Sample Review Problems for Intermediate Algebra Placement Test r

7/27/2019 Sample Review Problems for Intermediate Algebra Placement Test r

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SAMPLEREVIEWPROBLEMSFORINTERMEDIATEALGEBRA

PLACEMENTTEST

1. Simplify: 34232)2()4( −−−−

xy y x

2. Simplify:2

32

43

5

3

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−

y x

y x

3. Simplify: )4(3)2(6 y x y x −−+

4. Evaluatetheexpressionusingthegivenvaluesforthevariables:

22

23 y xy x +−− if 2−= x and 2= y

5. Solvethefollo0wingforh:3

2hr

V π

=

6. Solvethefollowingforx: )5(26)42(3)5(2 +−=−−− x x x

7. Solvethefollowingforx:4

122

3

4 −

=−

+ x x

8. Simplify:2

2

32

6

4−

−

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

xy

z y x

9. Solvethefollowingforx: 43

3

4

2

6−

+

=+

x x x

10. Theformula 1050)20(32

+÷−

= AT describestheaveragerunningtime, T ,inseconds,forapersonwhois Ayearsoldtorunthe100-yarddash.Howlongdoesittakea30-year-oldrunner

torunthe100-yarddash?

11. Solve: P

y x K

+

=

3for x .



12. Aftera40%discount,youpay690dollarsforarefrigerator.Whatwastheoriginalpriceoftherefrigerator?

13. Themathematicalmodel 2

6400

6400125 ⎟

⎠

⎞⎜⎝

⎛

+

=

xW describestheapproximateweightW (in

pounds)ofa125poundastronautatanaltitudeof x kilometersabovesealevel.Whatisthe

astronaut’sapproximateweightatanaltitudeof50,000kilometers?

14. Findthe(a) x -intercept,and(b)y -intercept,and(c)graphthefunction: 21217 =− y x

15. Findthe(a)slope,(b)y -intercept,and(c)graphthelinearfunction: 32 +−= x y

16. Findthe(a)slope,(b)y -intercept,and(c)graphthelinearfunction: 1243 =−− y x

17. Let 43)( 2+−= x x x f and 1)( += x x g .Findthefollowing:

a) )2(− f b) )5)(( g f +

c) )4()2( g f −

18. Findtheslopeofthelinepassingthrough(–2,4)and(6,–4).

19. ItcostMaurice$102tobuyrefreshmentsfor6people.ItcostShari$162tobuyrefreshmentsfor10peopleatthesamerestaurant.Writetheslope-interceptformofthelinethrough(6,102)

and(10,162).

20. If48%ofthe2800studentsinajuniorcollegeareovertheageof25,howmanystudentsareovertheageof25?

21. Themodel 20015)( += x xC representsthecost,indollars,ofacatereddinnerwhere x isthe

numberofpeopleattending.Find C (22)anddescribewhatthisnumberrepresentsintermsof

themodel.

22. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 9)3(2 +≥− x x

23. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 10824 ≤+−≤− x



24. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 3|74| <− x

25. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 1432 <++ x

26. Solvetheinequalityforx: 11855

4=++ x

27. Theinequality 20|39| ≤−T describestherangeofthemonthlyaveragetemperature, T in

degreesFahrenheit,forNewCity.Solvetheinequality.

28. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 86210 ≤+−≤− x

29. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 9|63| ≤− x

30. Solvetheinequalityforxandexpressyouranswerinintervalnotation: 34

12−>

− x

31. Performtheindicatedoperation: 232 )8( y x−

32. Performtheindicatedoperation: )43)(2( 2−+− x x x

33. Performtheindicatedoperation: 2)35( y x −

34. Factorcompletely,orstatethatthepolynomialisprime: 8016523

−−+ x x x

35. Factorcompletely,orstatethatthepolynomialisprime: x x x 1019623++

36. Factorcompletely,orstatethatthepolynomialisprime: 223625 y x −


+− x x



38. Factorcompletely,orstatethatthepolynomialisprime: y xy y x 456242

−−

39. Arockisthrownfromthetopofabuilding.Thedistance,infeet,betweentherockandthegroundt secondsaftertherockisthrownisgivenby 153416

2++−= t t d .Howlongafterthe

rockisthrowndoesithittheground?

