Test Bank For Essentials of College Algebra, 12th Edition

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CONTENTSCHAPTER TEST FORMS1ANSWERS TO CHAPTER TEST FORMS191DIAGNOSTIC PRETESTS AND ANSWERS234FINAL EXAMS AND ANSWERS244

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use set notation, and list all the elements of the set.1){19,20,21, . . . ,25}A){19,20,22,24,25}B){19,21,23,25}C){19,20,21,22,23,24,25}D){19,20,21,22,23,24,25,26}Answer:C2)1,13,19, . . . ,1243A)1,13,15,16,17,18B)1,13,19,127,1729,119,683C)1,13,19,127,1243D)1,13,19,127,181,1243Answer:D3){15,22,29, . . .,64}A){15,22,29,36,43,50,57,64}B){15,22,28,35,42,49,56,63}C){15,22,29,37,44,51,58,65}D){15,22,29,36,43}Answer:A4){82,77,72, . . .,32}A){82,77,72,67,62,57,52,47,42,37,32}B){82,77,72,66,61,56,51,46,41,36,31}C){82,77,72,62,52,42,32}D){82,87,92,97,102,107,112,117,122,127,132}Answer:A5)The firstfournatural numbers.A){0, 2, 4, 6}B){1, 2, 3, 4}C){0, 1, 2, 3}D){0, 1, 2, 3, 4}Answer:B6)The natural numbers between 3 and5.A){3,5}B){4}C){3, 4, 5}D){0, 1, 2, 3}Answer:BIdentify the set as finite or infinite.7){6,7,8, . . .,11}A)finiteB)infiniteAnswer:A8){3,5,7, . . .}A)finiteB)infiniteAnswer:B9)1,13,19,127, . . .,A)infiniteB)finiteAnswer:A1

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10){x|x is a natural number larger than1}A)infiniteB)finiteAnswer:A11){x|x is a fraction between 0 and 1}A)finiteB)infiniteAnswer:B12){x|x is anevennatural number}A)finiteB)infiniteAnswer:B13){x|x isa personalive now}A)infiniteB)finiteAnswer:BInsert%or'in the blank to make the statement is true.14)10{7,8,9,10}A)'B)%Answer:B15)10{6,9,12,10,8}A)%B)'Answer:A16)-9{9,11,13,15}A)%B)'Answer:B17)0{7,9, 0,11,10}A)'B)%Answer:B18)0{4,5,6,7,8,9}A)'B)%Answer:A19){9}{9,10,11,12,13,14}A)%B)'Answer:B20){10}{8,10,12,14}A)%B)'Answer:B21){0}{0,4,5,6,7}A)%B)'Answer:B2

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22)4+A)%B)'Answer:B23)++A)'B)%Answer:ATell whether the statement is true or false.24)6%{4,54,6,7}A)TrueB)FalseAnswer:A25)7%{-3,8,9,12}A)TrueB)FalseAnswer:B26)11'{0,9,10,12,14}A)TrueB)FalseAnswer:A27){0,8,11,16}={11,8,16, 0}A)TrueB)FalseAnswer:A28){1,6,4,7}={4,1,6}A)TrueB)FalseAnswer:B29){x | x is a natural number greater than1}={1,2,3, . . .}A)TrueB)FalseAnswer:B30)Let A={9,10,11,12,13,14}, B={11,13,15}, C={9,10,12,14}, D={9,14}, andU={9,10,11,12,13,14,15}.A5UA)TrueB)FalseAnswer:A31)Let A={8,9,10,11,12,13}, B={10,12,14}, C={8,9,11,13}, D={8,13}, andU={8,9,10,11,12,13,14}.A5BA)TrueB)FalseAnswer:B32)Let A={2,3,4,5,6,7}, B={4,6,8}, C={2,3,5,7}, D={2,7}, andU={2,3,4,5,6,7,8}.C5AA)TrueB)FalseAnswer:A3

