Microsoft Word - ACT Sample Math Test Solutions.docx

SAMPLEACTMATHEMATICSTESTQUESTIONS

(http://www.actstudent.org/sampletest/math/math_01.html)

AnactualACTMathematicsTestcontains 60questionstobeansweredin60minutes.

DIRECTIONS:Solveeachproblem,choosethe

correctanswer,andthenfillinthecorresponding

ovalonyouranswerdocument.

Donotlingeroverproblemsthattaketoomuch

time.Solveasmanyasyoucan;thenreturntothe

othersinthetimeyouhaveleftforthistest.

Youare

permittedtouseacalculatoronthistest.

Youmayuseyourcalculatorforanyproblemsyou

choose,butsomeoftheproblemsmaybestbe

donewithoutusingacalculator.

Note:Unlessotherwisestated,allofthefollowing

shouldbeassumed.

1. IllustrativefiguresareNOTnecessarily

drawnto

scale.

2. Geometricfigureslieinaplane.

3. Thewordlineindicatesastraightline.

4. Thewordaverageindicatesarithme tic

mean.

Set1

1.Acaraverages27milespergallon.Ifgascosts$4.04pergallon, whichofthefollowingisclosestto

howmuchthegaswouldcostforthiscartotravel2,727typicalmiles?

A.$44.44

B.$109.08

C.$118.80

D.$408.04

E.$444.40



2.Whenx=3andy=5,byhowmuchdoesthevalueof3x

–2yexceedthevalueof2x

–3y?

F.4

G.14

H.16

J.20

K.50

$4.04pergallon

x101gallons

404

404

408.04 total

3



–2

2



3









5

9514

2,727miles

÷27mpg

101gallons

Page2of25



3.Whatisthevalueofxwhen2x+3=3x–4?

A.–7

B. 

C.1

D. 

E.7



4.Whatisthegreatestcommonfactorof42,126,and210?

F.2

G.6

H.14

J.21

K.42



5.Salesforabusinesswere3milliondollarsmorethesecondyearthanthefirst,andsalesforthethird

yearweredoublethesalesforthesecondyear.Ifsalesforthethirdyearwere38milliondollars,what

weresales,inmillionsofdollars,forthefirst

year?

A.16

B.17.5

C.20.5

D.22

E.35





23  3–4

2 2 

34

44

7

422∙3∙7 

1262∙3∙7∙3 

2102∙3∙7∙5

422∙3∙7 

38









y38219

19316

yx3

z2y

So:

TogettheGCFofasetof

numbers,lineuptheprime

factorizationofeachand

multiplyanyprimefactors

thatexistineveryline.

1

2

3

Let:

Page3of25



6.Inthefigurebelow,ray wasconstructedstartingfromrays and .Byusingacompass,Dand

GweremarkedequidistantfromEonrays and .ThecompasswasthenusedtolocateapointF,

distinctfromE,sothatFisequidistantfromDand

G.Forallconstructionsdefinedbytheabovesteps,

themeasuresof DEFand GEF:



F.areequal.

G.areNOTequal.

H.sumto30°.

J.sumto45°.

K.sumto60°.



7.Abandonedminesfrequentlyfillwithwater.Beforeanabandonedminecanbereopened,thewater

mustbepumpedout.Thesizeofpumprequireddependsonthedepthofthemine.Ifpumpingouta

minethatisDfeetdeepr equiresapumpthatpumpsaminimumof







4–250gallonsperminute,

pumpingoutaminethatis150feetdeepwouldrequireapumpthatpumpsaminimumofhowmany

gallonsperminute?

A.362

B.500

C.800

D.1,250

E.1,750



8.Thelength,ininches,ofaboxis3incheslessthantwiceitswidth,ininches.Whichofthefollowing

givesthelength,linches,intermsofthewidth,winches,ofthebox?

F.l= w+3

G.l=w+3

H.l=w–3 

J.l=2w+3

K.l=2w–3



"3less" "3"

"twice"  "2"

, 23



150∙150

4∙150250

6∙1504∙150250

1,5002501,250

Notethat:∆≅∆bySSS.

Therefore,∠≅∠,meaningthatthe

measuresofthetwoanglesareequal.

Greensegmentsarecongruent.

Orangesegmentsarecongruent.

Page4of25



9.InquadrilateralPQRSbelow,sidesPSandQRareparallelforwhatvalueofx?

A.158

B.132

C.120

D.110

E.70



10.Howmanyirrationalnumbersaretherebetween1and6?

