Algebra and Trigonometry, 6th Edition Test Bank

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Ch. 0Chapter P: Prerequisites: Fundamental Concepts of Algebra0.1Algebraic Expressions, Mathematical Models, and Real Numbers1Evaluate Algebraic ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the algebraic expression for the given value or values of the variable(s).1) 9x+8;x=7A) 71B) 126C) 17D) 552) 8x+3;x=-2A)-13B) 19C)-19D) 133) 2(x+1)+21;x=-4A) 15B)-15C) 35D) 74) 6x2+8y;x=7 and y=5A) 334B) 1804C) 1710D) 2065) (x+4y)2;x=4 and y=2A) 144B) 12C) 24D) 646) 2+6(x-6)3;x=8A) 50B) 14C) 64D)-467) x2-4(x-y);x=6 and y=2A) 20B) 10C) 14D)-528) 6(x+3)2x+2 ;x=5A) 4B) 1C) 8D) 1129)y-4x7x+xy ;x=-1 and y=3A)-710B)110C) 14D)-9102Use Mathematical ModelsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve.1) The formula C=59 (F-32) expresses the relationship between Fahrenheit temperature, F, and Celsiustemperature, C. Use the formula to convert 68°F to its equivalent temperature on the Celsius scale.A) 20°CB) 4°CC) 56°CD) 65°CPage 1

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2) A stone is dropped from a tower that is 770 feet high. The formula h=770-16t2 describes the stone'sheight above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 secondsafter it is released?A) 514 ftB) 524 ftC) 489 ftD) 539 ft3) If a rock falls from a height of 50 meters above the ground, the height H (in meters) after x seconds can beapproximated using the formula H=50-4.9x2. What is the height of the rock after 3 seconds?A) 5.9 mB) 405.9 mC)-166.09 mD) 35.3 m4) As the relative humidity increases, the temperature seems higher than it is. The formula T=0.113x+77.98approximates the apparent temperature for an actual temperature of 85°F, where x is the relativehumidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 40%?A) 83°FB) 352°FC) 118°FD) 78°F5) The winning times (in seconds) in a speed-skating event for men can be represented by the formulaT=46.18-0.095x, where x represents the year, with x=0 corresponding to 1920. (For example in 1992, xwould be 1992-1920=72.) According to the formula, what was the winning time in 1998? Round to thenearest hundredth.A) 38.77 secB) 3594.63 secC) 39.72 secD) 40.67 sec6) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United Statesin year x, where x represents the number of years since 1990, is given by the formula y=1.3x+3.07. Thatis, x=0 represents 1990, x=1 represents 1991, and so on. According to the formula, how many items soldin 1995?A) 9.57 millionsB) 3.07 millionsC) 21.85 millionsD) 10.87 millions3Find the Intersection of Two SetsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the intersection of the two sets.1) {1, 3, 5, 8}∩{5, 11, 1}A) {1, 5}B) {1}C) {1, 5, 8, 3, 11}D)∅2) {2, 10, 8}∩{4, 6}A)∅B) {10, 8}C) {2, 4, 8, 10, 6}D) {2, 8}3) {6, 8, 9, 11}∩∅A)∅B) {6, 8, 9, 11}C) {6, 8}D) {9, 11}4Find the Union of Two SetsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the union of the two sets.1) {2, 5, 8, 10}∪{2, 5, 12}A) {2, 5, 8, 10, 12}B) {2, 5}C) {8, 10, 12}D)∅2) {2, 10}∪{2, 4, 8}A) {2, 4, 8, 10}B) {2}C) {4, 8, 10}D)∅3) {1, 3, 4, 6}∪∅A) {1, 3, 4, 6}B) {1, 3}C) {4, 6}D)∅Page 2

