76PRACTICETEST1ANSWERSANDEXPLANATIONS = 4 3 π 64 27 = 256 81 π Recallthat π = approx.3.14,so 256 81 (3.14) isabout9.92,or10whenroundedtothenearest cubicinch. 12.ThecorrectanswerisF. Theprobabilitythatthe gumballchosenwillNOTbegreenwhenthereare 6yellowgumballs,5greengumballs,and4red gumballsisthenumberoffavorableoutcomes(the numberoftimesayelloworredgumballcanbe chosen)dividedbythenumberoftotaloutcomes (thetotalnumberofgumballs).Thenumberof favorableoutcomesis10becausethereare6yel- lowgumballsand4redgumballs.Thetotalnumber ofoutcomesis6 5 4,or15.Thustheprobability ofthegumballNOTbeinggreenis 10 15 ,whichcan bereducedto 2 3 . AnswerchoiceGisincorrectbecauseitisthe probabilitythatachosengumball will begreen. 13.ThecorrectanswerisD. Tondthenumberof sportsawardsearned,multiplythenumberofpar- ticipantsineachsportbytheratioforthatsport, andthenaddthese4products.Thisisamatrix multiplication,asshownbelow: [ 25305080 ] 0.2 0.5 0.3 0.4 = 25(0.2) 30(0.5) 50(0.3) 80(0.4) = 5 15 15 32 = 67 14.ThecorrectanswerisG. Tondtheaveragenum- berofstudentspersectionenrolledinUSHistory, ndthetotalnumberofstudentsinallsectionsand dividebythenumberofsections.Add25 29 24 toget78,thendivideby3.Thisresultsinan averageof26studentsenrolledpersectioninUS History. IfyouselectedanswerchoiceF,youfoundthe median,ormiddlenumber(whichisnotalwaysthe average),of24,25,and29. 15.ThecorrectanswerisB. Thetotalnumberof booksavailableis(30 − 3) (30 − 5),or27 25, whichis52.Tondtheclassperiodsforwhich therearenotenoughbooks,ndthetotalnumber ofbooksneededforeachperiod,asgiveninthe tablebelow. PERIOD 1 2 3 4 5 BOOKSNEEDED 23 49 56 50 27 Theonlyentryinthetablewithmorethan52 is56forperiod3. IfyouselectedanswerchoiceE,youprobably used60asthenumberofavailablebooksanddid nottakeintoaccountthe8missingbooks. 16.ThecorrectanswerisG. Becausethesumofeach rowisequivalent,thesumofrow1isthesameas thesumofrow2. Row1:( − 4 x ) 9 x 2 x = 7 x Row2:7 x ? ( − 3 x ) = 4 x ? Thequestionmarkmustrepresent3 x ,because 7 x = 4 x 3 x .Youcouldalsoperformthesecal- culationsusingthesumvaluesincolumn1and column2. IfyouselectedanswerchoiceK,youmayhave thoughtthateachsummustbe0andfoundthat − 4 x wouldmakethesumsofrow2andcolumn2 equal0. 17.ThecorrectanswerisE. The x -coordinateis positiveif A istotherightofthe y -axis.The y -coordinateispositiveif y isabovethe x -axis. Thetablebelowshowsthesignof x andthesign of y inthefourquadrants. QUADRANT SIGNOF x y I II − III − − IV − ThusthesignsarethesameinQuadrantsIand IIIonly. 18.ThecorrectanswerisJ. Tondthenumberof distinctcompletemealsthatReggiecanmakefrom 5differententrees,4differentsides,and6different desserts,multiplythequantitiesinthe3different groupstogether.Thus,thereare(5)(4)(6),or120 distinctmealsthatReggiecanmake.Thegure belowshowsthatforeachmeal,thereare4sides, andforeachsidethereare6desserts.

**Published:**Dec 20, 2014

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taught in algebra class.You will,however,need a strong foundation in all the subjects listed on the previous page in order to do well on the math test.You may use a calculator,but as you will be shown in the follow- ing lessons,many questions can be solved quickly and easily without a calculator. Essentially,the ACT Math Test is designed to evaluate a student’s ability to reason through math prob- lems.Students need to be able to interpret data based on information given and on their existing knowledge ofmath.The questions are meant to evaluate critical thinking ability by correctly interpreting the problem, analyzing the data,reasoning through possible conclusions,and determining the correct answer—the one supported by the data presented in the question. Four scores are reported for the ACT Math Test:Pre-Algebra/Elementary Algebra,Intermediate Alge- bra/Coordinate Geometry,Plane Geometry/Trigonometry,and the total test score. Pretest As you did with the English section,take the following pretest before you begin the math review in this chap- ter.The questions are the same type you will nd on the ACT.When you are nished,check the answer key on page 138 to assess your results.Your pretest score will help you determine in which areas you need the most careful review and practice.For a glossary ofmath terms,refer to page 201 at the end ofthis chapter. 1. Ifa student got 95% ofthe questions on a 60-question test correct,how many questions did the stu- dent complete correctly? a. 57 b. 38 c. 46 d. 53 e. 95 2. What is the smallest possible product for two integers whose sum is 26? f. 25 g. 15 h. 154 i. 144 j. 26 – ACTMATH TEST PRACTICE – 132

**Published:**Dec 20, 2014

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