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HiSET ® Exam Free Practice Test FPT3
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Mathematics
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Released September 2015
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Directions
Thisisatestofyourskillsinapplyingmathematicalconceptsandsolvingmathematicalproblems.Readeachquestioncarefullyanddecidewhichofthefivealternativesbestanswersthequestion.Thenmarkyourchoiceonyouranswersheet.
Therearerelativelyeasyproblemsscatteredthroughoutthetest.Thus,donotwastetimeonproblemsthataretoo difficult;goon,andreturntothemifyouhavetime.
Workasquicklyasyoucanwithoutbecomingcareless.Trytoanswereveryquestionevenifyouhavetoguess.
Markallyouranswersontheanswersheet.Giveonlyoneanswertoeachquestion.
Ifyoudecidetochangeoneofyouranswers,besuretoerasethefirstmarkcompletely.
Besurethatthenumberofthequestionyouareansweringmatchesthenumberoftherowofanswerchoicesyouare markingonyouranswersheet.
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20,000
5,000
20,000
25
5,00025×
20,000
Mathematics
Time—60 minutes
32 Questions
1. Apicture-framingshophasthesignshownbelowinthewindow.
Acustomerhasa4-inch-by-6-inchpicture.Ifthecustomerwantstoenlargethephotographsothatitwillcomeascloseaspossibletofittingasaleframe,howmanytimeslargershouldthephotobe?
A. 2
B. 3
C. 4
D. 5
E. 13
2. Considertheadvertisementbelow.
Whichofthefollowingexpressionsrepresentsthecost,indollars,of20,000sheetsofpaper?
20,000×2 5
5,000A.
B. 20,000×25
C.
D.
E.
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20 × 6
15
15 × 20
6
6
15 × 20
15 × 6
20
3. Whichofthefollowingsetsofdatawouldbebestrepresentedbyacirclegraph?
A. ThepercentofrecentUnitedStatesimmigrantsfromdifferentcontinents
B. Thelifeexpectanciesofvariousanimals
C. Collegetuitionincreasesoverthelast5yearsforastateuniversity
D. Thepercentsofpeoplelivinginurbanandruralregionsineachofthelast6years
E. Thenumberofkilowatthoursofelectricityusedbyahouseholdeachmonthovera1-yearperiod
4. If6bottlesofPerfectWaterweighatotalof4kilograms(kg),whatistheweightof9bottles?
A. 5 kg
B. 6 kg
C. 7 kg
D. 7.5kg
E. 8 kg
5. Atourist’scabfarewas$12.89.Ifshewouldliketogivethedriveratipof15percent,approximatelyhowmuchmoneyshouldshegiveasatip?
A. $1.00
B. $1.50C. $2.00
D. $2.50
E. $3.00
6. Thefloorofa15-foot-by-20-footrectangularroomisbeingcoveredwithcarpettiles.Eachcarpettilecovers6squarefeetoffloor.Whichofthefollowingexpressionsrepresentsthenumberofcarpettilesneededtocovertheentirefloor?
A. 15 × 20 × 6
B.
C.
D.
E.
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___________________________________________________________________________________
7. Whichofthefollowinggraphsrepresentstherelationshipbetweenvariables x and y ifadecreasein x isalwaysaccompaniedbyanincreasein y withinthedomainshown?
A. Ionly
B. IIonly
C. IIIonly
D. IandIIIonly
E. I,II,andIII
8. Acompanycharges$8anhourforlawnmowing.Whatwouldthecompanychargeforalawnthattakes1hourand45minutestomow?
A. $16
B. $14
C. $12
D. $10
E. $8
9. Inacertainapartmentbuilding,apartmentscancomewith2,3,or4bedrooms;theycanhave1or2bathrooms;andtheycanbelocatedonthelower,middle,orupperlevel.Howmanydifferenttypesofapartmentsarepossibleifanynumberofbedrooms,bathrooms,andlocationscanbecombined?
A. 6
B. 8
C. 12
D. 18
E. 20
10. Arestaurantownerisplanningtohaveacourtyardareasodded.Thesodcomesinrollsthatare3feetlongby1footwide.Ifthecourtyardmeasures60feetby50feet,whichofthefollowingexpressionsrepresentsthenumberofrollsofsodneeded?
