexteriortointeriorfocus,whichisexactlywhatissoughtbythequestion.

58. Answer:F.Transitions

Noneofthesetransitionsareappropriateinthislocation,sotheyarebetteroffforegone.

59. Answer:D.ShorterisBetter:

RedundancyandWordinessAlloptionshereareredundant,asthe“adding”implicationisalreadypresentintheword“enhancing.”

60. Answer:G.SupposetheAuthor’sGoal

F&Jincorrectlyclaimthepassagefocusesonanumberofbuildingsandstyles,despitetheclearfocusontheLyceumTheatre’sBeauxArtsinfluence.Hiseasilyruledoutifyou’vereadthepassage,asitdoesnotfocusonthesets.

61. Answer:C.SentencesandFragments

Thepreposition“with”signalsthatweneedanounhere.“Inaccuracies”isthenounoption,andassuchitmustbemodifiedbytheadjectiveform“factual,”nottheadverb“factually.”

62. Answer:G.Colons

Thecolonhereisusedproperly,inthatitfollowsanindependentclauseandleadsintoanexampleorextrapolation.

63. Answer:D.Verbs:AgreementBecausethesubjecthereis“untruths,”despitetheclausebetweendashes,theverbmustbepluraltomatch.“Matter”isthecorrectplural,presentoption.

64. Answer:F.JoiningandSeparating

Sentences:Comma+FANBOYS“For”isaconjunctionwhich,withacomma,allowsustocombinetwoindependentclauses.Thisiscorrectas-is.Donotbetemptedtopicktheperiodorsemicolon;theconjunctionmakestheclausedependent!Alsonotethatiftwooptionsuseaperiodandsemicoloninthesameway,theymustbothbewrongbecausetheyarefunctionallythesameontheACT.

65. Answer:C.Transitions

Thewords“rather”and“instead”aresignaltransitionwordswhichshouldimmediatelycatchyoureye.BetweenC&D,onlyoneleadsintothethesisoftheessayasawhole.Considerreadingaheadandcomingbacktothistodeterminejustwhatthattopicis.

66. Answer:H.Apostrophes:Possessivevs.

PluralThissentencecontainsasingular-possessiveandaplural(“movement’s”and“advocates”respectively).Althoughitcanbeconfusingtoseeboth,thisisastraightforwardquestionifyoudon’trushthroughit.

67. Answer:D.AdditionalCommaUsesand

MisusesThereisnoneedforacommahere,as“Sheherself”isnotaclause,butonlythesubjectofthissentence.

68. Answer:G.IsitRelevant:Inserting

Remember,theonlyimportantpartoftheansweristheevidence.Inthiscase,theincorrectanswersdisregardtheimportanceofthisdetailincreatingcharacter,whileGsupportswhythedetailisimportant.

ACTTest1572

69. Answer:D.JoiningandSeparatingSentences:SemicolonDon’tknowhowtouseasemicolon?Useaperiod!Bothseparateindependentclauses,andarefunctionallythesameonthistest.

70. Answer:J.IsitRelevant:Deleting

TheonlyanswerwhichisrelevanttothetextisJ.Itisimportanttoreadthepassagewell,andifnecessarygobackintothetext.Withoutthecontext,questionslikethisareverydifficult.

71. Answer:A.IsitRelevant:Inserting

It’simportanttoreadtheanswerscarefully,becausesomewilltryandtrickyou.Obviouslythecomparisonisnotunrelated,norisitrepeated,butBmaytemptyoubecauseshemaywellhavecaredforherworkersinthatway.Aisthebestanswer,though,becausethismetaphoriscentraltothetext.

72. Answer:F.Colons

Notethatcolonsmustfollowanindependentclause.Thefollowingclauseisanexample,soacolonisappropriate.Theotheroptionsareconvolutedandincorrect.Itisimportanttolearnhow,where,andwhencolonsareacceptable;or,attheveryleast,whennothingelseis.

73. Answer:B.Transitions

Theonlytransitionwordherewhichimpliescausation,asthetextwouldimply,is“because.”Theotherswouldimplyshewascontrarytotheworkers,orasimilarlyincorrectrelationship.

