Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023)

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ThePrincetonReviewPublishingTeamRobFranek,Editor-in-ChiefDavidSoto,SeniorDirector,DataOperationsStephenKoch,SeniorManager,DataOperationsDeborahWeber,DirectorofProductionJasonUllmeyer,ProductionDesignManagerJenniferChapman,SeniorProductionArtistSelenaCoppock,DirectorofEditorialOrionMcBean,SeniorEditorAaronRiccio,SeniorEditorMeaveShelton,SeniorEditorChrisChimera,EditorPatriciaMurphy,EditorLauraRose,EditorAlexaSchmittBugler,EditorialAssistantPenguinRandomHousePublishingTeamTomRussell,VP,PublisherAlisonStoltzfus,SeniorDirector,PublishingBrettWright,SeniorEditorEmilyHoffman,AssistantManagingEditorEllenReed,ProductionManagerSuzanneLee,DesignerEugeniaLo,PublishingAssistantThePrincetonReview110East42ndStreet,7thFloorNewYork,NY10017Email:editorialsupport@review.comCopyright©2022byTPREducationIPHoldings,LLC.AllrightsreservedPublishedintheUnitedStatesbyPenguinRandomHouseLLC,NewYork.SomeofthecontentinACTMathPrephaspreviouslyappearedinMathandScienceWorkoutfortheACT,4thEditionpublishedasatradepaperbackbyRandomHouse,animprintanddivisionofPenguinRandomHouseLLC,in2019.TermsofService:ThePrincetonReviewOnlineCompanionTools(“StudentTools’)forretailbooksareavailableforonlythetwomostrecenteditionsofthatbook.StudentToolsmaybeactivatedonlyoncepereligiblebookpurchasedforatotalof24monthsofaccess.ActivationofStudentToolsmorethanonceperbookisindirectviolationoftheseTermsofServiceandmayresultindiscontinuationofaccesstoStudentToolsServices.ISBN9780525570356EbookISBN9780525570394ACTisaregisteredtrademarkofACT,Inc.ThePrincetonReviewisnotaffiliatedwithPrincetonUniversity.Thematerialinthisbookisup-to-dateatthetimeofpublication.However,changesmayhavebeeninstitutedbythetestingbodyinthetestafterthisbookwaspublished.Ifthereareanyimportantlate-breakingdevelopments,changes,orcorrectionstothematerialsinthisbook,wewillpostthatinformationonlineintheStudentTools.RegisteryourbookandcheckyourStudentToolstoseeifthereareanyupdatespostedthereEditor:ChrisChimeraProductionEditors:LizDacey,KathyG.CarterProductionArtists:GabrielBerlinandJasonUllmeyerCoverartbyLightFieldStudiosInc./AlamyStockPhotoCoverdesignbySuzanneLee|vv1StudyXY

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AcknowledgmentsSpecialthankstoNicoleCosme,StaceyCowap,LoriDesRochers,SpencerLeDoux,AaronLindh,ScottO'Neal,JacobSchiff,andJamesWilliamsfortheirworkincreatingthistitle.—AmyMinsterContentDirector,HighSchoolProgramsThanksforGabrielBerlin,JasonUlimeyer,KathyCarter,andLizDaceyfortheirhardworkandcarefulattentiontoeverypageintheproductionofthisbook.SpecialthankstoAdamRobinson,whoconceivedofandperfectedtheJoeBloggsapproachtostandardizedtests,andmanyoftheothersuccessfultechniquesusedbyThePrincetonReview.+StudyXy

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ContentsGetMore(Free)ContentPartI:Orientation1AllabouttheACT2HowtoApproachtheACTOnlineTest3ACTStrategiesandtheMathTestPartIl:BigImpact4PluggingInPluggingInDrill5PluggingIntheAnswersPluggingIntheAnswersDrill6PlaneGeometryPlaneGeometryDrill7CoordinateGeometryCoordinateGeometryDrillPartIll:PracticeTests8MathPracticeTest19MathPracticeTest1:AnswersandExplanations10MathPracticeTest211MathPracticeTest2:AnswersandExplanations12MathPracticeTest313MathPracticeTest3:AnswersandExplanations14MathPracticeTest415MathPracticeTest4:AnswersandExplanations

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1GotoPrincetonReview.com/prepandenterthefollowingISBNforyourbook:97805255703942AnswerafewsimplequestionstosetupanexclusivePrincetonReviewaccount.(Ifyoualreadyhaveone,youcanjustlogin.)3EnjoyaccesstoyourFREEcontent!Needtoreportapotentialcontentissue?ContactEditorialSupport@review.comandinclude:«fulltitleofthebook«ISBN«pagenumberNeedtoreportatechnicalissue?ContactTPRStudentTech@review.comandprovide:«yourfullname«emailaddressusedtoregisterthebook«fullbooktitleandISBN«Operatingsystem(Mac/PC)andbrowser(Chrome,Firefox,Safari,etc.)Onceyou’veregistered,youcan...«GetourtakeonanyrecentorpendingupdatestotheACT«Takeafull-lengthpracticeACT«Getvaluableadviceaboutthecollegeapplicationprocess,includingtipsforwritingagreatessayandwheretoapplyforfinancialaid«Ifyou'restillchoosingbetweencolleges,useoursearchablerankingsofTheBest388Collegestofindoutmoreinformationaboutyourdreamschool.«Checktoseeiftherehavebeenanycorrectionsorupdatestothisedition+StudyXy

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LookForTheseIconsThroughoutThePROVENTECHNIQUESAPPLIEDSTRATEGIESMOREGREATBOOKSONLINEARTICLES