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5Recognize Subsets of the Real NumbersMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.List all numbers from the given set B that are members of the given Real Number subset.1) B={17,5,-22, 0, 0.6,25} IntegersA) 17,-22, 0,25B) 17, 0C) 17,-22, 0D) 17, 0,252) B={11,6,-16, 0, 0.1,4} Whole numbersA) 11, 0,4B) 11,-16, 0C) 11,-16, 0,4D) 11, 03) B={10,6,-9, 0, 0.6,9} Natural numbersA) 10,9B) 10, 0,9C) 10, 0D) 104) B={16,5,-2, 0, 89 ,25, 0.3, 0.73} Rational numbersA) 16,-2, 0, 89 ,25, 0.73, 0.3B) 16, 0,25C)5,25D)5, 89 , 0.735) B={11,7,-11, 0, 56 ,4, 0.7, 0.35}Irrational numbersA)7B)7, 0.7C)7,4, 0.7D)7,4, 0.356) B={4,8, 0, 56 ,9,-0.9, 0.53,-23}Real numbersA) 4,8, 0, 56 ,9,-0.9, 0.53,-23B) 4,8, 0, 56 ,9, 0.53C) 4,8, 56 ,9,-0.9, 0.53,-23D) 4, 0, 56 ,-0.9, 0.53,-236Use Inequality SymbolsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine whether the statement is true or false.1) 21>24A) FalseB) True2) 17≥4A) TrueB) False3)-81<0A) TrueB) False4) 24<-6A) FalseB) True5) 12≤11A) FalseB) TruePage 3

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6)-5≤8A) TrueB) False7) 15>13A) TrueB) False8)-8≥15A) FalseB) True9)-π≥-πA) TrueB) False10)π<3A) FalseB) True7Evaluate Absolute ValueMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Rewrite the expression without absolute value bars.1) |13|A) 13B)-13C) 26D) 02) |-2|A) 2B)-2C) 4D) 03)19-1A) 19B)-1C) 1D)-194)10-13A) 13-10B)10-13C)-3D) 35) |5+(-10)|A) 5B) 15C)-5D)-156)-4--9A) 5B) 13C)-5D)-137)-6+-8A) 14B) 2C)-2D)-14Evaluate the expression for the given values of x and y.8) |x|x+|y|y;x=6 and y=-3A) 0B) 2C) 1D)-1Page 4

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8Use Absolute Value to Express DistanceMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Express the distance between the given numbers using absolute value. Then find the distance by evaluating theabsolute value expression.1) 26 and 34A) |26-34|=8B)-|34-26|= -8C) |26+34|=60D)-|26+34|= -602)-18 and-34A) |(-18)-(-34)|=16B) |(-34)-(-18)|= -16C) |(-34)+(-18)|=-52D) |-(-18)+(-34)|=523) 72 and-9A) |72-(-9)|=81B) |(-9)-72|= -81C) |72+(-9)|=63D) |-72+(-9)|= -634) 28.9 and 23.7A) |28.9-23.7|=5.2B) |23.7-28.9|= -5.2C) |28.9+23.7|=52.6D) |-28.9+23.7|= -52.65)-14.7 and 24.3A) |-14.7-24.3|=39.0B) |24.3+(-14.7)|=-39.0C) |24.3-(-14.7)|=9.6D) |-14.7+(-24.3)|=-9.66) 1.5 and 48.3A) |1.5-48.3|=46.8B) |48.3-1.5|= -46.8C) |48.3+1.5|=49.8D)-|1.5+48.3|= -49.89Identify Properties of the Real NumbersMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.State the name of the property illustrated.1) 6+(-7)=(-7)+6A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Identity property of addition2) 17·(6+8)=17·6+17·8A) Distributive property of multiplication over additionB) Commutative property of multiplicationC) Associative property of multiplicationD) Commutative property of addition3) 2+(8+7)=(2+8)+7A) Associative property of additionB) Commutative property of additionC) Distributive property of multiplication over additionD) Identity property of additionPage 5

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4) (7+3)+4=(3+7)+4A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Inverse property of addition5) 5·(6·17)=5·(17·6)A) Commutative property of multiplicationB) Associative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication6) (9+6)+(7+19)=(7+19)+(9+6)A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Inverse property of addition7) 3·(19·2)=(19·2)·3A) Commutative property of multiplicationB) Associative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication8) (8·12)·7=8·(12·7)A) Associative property of multiplicationB) Commutative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication9) 7(x+6)=7x+7·6A) Distributive property of multiplication over additionB) Commutative property of multiplicationC) Associative property of multiplicationD) Identity property of multiplication10) 3(-5+7)=-15+21A) Distributive property of multiplication over additionB) Associative property of multiplicationC) Associative property of additionD) Commutative property of multiplication11)-7(6+7)=-42+(-49)A) Distributive property of multiplication over additionB) Associative property of multiplicationC) Associative property of additionD) Commutative property of multiplication12)1(x+2) (x+2)=1, x≠-2A) Inverse property of multiplicationB) Inverse property of additionC) Commutative property of multiplicationD) Identity property of multiplicationPage 6