74. Answer:H.Apostrophes:They’re,Their,

There“Their”istheformwhichreferstopossessionbyaplural.“Behalf”doesnotneedtobetransformedinanyway,andthestrangeapostropheinJshouldbereasonenoughtoignoret.

75. Answer:D.SupposetheAuthor’sGoalDiscorrectbecauseitsupportsitsclaimwithevidencetruetothetext,whichdoesfocusonMotherJones.Theotheranswerchoicesreferenceeitherherorthelabormovement,butnotboth,asrequiredbytheprompt.

ACTTest1572

1.D.ProbabilityTypeAorAB67 + 6 = 73

D. 𝟕𝟑𝟏𝟓𝟎

2.H.Mean,Average+,-.+/-.+0-.+1-.+/-

2

H.342

3.E.Rate&Proportion/3" = 18𝑚𝑖𝑙𝑒𝑠.2/0= 3.2

>

Solveforx.𝑥 = (/0)(3.2)

.2

E.90

4.F.SolvingEquations450 = c(10)+

𝑐 =4501000

F.0.455.E.Functionsf(x)𝑓 𝑥 = (3𝑥 + 7)3𝑓 1 = (3 ∗ 1 + 7)3𝑓 1 = 100

E.1006.H.Percent6%increase(12)(1.06)=12.72

H.$12.72

7.E.Sequence1,-3,9,-27,_________Geometricmeansmultiple.Hereitismultiplyby-3.-27*-3=81 5th8*-3=-243 6th-243*-3=729 7thterm

E.𝟕𝟐𝟗

Note:Thesearethepowersof3whichyoushouldbefamiliar.8.H.Rate&Proportion1box15lbsFee+Priceperpound$10 + . 65 15 = $19.75 H.$19.759.A.Solids. 32 − 2(.03)

. 02= 13

H.13

10.K.Median13,15,16,19,19,22|25, 25, 26, 27, 28, 2933.323

= 23.5

K.23.5

11.C.LinearFunctions:y=mx+b1. 𝑃𝑙𝑢𝑔𝑖𝑛𝑡 = 10, 𝑑 = 14

A. 14=0+14C. 14=6*0+14EliminateB,D,E

2. 𝑃𝑙𝑢𝑔𝑖𝑛𝑡 = 1, 𝑑 = 20A. 20=1+14NOC. 20=6+14YES

C.𝒅 = 𝟔𝒕 + 𝟏𝟒

12.K.Quadrilaterals𝑙 ∗ 𝑤 = 549 ∗ 𝑤 = 54𝑤 = 62 9 + 2 6 = 30

ACTTest1572

K.3013.B.Angles,Triangles

B.100

14.H.Sectors&Arcs,Charts&Graphs4𝑐𝑜𝑟𝑒9𝑡𝑜𝑡𝑎𝑙

=𝜃(𝑎𝑛𝑔𝑙𝑒)360°

Solvefor𝜃.

𝜃 =4 ∗ 36090

𝜃 = 160°

H:𝟏𝟔𝟎°Note:Knowhowtodothis.ACTlovesthisproblem.15.B.SystemsWordProblemsS+L=70$12L=$8SHowmanylargeS=70–L12L=8(70–L)distribute12L=560–8L20L=560L=2�-

3-

L=28

B.𝟐𝟖16.H.LinearFunctions:y=mx+b220 − 88

3= 44

H:44

17.D.Angles

< 𝐵𝐴𝐷 = 133

B.133°18.F.Fractions/32�20

LCD=24/3313-31/231

“ascending”/331< /2

31< 3-

31

F:𝟏𝟐< 𝟓

𝟖< 𝟓

𝟔

19.D.Exponents&Roots

D.𝟏. 𝟑𝟕×𝟏𝟎𝟗

20.F.Quadrilaterals

F.(180–x)

• alotlike304;Angles

ACTTest1572

21.B.Percent1,000 ( 0-

/--)( �-/--)

(1,000)(.8)(.6)=480

B.𝟒𝟖𝟎22.H.Exponents&Roots𝑎� = x𝑐� = yx×y =?substitute𝑎�×𝑐� = (𝑎𝑐)�

H:(𝒂𝒄)𝒃23.A.AlgebraicOperations/3𝑦3(6𝑥 + 2𝑦 + 12𝑥 − 2𝑦)combineliketerms/3𝑦3 18𝑥 = 9𝑥𝑦3A.𝟗𝒙𝒚𝟐