F.1

G.3

H.4

J.10

K.Infinitelymany



11.Atypicalhighschoolstudentconsumes 67.5poundsofsugarperyear.Aspartofanewnutrition

plan,eachmemberofatrackteamplanstolowerthesugarheorsheconsumesbyatleast20%forthe

comingyear.Assumingeachtrackmemberhadconsumed sugar

atthelevelofatypicalhighschool

studentandwilladheretothisplanforthecomingyear,whatisthemaximumnumberofpoundsof

sugartobeconsumedbyeachtrackteammemberinthecomingyear?

A.14

B.44

C.48

D.54

E.66





°

°

.

∠  180°70°110°

, ∠ ∠

,∠ 110°

Thereareinfinitelymanyrational

numbersandinfinitelymany

irrationalnumbersbetweenany

twoRealnumbers.

67.5∙80%

67.5∙



67.5∙4



270

54

Page5of25



12.Inthestandard(x,y)coordinateplanebelow,3oftheverticesofarectangleareshown.Whichof

thefollowingisthe4thvertexoftherectangle?



F.(3,–7)

G.(4,–8)

H.(5,–1)

J.(8,–3)

K.(9,–3)





2,1

:1,1

:3,2

6,5

:3,2

:3,7

Step1:Drawtwosidesoftherectangle.

Step2:Themissingpointappearstobebelowandto

theleftofpointC.So,determinethevectorthatadds

toBtogetA.

Step3:Subtractthevector,,fromCto

getthe

missingpoint,D.

OptionalStep4:PlotDtoseeiftheresultlookslikea

rectangle.

A

B

C

D

Page6of25



Set2

1.Theleadofascrewisthedistancethatthescrewadvancesinastraightlinewhenthescrewis

turned1completeturn.Ifascrewis





incheslongandhasaleadof





inch,howmanycomplete

turnswouldgetitallthewayintoapieceofwood?

A.5

B.10

C.15

D.20

E.25



2.Ifxy=144,x+y=30,andx>y,whatisthevalueofx–y?

F.4

G.6

H.18

J.22

K.24



3.Whichofthefollowingisthesineof Aintherighttrianglebelow?



A. 

B. 

C. 

D. 

E. 













∙



20

Notethat:30

Fastestmethodistotryvaluesthataddto30:

 2∙2856

 4∙26104

 6∙24144

Then,don’tforgettosubtract:24618

Remember:SOH–CAH–TOA

Then, sin













Page7of25



4.Ding’sDineradvertisedthisdailylunchspecial:“Choose1itemfromeachcolumn—only$4.95!”

Thus,eachdailylunchspecialconsistsofasalad,asoup,asandwich,andadrink.

Howmanydifferentdailylunchspecialsarepossible?

F.4

G.14

H.30

J.120

K.180



Salads Soups Sandwiches Drinks

coleslaw

lettuce

potato

onion

tomato

meatloaf

chicken

hamburger

ham

tenderloin

milk

cola

coffee

tea

5.Thevolume,V,oftherightcircularconewithradiusrandheighth,shownbelow,canbefound

usingtheformula









.Acone‐shapedpapercuphasavolumeof142cubiccentimetersanda

heightof8.5centimeters.Whatistheradius,tothenearestcentimeter,ofthepapercup?



A.2

B.4

C.8

D.12

E.16



6.AboatdepartsPortIsabelle,Texas,travelingtoanoilrig.Theoilrigislocated9mileseastand12

milesnorthoftheboat’sdeparturepoint.Abouthowmanymilesistheoilrigfromthedeparture

point?

F.3

G. 

H.15

J.21

K.225





Trick:

Approximate

valuesateach

ste



Step1:













Step2:Substitutevalues:

142



∙9













 



~16

 ~4

345

6810

91215

Recall:PythagoreanTriples

orusePythagoreanTheorem

So,15

9

12







~

~

∙∙∙

 

 

Page8of25



7.Inthefigurebelow, ABC DFE, BAC FDE,DandFareonAB,AD FB,anddistancesin

centimetersareasshown.WhatisthelengthofAD,incentimeters?



A.5

B.4

C.3

D.2

E.1



8.Whichofthefollowingisafactorofthepolynomial:



––?

F.x–1

G.2x–3

H.2x–5

J.2x+5

K.3x+5



9.Whatisx,thesecondterminthegeometricseries

















…?

(Note:Inageometricseriestheratioofanytermtothefollowingtermisconstant.)