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13) (x+3)+[-(x+3)]=0A) Inverse property of additionB) Inverse property of multiplicationC) Commutative property of additionD) Identity property of multiplication10Simplify Algebraic ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the algebraic expression.1)-8(6r+3)+4(9r+4)A)-12r-8B)-2r-5C)-12r+3D)-72r2) (11z+6)-(4z-4)A) 7z+10B) 7z+2C) 15z+10D) 7z-103)-6(2x-9)-4x+5A)-16x+59B) 8x+59C) 16x+59D)-16x-49Write the algebraic expression without parentheses.4)-(49x)A)-49xB) 49xC)-49-xD) 49-x5)-8(-8z)A) 64zB)-64zC) 64-8zD) 64+z6)-(3x-9)A)-3x+9B) 3x-9C)-3x-9D) 27x7)-(-9+5y)A) 9-5yB) 9+5yC)-9+5yD) 45y8)-(7z-2w+6y)A)-7z+2w-6yB)-7z+2w+6yC)-7z-2w+6yD)-7z-2w-6y9) 15 (5x)+[(4x)+(-4x)]A) xB) 9xC)-7xD) 10.2Exponents and Scientific Notation1Use the Product RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 83·88A) 811B) 824C) 6411D) 64242) y·y11A) y12B) 2y11C) y11D) 2y123) x8·x9A) x17B) x72C) 17xD) 72xPage 7

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4) (3x4)(9x9)A) 27x13B)-27x13C) 27x36D)-27x365) (-8x5y)(-3x3y6)A) 24x8y7B)-24x8y6C)-11x8y6D) 24x15y62Use the Quotient RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 5556A) 15B) 5C)-12,500D) 562) x14x10A) x4B) x24C) x8D)1x43) x2x6A)1x4B)-x4C) x4D)-1x44) 6x10x7A) 6x3B) 216x3C) 6x17D) 18x5)-30x115x8A)-6x3B) x2C) x3D)-6x26) x13y13x2y2A) x11y11B) x10y10C) xy11D) x10y117)-32x12y118x8y3A)-4x4y8B) x4y8C)-4x3y4D)-4x3y7Page 8

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8)-27x73x10A)-9x3B)-9x3C)-9x2D)-9x29)-10x13y12z65x7y3z5A)-2x6y9zB) x6y9zC)-2x5y8zD)-2x6y93Use the Zero-Exponent RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 40A) 1B)-1C) 0D) 42) (-2)0A) 1B)-1C) 0D) 23)-60A)-1B) 1C) 0D) 64) x6y0A) x6B) 1C) 0D)1x65)-7y0A)-7B) 1C) 0D)-66) (7b)0A) 1B) 0C) bD) 77)-72x9y138x3y40A) 1B) x6y9C)-9x6y9D) 04Use the Negative-Exponent RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 3-4A)181B)-81C) 81D)1122) (-3)-2A) 19B)-9C) 9D)-19Page 9

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3)-4-3A)-164B)-64C) 64D)1124) 3-3·3A) 19B)127C) 9D) 275) 33·3-4A) 13B)-3C) 2187D)-136) x7·x-2A) x5B)1x5C)-x5D)-1x57) x-9·x7A)1x2B)-x2C) x2D)-1x28) x2y-3A) x2y3B) y3x2C)x2y15D) y15x29) 8x-8y2A) 8y2x8B)8x8y2C)y28x8D) 8x8y210) x-6x4A)1x10B)1x24C)1x2D) x1011) x-3y-2A) y2x3B)1x3y2C) x3y2D) x3y212) x8y-3z-8A) x8z8y3B)z8x8y3C)y3x8z8D) x8z3y8Page 10

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13) 10x3y145x2y-10A) 2xy24B) 10xy24C) 2x5y24D) 2xy45Use the Power RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) (34)2A) 6561B) 729C) 24D) 1622) (43)-2A)14096B)11024C)-24D)-1283) (x7)8A) x56B) x15C) 8x7D) 8x564) (x-6)4A)1x24B)-x24C)-6x4D)-6x245) (x9)-6A)1x54B)-x54C)-6x9D)-6x546) (x-4)-3A) x12B)1x12C)1x7D)-x76Find the Power of a ProductMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) (5x)3A) 125x3B) 15xC) 125xD) 15x32) (-2x)5A)-32x5B)-10xC)-32xD)-10x53) (6x3)2A) 36x6B) 6x6C) 36x3D) 6x54) (x7y)4A) x28y4B) x28yC) x11y5D) x11yPage 11