24.H.Factoring&FOIL500p − 𝑝3 = 60,000𝑝3 − 500p + 60,000𝑝 − 200 𝑝 − 300 = 0

H.200Tip:Whenthereisafactoringproblem,lettheanswersgiveyouaclue.25.B.Charts&Graphs

B.28%

26.G.Angles

G.(𝟕𝟎 − 𝒙)°

27.E.Triangles

E.𝟏𝟔 + 𝟖 𝟐

28.H.Quadratics&Parabolas

solutioniswherey=0orxintercept

H.1positive,1negativerealsolutions“realsolution”meansparabolacrossesx-axis.Ifthesolutionisnotrealitisimaginary.29.C.ComplexNumbers−3𝑖 + 4 3𝑖 + 4 𝐹𝑂𝐼𝐿−3 ∗ 3𝑖 − 4 ∗ 3𝑖 + 4 ∗ 3𝑖 + 16−9 −1 + 16 = 25

C.25

ACTTest1572

30.G.Trigonometry

G. 𝟓

𝟕𝟓𝟓

31.D.Probability

750 + 5𝑒𝑥𝑡𝑟𝑎 = 7555𝑒𝑥𝑡𝑟𝑎755𝑡𝑜𝑡𝑎𝑙

=5755

Don’tyouthinktheACTshouldreduceto //22

?

D. 𝟓𝟕𝟓𝟓

32.K.FractionsThemidpointissimplytheaverage.(3++ +

1)/2

math>frac

K.𝟏𝟕𝟐𝟒

Note:33–35arethreeofthemostmissedquestions!33.B.Rate&Proportion.25inch=2ft>.32= /2

3

x=1.875B.𝟏. 𝟖𝟕𝟓

34.H.MultipleFiguresNotcovered=whole–cabinetWhole=12x15=180

180–(16+24)=140

H.𝟏𝟒𝟎

35.D.LinearFunctionsy=mx+b2,150 = 650 + (10)(𝑥)Thereare10cabinets.Pricepercabinet=3/2-.�2-

/-=150

Twiceasmany650 + 20 ∗ 150

D.𝟑𝟔𝟓𝟎36.J.SystemsofEquations,203;Inequalities1 < 𝑥 + 𝑦 < 2breakacompoundintotwoinequalities1 < 𝑥 + 𝑦𝑥 + 𝑦 < 2graphlineinstandardform,useintercepts1 < 0 + 𝑦(0,1)1 < 𝑥 + 0)(1,0)

𝑥 + 𝑦 < 20 + 𝑦 < 2(0,2)𝑥 + 0 < 2(2,0)

90%ofstudentsmissthisone!

ACTTest1572

37.A.Mean,Median+.0./-./2

1= 9

3, 8, __,10,15; median = 9 Difference 9 – 9 = 0

A.𝟎38.F.2Quadratics&Parabolas,LinearFunctionsy=mx+b,SystemsofEquations

Wheredotheyintersect?Thatiswherethefunctionsareequal.F.𝒇 𝒙 = 𝒈 𝒙 𝒇𝒐𝒓𝒆𝒙𝒂𝒄𝒕𝒍𝒚𝟐𝒗𝒂𝒍𝒖𝒆𝒔𝒐𝒇𝒙39.B.Slope

𝑚 = 1°/

±°/3= +

°+

B.-1

40.F.CoordinateGeometry&XY-Plane

F.−𝟏𝟐, 𝟏

41.E.Quadrilaterals

+.±3=6 3./3

3= 7

(�.,)3

= 6.5MIDPOINT!meansaverageCutintoequalareaismidpointsofb1andb2.

E.6.5

42.K.Functionsf(x)𝑓 𝑥 = 𝑥 − /

>

𝑔(𝑥) = 1/𝑥𝑓(𝑔(1/2)) = (1/(1/2)) − (1/(1/2))ℎ𝑢𝑙𝑜?𝑔(1/2) = 1/(1/2) = 2𝑓 2 = 2 − /

3=+

3

F.𝟑

𝟐

43.D.AlgebraicOperationsP =

µ¶·¸¹.·

/3¹

Factorout“a”

𝑃 =µ¶¸¹./

/3¹𝑎

Mutiplyaby2,meansbalanceequationbyP×2.