A. 

B. 

C. 

D. 

E. 











 12∙120

 



10

Then,let:xADFB











106

42

2

2



–3–5

2



–52–5

2–52–5) 





1







2–5



5 ∙ 2 10

52 3

108

3

Thenumeratorsareall1,so

let’slookattheratiosofthe

denominators:

So,theratioofsucceeding

denominatorsis3.





Then,thedenominatorofx

is:4∙312

And,finally:

Page9of25



10.Whatistheslopeofanylineparalleltotheline9x+4y=7?

F.–9

G. 

H. 

J.7

K.9



11.ADVDplayerwithalistpriceof$100ismarkeddown30%.IfJohngetsanemployeediscountof

20%offthesaleprice,howmuchdoesJohnpayfortheDVDplayer?

A.$86.00

B.$77.60

C.$56.00

D.$50.00

E.$44.00



12.













?

(Note:i= )

F.9i

G.9+i

H.9–i

J.9

K.–9



$100∙70%∙80%

$70∙80%

$56

√

81

9

947

9 9

497

44







Parallellineshavethesameslope.

Inslope‐interceptform,the

coefficientofistheslope.

Page10of25



Set3

1.Whatisthedegreemeasureoftheacuteangle formedbythehandsofa12‐hourclockthatreads

exactly1o’clock?

A.15°

B.30°

C.45°

D.60°

E.72°



2.Whatistheprobabilitythatanumberselectedatrandomfromtheset{2,3,7,12,15,22,72,108}

willbedivisiblebyboth2and3?

F. 

G. 

H. 

J. 

K. 



3.Acirclehasacircumferenceof16feet.Whatistheradiusofthecircle,infeet?

A. 

B.4

C.8

D.16

E.32





Thearcfrom12to1ona

clockis





ofacircle.

Then,

˚



30˚



2,3,7,12,15,22,72,108





 

12

1

Numbersdivisibleby2areeven.

Numbersdivisibleby3havedigi tsthataddtoanumberdivisibleby3.

Now,let’stesteachofthenumbers.





So,3outofthe8numbersare

divisiblebyboth2and3.

162

2 2

8

Page11of25



4.Arectanglewithaperimeterof30centimetersistwiceaslongasitiswide.Whatistheareaofthe

rectangleinsquarecentimeters?

F.15

G.50

H.200

J.3 

K.6 



5.Inthestandard(x,y)coordinateplane, whatarethecoordinatesofthemidpointofalinesegment

whoseendpointsare(–3,0)and(7,4)?

A.(2,2)

B.(2,4)

C.(5,2)

D.(5,4)

E.(5,5)



6.PointsA,B,C,andDareonalinesuchthatBisbe tweenAandC,andCisbetweenBandD.The

distancefromAtoBis6units.ThedistancefromBtoCistwicethedistancefromAto

B,andthe

distancefromCtoDistwicethedistancefromBtoC.Whatisthedistance,inunits,fromthemidpoint

ofBCtothemidpointofCD?

F.18

G.14

H.12

J.9

K.6



7.Whichofthefollowingstatementsmustbetruewhenevern,a,b,andcarepositiveintegerssuch

thatn<a,c>a,andb>c?

A.a<n

B.b–n>a–n

C.b<n

D.n+b=a+c

E.2n>a+b

630

5



5∙1050

allvaluesarepositive



4,4



2



2,2





7,4

3,0

Requestedlengthisbetweenthetwopoints:







∙12





∙24  612  18









 



  



Simplifiesto:

Page12of25



8.ThedistributionofJamal’shighs choolgradesby percentageofcoursecreditsisgiveninthecircle

graphbelow.WhatisJamal’sgradepointaverageifeachAisworth4points;eachB,3points;andeach

C,2points?



F.3.0

G.3.4

H.3.6

J.3.7

K.Cannotbedeterminedfromthegiveninformation



9.Whatisthedifferencebetween1.8and1.08?

(Note:Abarindicatesadigitpatternthatisrepeated.)

A.0.71

B.0.71

C.0.719

D.0.72

E.0.72



10.Whichofthefollowingequationsrepresentsthelinearrelationshipbetweentime,t,andvelocity,v,

showninthetablebelow?

F.v=32t

G.v=32t+120

H.v=120t

J.v=120t+32

K.v=120t+120



t 0 1 2

v 120 152 184





"m"istheuniformdifferencebetweenterms.

