Algebra I State Exam (1) final - University of Central …uca.edu/actm/files/2013/01/Algebra-I-State-Exam-1-final...Which equation can be used to determine the value of the car, V,

ArkansasCouncilofTeachersofMathematics–AlgebraIStateExamApril23,2016

Forquestions1-25,markyouranswerchoiceontheanswersheetprovided.Aftercompletingitems1through25,answereachofthetiebreakeritemsinsequenceorder(do#1first,followedby#2,then#3).Besurethatyournameisprintedoneachofthetiebreakerpages.

1. Thegraphsoftheequations𝑦 = 2!and𝑦 = −2𝑥 + 𝑎 intersectinQuadrantIforwhichvalues

of𝑎?

a. 0 < 𝑎 < 1 b.𝑎 < 1 c.𝑎 ≥ 1 d.𝑎 > 12. WhichorderedpairisNOTinthesolutionsetof𝑦 > − !

! 𝑥 + 5and𝑦 ≤ 3𝑥 − 2?

a.(3,5) b.(4,3) c.(3,4) d(4,4)3. Acardepreciatesatarateof4.5%annually.Gregpurchasedacarfor$12,500.Whichequation

canbeusedtodeterminethevalueofthecar,V,after5years?a.V=12,500(0.55)5 b.V=12,500(0.955)5c.V=12,000(1.045)5 d.V=12,500(1.45)5

4. Asunfloweris3inchestallatweek0andgrows2incheseachweek.Whichfunction(s)shown

belowcanbeusedtodeterminetheheight,f(n),ofthesunflowerinnweeks?

I. f(n)=2n+3II. f(n)=2n+3(n–1)III. f(n)=f(n-1)+2wheref(0)=3

a.IandII b.IIonly c.IIIonly d.IandIII

5. Findthesolutionsetto!

! 𝑥 + 13.5 > !

! 𝑥 − 2.4

a.(−∞,−31.8)b.(−31.8,∞)c.(−∞, 9.25)d.(9.25,∞)

6. Theweightsof11peopleinJohn’sclassareaveragedtobe94pounds.Johntakesoutone

person’sweightandtheaveragebecomes97pounds.Whatweightwasremovedfromthedataset?

a.33pounds b.64pounds c.97pounds d.100pounds7. Atmostgasstations,gasolinepricesinclude !

!"ofacentinadditiontoanamountstatedin

dollarsandcents.However,customerscanonlypayfortheirpurchasesusingdollarsandwholecents.Whatisthemaximumdifferencebetweentheactualpriceofagasolinepurchaseandthepricethecustomerpays?

a.$0.001b.$0.005c.$0.009d.Thereisnomaximumdifference


8. Joehasarectangularpatiothatmeasures10feetby12feet.Hewantstoincreasetheareaby50%andplanstoincreaseeachdimensionbyequallengths,x.Whichequationcouldbeusedtodeterminex?

a. 10 + 𝑥 12 + 𝑥 = 120 b. 10 + 𝑥 12 + 𝑥 = 180 c. 15 + 𝑥 18 + 𝑥 = 180d. 15 18 = 120 + 𝑥!

9. Theequation𝑦 = 0.45𝑥 + 2.99determinesthetotalcostthatarestaurantchargesforits$2.99

regularhamburgerplustoppingsat$0.45each.Whichofthefollowingisatruestatement?

a. They-interceptrepresentsthecostofaregularhamburgerwithnotoppings.b. They-interceptrepresentstheadditionalcostpereachtopping.c. Thesloperepresentsthenumberofhamburgertoppingsadded.d. Thesloperepresentsthetotalcostahamburgerwithxtoppings.

10. Whichquadrantwillbecompletelyshadedinthegraphoftheinequality4𝑥 + 3 < 9?

a.QuadrantI b.QuadrantII c.QuadrantIII d.QuadrantIV

11. Delawarehasanareaof2,000squaremiles.WhichistrueifDelawareisincludedinthedata

set?

a.Thestandarddeviationincreases. b.Therangedecreases.c.Theinterquartilerangedecreases.d.Themeanincreases.12. Inabeautycontest,thescoresawardedbyeightjudgeswere:

5.9 6.7 6.8 6.5 6.7 8.2 6.1 6.3

Onlysixscoresaretobeused.Whichtwoscoresmaybeomittedthatwillleavethevalueofthemedianthesame?

a.6.5and6.7 b.5.9and6.3 c.5.9and8.2 d.Themediancannotbeduplicatedusingsixscores.