D.𝑷×𝟐

ACTTest1572

44.G.CoordinateGeometryandXY-Plane

𝐸𝐹 = 4×(𝐸𝐷)

8is4×24+2=6

G.8.6

45.D.MatrixAmatrixcanhaveacoefficient.Distributethe“a”2𝑎 6𝑎𝑎 4𝑎 = 𝑥 27

𝑦 𝑧

6𝑎 = 27𝑎 = ±

3𝑜𝑟4.5

2𝑎 = 𝑥2 4.5 = 𝑥9 = 𝑥4𝑎 = 𝑧4 4.5 = 𝑧18 = 𝑧9 + 18 = 27

D.𝟐𝟕

46.J.Fractions/0ofthewhole/0𝑥 + 10 = 34𝑥Solvefor𝑥.𝑥 = 16

J.1647.B.Solids“Mostlikely”86:25518:51Thesearethesame“whole”51𝑥 = 255𝑥 = 518×5 = 90

Mostlikely=11th ±

322

B.11th

48.G.Fractions,Exponents&Roots13+ 3

+=?

FindLCM1 +3 +

+ 3 3+ 3

G.𝟒 𝟑.𝟐 𝟐

𝟔

49.A.SystemsofEquations,215;EquationsofaCircle,207;LinearFunctionsy=mx+bFirstfindthelinearinequality.

Second,thecircleisshadedinside.Solutionsmustbelessthanradius.(𝑥 − 1)3 + (𝑦 − 2)3 < 9

A.𝒚 < −𝒙 + 𝟐

(𝒙 − 𝟏)𝟐 + (𝒚 − 𝟐)𝟐 < 𝟗

ACTTest1572

ACTTest1572

50.F.Solids

Volumeofwater 40×30×20 = 24,000Itincreasesby.25 40×30×20.25 = 24,300Displacement=Difference 24,300 − 24,000

F.30051.E.Ratio𝑥: 𝑦 = 5: 2𝑦: 𝑧 = 3.2(5:2)3=15:16(3:2)(2)=6:4𝑥: 𝑧 = 15: 4

E.15:452.H.Inequalities−5 < 1 − 3𝑥 < 10breakintoparts−5 < 1 − 3𝑥−1−1−6 = −3𝑥°�°+< °+>

°+switchsign

2 > 𝑥1 − 3𝑥 < 10−1−1−3𝑥 < 9°+>°+

< ±°+switchsign

𝑥 > −3

H.−𝟑 < 𝒙 < 𝟐

53.B.SolidsA=2𝑙𝑤 + 2𝑙ℎ + 2𝑤ℎDoubleeach2 21 2𝑤 + 2 21 2ℎ + 2 2𝑤 2ℎ81𝑤 + 81ℎ + 8𝑤ℎincreasebyfactorof4

𝐁. 𝟒

54.K.LinearFunction:Rate(,¿·ÀÁ)(+·¹Á)

3 + 𝑑 =?3 ,

++ 𝑑 ,

+

K.7+𝟕𝒅

𝟑

55.E.Counting,Permutations,&Combinations

28+45–65=8

E.8

56.K.MultipleFigures,Fractions

13×12+

13×13+

13×14=

1336

K.𝟏𝟑

𝟑𝟔

ACTTest1572

57.A.Trigonometry

A.𝒂 < 𝟎𝒂𝒏𝒅𝒃 = 𝟎

58.K.ABSAbsoluteValue𝑥 − 5 < −1Thesmallestvaluefor 𝑥 is0!ThereCANNOTbeanegativeABS.

K.EmptySet59.E.Probability𝟏𝟑× 𝟏𝟑× 𝟏𝟑× 𝟏𝟑= 𝟏

𝟖𝟏

E. 𝟏

𝟖𝟏

60.J.Trigonometry

Note:Thesmallestangleisoppositethesmallestside.

J.𝟏𝟒𝟐 = 𝟏𝟖𝟐 + 𝟐𝟎𝟐 − 𝟐 𝟏𝟖 𝟐𝟎 𝒄𝒐𝒔𝜽