"b"isthevalueo

thefunctiona

0

70% ∙42.8

20% ∙30.6

10% ∙20.2

3.6

1.79999999999…

1.08080808080…

0.71919191919…



:1.801.799999999…1.79

Page13of25



11.Anindustrialcleanerismanufacturedusingonlythe3secretingredientsA, B,andC,whichare

mixedintheratioof2:3:5,respectively,byweight.HowmanypoundsofsecretingredientB areina42‐

pound(netweight)bucketofthiscleaner?

A.

4.2

B.12.6

C.14.0

D.18.0

E.21.0



12.Ifn=8and16∙2

=4

n–8

,thenm=?

F.–4

G.–2

H.0

J.1

K.8







:2

:3

:5

10

16∙2



4







∙2



4







1

1042

4.2

:33∙4.212.6

Then,since:2



1:

m40

4

Page14of25



Set4

1.Inthefigurebelow,A,B,C,andDarecollinear,FCisparalleltoED,BEisperpendiculartoED,andthe

measuresof FABand EBAareasmarked.Whatisthemeasureof FCB?



A.33°

B.57°

C.63°

D.84°

E.Cannotbedeterminedfromthegiveninformation



2.Whichofthefollowingisanequationofthecirclewithitscenterat(0,0)thatpassesthrough(3,4)in

thestandard(x,y)coordinateplane?

F.x–y=1

G.x+y=25

H.x

+y=25

J.x

+y

=5

K.x

+y

=25





Usetheexternalangletheorem:

147˚90˚

57˚















Generalequationofacircle:

,isthecenterofthecircle.

istheradiusofthecircle.

Resultingequation:

0



0



5













25

enlarge



147˚

4

3

0,0



Recall:PythagoreanTriples

orusePythagoreanTheorem

345

So,5

Page15of25



Usethefollowinginformationtoanswerquestions3–5.

Taherhasdecidedtocreateatriangularflowerbedborder.Heplanstouse

3piecesofrectangularlumberwithlengths4,5,and6feet,asshowninthe

figurebelow.PointsA,B,andCarelocatedatthecorners

oftheflowerbed.



3.Taherplanstocutthe3piecesof lumberfortheflowerbedborderfromasinglepieceoflumber.

Eachcuttakes





inchofwoodoffthelengthofthepieceoflumber.Amongthefollowinglengths,in

inches,ofpiecesoflumber,whichistheshortestpiecethathecanusetocutthepiecesfortheflower

bedborder?

A.178

B.179

C.180

D.181

E.182



4.Themeasureof ABCinthefigureisx°.Whichofthefollowingisanexpressionforb°?

F.x°

G.2x°

H.(90+x)°

J.(180–x)°

K.(180–





)°



5.Afterarrangingtheflowerbed,Taherdecidesthattheflowerbedwouldlookmoreattractiveif1of

theanglesinthetrianglewerearightangle.HedecidestoplacetherightangleatvertexAandtoleave

thelengthsofABandACas4and

5feet,respectively.Tothenearest0.1foot,howlongofapieceof

lumberwouldheneedtoreplacethe6‐footpiecerepresentedbyBC?

A.3.0

B.3.3

C.6.0

D.6.4

E.7.8



bappearstobethemeasureoftheexternalanglea

B.

So,

b180

Therefore,

b˚ 180˚



5







1625





41





UsethePythagoreanTheorem

Then,since: 36



49

Weconcludethat:67

5

4



Totalmeasureofthelumberis:

4feet+





inch+5feet+





inch+6feet=16feet+





inch

15∙12





180





















4





lumber

Page16of25



6.Whichoneofthefollowingexpressionshasanevenintegervalueforallintegersaandc?

F.8a+2ac

G.3a+3c

H.2a+c

J.a+2c

K.ac+a



7.Aneighborhoodrecreationprogramservesatotalof280childrenwhoareeither11yearsoldor12

yearsold.Thesumofthechildren’sagesis3,238years.Howmany11‐year‐oldchildrendoesthe

recreationprogramserve?

A.55

B.122

C.132

D.158

E.208



InfoTable Number TotalAge

11‐yearolds

 11

12‐yearolds

280 12∙280

Total

280 3,238

8.Thegeometricfigureshownbelowconsistsofasquareand4semicircles.Thediametersofthe

semicirclesarethesidesofthesquare,andeachdiameteris10centimeterslong.Whichofthefollowing

istheclosestapproximationofthetotalarea,insquarecentimeters,ofthisgeometricfigure?