40. Arectanglehasalength1footlongerthantwicethewidth.Theareaoftherectangleis253squarefeet.Findthe(a)lengthandthe(b)width.

41. Factorcompletely,orstatethatthepolynomialisprime: 81164− x

42. Factorcompletely,orstatethatthepolynomialisprime: 15181012 −−+ x y xy


−+ x x

44. Factorcompletely,orstatethatthepolynomialisprime: x x x 7530323+−

45. Factorcompletely,orstatethatthepolynomialisprime: 228118 y x x −++


++ x x

47. Thelongestsideofatriangleis4centimetersmorethantheshortestside.Thethirdsideis2centimetersmorethantheshortestside.Findthelengthoftheshortestsideiftheperimeteris15centimeter.

48. Aballisthrownstraightupfromaplateau400feethigh.Thefunction4002016)( 2

++−= t t t s describestheball’sheightabovetheground, s(t),infeet,tseconds

afteritwasthrown.Howlongwillittakefortheball’sheighttobe224feet?

49. Performtheindicatedoperation: )1)(2( 2−−+ x x x

50. Performtheindicatedoperation: )72)(83(

+−

y y

51. Performtheindicatedoperation: 2)52( −a

52. Performtheindicatedoperation: )89)(89(22−+ x x



53. Performtheindicatedoperations.Simplifywherepossible: 4

2

6

1

22−

−

+

−−

+

x

x

x x

x

54. Performtheindicatedoperations.Simplifywherepossible:16

4

82

2

22−

+

−

−+

−

x

x

x x

x

55. Performtheindicatedoperations.Simplifywherepossible: x x

x x

x

x

8

86

42

22

+

++

⋅

+

56. Performtheindicatedoperations.Simplifywherepossible:2410

36

242

2410

2

2

2

2

++

−

÷

−+

+−

y y

y

y y

y y

57. Simplify:16

82

2

2

−

−−

x

x x

.

58. For82

67)(

2

2

−

++

=

x

x x x f ,find f (–2)orstateifitisundefined.

59. Whenaballisthrownverticallyupward,itsheight,h,infeet,abovethegroundafter t secondsisdescribedbytheformula .809616

2++−= t t h Atwhattimeistheball124feetabovethe

ground?

60. For x x f −= 2)( ,find

a) Completethetableandgraph.

b) find )14(− f

61. Simplifytheexpressions.Assumethatallvariablesrepresentpositivenumbers:a) 410

50 ba

b) 4 38243

y x

c) 48756128 +−

62. Performtheindicatedoperationand,ifpossible,simplify.Assumethatallvariablesrepresentpositiverealnumbers.



a) 4 5524 132164 bababa −

b) ( )2532 +

c) 5443 +− x x

d) y x y x 22 −+

63. Simplifytheexpression:2

1

8

4

100

25−

⎟⎟⎠

⎞⎜⎜⎝

⎛

x

x

64. Simplifytheexpression:3

3

4

2

3

2

1

3

2

249 ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ y x y x

65. Simplifytheexpression:( ) 3

4

64−

−

66. Solvetheradicalequation: 64 =− x

67. Simplify:81

49−

68. Simplify: 98600 ba

69. Performtheindicatedoperationsinthebelow.Assumethatallvariablesrepresentpositivenumbers.

a) 3 623 446 y x x

b) x x x 1824223 +−



c) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −3

2

2

1

aa

d) 3

9

13

65

x

x

e) ( ) 2

1

48

4

2

3

2

5

814−−−

⎟⎟⎠

⎞⎜⎜⎝

⎛ y x y x

70. Solveforx: 0722

=+ x

71. Rationalizethedenominatorandsimplify:i34

10

+

.

72. Abreederdeterminesthatamousepopulationcanbeapproximatedoveraoneyearperiodwiththefunction

t

t f ⎟⎠

⎞⎜⎝

⎛=

2

540)( wheret ismeasuredinyears.Predicthowmanymicewill

bepresentafter5years.Roundtothenearestinteger.