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33)Let A={6,7,8,9,10,11}, B={8,10,12}, C={6,7,9,11}, D={6,11}, andU={6,7,8,9,10,11,12}.+5DA)TrueB)FalseAnswer:A34)Let A={6,7,8,9,10,11}, B={8,10,12}, C={6,7,9,11}, D={6,11}, andU={6,7,8,9,10,11,12}.C5+A)TrueB)FalseAnswer:B35)Let A={2,3,4,5,6,7}, B={4,6,8}, C={2,3,5,7}, D={2,7}, andU={2,3,4,5,6,7,8}.{6,8}5BA)TrueB)FalseAnswer:A36)Let A={5,6,7,8,9,10}, B={7,9,11}, C={5,6,8,10}, D={5,10}, andU={5,6,7,8,9,10,11}.{0,6,10}5CA)TrueB)FalseAnswer:B37)Let A={7,8,9,10,11,12}, B={9,11,13}, C={7,8,10,12}, D={7,12}, andU={7,8,9,10,11,12,13}.B*CA)TrueB)FalseAnswer:A38)Let A={5,6,7,8,9,10}, B={7,9,11}, C={5,6,8,10}, D={5,10}, andU={5,6,7,8,9,10,11}.D*CA)TrueB)FalseAnswer:B39)Let A={1,2,3,4,5,6}, B={3,5,7}, C={1,2,4,6}, D={2,6}, andU={1,2,3,4,5,6,7}.U5CA)TrueB)FalseAnswer:BInsert5or*in the blank to make the statement true.40){9,10,11}{0,9,10,11,12,13}A)5B)*Answer:A41){8,12}{5,-6,10,-8,12,7}A)*B)5Answer:A4

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42){4,6,9,11}{4,4,6,7,8,9}A)5B)*Answer:B43){7,8,9,12}{7,11,9,10,8,12}A)*B)5Answer:B44){0,2,4,7}{2,4,7,8,9,10}A)*B)5Answer:A45)+{6,9,13, 0,10,14}A)5B)*Answer:A46){-13,8,-14, 0,12}+A)5B)*Answer:B47)++A)5B)*Answer:ATell whether the statement is true or false.48){10,13,14,16}.{13,14,17,18}={13,14}A)TrueB)FalseAnswer:A49){6,8,9,11}1{0,10,8,13,6}={6,8}A)TrueB)FalseAnswer:B50){5,7,8,10}.+={5,7,8,10}A)TrueB)FalseAnswer:B51){8,10,11,13}1+={8,10,11,13}A)TrueB)FalseAnswer:AUse these sets to find the following. Identify any disjoint sets.52)Let U={5,6,7,8,9,10,11,12,13,14,15}, M={5,7,9,11},N={6,8,10,12,14},Q={5,7,9,11,13,15},andR={5,6,7,8}.M.RA){5,6,7,8}B){5,7}C){5,6,7,8,9,11}D)+; M and R are disjoint sets.Answer:B5

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53)Let U={4,5,6,7,8,9,10,11,12,13,14}, M={4,6,8,10},N={5,7,9,11,13},Q={4,6,8,10,12,14},andR={4,5,6,7}.M1NA){5,6,7,8,9,10,11,12,13}B){4,5,6,7,8,9,13}C)+; M and N are disjoint sets.D){4,5,6,7,8,9,10,11,13}Answer:D54)Let U={2,3,4,5,6,7,8,9,10,11,12}, M={2,4,6,8},N={3,5,7,9,11},Q={2,4,6,8,10,12},andR={2,3,4,5}.M.NA){4,5,6,7,11}B)+; M and N are disjoint sets.C){3,4,5,6,7,8,9,10,11}D){2,3,4,5,6,7,8,9,11}Answer:B55)Let U={5,6,7,8,9,10,11,12,13,14,15}, M={5,7,9,11},N={6,8,10,12,14},Q={5,7,9,11,13,15},andR={5,6,7,8}.N'A){7,9,11,13,15}B)Q, or {5,7,9,11,13,15}C)M, or {5,7,9,11}D){6,8,10,12,14}Answer:B56)Let U={2,3,4,5,6,7,8,9,10,11,12}, M={2,4,6,8},N={3,5,7,9,11},Q={2,4,6,8,10,12},andR={2,3,4,5}.Q.R'A){5,6,7,8,9,10,11,12}B)+; Q and R' are disjoint sets.C){4,6,8,10,12}D){6,8,10,12}Answer:D57)Let U={3,4,5,6,7,8,9,10,11,12,13}, M={3,5,7,9},N={4,6,8,10,12},Q={3,5,7,9,11,13},andR={3,4,5,6}.+1NA)+; N and+are disjoint sets.B){5,7,9,11,13}C)N, or {4,6,8,10,12}; N and+are disjoint sets.D){3,4,5,6,7,8,9,10,11,12,13}Answer:C58)Let U={5,6,7,8,9,10,11,12,13,14,15}, M={5,7,9,11},N={6,8,10,12,14},Q={5,7,9,11,13,15},andR={5,6,7,8}.(N1R).QA){5,7}B)+; N and R are disjoint sets.C){7}D){5}Answer:A6