A. 60 × 50
B. 60 × 50 ÷ 3
C. 60 × 50 × 3
D. (60 + 50) ÷ 3
E. (60 + 50) × 3
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x y z+ +
10 100 1,000
x y z+ +
1,000 100 10
x y+ + z10 10
11. Considertheequation6 x + 7 = 3 x� 5. Whichofthefollowingpossiblefirststepswouldpreventhavingtodealwithfractionswhensolvingtheequation?
I. Combiningthe6 x and3 x terms
II. Combiningthe7and5
III. Dividingbothsidesoftheequationby6
A. Ionly
B. IIonly
C. IIIonly
D. I or II only
E. I or II or III
12. Abookstatesthatthelongestriverinacountryisabout3,700kilometerslong.Theactuallengthoftheriverismostlikelybetween
A. 3,600kmand3,700km.
B. 3,650kmand3,700km.
C. 3,650kmand3,750km.
D. 3,700kmand3,750km.
E. 3,700kmand3,800km.
13. Whichofthefollowingcorrectlyexpresses xdecimeters, y centimeters,and z millimetersintermsofmeters?
A.
B.
C. 10 x +100 y +1,000 z
D. 1,000 x + 100 y + 10 z
E.
14. Agroupofhospitalworkersbelongingtoaunioneachearnthesamehourlywage.Theunionduesare2percentofeachpaycheckregardlessofwhethertheemployeeworksfull-time,half-time,orquarter-time.Doesthismeanthattheamountofmoneydeductedwillbethesameforalltheemployees?
A. Yes.
B. No,thequarter-timeemployeeswillhavethegreatestamountdeductedfromtheirpaychecks.
C. No,thehalf-timeemployeeswillhavethegreatestamountdeductedfromtheirpaychecks.
D. No,thequarter-timeandhalf-timeemployeeswillhavethegreatestamountdeductedfromtheirpaychecks.
E. No,thefull-timeemployeeswillhavethegreatestamountdeductedfromtheirpaychecks.
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15. Anauditoriumhasaseatingcapacityof1,500.Foranupcomingcommunitytheaterplay,ticketscost$4foradultsand$2forchildren.Atlastyear’splay,twiceasmanychildrenattendedasdidadults.Iftheattendanceatthisyear’splayhasthesameratio,whichofthe
followingexpressionsrepresentsthebestestimateofthetotalamountofmoneyfromticketsaleswhentheauditoriumisfilledtocapacity?
A. 1,500×$4
B. 1,500×$2
C. (750 × $4) +(750 × $2)
D. (1,000×$4) +(500 × $2)
E. (500 × $4) +(1,000×$2)
16. Ifabathroomdooris2unitstall,1unitmostlikelyrepresentsa
A. meter.
B. kilometer.
C. centimeter.
D. decimeter.
E. millimeter.
Questions 17 and 18 refer to the informationbelow.
Thetablebelowshowstheaveragemonthlyincomesofpeoplewithdifferentlevelsofeducation.
17. Aftercompletingherfour-yearcollegedegree,Lynnhasa$20,000loan.Sheearnstheaveragemonthlyincomeforherlevelof
education.Ifherlivingexpensesare$1,700permonth,inhowmanymonthscouldLynnpayoffherloan?
A. 25
B. 20
C. 15
D. 12
E. 8
18. Onaverage,approximatelyhowmuchmoremoneywillapersonwhohasatwo-yearcollegedegreeearninanentireyearcomparedwithapersonwhohasavocationaldegree?
A. $250
B. $2,400
C. $3,000
D. $3,600
E. $4,800
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19. Thecitywaterdepartmentreportedthattheaverageamountofwaterusedperhouseholdeachmonthinthelastyearwas1,000cubicfeet.Employeesfromthedepartmentrandomlysampled50homesinthecommunityandreviewedthewaterbillsforarecent
month.Whichofthefollowingwouldmostlikelybetrueofthewaterconsumptionofthe50households?
A. Eachhouseholdwillhaveusedexactly1,000cubicfeet.
B. Eachhouseholdwillhaveusedatleast1,000cubicfeet.
C. Eachhouseholdwillhaveusedatmost1,000cubicfeet.
D. Twenty-fiveofthehouseholdswillhave
usedmorethan1,000cubicfeet,and25ofthehouseholdswillhaveusedlessthan1,000cubicfeet.
