Math Test FPT3

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HiSET ® Exam Free Practice Test FPT3

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Mathematics

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■ Answer questions developed by the test maker

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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

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Math Test FPT3

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