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59)Let U={3,4,5,6,7,8,9,10,11,12,13}, M={3,5,7,9},N={4,6,8,10,12},Q={3,5,7,9,11,13},andR={3,4,5,6}.Q'.(N'.U)A){4,6,8,10,12}B){3,5,7,9,11,13}C){4,5,6,7,8,9}D)+; Q' and (N'.U) are disjoint sets.Answer:D60)Let U={9,10,11,12,13,14,15,16,17,18,19}, M={9,11,13,15},N={10,12,14,16,18},Q={9,11,13,15,17,19},andR={9,10,11,12}.(R1N).M'A)M, or {9,11,13,15}B)+; M' and (R1N) are disjoint sets.C){9,10,12,14,16,18}D)N, or {10,12,14,16,18}Answer:D61)Let U={7,8,9,10,11,12,13,14,15,16,17}, M={7,9,11,13}, N={8,10,12,14,16},Q={7,9,11,13,15,17},andR={7,8,9,10}.(U1+).R'A)U, or {7,8,9,10,11,12,13,14,15,16,17}B)+; R' and (U1+) are disjoint sets.C)R, or {7,8,9,10}D){11,12,13,14,15,16,17}Answer:DList all the elements of set B that belong to the indicated set.62)B=14,7,-14, 0,01,25IntegersA)14, 0B)14,-14, 0C)14,-14, 0,01,25D)14, 0,25Answer:C63)B=11,5,-17, 0,04,16Whole numbersA)11,-17, 0B)11, 0,04,16C)11, 0D)11,-17, 0,16Answer:B64)B=14,8,-14, 0,04,4Natural numbersA)14, 0,4B)14, 0,04C)14,4D)14, 0Answer:C7

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65)B=5,7,-16, 0,08,9,-50,0.59Rational numbersA)5,-16, 0,08,9,0.59B)7,08,0.59C)7,9D)5, 0,9Answer:AEvaluate the expression.66)36A)729B)324C)72.9D)18Answer:A67)-36A)18B)729C)-729D)-18Answer:C68)(-4)3A)-64B)64C)144D)-12Answer:A69)-4·52A)-400B)400C)100D)-100Answer:D70)-5(-2)3A)40B)-1,000C)-40D)1,000Answer:A71)26+28·2+7A)89B)63C)486D)115Answer:A72)11+62-(-3)·7A)308B)26C)182D)68Answer:D73)81-8·3+4A)80B)61C)223D)511Answer:B74)92-22·4+224÷(-16)A)-997B)-19C)266D)-10Answer:D8

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75)(-2)3-(-2)2A)-12B)4C)12D)-4Answer:A76)(9+(-2))[7+(4+8)]A)89B)26C)133D)22Answer:C77)-8[-1+2(-9+3)]A)104B)44C)48D)-4Answer:A78)(9-82)(-8+81)A)-4895B)-47C)-55D)73Answer:C79)-38--14-32-78A)12B)-54C)-34D)0Answer:C80)-7·5+3-(-1+6)-7·8+2A)6170B)5954C)3754D)3770Answer:CEvaluate the expression for x=-2, y=3, and a=-4.81)-3x+7y+5aA)7B)-43C)-7D)23Answer:A82)-4a-6y-3xA)8B)19C)23D)4Answer:D83)(-5x-3y)(-8a)A)-32B)-288C)32D)140Answer:C84)9x2-4y-aA)26B)22C)25D)28Answer:D85)x3-7y+3aA)-28B)-37C)-41D)-25Answer:C9

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86)y+2xy-4aA)-119B)-123C)0D)-319Answer:A87)6y-a2x2+9yA)43B)52C)0D)2Answer:D88)-(x+5)2-2y-2-aA)152B)-152C)-32D)352Answer:B89)2x+2(3+a)2y-1A)19B)9C)-1D)33Answer:CIdentify the property illustrated by the statement. Assume all variables represent real numbers.90)6·1=6A)DistributiveB)InverseC)IdentityD)ClosureAnswer:C91)(2+3)+6=(3+2)+6A)AssociativeB)CommutativeC)DistributiveD)ClosureAnswer:B92)8+0=8A)IdentityB)InverseC)ClosureD)AssociativeAnswer:A93)3(x+8)=3x+24A)ClosureB)CommutativeC)DistributiveD)AssociativeAnswer:C94)4+(-4)=0A)InverseB)ClosureC)AssociativeD)IdentityAnswer:A10