E. Twenty-fiveofthehouseholdswillhaveusedexactly1,000cubicfeet,and25ofthehouseholdswillhaveusedeithermoreorlessthan1,000cubicfeet.
20. Afamilyhasdecidedtoplantarectangulargardenalongtheentirelengthofa25-foot-longfenceinthebackyard.Ifthe
familywantstohaveaplotof125squarefeetwithinwhichtoplant,howmanyfeetwideshouldthegardenbe?
A. 5
B. 25
C. 50
D. 75
E. 100
21. Theefficiencyofconvertingfromoneformofpowertoanotherformisdefinedbytheformulabelow.
Iftheefficiencyremainsconstant,whichofthefollowingistrue?
A. Wheninputpowerremainsconstant,outputpowerincreases.
B. Wheninputpowerincreases,outputpowerdecreases.
C. Wheninputpowerdecreases,outputpowerincreases.
D. Wheninputpowerdecreases,output
powerremainsconstant.
E. Wheninputpowerincreases,outputpowerincreases.
22. Atatrackmeet,theofficialsmeasurethelong1
100 jumpstothenearest ofameter.Ifa
participant’sjumpisrecordedas6.50meters,
theactualjumpisprobablybetween
A. 6.45and6.50meters.
B. 6.495and6.50meters.
C. 6.495and6.505meters.
D. 6.50and6.505meters.
E. 6.50and6.55meters.
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23. Considerthetablebelow.
Usingtheapproximationsinthetable,whichofthefollowingexpressionsrepresentsthenumberofbytesin2.4GB?
A. 2.4 × 10� 9
B. 2.4 × 103
C. 2.4 × 106
D. 2.4 × 109
E. 2.4 × 1027
24. Anewyo-yofactoryisoperatingat80percentofcapacityandproduces4,000yo-yosdaily.Whenthefactoryreaches100percentofcapacity,howmanyyo-yosshouldbeproducedeachday?
A. 800B. 3,200
C. 4,800
D. 5,000
E. 7,200
25. Anartistknowsthatitcostsheranaverageof$40perpaintingtohaveframesbuiltataframeshop.Sheistaking30framedpaintingstoanartfair.Ifshesellseachpaintingfor$100,howmanypaintingsdoessheneedtoselltopayfortheframes?
A. 3
B. 12
C. 30
D. 40
E. 75
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y
x x − x x
3 2+
4 x − 4
y =
x
++ x x
x x −
y =
x3 ++ x x2 + 4 x + 1
y =
x ++ x x + 4 x + 4
y
x x − x x
3 2+
4 x −1
3 8 525
− 5tan
20
25+ 5
tan 20
y x
26. Naomi is looking at a flying eagle, as shownin the diagram below.
x feet
5 feet
20º
25 feet
Which expression represents the eagle’s
height, in feet, above the ground?
A.
B.
C. 20tan
(25) + 5
D. 20tan (25) − 5
E. 25tan (20) + 5
27. Find the cubic equation that has −1 and 2i
as roots.
A.
B. 2
4
C.
D. 2
E.
28. Suppose the functions f x x)
and g x x( are)
inverse functions. About what line is the
graph of g x x a reflection of the graph)
of f x x)?
A. The x -axis
B. The y-axisC. The line y = 0
D. The line y x
E. The line
29. Simplify the following expression completely.
)2(
A. 2 3 + 4 5
4 1523 +
B. 23C. 1
D.
E. 25 15
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2 123 2101010 x10 .
32. Factor the following expression:
A. 2
(
)66 ( )1)( x
B. 2 ( )66 ( )1)( x
C. 2 ( )3 ( )2 x)3 ( x
D. 2
(
)33 ( )2)( x
E. 2 ( )66 ( )1)( x
any part of this page is illegal
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30. What is the solution to
− + −5 7+ 3 2= −4 x ?
A. x = 3
B. x = 4
C. x = 6
D. x = 9
E. x = 12
31. What equation represents therelationship that s is directly related to
r and inversely related to t ?
A. s rt
B. s
=t
r
C. s r
t
=
D. srt
=1
E. s t
= +r
1
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