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PartIOrientation

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Chapter1AllAbouttheACT

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TheACTcanbeanimportantpartofcollegeadmissions.ManyschoolsrequireorrecommendtheirapplicantssubmiteitherSATorACTscores.It’sworthkeepinginmind,though,thattheimportanceofthesetestswillvaryamongthemanycollegesanduniversitiesintheUnitedStates.Ifyouhaven’talready,makesuretoresearchwhethertheACTisrequiredorrecommendedforadmissiontotheschoolsyouplantoapplyto.DuringtheCOVID-19pandemic,manyschoolswenttest-optionaltoaccountforthenumerousstudentswhoseSATandACTtestswerecanceled.Someofthoseschoolshavereturnedtorequiringtestscores,whileothershavenotyetbutstillmay.Forthemostup-to-dateinformationontheschoolsyouareinterestedin,checkouttheiradmissionswebsites.Formoreonadmissions,seeThePrincetonReview'sTheBest388Collegesorvisitourwebsite,PrincetonReview.comEvenifACTscoresareoptional,youmaystillwanttosubmitthemifyouthinkyourgreatACTscoreswillboostyourchancesofacceptance.Furthermore,ACTscoresareoftenusedforscholarships,soitcanbeworthputtingtimeintopreparingforthetestifyoucansaveagoodamountonyourcollegeeducationinreturn.Whencollegesrequirestandardizedtestscores,theywillaccepteitherSATorACTscores.TheexpertadviceofThePrincetonReviewistotakewhichevertestyoudobetteronandfocusyoureffortsonpreparingforthatone.Becauseyouboughtthisbook,weassumeyou'vealreadymadethedecisiontoboostyourACTscore.Thisbookprovidesastrategicandefficientwaytoimproveyourscores,specificallyontheMathtest.Foramorethoroughreviewofcontentandexhaustivepractice,werecommendpurchasingthelatesteditionsofACTPrepandourACTPracticeQuestionsbook.TheACTMathtestisnothinglikethemathtestsyoutakeinschool.AllofthecontentreviewandstrategiesweteachinthefollowinglessonsarebasedonthespecificstructureandformatoftheACT.Beforeyoucanbeatatest,youhavetoknowhowit’sbuilt.StructureTheACTismadeupoffourmultiple-choicetestsandanoptionalWritingtest.Thefivetestsarealwaysgiveninthesameorder.+StudyXY

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«English:45minutes,75questions«Math:60minutes,60questions«Reading:35minutes,40questions«Science:35minutes,40questions«Writing:40minutes,1EssayorScience,pleaseseeourcompanionbooks:ACTEnglishPrep,ACTReadingPrep,andACTSciencePrep.ScoringWhenstudentsandschoolstalkaboutACTscores,theymeanthecompositescore,arangeof1-36.Thecompositeisanaverageofthefourmultiple-choicetests,eachscoredonthesame1-36scale.IfyoutaketheWritingtest,you'llalsoreceiveanadditionalWritingscoreonascaleof2-12.TheWritingscoreisanaverageoffour2-12subscores:IdeasandAnalysis,DevelopmentandSupport,Organization,andLanguageUseandConventions.NeithertheWritingtestscorenorthecombinedEnglishplusWritingEnglishLanguageArtsscoreaffectsthecomposite.BesuretocheckACT’swebsitetodeterminewhetheryourtargetschoolswantyoutotaketheACTWritingtest.Studentsalsoreceivesubscoresinadditiontotheir(1-36)compositeACTscore.Theseindicatorsaredesignedtomeasurestudentperformanceandpredictcareerreadiness,aswellascompetencyinSTEM(Science,Technology,Engineering,Mathematics)andEnglishlanguagearts.ACTbelievesthattheseadditionalscoreswillgivestudentsbetterinsightintotheirstrengthsandhowthosestrengthscanbeharnessedforsuccessincollegeandbeyond.Inadditiontothe1-36scoreforeachofthetestsandtheircompositescore,studentsnowseescorebreakdownsinthefollowingcategories:«STEMscore.ThisscorewillshowyouhowwellyoudidontheMathandScienceportionsofthetest.«ProgressTowardCareerReadinessindicator.TheACTwouldhaveyoubelievethisindicatormeasureshowpreparedyouareforacareer,butreallyitjustmeasureshowpreparedyouaretotakeyetanothertest:theACTNationalCareerReadinessCertificate™.«EnglishLanguageArtsscore.IfyoutaketheWritingtest,thisscorewillgiveyouacombinedscorefortheEnglish,Reading,andWritingtests.«TextComplexityProgressindicator.Thisscorewilltellyouhowwellyoufaredonthosehardpassagesthroughoutthetest.Thereisalsoasectiononthescorereportthatbreakseachsectiondownintocategoriesandtellsyoubothhowmanyquestionstherewereineachcategoryandhowmanyofthemyougotcorrect.Someofthesecategoriescanbeusefulinhelping