State Area(thousandsofsquaremiles)

Connecticut 6Georgia 59Maryland 12

Massachusetts 11NewHampshire 9

NewYork 54NorthCarolina 54Pennsylvania 46


13. Giventhefunction𝑓 𝑥 = 2𝑥! + 5, 𝑥 ≥ 0find𝑓!!(𝑥).

a. !!!! b. !!!

! c.± !!!!

! d.± !!!!

!

14. Anarithmeticsequencehasafirsttermof10andasixthtermof40.Whatisthe20thtermof

thissequence?

a.105 b.110 c.124 d.13015. Whichsituationbelowcorrectlymodelstheexponentialequation𝑦 = 1500 . 975 ! .

a. Apopulationof1,500geeselosingitspopulationby2.5%eachyear.b. Apopulationof1,500geesegrowingatarateof97.5%eachyear.c. Apopulationof1,500geeselosing25%ofitspopulationayear.d. Apopulationof1,500geeseadding97.5newgeesetoitspopulationeachyear.

Usethefigurebelowtoanswerquestion16.

16. Whatistheareaoftheunshadedpartofthefigure?

a. −2𝑥! + !"!𝑥! − !

!

b. −2𝑥! − !"!𝑥! − !

!

c. −2𝑥! + 13𝑥! − !!𝑥 − !

!

d. – 2𝑥! + 13𝑥! + !!𝑥 − !

!

17. Onetypeofredwoodtreehasanaverageheightof65feetwhenitis20yearsold.Ifthetreeis

morethan20yearsold,theaverageheight,h,canbemodeledbythefunctionℎ = 1.95 𝑎 −20 + 65,whereaistheageofthetreeinyears.Whichstatementaboutthissituationistrue?a. Eachadditionalyearofageover20yearsadds1.95ft.totheaverageheightofthistypeof

redwoodtree.b. Everyadditional1.95ft.oflengthover20ft.adds45yearstotheageofthistypeof

redwoodtree.c. Forthistypeofredwoodtree,theaverageheightincreasesby1.95ft.peryearthroughout

itslifetime.d. Forthistypeofredwoodtree,theaverageheightincreasesby65ft.forevery20yearsof

growth.

3𝑥! −12

−23𝑥 + 5

𝑥𝑥

𝑥𝑥


18. Theperimeterofarectangleis42centimeters.Thelengthoftherectanglecanberepresentedby(x+4),anditswidthcanberepresentedby(2x−7).Whatarethedimensionsofthisrectangleincentimeters?a. Length=10andwidth=11b. Length=8andwidth=13c. Length=6andwidth=15d. Length=12andwidth=9

19. Whichofthefollowingisnotequivalentto 3 ! !"!"

!!!! ?

a. 3! !

!"!!

!!

b.! !"#!

! !!! c.9 !" !"

!"

!! d.3! ! !

!

!!!

20. Theinterceptsofagivenupwardfacingquadraticfunctionare(3,0)and(5,0).Whatistheaxisofsymmetryofthequadraticfunction?

a.𝑥 = 15 b. 𝑥 = −15 c.𝑥 = −4 d.𝑥 = 4

21. Giventhefunctionℎ 𝑡 = 𝑡! + 10𝑡 + 24,whatistheaveragerateofchangefrom[5,10]?

a.25 b.-25 c.125 d.-125

22. Letfbeafunctionwhosegraphistheparabolasketchedtotheright.

Inwhichinterval(s)is𝑓 𝑥 > 0?

a. (1, 3)b.[1, 3]c.(−∞, 1) ∪ (3,∞) d. −∞, 1 ∪ [3,∞)

23. At3:00PM,250bacterialcellsarebeinggrowninalab.Ifthenumberofcells

continuedtodoubleeveryhalfhour,atwhattimewilltherebe32,000cells?

a.6:00PM b.6:30PM c.10:00PM d.11:00PM

24. Whatistheareaoftherectangleshowninthefiguretotheright?

(Note:Thegraphisnotdrawntoscale.)

a.15units2 b.20units2 c.39units2 d.65units2

25. Theaccompanyingdiagramrepresentsthebiologicalprocessofcelldivision.

Ifthisprocesscontinues,whichexpressionbestrepresentsthenumberofcellsatanytime,t?

a. 𝑡 + 2 b.2𝑡 c.𝑡! d.2!


