HoustonCommunityCollege-Southwest
MathDepartment
MATH0312FINALREVIEWPROBLEMS
Theseexercisesrepresentacompilationoftypicalproblemsinthiscourse. ThisisNOTasampleofthefinalexam.However, doingtheseproblemswillhelpyouprepareforthefinalexam. Theinstructionsfortheproblems arefollowed bybracketedreferencestoappropriatesectionsinthebook.
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Solvetheinequality.Givethesolutionsetinbothintervalandgraphforms.[2.5]
1)5z-205(2z-6)
Solvetheequation. [2.7]
2) 6m+5 =6
Completethetableoforderedpairsfortheequation.[3.1]
3)5x+6y=30
x y
6
1
3
Findtheinterceptsandgraphthelinearequation. [3.1]
4)2x-y=4
Findtheequationofthelinesatisfyingthegivenconditions. Thengivetheslopeoftheline. [3.2,3.3]
5)Averticallinethroughthepoint(5,-1)
Findtheslopeoftheline.[3.2]
6)
y
10
5
-10-5510 x
-5
-10
Findanequationofthelinesatisfyingtheconditions.Writetheequationinslope-interceptform.[3.3]
7)Through(-3,8);perpendicularto-3x+4y=-23
Findanequationofthelinepassingthroughthetwopoints.Writetheequationinstandardform.[3.3]
8)(4,-2)and(0,3)
Graphthelinearinequalityintwovariables.[3.4]
9)-2x-4y≤8
Decidewhethertherelationisafunction,andgivethedomainandrange. [3.5]
10)
y
10
5
-10-5510x
-5
-10
Decidewhethertherelationisafunction.[3.5]
11){(-1,7),(1,-9),(4,-9),(7,-5),(10,-3)}
Solvetheproblem.[3.6]
12)Findf(-3)whenf(x)=-x2-5x-2.
Solvethesystem. [4.1]
13)x=-3y+4
-2x-6y=3
Solvethesystem [4.1]
14)7x-6y=-16
4x+3y=23
Performtheindicatedoperations.[5.4]
15)(8m-9)(5m2+m-3)
Performthedivision.[5.5]
16)9x3-21x2+6x+15
3x-4
Factorcompletely. [6.1-6.4]
17)125a3-27b3
18)15z2+8z-16
19)2x3-16x2-5x+40
20)x2+2xy-8y2
Determinethedomainofthefunction. [3.5,7.1]
21)f(x)=x2-4
x2+2x-48
Multiplyandsimplify,ifpossible. [7.1]
22)x2 +25·x2+8x
x2-64x
Performtheindicatedoperationandexpressinlowestterms.[7.1]
23)4p-4÷9p-9
p4p2
24)m2-10m+24
m-4
m-4
Addorsubtractasindicated.Writetheanswerinlowestterms.[7.2]
25)3
y2-3y+2
-7
y2-1
Addorsubtractasindicated.Writetheanswerinlowestterms.[7.2]
26)1
x-3
-5
3-x
Simplifytheexpression,usingonlypositiveexponentsinyouranswer.[7.3]
27)m-1+z-1m-1-z-1
Simplify. [7.3]
4+2x
28)
x+1
36
Solve. [7.4]
29)2
x-4
-3
x+7
=22
x2 +3x-28
Solvetheformulaforthespecifiedvariable.[7.5]
30)F=9C+32forC
5
Solvetheformulaforthespecifiedvariable. [7.5]
31)A=P(1+nr)forr
Solvetheproblem.[sec7.5]
32)Frankcantypeareportin2hoursandJamestakes3hours. Howlongwillittakethetwoofthemtypingtogether?
Simplifytheexpressioninvolvingrationalexponents.[8.2]
33) -27-4/3
8
Usethelawsofexponentstosimplify.Writetheanswerwithpositiveexponents. [8.2]
34)(9k2m-4)1/2
Findtheunknownlengthintherighttriangle.Simplifytheanswerifpossible. [8.3]
35)
b20
10
Simplify. [8.3]
3
36)
-8a8b5
Simplify. Assumethatthevariablerepresentsa positiverealnumber. [8.4]
37)6a+4 24a+3 216a
Rationalizethedenominator.Assumethatallvariablesrepresentpositiverealnumbers.[8.5]
38)49
5
Rationalizethedenominator. [8.5]
39)3
6-7
Multiply. [8.7]
40)-25·-4
Performtheindicatedoperation. Writetheresultinstandardform. [8.7]
41)(5+3i)-(-8+i)
Findthequotient. Writetheresultinstandardform. [8.7]
42)1-7i
5-3i
Findthepowerofi. [8.7]
43)i13
Solve. [9.1]
44)25x2+49=0
Solvetheequationbycompletingthesquare. [9.1]
45)x2-2x+12=0
Usethequadraticformulatosolvetheequation.[9.2]
46)2x2=-10x-7
1)(2,∞)
-5 -4 -3 -2 -1 0123456789
2) 1,-11
66
3)0;25;12
65
4)x-intercept: (2,0)y-intercept: (0,-4)
y
10
5
-10-5510 x
-5
-10
5)x=5 ; Undefinedslope
6)-2
5
7)y=-4x+4
3
8)5x+4y=12
9)
y
10
5
-10-5510 x
-5
-10
10)Function; domain(-∞,∞); range[1,∞)
11)Function
12)4
13)∅ (nosolution)
14) (2,5)
15)40m3-37m2-33m+27
16)3x2-3x-2+7
3x-4
17)(5a-3b)(25a2+15ab+9b2)
18)(3z+4)(5z-4)
19)(x-8)(2x2-5)
20)(x+4y)(x-2y)
21) x x≠-8,6
22)x2+25x-8
23)16p
9
24)m-6
25)-4y+17
(y-1)(y+1)(y-2)
26)6
x-3
27)z+mz-m
28)12x
29)∅ (Thesolutionx=4isanextraneoussolution.)
30)C=5(F-32)
9
31)r=A-PPn
32)6hr
5
33)16
81
34) 3km2
35)10 3
36)-2a2b
37)27 6a
38) 75
5
3
a2b2
39)18+3 7
29
40)-10
41)13+2i
42)13-16i
1717
43)i
44) ±7i
5
45)1± i 11
46)
-5+11,
2
-5-11
2