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youknowwhatyouneedtostudy:forexample,ifyoumissedalotofquestionsinthe“Geometry”category,youshouldbrushupyourgeometryskills.Butifyoudidpoorlyinthe“IntegrationofKnowledgeandIdeas”category,it’snotquiteasobviouswhatyouneedtostudy.Don’tworryaboutthesescoresthough—they’retherebecausetheyalignwithfederalacademicstandards,andschooldistrictsthatusetheACTforstandardizedtestingforalljuniorswantthosescores,butcollegesdon’ttypicallylookatthemforadmissionspurposes.It’sAllAbouttheCompositeWhetheryoulookatyourscoreonlineorwaittogetitinthemail,thebiggestnumberonthepageisalwaysthecomposite.Whileadmissionsofficeswillcertainlyseetheindividualscoresofallfivetests(andtheirsubscores),schoolswillusethecompositetoevaluateyourapplication,andthat’swhy,intheend,it’stheonlyonethatmatters.Thecompositeisanaverage:letthefullweightofthatsinkin.Doyouneedtobringupallfourscoresequallytoraiseyourcomposite?Doyouneedtobeasuperstarinallfourtests?Shouldyoufocusmoreonyourweaknessesthanyourstrengths?No,no,andabsolutelynot.Thebestwaytoimproveyourcompositeisnottoshoreupyourweaknessesbutexploityourstrengthsasmuchaspossible.compositescoreashighaspossibleYoudon’tneedtobearockstaronallfourtests.Identifytwo,maybethreetests,andfocusonraisingthosescoresasmuchasyoucantoraiseyourcomposite.Workonyourweakestscorestokeepthemfrompullingyoudown.Thinkofitthisway:ifyouhadonlyonehourtodevotetopracticetheweekbeforetheACT,spendthathouronyourbestsubjects.Single-SectionTestsandSuperscoringThepeoplewhowritetheACThaveannouncedtheirintentiontoallowstudentstotakeone,two,orthreeindividualsectionsinaday—thatis,youwillnothavetotaketheentiretestinonesingleday.However,beforeusingthisoption,youwillneedtotakeafullACT.Also,single-sectiontestsareofferedonlyoncomputer.Unfortunately,planstooffersingle-sectionretestingweredelayedbytheCOVID-19pandemic,andasofthepublicationofthisbook,adatefortherollouthasnotbeenannounced.WeencourageyoutochecktheACTwebsite,www.act.org,forthemostup-to-dateinformationabouttheavailabilityofsingle-sectionretestingwhenitiseventuallyoffered.OnepieceofgoodnewsisthatACThasbegunSuperscoring.IfyoutaketheACTmorethanonce,ACTwillautomaticallytakeyourhighestEnglish,Math,Reading,

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andSciencescoresandaveragethemtogethertocalculateanew“Superscore”composite.Soundsgreat,right?Wethinkitis—thisgivesyoutheopportunitytoshowyourbestACTscoretoschools.Now,collegesanduniversitiesstillhavetheoptionofwhethertoaccepttheSuperscore,butfortheschoolsthatletyouSuperscore,thisisallpositiveforyou.Single-sectiontestingisgreat,butresearchyourgoalschools’Ofcourse,youmighthavegrabbedthisbookbecauseyou'vealreadydecidedtofocusonimprovingasingletestforyoursuperscore.So,let’smoveonsowecandiveintothegoodstuff!MathScoreManystudentsfindMathscorestheeasiesttoimprove.Astrategicreviewoftherulesandformulas,coupledwithrigorouspractice,canaddseveralpoints.InordertomosteffectivelyraiseyourMathscore,focusonmasteringtheBigImpactskillsandtopics.ThesearestrategiestohelpyoutacklethemostcommonlycoveredMathcontentinastrategicandefficientway.TimeHowoftendoyoutakeafinalexaminschoolthatgivesyouatmostaminuteperquestion?Probablynever.TheACTisn’taschooltest,andyoucan’tapproachitasifitis.Whilespeedandaccuracydependonindividualskillsandgraspofcontent,almostallstudentsstruggletofinishtheMathtestontime.Themoreyoutreatthistestthesamewayyouwouldaschoolfinal,thelesslikelyyouaretofinish,muchlessfinishwiththegreatestaccuracy.AllofThePrincetonReview'sstrategiesarebasedonthistimecrunch.There’sadifferencebetweenknowinghowtodoaquestionunderthebestofcircumstanceandgettingitrightwithatickingclockandgloweringproctorintheroom.FormorecomprehensivereviewandpracticefortheACT,pickupacopyofACTPremiumPrep,whichincludessamplequestionsandguidanceforeachofthetestsontheexam.

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Chapter2HowtoApproachtheACTOnlineTestInthischapter,you'lllearnwhattoexpectontheACTOnlineTest,includinghowtoapplyitscomputer-basedfeaturesandourstrategiestothequestiontypesineachsection—English,Math,Reading,Science,andWriting.IfyourACTwillbepencil-and-paper,skipthischapter.+StudyXy

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WHATISTHEACTONLINETEST?TheACTOnlineTestistheACTthatyoutakeonacomputer,ratherthanwithapencilandpaper.Despitethename,youcan’ttaketheACTfromthecomfortofyourownhome;instead,you'llhavetogotoatestingcenter(possiblyyourhighschool)andtakethetestononeofthecenter’scomputers.TheACTOnlineTesthasthesameoverallstructure,timing,andnumberofquestionsasthepencil-and-paperACT.Thescoring,scorerange,andscoringmethodarealsothesame.IftheACTOnlineTestisbasicallythesameasthepencil-and-paperACT,whowouldtaketheACTOnlineTest?theACTonlineatatestingcenterwaspostponed.ACTalsoplanstoofferat-homeonlinetestingalthoughanexactrolloutdatehasnotyetbeenannounced.Forup-to-datenewsonbothoptions,checktheACTwebsiteWHOTAKESTHEACTONLINETEST?ACThasbeenofferingversionsoftheACToncomputersinceabout2016.ThefirststudentstotaketheACTonthecomputerwerestudentstakingthetestatschool.Schoolsandschooldistrictsdecidedwhethertogivethetestonthecomputer.AsofSeptember2018,allstudentstakingtheACToutsideoftheUnitedStatestakethetestonacomputer(exceptforthosestudentswithaccommodationsrequiringtheuseofatraditionalpencil-and-papertest).ACThasindicatedthateventuallystudentsintheUnitedStateswillhavetheoptionoftakingtheACTOnlineTestinsteadofthetraditionalpencil-and-paperversion.Studentschoosingthisoptionwillgettheirscoresinabouttwotothreebusinessdays(e.g.,takethetestonSaturday,haveyourscorethenextWednesday).However,atthetimeofthisprinting,nospecifictimelinewasavailable.Single-SectionRetestingIfyouarehappywiththescoreyoureceivefromasingletestadministration,youwillstillhavetheoptiontosendjustthatscoretocolleges.Ifyourscoreinonesectionisnotashighasyou’dlike,youwilleventuallyhaveachancetocorrectthat.StudentswhohavealreadytakenthefullACTmaychoosetotakeone,two,orthreesectionsagainusingSingle-SectionRetesting.ACTwillthenproducea“superscore”consistingofyourbestresultsinalltests(English,Math,Reading,Science,andWriting(ifyoutookit)).NotethatnotallcollegesacceptasuperscoredACT,sodoyourresearchbeforetakingadvantageofthisoption.