F.100

G.160

H.260

J.400

K.730





AreaAreao

square4∙



Areao

semicircle





Areao

square2∙



Areao

circle





10



2∙∙5





10050

~100157257



Findbasedoninformationin

the“TotalAge”column:

1112∙



280



3,238

 3,3603,238

 122

Onlyevencoefficientswill

guaranteeanevenresult.

10

Page17of25



9.Whichofthefollowingexpressionsistheclosestapproximationtotheheighth,infeet,oftheroof

trussshownbelow?



A.15tan20°

B.15sin20°

C.30tan20°

D.30sin20°

E.



10.QuadrilateralABCDisdrawnonthestandard(x,y)coordinateplaneasshownbelow,withpointsE

andFonAD.PointGisthecenterofrectangleBCEF.HowmanycoordinateunitslongisAG?



F. 

G. 

H. 

J. 

K.11



11.Whatisthex‐interceptofthegraphofy=x

–4x+4?

A.–2

B.–1

C.0

D.1

E.2





0



–44

022

2

Addthegreenandorangelinesto

theillustrationasshown.ThenGis

themidpointofBE



.

Plan:findthecoordinatesofG,then

findthedistancefromAtoG.

tan20˚





15tan20˚

Consideronlythegreentriangle.

Remember:SOH–CAH–TOA

Wehavethesidesoppositetoand

adjacenttothe20˚angle.So,use

the

tangent

function:

15





B:6,4

E:12,0

G:



18,4



2



9,2







90



20





√

814

√

85

Then,calculate:AG

Page18of25



12.Forallnonzerorealnumbersp,t,x,andysuchthat











,whichofthefollowingexpressionsis

equivalenttot?

F. 

G. 

H. 

J. 

K. 





Startingequation: 













Crossmultiply:   23



Multiplybothsidesby2: 













Combineandsimplify:  







Page19of25



Set5

1.Ms.Hernandezbeganhermathclassbysaying:

I'mthinkingof5numberssuchthattheirmeanisequaltotheirmedian.If4ofthenumbersare14,

8,16,and14,whatisthe5thnumber?

Whatisthe5thnumberMs.Hernandezisthinkingof?

A.13



B.14

C.15

D.16

E.18



2.Thegraphofacertainhyperbola,y=h(x),isshowninthestandard

(x,y)coordinateplanebelow.

Amongthefollowinggraphs,whichbestrepresentsy=–h(x)?

F. 

G. 

H. K.

J. 

8,14,14,16.

First,orderthenumbersgiven:

Thennoticethatnomatter

whatthe5

numberis,the

medianofthefivenumbers

willbe14.

8141416

14

5270

18

Negatingafunctionissimplyareflectionofthatfunctionoverthex‐axis.

AnswerFisareflectionoverthex‐axisofthefunctiongiven.

Page20of25



3.Inthefigurebelow, H  F;E,G,andIarecollinear;andGisthemidpointofFH.



ToprovethatHI FEgiventheconditionsstatedabove,whichofthefollowingisalogicalorderfor

the5stepsinthe

tablebelow?

Statement Reason

1.HG FG

Themidpointofalinesegmentdividesthesegment

into2congruentsegments

2. EGF IGH Verticalanglesarecongruent

3. GHI GFE Angle‐side‐anglecongruencetheorem

4. EGFand IGHareverticalangles Definitionofverticalangles

5.HI FE Correspondingpartsofcongruenttrianglesare

congruent

A.1,2,3,4,5

B.1,2,3,5,4

C.1,2,4,3,5

D.1,4,2,3,5

E.1,5,4,2,3



4.Eachofthevariablest,w,x,y,and zrepresentsadifferentpositiverealnumber.Giventheequations

below,whichofthe4variablesw,x,y,andznecessarilyhasthegreatestvalue? 

1.23w=t

1.01x=t

0.99y=t

0.23

z=t

F.w

G.x

H.y

J.z

K.Cannotbedeterminedfromthegiveninformation

Plan:reviewthestepsbelowand

findsomesemblanceoforder.

Mustbethefirststep.

MustbeafterStep4given.

Mustbethelaststepbecause

thisistheconclusion.

Oneofthekeystosolvingthisproblemistonotethatyoumust

establishthatverticalanglesexistStep4beforeyoucando

anythingwiththemStep2.Hence,Step4mustprecedeStep2.

TheonlyanswergiventhathasStep4beforeStep2,andhasStep5

lastisanswerD.So,thismustbethesolution.





