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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