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students.However,collegesstillhavetheoptiontoacceptornotacceptthesenewscores.Researchyourtargetschoolsearlysoyouknowyouroptions!ACTONLINETESTFEATURESSo,besidestheobviousfactthatit’stakenonacomputer,whatarethedifferencesbetweentakingtheACTonthecomputerandtakingitonpaper?Let’sstartwithwhatyoucan’tdoontheACTOnlineTest.Youcan’t“write”onthescreeninafreehandway.You'relimitedinhowyou'reabletomarktheanswerchoices,andeachquestionappearsonitsownscreen(soyoucan’tseemultiplequestionsatoneglance).Youwillalsobegivenasmall“whiteboard”anddryerasepenwithwhichtomakenotesanddowork.So,whatfeaturesdoestheACTOnlineTesthave?«Timer°Youcanhidethetimerbyclickingonit.oThereisa5-minutewarningtowardtheendofeachtest.Thereisnoaudiblesignalatthe5-minutewarning,onlyasmallindicatorintheupper-rightcornerofthescreen.«Navtool>Youcanusethistooltonavigatedirectlytoanyquestioninthesection.°TheNavtoolblocksthecurrentquestionwhenopened.oItalsoshowswhatquestionsyouhaveflaggedand/orleftblank.°Youcanflagquestionsinthismenu.+Questionnumbersatthebottomofthescreen°Youcanclickonthesenumberstonavigatedirectlytoanyquestioninthesection.°Thesenumbersalsoindicatewhetheraquestionhasbeenflaggedand/orleftblank.«Flagtool°YoucanflagaquestiononthequestionscreenitselforbyusingtheNavtool.°Flaggingaquestionhasnoeffectbesidesmarkingthequestionforyourownpurposes.«AnswerEliminator>Answerchoicescanbe“crossed-off”on-screen.>Ananswerchoicethat’sbeeneliminatedcannotbechosenandmustbe“un-crossed-off”firstbyclickingtheanswerchoice.«Magnifier°Youcanusethistomagnifyspecificpartsofthescreen.«LineMask

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°Thistoolcoverspartofthescreen.Thereisanadjustablewindowyoucanusetolimitwhatyoucansee.°Thisisanexcellenttoolifyouneedanaidtohelpyoufocusonspecificpartsofthetextorfigure.>However,noteveryonewillfindthistooluseful,sodonotfeelobligatedtouseit!>NotethatyoucannothighlightthetextinthewindowoftheLineMask.«AnswerMask°Thistoolhidestheanswerchoicesofaquestion.>Answerscanberevealedoneatatime.*ScreenZoom°Thistoolchangesthezoomoftheentirescreen(asopposedtothemagnifier,whichmagnifiesonlyonepartofthescreen).°Yourscreenzoomsettingwillremainthesamefromquestiontoquestion.«Highlighter>Youcanusethistooltohighlightpartsofpassagetext,questiontext,oranswertext.°Youcannothighlightwithinfigures.oIfyouhighlightinapassagewithmultiplequestions,yourhighlightswillonlyshowuponthatquestion.(Inotherwords,ifyouhighlight,forexample,question1ofaReadingpassage,questions2-10ofthatsamepassagewillnotshowthosehighlights.)°Turningoffthehighlightertoolremovesyourhighlights.«Shortcuts:A-Eor1-5SelectAlternativeToggleAnswerEliminator«TheWritingtestistyped,ratherthanwrittenbyhand.+StudyXY

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Youwillalsobegivenasmall“whiteboard”anddryerasepenwithwhichtomakenotesanddowork.HOWTOAPPROACHTHEACTONLINETESTThestrategiesmentionedinthischapterarethoroughlydiscussedinourcomprehensiveguide,ACTPrep,sobesuretopickupacopyofthatbookifyouhavenotalreadydoneso.Theseapproacheswerecreatedinreferencetothepencil-and-paperformat,buttheystillapplytotheACTOnlineTestwithsomeadjustments.Thischapterassumesyourfamiliaritywiththesestrategiesandwillshowyouhowtomakethebestuseofthemgiventhetoolsavailableinthecomputer-basedformat.Youwillalsowanttoincorporatesomecomputer-basedpracticeintoyourprepplan.ACT’swebsitehaspracticesectionsforeachofthefourmultiple-choicepartsofthetestandfortheessay.Werecommendthatyoudothosesectionstowardtheendofyourpreparation(andclosetoyourtestdate)togiveyourselfanopportunitytopracticewhatyou’velearnedonaplatformsimilartotheoneyou’llbeusingonthedayofthetest.IfyouareplanningtotaketheACTonline,youshouldpracticeasifyou'redoingallyourworkonthecomputer,evenwhenyou'reworkinginaphysicalbook.Useahighlighter,butdon’tusethehighlighteronanyfigures(astheACTOnlineTestwon'tletyoudoso).Useyourpenciltoeliminateanswerchoicesandhaveaseparatesheetofpaperorawhiteboardtodoanyworkyouneedtodo,insteadofwritingontheproblemitself.Also,rememberthatourapproacheswork.Don’tgetmisledbyACT’sinstructionsonthedayofthetest—theirwayofapproachingthetestwon’tgiveyouthebestresults!YourgoalistogetthebestpossiblescoreontheACT.ACT'sgoalistoassignanumbertoyouthat(supposedly)meanssomethingtocolleges.Focusonyourgoal!OverallYourPersonalOrderofDifficulty(POOD)andPacinggoalswillbethesameontheACTOnlineTestasonthepencil-and-paperversion.Becauseitiseasytochangeyouranswers,putinyourLetteroftheDay(LOTD)whenskippingaLaterorNeverquestion.UsetheFlagtoolontheLaterquestionssoyoucanjumpbackeasily(usingeitherthenavigationbaratthebottomofthescreenortheNavtool).ProcessofElimination(POE)isstillavitalapproach.Onboththepaper-and-pencilACTandtheACTOnlineTest,therearemorewronganswersthancorrectones.Eliminatingoneyouknowarewronghelpsyoutosavetime,avoidtrapanswers,and