1.23





1.01





0.99





0.23

Thegreatestvalueresultsfromthedivision

withthesmallestdenominator.

Page21of25



5.Whichofthefollowingisequivalentto











?

A. 

B. 

C. 

D. 

E. 



6.Inthe2×2matrixbelow,b

andb

arethecostsperpoundofbokchoy(Chinesegreens)atMarket1

andMarket2,respectively;r

andr

arethecostsperpoundofriceflouratthese2markets,

respectively.Inthefollowingmatrixproduct,whatdoesqrepresent? 

F.Thecostofr

poundsofriceflourat$0.50perpound

G.Thecostofahalf‐poundofriceflouratMarket1

H.Thetotalcostofahalf‐poundofbokchoyandahalf‐poundofriceflouratMarket1

J.Thetotalcostofahalf‐poundofbokchoyandahalf‐poundofriceflouratMarket2

K.Thetotalcostofahalf‐poundofriceflouratMarket1andahalf‐poundofriceflouratMarket2









3

5

∙





3

5

∙





525



3

5







825

5

0.5



0.5



Sothevalueofiscalculatedbasedonthevalues

ofthecostofriceflouratbothmarkets.

Page22of25



7.The2diagramsbelowshowacircleofradius1inchwithshadedsectorsofanglex°,for2different

valuesofx.



Oneofthefollowingisthegraphinthestandard(x,y)coordinateplaneofthearea,y,of

ashaded

sectorwithanglex°,forallvaluesofxbetween0and360.Whichisthatgraph?

A. 

B. 

C. 

D. 

E. 

8.Ifh(x)=x³+xandg(x) =2x+3,theng(h(2))=?

F.7

G.10

H.17

J.19

K.23







360

∙



Theformulafortheareaofasectorofacircle,basedon

theillustrationsabove,is:







2



210











2∙10



323



Aschanges,Areachangesproportionally,ina

linearfashion.It’sasiftheequationwere:

Wherekisaconstantequalto:











TheonlycurvethatislinearisA.

Page23of25



9.Inthefigurebelow,pointsAandBareonoppositebanksofasmallstream.PointC

isonthesamebankofthestreamaspointBandapproximately18metersfromB.

Themeasureof CBAis45°,andthemeasureof

 BCAis60°.

Whichofthefollowingexpressionsgivestheapproximatedistance,inmeters,

betweenpointAandpointB?

(Note:For PQR,wherep,q,andrarethelengthsofthesidesopposite P,

Q,and R,respectively,

∠





∠





∠



.)

A. 

B. 

C. 

D. 

E. 



10.Eachsideofthesmallersquareinthefigurebelowisxinches long,andeachsideofthelarger

squareiscincheslongerthanasideofthesmallersquare.Theareaofthelargersquareishowmany

squareinchesgreaterthantheareaofthesmaller

square?



F.c



G.xc

H.4c

J.(x+c)



K.2xc+c





sin60˚





sin75˚



18∙sin60˚∙sin75˚

18∙sin60˚

sin75˚







∠



180˚60˚45˚75˚



























2









  2



Tosolvethisproblem,wemustfirstfindthemeasureof

angleA;thenwecanutilizetheequalitiesshown.

Note:

∠





∠





∠



iscalledtheLawofSines.

Tofindthedifferenceinarea,calculateeachareaandsubtract.

Page24of25



11.Acubewithedges





inchlongisshownbelow.Whatisthelength,ininches,ofadiagonalthatruns

fromonecornerofthecubetotheoppositecorner?



A. 

B. 

C. 

D. 

E. 



12.Whichofthefollowingisequivalenttosincscwhereversincscisdefined? 

F.–1

G.1

H.–tan

J.tan

K.–sin







sincsc

sin∙

sin



sin∙

sin











sin

sin

1







































√



√

Usingthe3‐dimensionaldistanceformula,

weget:

csc

sin

Ithelpstoknowwhatthe

sinefunctionlookslike.

Italsohelpstoknowthat:

sinsin

Fromthegraph,weseethat:

Page25of25



ACTOnlineSampleTestAnswerKey



 Set1 Set2 Set3 Set4 Set5

1 D D B B E

2 G H G K F

3 E C C D D

4 K J G J  J

5 A B A D E

6 F H F F  K

7 D D B B A

8 K H H H K

9 D C C A E

10 K G G  H K

11 D C B E E

12 F F F K F