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95)2+9=9+2A)IdentityB)CommutativeC)AssociativeD)InverseAnswer:B96)1(a+2)·(a+2)=1, if a+2J0A)InverseB)DistributiveC)ClosureD)IdentityAnswer:A97)(8·4)·6=8·(4·6)A)CommutativeB)AssociativeC)IdentityD)DistributiveAnswer:B98)6ǻΔ) is a real number.A)IdentityB)ClosureC)DistributiveD)AssociativeAnswer:BWrite the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero realnumbers.99)54(-8y)A)20yB)-10yC)10yD)-9yAnswer:B100)13y(-15)A)4yB)3yC)-5yD)5yAnswer:C101)54(16y-16x+20z)A)20y-20x-25zB)20y+20x+25zC)20y+20x-25zD)20y-20x+25zAnswer:D102)1510y+103x-20A)2y-23x-4B)2y+23x+4C)2y+23x-4D)2y-23x+4Answer:CUse the distributive property to rewrite a sum as a product or the product as a sum.103)-11y+3yA)8yB)-8yC)14yD)-14yAnswer:B104)2-10bA)2(1-5b)B)2(1-6b)C)12bD)-8bAnswer:A11

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105)-4(x+k)A)-4xkB)-4x+kC)-4x+4kD)-4x-4kAnswer:D106)-(-3-9b)A)3+9bB)-3+9bC)-3-9bD)3-9bAnswer:A107)-(-5y+8k)A)5y+8kB)-5y-8kC)5y-8kD)-5y+8kAnswer:CDecide whether the statement is true or false. If false, correct the statement so it is true.108)5-10=5-10A)TrueB)False;5-10=10-5Answer:B109)2-8=8-2A)TrueB)False;2-8=2-8Answer:A110)-12=-12A)TrueB)False;-12=-(-12)=12Answer:B111)-3=3A)TrueB)False;-3=-3=-3Answer:A112)(-4)3=-(4)3A)TrueB)False;(-4)3=43Answer:B113)-45=-45A)TrueB)False;-45=4-5Answer:A114)-5·10=-5·10A)TrueB)False;-5·10=-5·10Answer:AEvaluate the expression.115)-12A)0B)±12C)12D)-12Answer:C12

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116)23A)-23B)23C)±23D)0Answer:B117)-20A)±20B)-20C)0D)20Answer:B118)--2A)±2B)-2C)0D)2Answer:B119)-17A)0B)-17C)±17D)17Answer:B120)--83A)±83B)-83C)0D)83Answer:B121)-87A)0B)-87C)87D)±87Answer:C122)Let x=-19, y=-18. Evaluate |21x|.A)399B)-342C)-399D)342Answer:A123)Let x=-8, y=5. Evaluatex+y.A)13B)-13C)-3D)3Answer:D124)Let x=-8, y=4. Evaluatex+y.A)12B)-4C)-12D)4Answer:A125)Let x=18, y=-6. Evaluate |y-x|.A)-24B)-12C)12D)24Answer:D13

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126)Let x=2, y=5. Evaluate6x-7y.A)-47B)23C)47D)-23Answer:B127)Let x=-9, y=13. Evaluate |9y-2x|.A)-99B)-135C)135D)99Answer:C128)Let x=9, y=-2. Evaluate 4x+5y.A)26B)-26C)46D)-46Answer:C129)Let x=-18, y=12.Evaluate |4y-5x|-|4y|.A)90B)60C)84D)36Answer:A130)Let x=6and y=-3. Evaluate|x|x+|y|y.A)0B)2C)-1D)1Answer:A131)Let x=5, y=-1. Evaluate|x+2|-|2y||3y+5x|.A)922B)522C)528D)12Answer:BDetermine which property of absolute value justifies the statement.132)xL0A)Property 5: the triangle inequalityB)Property 1: the absolute value of a number is positive or 0.C)Property 1: the absolute value of a number is greater than 0.D)Property 1: the absolute value of a number is positive.Answer:B133)-x=xA)Property 2: the opposite of the absolute value of a number is equal to the absolute value of the number.B)Property 5: the triangle inequalityC)Property 2: the absolute value of a number and its opposite are equal.D)Property 1: the opposite of a number is equal to the absolute value of the number .Answer:C14

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