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makeabetterguessifyouhaveto.OntheACTOnlineTest,youcannotwriteonthetest,butyoucanusetheHighlightertool.Turnonthesetools(andtheLineMask,ifdesired)atthebeginningoftheEnglishsectionandusethemthroughout.TheBasicApproachestobothProofreaderandEditorquestionsarethesameonthecomputerizedandthepaperversionsoftheACT.WhenyoudecidetoskipaquestiontocomebacktoitLater(forexample,aquestionaskingfortheintroductiontothetopicofthepassagebeforeyou'vereadanypartofthepassage),flagthequestionsoyoucaneasilyjumpbacktoitbeforemovingontothenextpassage.Whenyouhavefiveminutesremaining,flagyourcurrentquestionandusetheNavtooltomakesureyou’veputinyourLOTDforanyquestionsthatyouhaven’tdone,thenreturntoyourspotandworkuntiltimerunsout.ForacomprehensivereviewofallsectionsoftheACTandthestrategiesmentionedthroughoutthischapter,checkoutourbook,ACTPrep.WhenyouworkProofreaderquestions,youcanusetheHighlightertooltohelpyoufocusonthekeypartsofthetext.Let’sseeanexample:Sneakingdownthecorridor,theagent,takingcarenottoalerttheguards,thelockeddoor.A.NOCHANGEB.spotC.arespottingD.spotsUsethetoolsavailabletohelpyoufocusonthekeyportionsofthetext.Practicewithahighlighterwhenyou'reworkingonpaper(insteadofunderliningwithyourpencil).Here’sHowtoCrackItVerbsarechangingintheanswerchoices,sothequestionistestingsubject/verbagreement.Theverbmustbeconsistentwiththesubject.Theagentisthesubject;highlightit:Sneakingdownthecorridor,fheagent,takingcarenottoalerttheguards,thelockeddoor.A.NOCHANGEB.spotC.arespotting+StudyXy

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D.spotsTheagentissingular,sotheverbmustbesingular.Eliminate(B)and(C),asbothareplural.Spottingcannotbethemainverbofasentence,soeliminate(A).Thecorrectansweris(D).Similarly,theHighlightertoolishelpfulonEditorquestions.Usethetoolonboththepassageandthequestiontohelpyoufocusontherelevantpartsofeach.Asit’snamesuggests,theIndianfantailisnotnativetoNorthAmerica.Infact,itsestablishmentherewasquiteaccidental.In1926,theSanDiegoZooacquiredfourpythonsfromIndiaforitsreptileexhibit.ThelongtripfromIndiarequired,that,thepythonsbeprovidedwithfoodforthejourney,[andagroupofunfortunatefantailswasshippedforjustthatpurpose]Twoluckyfantailssurvived,andtheirbeautifulappearancecausedtheSanDiegoZootokeepandbreedthemforthepublictosee.Eventually,someoftheanimalsescapedcaptivityanddevelopedpopulationsinthewild,allthankstothosetwobirds!Giventhatallthechoicesaretrue,whichoneprovidesthemostrelevantandspecificinformationatthispointintheessay?A.NOCHANGEB.andtheyhavequiteanappetite.C.becausenoonewantedthemtostarve.D.andtheyarequitepickyinwhatthey’lleat.Here’sHowtoCrackItThequestionasksforthemostrelevantandspecificinformation.Highlightthosewordsinthequestion.ThefirstsentenceoftheparagraphfocusesontheIndianfantail,andthesentenceaftertheunderlinedportiondiscusses(2)woluckyfantails.Thefinalsentencediscussestheanimalsthatescaped.Highlightthesewordsintheparagraph.Yourscreenshouldlooklikethis:Asit’snamesuggests,theIndianfantailisnotnativetoNorthAmerica.Infact,itsestablishmentherewasquiteaccidental.In1926,theSanDiegoZooacquiredfourpythonsfromIndiaforitsreptileexhibit.ThelongtripfromIndiarequired,that,thepythonsbeprovidedwithfoodforthejourney,landagroupofunfortunatefantailswasshippedforjustthatpurpose][Twoluckyfantailgsurvived,andtheirbeautifulappearancecausedtheSanDiegoZootokeepandbreedthemforthepublictosee.Eventually,someof[theanimals|escapedcaptivityanddevelopedpopulationsinthewild,allthankstothosetwobirds!