73. Solveforx: 125594=

− x

74. Solveforx: 0352

=− x

75. Multiply: ( ) ( )ii 675 −−

76. Thedistance,d ,measuredinmilesthatanobservercanseefromanobservationtowerisrelatedtotheheightofthetower, h,infeetbytheformula hd 4.1= .Howtallmustthe

towerbetoseeadistanceof8.4miles?

77. Findthe(a)vertex,(b) x -intercepts,(c)y -intercept,(d)axisofsymmetry,and(e)graphthefollowingfunction.Roundirrationalnumberstothenearesthundredth: 1)4()( 2

−+−= x x f



78. Theperimeterofarectangularconcreteslabis108feetanditsareais608squarefeet.Whatisthelengthofthelongersideoftheslab?

79. Astackoffirewoodhas14layers.Thefirstlayerhas40piecesofwood.Thesecondhas38piecesofwood,thethirdhas36,andsoon.Howmanypiecesofwoodareinthestack?

80. Forthearithmeticsequence7,4,1,…,(a)writeaformulaforthe nthterm.Then,(b)usetheformulatofind

10a .

81. Forthegeometricsequence ,25

1,

10

1,

4

1…,

a. writeaformulaforthenthterm

b. usetheformulatofind .8a

82. Find19a forthesequence .46 −= na

n

83. Findthe10thtermofthesequence:14,20,26,32,…

84. Findthecommonratioofthegeometricsequence: ,5

48,

5

12,

5

3…

85. Alberto’swifewantshimtoputafencearoundhergarden.Hehasenoughfencingmaterial

tofenceinasmallareawithaperimeterof90feet.Ifthelengthofthegardenistobethree

feetlessthantwicethewidth,whatwillbethedimensionsofthegarden?

86. Simplify:

x x

x x

2

3

3

4

4

12

+

+

87. Whichequationcorrespondstothegraph?



a. 342

++= x x y

b. 342

+−= x x y

c. 322

−−= x x y

d. 322

−+= x x y

88. Graph 3)2(2−+= x y .

89. Graphtheequation: x y 5=

90. Graphthesolutionsetofeachsystemofinequalities. 4

2

y

y x

Ï <ÔÔÌÔ > +ÔÓ

91. Graph 33 −<− y x .

92. Graph 21217 ≥− y x

93. Findtheequationofthegraph.



94. Graph: 2)1()(2−+= x x f

95. Solvethesystembythesubstitutionortheadditionmethod.Ifthereisnosolutionor

infinitelymanysolutions,usesetnotationtoexpresstheirsolutionsets.

4 3 20

6

x y

x y

Ï - =ÔÔÌÔ - =ÔÓ

96. Ticketstoalocalmovieweresoldat$7.00foradultsand$5.50forstudents.If400tickets

weresoldforatotalof$2575.00,howmanyadultticketsweresold?

97. Performtheindicatedoperation.Ifanswersarecomplex,writein bia + form.Assumethat

allvariablesrepresentpositivenumbers: 58 −⋅−


allvariablesrepresentpositivenumbers: ( )ii 236 −−


allvariablesrepresentpositivenumbers: ( )( )ii 2534 −−

100. Rationalizethedenominator.Ifanswersarecomplex,writein bia + form.

i

i

32

7

−

+

101. Theformula Lv 62= isusedbypolicetoestimatethespeedofacar, v ,inmilesperhour,

basedonthelengthofitskidmarks,L,infeet,ondrypavement.Howfarwillacarskidata

speedof72milesperhour?

102. Graph 32 −≥ x y .

103. Graph 22

1+−< x y and x y 2> .

104. Findtheequationfromthegraph.



105. Usetheslopeandy -intercepttograph 2+−= x y .

106. Graph 42 −= y .

107. Usethe x -interceptandy -intercepttograph 453015 =+− y x .

108. Usetheslopeandy -intercepttograph 45 +−= x y .

109. Graph 44 −= x

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Sample Review Problems for Intermediate Algebra Placement Test r