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5) (-6x4y5)2A) 36x8y10B)-6x8y10C)-36x8y10D) 36x6y76) (4x3)-2A)116x6B)14x6C) 16x6D) 16x67) (x-1y4)-2A) x2y8B) x-3y2C)1x2y8D)y2x-38) (3x-6y2z-5)-3A) x18z1527y6B)y527x9z8C) x18z15-9y-6D)y5-9x9z87Find the Power of a QuotientMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1)x63A)x3216B)x41296C) x6D) x362)-5x3A)-125x3B)125x3C)-125xD)-5x33)x422A) x84B) x82C) x64D) x624)-3xy2A) 9x2y2B) 9xy2C)-6x2y2D)-6xy5)3x4y2z23A) 27x12y6z6B) 3x12y6z6C) 27x7y5z5D) 3x12y6z5Page 12

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6)-21x12y67x17y-23A)-27y24x15B) 27y24x15C)-27y12x15D)-27x15y247)x-1y5-3A) x3y15B) x-4y2C)1x3y15D)y2x-48)2x3y2-3A)y68x9B) 8x9y6C) 8y6x9D)y28x98Simplify Exponential ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression. Assume that variables represent nonzero real numbers.1) 33·5A) 135B) 45C) 3375D) 322) (-5)3A)-125B) 125C)-15D) 153)-63A)-216B) 18C) 216D)-184) (3x3)3x15A) 27x6B)3x6C) 27x9D)27x245) (-5x4y-5)(3x-1y)A)-15x3y4B)-15x3y6C)-2x3y4D)-15x5y66) 5-9x-2y35-6x-5y6A)x3125y3B)1125x5y3C) 3x3y3D)125x3y3Page 13

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7)xy6x6y-2A) x10y10B)1x8y13C)1x14y14D) y10x108)6x-4y-2z32xy-2z-3-1A)x53z6B)x33z6C) 3x5z6D) x5y43z69Use Scientific NotationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Write the number in decimal notation without the use of exponents.1) 4×10-4A) 0.0004B) 40,000C) 0.004D) 40002) 2×105A) 200,000B) 0.00002C) 2,000,000D) 0.0000023) 5.01×107A) 50,100,000B) 501,000,000C) 5,010,000D) 350.74) 4.14×10-4A) 0.000414B) 0.00414C) 0.0000414D)-414,0005) 5.201×10-6A) 0.000005201B) 0.00005201C) 0.0000005201D)-5,201,0006)-6.77×104A)-67,700B)-677,000C)-6770D) 67,7007)-1.0077×104A)-10,077B)-100,770C)-1007.7D)-40.308Write the number in scientific notation.8) 2,012,310A) 2.01231×106B) 2.01231×107C) 2.01231×10-6D) 2.01231×1019) 24,000A) 2.4×104B) 2.4×10-4C) 2.4×103D) 2.4×10-310) 57,000,000A) 5.7×107B) 5.7×10-7C) 5.7×108D) 5.7×10-811) 472A) 4.72×102B) 4.72×103C) 4.72×10-2D) 4.72×101Page 14

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12) 0.000585A) 5.85×10-4B) 5.85×104C) 5.85×10-5D) 5.85×10-313) 0.000048919A) 4.8919×10-5B) 4.8919×105C) 4.8919×10-4D) 4.8919×10414) 0.000000088007A) 8.8007×10-8B) 8.8007×108C) 8.8007×10-7D) 8.8007×10-9Perform the indicated computation. Write the answer in scientific notation.15) (5×10-9)(7×10-4)A) 3.5×10-12B) 35×10-12C) 350×10-13D) 3.5×103616) (2×10-4)(3.2×10-7)A) 6.4×10-11B) 6.4×10-10C) 64×10-11D) 6.4×102817) 8×1024×103A) 2×10-1B) 2×105C) 4×10-1D) 4×10518) 17.15×10-65×10-3A) 3.43×10-3B) 3.43×10-9C) 6.86×10-3D) 6.86×10-919) 5.52×1012.4×10-8A) 2.3×109B) 2.3×10-7C) 4.6×109D) 4.6×10-720) 30,000,000,0000.00006A) 5×1014B) 5×1013C) 24×1014D) 24×101321) 0.00018×0.00030.0009A) 6×10-5B) 6×105C) 54×106D) 54×10-6Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.22) In a state with a population of 5,000,000 people, the average citizen spends $6,000 on housing each year.What is the total spent on housing for the state?A) $3×1010B) $3×109C) $30×1011D) $30×101023) Approximately 8×103 employees of a certain company average $30,000 each year in salary. What is thetotal amount earned by all the employees of this company per year?A) $2.4×108B) $24×108C) $2.4×109D) $24×109Page 15