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Giventhatallthechoicesaretrue,whichoneprovidesthe[mostrelevantandspecificinformation]atthispointintheessay?A.NOCHANGEB.andtheyhavequiteanappetite.C.becausenoonewantedthemtostarve.D.andtheyarequitepickyinwhatthey’lleat.UsePOE,focusingonwhetherthechoiceisconsistentwiththehighlightsinthepassage.Thesentenceaswrittendiscussesagroupofunfortunatefantails;keep(A).Choices(B),(C),and(D)donottalkabouttheIndianfantail;instead,theyfocusonthepythons.Thisisinconsistentwiththegoalofthesentenceandthecontentoftheparagraph;eliminatethoseanswers.Thecorrectansweris(A).Finally,youcan’twriteinthepassage,soyou’llneedtoapproachtheVerticalLineTestslightlydifferently.Onthepaper-and-pencilACT,youwouldusethisstrategyforquestionsaboutpunctuation,drawingaverticallinewherethepunctuationbreaksuptheideasinthetext.OnthecomputerizedACT,youshouldusethewhiteboardtohandlethesequestions.I'mnotsearchingforaghostoristheIndianfantail.Thesebeautifulcreaturesaremembersofthepigeonfamily,butyoucouldnottellthatbylookingatthem.A.NOCHANGEB.yeti:myphantomC.yetimyphantomD.yeti,sincethisHere’sHowtoCrackItPunctuationischangingintheanswerchoices,sothequestionistestingSTOPandGOpunctuation.ThereisHalf-Stoppunctuationin(B),sousetheVerticalLineTest.Youcannotdrawalineinthetext,sodrawa“t”onyourwhiteboard,with“yeti”inthebottom-leftand“my”inthebottom-right:Readeachpartofthesentenceanddeterminewhetheritiscompleteorincomplete.I'mnotsearchingforaghostoryetiisacompleteidea;write“C”intheupper-leftofthe“t.”MyphantomistheIndianfantailisalsoacompleteidea;write“C”(for“complete”)intheupper-rightofthe“t.”Yourboardshouldlooklikethis:Eliminateanyanswerthatcannotlinktwocompleteideas.Both(A)and(C)useGOpunctuation,whichcannotlinkcompleteideas;eliminate(A)and(C).Choice(D)addssince,whichmakestheideatotherightofthelineincomplete.However,sinceisusedtoshowtimeorcausation,whichdoesnotworkinthecontextofthesentence.Eliminate(D).Thecorrectansweris(B).

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 25 preview image

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Firstoff,you’llstillneedtobringyourcalculatortotheACTOnlineTest—whichisagoodthing!You'realreadycomfortablewithyourpersonalcalculator,sotherewillbeonelessthingtoworryaboutonthedayofthetest.WhenchoosingquestionstodoLater,flagthequestionsoyoucaneasilynavigatebacktoitafterdoingyourNowquestions.DoputinyourLOTDwhendoingso;youdon’twanttoaccidentlyleaveaquestionblank!Whenyougetthefive-minutewarning,finishthequestionyou'reworkingon,flagit(soyoucanfindyourspoteasily),thenputinyourLOTDforeveryunansweredquestion.Thenyoucangobacktoworkinguntiltimerunsout.UsetheHighlightertooltohighlightwhatthequestionisactuallyasking,especiallyinWordProblems.Ofcourse,you'llwanttouseyourwhiteboardwhenworkingthestepsofamathproblem(don’tdotheworkinyourhead!).Writeitdown!Itistemptingtodoallyourworkinyourhead.Don'tfallintothistrap!It'seasiertomakemistakeswhenyou'renotwritingdownyourwork,andyou'lloftenhaveto“goback”ifyoudon’thavesomethingwrittendown.Useyourwhiteboard!ACTOnlineGeometryBasicApproachBecauseyoucan’twriteonthescreen,theBasicApproachforGeometryquestionsneedsafewslighttweaks:1.Drawthefigureonyourwhiteboard(copyifit’sprovided;drawityourselfotherwise).IfthefigurewouldbebetterdrawndifferentlyfromthewayACThasdrawnit(forinstance,asimilartrianglesquestion),redrawthefigureinawaythatwillhelpyouanswerthequestion.2.LabelthefigureyoudrewonyourwhiteboardwiththeinformationfrombothACT’sfigureandthequestion.3.Writedownanyformulasyouneedandfillintheinformationyouknow.Let’sseehowthatworksonaquestion.Inthefigurebelow,triangleABCissimilartotriangleDEF.WhatisthelengthofEF?A.15B.225C.3+StudyXY

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 26 preview image

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D.4E.45Here’sHowtoCrackItThequestionasksforthelengthofEF,sohighlightthatinthequestion.FollowtheGeometryBasicApproach.Startbydrawingthefigureonyourwhiteboard.Becausethetrianglesaresimilar,redrawtriangleDEFtobeorientedthesamewayasABC.Labelyourfigurewiththegiveninformation.Writedowntheequationyouneedandfillinthenecessaryinformation.ACcorrespondstoDF,andBCcorrespondstoEF.Setupaproportion:.Fillintheinformationfromyourfigure:,wherexisequaltoEF.Cross-multiplytoget6x=3(4.5),or6x=13.5.Dividebothsidesby6togetx=2.25.Thecorrectansweris(B).READINGFirstoff,thereareafewdifferencesbetweenthepencil-and-paperACTandtheACTOnlineTest.IntheACTOnlineTest,therearenolinereferences;rather,therelevantpartofthetextishighlighted.Thepassagewillalso“jump”tothehighlightedtextifit’soffthescreenwhenyougotothatquestion.Thismaydisorientyouatfirst:bepreparedforthistohappen.Let’sseeanexample....protestedeverystep.Wecouldstillrun,but,Hookworried,forhowlong?Inacross-countryrace,onlyateam’stopfiverunnersscore,andweweren'tthosefive.Ourjobwastofinishaheadofasmanyofourrivalteams”topfivesaswecould.Leahwasaseniorthatyear,myfreshmanyear.Allseason,she’dbeencountingdowntothislastrace,prayingherbodywouldn’tsayNo.SheandIjokedthatweneededtogototheandpickoutnewknees,onesthatwouldn’tcrackandpopandburnallthetime.Itwashardtowatchateammateinthatmuchpain,butLeahwasatrooper,neverslackingfromworkouts,neverstoppingtowalk,neverlosingsightofthenextpersoninfrontofhertocatch.Thecrackofthestarter’spistolsentussurgingoutofthatlittlecropoftreesandontotheracecourse.Ihollered,“Seeyouatthe[KneeStore|!”Behindme,shelaughed.Thepackstayedtightthroughthefirstquarter-mile,andIwassurroundedbysomanybodiesIcouldn’tthink.Ijustran,puttingone+StudyXy