Name:____________________________________OpenResponse#1Theformula𝑠 = 30𝑑𝑓isusedtofindhowfastacarwastravelingbeforeanaccident,wheres=speed(inmph),d=thelength(infeet)oftheskidmarkleftbythecar,andf=thecoefficientoffriction(roadcondition).OfficerBartonmustdecideifthedriverinacaraccidentwasspeedingina35mphspeedzone.Thecar’sskidmarklengthwasmeasuredtobe76feet.Thecoefficientoffrictionis0.80.

a. Writetheequationthatmodelsthespeedofthecarbeforetheaccident.

b. Solvetheequationinpart(a).Roundyouranswertothenearesttenth.

c. Wasthedriverspeedinginthe35mphspeedzone?Showyourworkand/orexplainyouranswer.

d. Iftheskidmarkhadbeen4timeslonger,howmanytimesasfastwouldthedriverhavebeengoingascomparedtothespeedinpart(b)?Showyourworkand/orexplainyouranswer.


Name:_________________________________________________________OpenResponse#2

Ms.Daniels’sewingclassstudentsaremakingstuffedteddybearsforafundraiser.Theyaremakingboyandgirlbears.Eachweektheypurchaseenoughmaterialstocreate40bears.Letxrepresentthenumberofgirlbearsandyrepresentthenumberofboybears.

a. Writeaninequalitythatshowsthepossiblenumberofboyandgirlbearstheycanmake

eachweek.

b. Itcost$3tocreateeachbear.Theclasswillcharge$15forgirlbearsand$12forboy

bears.Theywanttoearnatleast$540aweek.Writeaninequalitytodescribethissituation.

c. Givethreepossiblesolutionsforthenumbersofboyandgirlbearsthatcanbemadeto

earnaprofitover$540.


Name:_________________________________________________________OpenResponse#3 The $150 million Deep Space 1 spacecraft launched on October 22, 1998 used an ion engine to travel from Earth to the Comet Borrelly. It arrived on September 22, 2001. By ejecting a constant stream of xenon atoms into space, at speeds of thousands of kilometers per second, the new ion engine could run continuously for months. This allowed the spacecraft to accelerate to speeds that eventually could exceed the fastest rocket-powered spacecraft.

The Deep Space 1 ion engine produced a constant acceleration, starting from a speed of 44,000 km/hr, reaching a speed of 56,060 km/hr as it passed the comet 36 months later. The sequence for the first 7 months of operation is given by:

n 1 2 3 4 5 6 7 Vn 44,000 44,335 44,670 45,005 45,340 45,675 46,010

a. What is the general formula for Vn?

b. How much time had passed when the spacecraft reached a speed of 50,000? Round to the nearest whole number.

c. Suppose the Deep Space I ion engine could be left on for 30 years. What would be the speed of the spacecraft at that time?


AnswerKey:1.D2.B3.B4.D5.B6.B7.C8.B9.A10.C11.A12.C13.B14.C15.A16.D17.A18.D19.C20.D21.A22.C23.B24.C25.D


Name:____________________________________OpenResponse#1Theformula𝑠 = 30𝑑𝑓isusedtofindhowfastacarwastravelingbeforeanaccident,wheres=speed(inmph),d=thelength(infeet)oftheskidmarkleftbythecar,andf=thecoefficientoffriction(roadcondition).OfficerBartonmustdecideifthedriverinacaraccidentwasspeedingina35mphspeedzone.Thecar’sskidmarklengthwasmeasuredtobe76feet.Thecoefficientoffrictionis0.80.

e. Writetheequationthatmodelsthespeedofthecarbeforetheaccident.

𝑺 = 𝟑𝟎 ∙ 𝟕𝟔 ∙ 𝟎.𝟖𝟎

f. Solvetheequationinpart(a).Roundyouranswertothenearesttenth.

𝑺 = 𝟒𝟐.𝟕

g. Wasthedriverspeedinginthe35mphspeedzone?Showyourworkand/orexplainyouranswer.