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0.3Radicals and Rational Exponents1Evaluate Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression or indicate that the root is not a real number.1)16A) 4B) 256C)116D) Not a real number2)-625A)-25B) 25C)-312D) Not a real number3)-144A)12144B) 20,736C) 12D) Not a real number4)16+9A) 5B) 7C) 25D)75)25-9A) 4B) 7C) 16D)76)64+36A) 14B) 10C) 100D)282Simplify Expressions of the Form SqRt(a^2)MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression or indicate that the root is not a real number.1)(7)2A) 7B) 2401C)149D) Not a real number2)(-5)2A) 5B) 25C)-5D) Not a real number3Use the Product Rule to Simplify Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the product rule to simplify the expression.1)96A) 46B) 64C) 24D) 92)15A)15B) 53C) 35D) 33)175A) 57B)175C) 35D) 257Page 16

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4)192x2A) 8 x3B) 83xC) 192xD) 3x285)448x2A) 8 x7B) 87x2C) 8x27D) 876)14x·28xA) 14 x2B) 142xC) 14x22D) 142x27)7x2·21xA) 7 x3xB) 7 x3C) 7x23xD) 7 x3x2Solve the problem.8) Racing cyclists use the algebraic expression 4x to determine the maximum speed, in miles per hour, toturn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist shouldtravel around a corner of radius 38 feet without tipping over. Write the answer in simplified radical form.A) 438 miles per hourB) 242 miles per hourC) 24+2 miles per hourD) 4(6+2)xmiles per hour9) The formula v=2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on acurved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at anexit ramp as 490 feet. What is the maximum safe speed?A) 35 miles per hourB) 49 miles per hourC) 40 miles per hourD) 32 miles per hour10) The formula v=20L can be used to estimate the speed of a car, v, in miles per hour, based on the length,L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accidentand its skid marks measure 245 feet, at what estimated speed was the car traveling when it applied itsbrakes just prior to the accident?A) 70 miles per hourB) 75 miles per hourC) 65 miles per hourD) 80 miles per hour11) The average height of a boy in the United States, from birth through 60 months, can be modeled byy=2.9x+20.1 where y is the average height, in inches, of boys who are x months of age. What would bethe expected difference in height between a child 36 months of age and a child 25 months of age?A) 2.9 inchesB) 43.1 inchesC) 17.4 inchesD) 4.9 inches4Use the Quotient Rule to Simplify Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the quotient rule to simplify the expression.1)14A) 12B)116C) 2D) 4Page 17

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2)6425A) 85B) 1C)85D)853)32x32xA) 4 xB) 4 x2C) 2x2D) 4x224)100x45xA) 2 x5xB) 100x3C) 5 xxD) x21005Solve the problem.5) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic expressiond16 . Find how long it will take a ball dropped from the top of a building 83 feet tall to hit the ground.Write the answer in simplified radical form.A)834secondsB) 924secondsC)8316secondsD) 9+24seconds5Add and Subtract Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Add or subtract terms whenever possible.1) 63+23A) 83B) 126C) 86D) 432) 76+554A) 226B) 86C) 126D)-2263) 83x+33xA) 113xB) 246xC) 11x6D) 534) 33+912A) 213B) 153C) 123D)-2135)-6162+2128+798A) 112B)-62C) 662D)-6626)16+245+4+405A) 165+6B) 165+16+4C)245+405+6D) 1305+67)5x-545x+280xA)-65xB)-6130xC)-3130xD)-35xPage 18

Algebra and Trigonometry, 6th Edition Test Bank - Page 20 preview image

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6Rationalize DenominatorsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Rationalize the denominator.1)117A)1717B)17C) 1+17D) 1+17172)1010A)10B) 1010C) 10D) 13)14411A) 121111B) 1211C) 1441111D) 1334)14411A) 121111B) 1211C) 1441111D) 1335)37A)217B)2149C)21D)36)58-10A) 40+51054B) 40-51054C) 40+5102D) 58-5107)617+2A)102-2613B)102+2613C)102-2619D) 3102+173468)34-2A) 12+3214B) 12-3214C) 12+322D) 34-329)56+11A)11-6B)6-11C)11+6D)5Page 19