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 27 preview image

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footinfrontoftheother,tryingnottofall.Tryingtolookbeyondthejostlingmasssurroundingme,Icouldbarely...Thenarrator’sreferencestotheKneeStoreprimarilyservetosuggestthat:A.Leahwishestobuybetterkneesupports.B.thenarratorandLeahusehumortocopewiththeirpain.C.thenarratordesirestolearnmoreaboutherinjury.D.Leah'sinjuries,unlikethenarrator’s,havebecomeunbearable.Practicebyreadingarticlesorotherpassagesonthecomputerwhenpossible.Here’sHowtoCrackItThequestionaskswhatthereferencestotheKneeStore...suggest.ThereferencestotheKneeStorearehighlightedinthetext.Notethatthetexthasshifteddowntothehighlightedportions.ThewindowindicatesthatLeahandthenarratorjokedthatweneededtogototheKneeStore.LeahlaughedafterthenarratorreferredtotheKneeStore.Therefore,theanswershouldbeconsistentwithjokingandlaughing.Choice(A)takesthereferencetooliterally;eliminate(A).“Humor”isconsistentwiththetext’sreferencestojokedandlaughed;keep(B).There’snoindicationofthenarrator’sgoaltolearnmoreaboutherinjury,nordoesthetextsupporttheideathatLeah’sinjurieshavebecomeunbearable,eliminate(C)and(D).Thecorrectansweris(B).Whenyouhavefiveminutesremaining,flagyourcurrentquestionandusetheNavtooltomakesureyou’veputinyourLOTDforanyquestionsthatyouhaven’tdone.Thenreturntoyourspotandworkuntiltimerunsout.Ifyou'vejuststartedorfinishedapassage,clickthroughthequestionstolookforEasytoFindquestionsintheremainingtime,anddon’tforgettoputinyourLOTDforanyquestionyoudon’tanswer!ThebiggestdifferencebetweentheACTOnlineTestandthepaper-and-pencilACTisthatyoucanonlyseeonequestiononthescreenatatime.Ratherthanlookingoverthequestionsataglance,youmustclickfromquestiontoquestion.ThisfeaturemeansthattheReadingBasicApproach(coveredbelow)needstobemodifiedinordertobeastimeefficientaspossible.ACTOnlineReadingBasicApproach1.PreviewReadonlytheblurb—donotgothroughandmapthequestions.Instead,writethequestionnumbersonyourwhiteboardtopreparetoWorkthePassage.2.WorkthePassage

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 28 preview image

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ThisstepisevenmoreoptionalontheACTOnlineTestthanonthepencil-and-paperACT.Youhaven’tmappedthequestions,andyourhighlightsonlyshowupononequestion.IfyoudodecidetoWorkthePassage,ensurethatyou'regettingthroughthepassagein2-3minutes.Morelikely,you'llfinditbesttojustskipthisstepandmoveontothequestionsafterreadingtheblurbandsettingupyourwhiteboard.answeringquestionscorrectly.DeterminewhetherWorkingthePassagehelpsyouanswerquestionscorrectlyandquickly.3.SelectandUnderstandaQuestion‘WhenSelectingaQuestion,ifaquestionisEasytoFind(aportionofthetextishighlightedoryouWorkedthePassageandknowwhereinthepassagethecontentyouneedis),doitNow.Understandthequestion,thenmoveontoStep4.IfthequestionisnotEasytoFind(inotherwords,youdon’timmediatelyknowwhereinthepassagetogo),writedownthequestion’sleadwordsonyourwhiteboardnexttothequestionnumber.IncludeEXCEPT/LEAST/NOTifthequestionincludesthosewords.Iftherearenoleadwords,flagthequestion.Afteryoudoallthequestionswithhighlights,thenWorkthePassage,scanningactivelyforyourleadwords.Onceyoufindaleadword,dothecorrespondingquestion.Afteransweringthequestionswithleadwords,finishwiththeflaggedquestions.4.ReadWhatYouNeedFindthe5-10linesyouneedtoanswerthequestion.Rememberthatonlythequotationwillbehighlighted—theanswerisnotnecessarilyhighlighted.Youmustreadthelinesbeforeandafterthehighlightedportiontoensurethatyoufindthecorrectanswertothequestion.IfyoufindtheLineMasktoolhelpful,useittoframeyourwindow.5.PredicttheCorrectAnswerAsyouread,lookforevidencefortheanswertothequestioninyourwindowandhighlightitusingthehighlightertool.(YoucanhighlighttextthatACThasalreadyhighlighted—thecolorwillchangeto“your”highlightingcolor.)Asalways,baseyourpredictiononthewordsinthepassageasmuchaspossible.6.UsePOEUsetheAnswerEliminatortooltonarrowtheanswerchoicesdowntooneanswer.IfthequestionisanEXCEPT/LEAST/NOTquestion,insteadwriteABCDonyourwhiteboardandmarkeachanswerTorFforTrueorFalse(orYorNforYesorNo)andchoosetheoddoneout.

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DualReadingApproachThequestionsforDualReadingpassagesaregroupedwiththequestionsaboutPassageA,thenthoseaboutPassageB,thenthoseaboutbothpassages.Eachquestionshouldbelabeledwithanindicatorforthepassagethequestionrefersto.Workeachpassageseparately,answeringallthePassageAquestionsyouplantoanswerbeforemovingontothePassageBquestions.YoushouldalsowritedowntheGoldenThreadofeachpassageonyourwhiteboard—eitherafterWorkingthePassageorafterfinishingthequestionsonthatpassage.Thatwillaidyouinansweringthequestionsaboutbothpassages.SCIENCETheoverallapproachtotheSciencetestisthesameontheACTOnlineTestasitisonthetraditionalpencil-and-paperversion.Thereareafewsmalladjustmentstomake,buttheoverallstrategyremainsthesame.TheFlagtoolisveryimportantwhenidentifyingLaterpassagesandquestions.OnaLaterpassage,flagthefirstquestion,thenputyourLOTDforeveryquestiononthepassage.Makeanoteonyourwhiteboardofthefirstquestioninthepassagesoyoucaneasilyjumpbacktothepassage.WhenworkingaNowpassage,youmaystillencounteraLaterquestion.Forthesestand-aloneLaterquestions,flagthequestionbutdon’tputinyourLOTD.Whenyougettotheendofapassage,checkthebaratthebottomofthescreentomakesureyouhaveansweredeveryquestionuptothatpoint.ScienceBasicApproachThereareafewsmallchangestotheScienceapproachwhentakingtheACTOnlineTest.1.WorktheFiguresYoucan’thighlightthefigures.Experimentwithtakingquicknotesaboutthevariables,units,andtrendsonyourwhiteboardanddeterminewhetherithelpsyoufindtheneededinformationquickly.2.WorktheQuestionsHighlightthewordsandphrasesfromthefiguresinthequestiontohelpguideyoutotherelevantinformation.3.WorktheAnswersUsetheAnswerEliminatortooltoworkPOEonanswerchoiceswithmultipleparts.Let’slookatanexample.+StudyXy