Yes.Thedriver’sspeedwas42.7mph(asshowninpartb),whichisgreaterthanthespeedlimit(35mph).

h. Iftheskidmarkhadbeen4timeslonger,howmanytimesasfastwouldthedriverhavebeengoingascomparedtothespeedinpart(b)?Showyourworkand/orexplainyouranswer.Hypotheticalskidmark 𝟕𝟔×𝟒 = 𝟑𝟎𝟒feetHypotheticalSpeed 𝑺 = 𝟑𝟎 ∙ 𝟑𝟎𝟒 ∙ 𝟎.𝟎𝟖 = 𝟕𝟐𝟗𝟔

𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒕𝒊𝒄𝒂𝒍 𝒔𝒑𝒆𝒆𝒅

𝒂𝒄𝒕𝒖𝒂𝒍 𝒔𝒑𝒆𝒆𝒅=𝟕𝟐𝟗𝟔𝟒𝟐.𝟕

= 𝟏𝟕𝟎.𝟖𝟕

Thedriverwouldhavebeengoing170.87timesfaster


Name:_________________________________________________________OpenResponse#2

Ms.Daniels’sewingclassstudentsaremakingstuffedteddybearsforafundraiser.Theyaremakingboyandgirlbears.Eachweektheypurchaseenoughmaterialstocreate40bears.Letxrepresentthenumberofgirlbearsandyrepresentthenumberofboybears.

d. Writeaninequalitythatshowsthepossiblenumberofboyandgirlbearstheycanmake

eachweek.

𝑥 + 𝑦 ≤ 40 or

𝑦 ≤ 40 − 𝑥e. Theclasswillcharge$15forgirlbearsand$12forboybears.Theywanttoearnatleast

$540aweek.Writeaninequalitytodescribethissituation.

15𝑥 + 12𝑦 ≥ 540 or

𝑦 ≥ 45 −54𝑥

f. Givethreepossiblesolutionsforthenumbersofboyandgirlbearsthatcanbemadetoearnatleast$540.

Anyofthecombinationsgiveninthetableareacceptableanswers.(x=girls,y=boys)

X=20Y=20

X=21Y=19

X=22Y=18

X=23Y=17

X=24Y=15or16

X=25Y=14or15

X=26Y=13or14

Y=27Y=12or13

X=28Y=10,11or12

X=29Y=9,10or11

X=30Y=8,9or10

X=31Y=7,8or9

X=32Y=5,6,7or8

X=33Y=4,5,6or7

X=34Y=3,4,5or6

X=35Y=2,3,4or5

X=36Y=0,1,2,3or4

X=37Y=0,1,2or3

X=38Y=0,1or2

X=39Y=0or1

X=40Y=0


Name:_________________________________________________________OpenResponse#3 The $150 million Deep Space 1 spacecraft launched on October 22, 1998 used an ion engine to travel from Earth to the Comet Borrelly. It arrived on September 22, 2001. By ejecting a constant stream of xenon atoms into space, at speeds of thousands of kilometers per second, the new ion engine could run continuously for months. This allowed the spacecraft to accelerate to speeds that eventually could exceed the fastest rocket-powered spacecraft.

The Deep Space 1 ion engine produced a constant acceleration, starting from a speed of 44,000 km/hr, reaching a speed of 56,060 km/hr as it passed the comet 36 months later. The sequence for the first 7 months of operation is given by:

n 1 2 3 4 5 6 7 Vn 44,000 44,335 44,670 45,005 45,340 45,675 46,010

d. What is the general formula for Vn?

𝑽𝒏 = 𝟒𝟒𝟎𝟎𝟎+ 𝟑𝟑𝟓(𝒏− 𝟏)

e. How much time had passed when the spacecraft reached a speed of 50,000? Round to the nearest whole number.

𝟓𝟎𝟎𝟎𝟎 = 𝟒𝟒𝟎𝟎𝟎+ 𝟑𝟑𝟓(𝒏− 𝟏) 𝒏 = 𝟏𝟗

Answer: 19 months, or 1 year and 7 months

f. Suppose the Deep Space I ion engine could be left on for 30 years. What would be the speed of the spacecraft at that time?

𝑽𝟑𝟔𝟎 = 𝟒𝟒𝟎𝟎𝟎+ 𝟑𝟑𝟓(𝟑𝟔𝟎− 𝟏)

𝑽𝟑𝟔𝟎 = 𝟏𝟔𝟒𝟐𝟔𝟓 𝒌𝒎/𝒉𝒓

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Algebra I State Exam (1) final - University of Central …uca.edu/actm/files/2013/01/Algebra-I-State-Exam-1-final...Which equation can be used to determine the value of the car, V,