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 30 preview image

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AblockisplacedonafrictionlesshorizontalsurfaceatpointQ.Theblockispushedwithaplungerandgiveninitialvelocityvalongthehorizontalsurface.AtpointR,theblockslidesuparampwithcoefficientoffrictionf'toamaximumdistanceLalongtheramp.ThedistancebetweenpointsQandRis1.0m.Figure1ScrollingPassagesMostpassagesinSciencewillrequirescrollingdowntoseeallthefigures.Lookforascrollbarforeverypassage!Figure2,below,showshowLvarieswithvfordifferentfonarampwith6=20°.Figure3(onthefollowingpage)showshowLvarieswithvfordifferent6onarampwithf=0.1.Figure2Figure3Iff=0.90fortheslidingblockandv=5.5m/s,Lwillmostlikelybeclosesttowhichofthefollowing?A.03mB.0.7mC.l15mD.3.0mHere’sHowtoCrackItStartbyWorkingtheFigures.Figure1showsthepointsQandRandvariablesLand0,buttherearenonumbersortrends.Figure2showsadirectrelationshipbetweenL(m)andv(m/s);markthisonyourwhiteboard.Furthermore,thelegendgivesvaluesoff;asfincreases,Ldecreases.Marktheserelationshipsonyourwhiteboard.Figure3alsoshowsadirectrelationshipbetweenL(m)andv(m/s);thelegend,however,gives0(°).As0increases,Ldecreases.Puttheseonyourwhiteboardaswell.NotethatFigures2and3showbothLandv;Figure2hasf,whereasFigure3has6.Yourwhiteboardshouldlooklikethefollowing:Figure2:1(m)1v(m/s)tandf1L|Figure3:1(m)1v(m/s)tand©1L|+StudyXY

Princeton Review ACT Math Prep: 4 Practice Tests + Review + Strategy for the ACT Math Section (2023) - Page 31 preview image

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Thequestionreferstothevariablesf,v,andL;highlightthosevariables.Figure2hasallthreevariables.Thehighestvalueofvgiveninthefigureis4.5,sostartthereandusethetrendtomakeapredictionaboutavof5.5.Atv=4.5andf=0.90,Lisapproximately0.9.Thetrendisincreasing,soavof5.5mustresultinanLvalueofgreaterthan0.9;eliminate(A)and(B).AnLvalueof3.0wouldbehigherthananyvaluealreadyinFigure2,andextendingthetrendforthelinecreatedbythef=0.90markswouldnotresultinLincreasingto3.0bythetimevreaches5.5;eliminate(D).Althoughyoucan’tphysicallyextendthelinebecauseit’sonacomputerscreen,itmaybeagoodideatouseyourfingertotracewhereyouwoulddrawonthescreen.Thecorrectansweris(C).You'llstillapproachthepassagethat’sallormostlytextasifitisaReadingpassage.UnlikeinReading,youwillwanttoMaptheQuestionsduringthePreviewstep,astherewillnotbeagroupofquestionsabouteachpassagelikethereisintheDualReadingpassage.Instead,thequestionswillnotbeaskedinanyparticularorder,souseyourwhiteboardtomapoutwhichscientist(s)orexperiment(s)eachquestionrefersto.Aswiththeothersections,atthefive-minutewarning,flagyourquestion,putinyourLOTDonanyunansweredquestion,thenkeepworkinguntiltimerunsout.WRITINGAsyouhaveprobablyguessed,you'llbetypingtheWritingtestontheACTOnlineTest.Butbeforewegettowritingtheessay,thereareafewminorpointstonoteabouttheformatofthistestonthecomputer.First,youwon’tbeabletohighlightwhenWorkingthePromptorPerspectives,sobesuretowritenotesonyourwhiteboard.Second,ACThasgiventhepromptandperspectivesononescreen,thenrepeatedthemonthescreenthatcontainsatextbox.Feelfreetodoyourworkonthescreenwithinthetextbox.Ifyou'reusedtomakingyouressayoutlinesonacomputer,youcanusethetextboxtodosohere,aslongasyouremembertodeleteanynotesbeforethesectioncomestoanend.Whenwritingtheessay,allthesamepointsapplytoboththepencil-and-paperandonlinetests(haveaclearthesis,makeandorganizeyourargumentsinawaythatiseasytofollow,etc.).Whenyouhave5minutesleft,quicklytypeupaconclusionparagraph(ifyouhaven’talready),thengobackandfinishupyourbodyparagraphideas.It’smoreimportanttohaveaconclusionthanitistohaveperfectbodyparagraphs.Finally,spendaminuteortwoattheendtoquicklyfixanyobvioustyposorgrammaticalissues.WhenyoupracticetheWritingtestathome,typeyouressayinawordprocessingprograminsteadofwritingitbyhand.Besuretoturnoffspellcheck,astheACTdoesnotprovideit,soyoudon’twanttorelyonit.

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