Algebra and Trigonometry, 6th Edition Test Bank - Page 21 preview image

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7Evaluate and Perform Operations with Higher RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the radical expressions or indicate that the root is not a real number.1) 3 64A) 4B)-4C) 64D) not a real number2) 3 (-3)3A)-3B) 3C)-27D) not a real number3) 4 625A) 5B)-5C) 625D) not a real number4) 4 (-3)4A) 3B)-3C) 81D) not a real numberSimplify the radical expression.5) 3 x4A) x 3 xB) x2 3 xC) x 3 x2D) x2 3 x26) 3 14·3 4A) 2 3 7B) 3 56C) 2 3 14D) 6 56Add or subtract terms whenever possible.7) 2 3 40+3 320A) 8 3 5B) 2 3 360C) 3 3 360D) 6 3 58) y 3 192x-3 24xy3A) 2y 3 3xB) 4y 3 3x-192 3 3xy3C) (y+1) 3 26D) y 3-22xy38Understand and Use Rational ExponentsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression without using a calculator.1) 1441/2A) 12B) 24C) 6D) 482) 2561/4A) 4B) 16C) 64D) 10243) 84/3A) 16B) 64C) 32D) 128Page 20

Algebra and Trigonometry, 6th Edition Test Bank - Page 22 preview image

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4) 16-3/2A)164B)-164C) 64D)-64Simplify using properties of exponents.5) (7x3/4)(10x1/2)A) 70x5/4B) 70x1/2C) 70x5/3D) 70x3/46) 50x3/210x1/3A) 5x7/6B) 5x1/3C) 40x1/3D) 5x7/27) (25x4y6)1/2A) 5x2y3B) 625x8y6C) 52 x2y3D) 25x2y3Simplify by reducing the index of the radical.8) 10 x4A) 5 x2B)x2C) 5 xD)x9) 6 27x3A)3xB) 3 3xC) 33xD)19xSolve the problem.10) The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d miles.Use a calculator to determine the duration of a storm with a diameter of 5 miles. Round to the nearesthundredth.A) 0.78 hoursB) 0.16 hoursC) 11.18 hoursD) 0.21 hours0.4Polynomials1Understand the Vocabulary of PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Is the algebraic expression a polynomial? If it is, write the polynomial in standard form.1) 4x-1-8+7xA) NoB) Yes; 7x+4x-1-82) 2x-3+5x2A) Yes; 5x2+2x-3B) No3) 2x-7xA) NoB) Yes; 7x-2Page 21

Algebra and Trigonometry, 6th Edition Test Bank - Page 23 preview image

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4) x2+x4-x3+9A) Yes; x4-x3+x2+9B) NoFind the degree of the polynomial.5)-6x-8x7-5A) degree 7B) degree 8C) degree-6D) degree-86)-7x+3x8+4x7-16A) degree 8B) degree 4C) degree 3D) degree 77)-15x4+2x3+2x-4x5-3A) degree 5B) degree 4C) degree-15D) degree 38) x5-3x4y7+8xy-10x+6A) degree 11B) degree 5C) degree 18D) degree-32Add and Subtract PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Perform the indicated operations. Write the resulting polynomial in standard form.1) (7x5+6x2-9x)+(3x5-3x2-9x)A) 10x5+3x2-18xB)-6x5+4x2-3xC) 10x+3x5-18x2D)-5x82) (6x4+9x3-3x2-4)+(3x4+7x3-9x2+5)A) 9x4+16x3-12x2+1B) 9x8+16x6-12x4+1C) 13x18+1D) 3x4+3x3+11x2+123) (-6x5+18x3+15)+(8x5+4x3-11)A) 2x5+22x3+4B) 2x5+10x3-26C) 2x5+22x3-26D) 28x84) (-4x5-8x4-2x3+6)+(6x5+2x4+9x3+5)A) 2x5-6x4+7x3+11B) 10x5+10x4+11x3-1C) 2x5+10x4+11x3-1D) 10x5+10x4+11x3+115) (9x5-16x3-3)-(6x5-19x3+20)A) 3x5+3x3-23B) 3x5-10x3+17C) 3x5+3x3+17D)-17x86) (4x6-4x5+3x4-5)-(2x6-2x5+8x4-4)A) 2x6-2x5-5x4-1B) 6x6-6x5+11x4-9C) 2x6-6x5+11x4-9D) 6x6-6x5+11x4-17) (6x6+18x4+12)-(9x6-4x4+14)A)-3x6+22x4-2B)-3x6+27x4+26C)-3x6+22x4+26D) 17x108) (4x2+4x+7)+(2x2+3x+2)-(5x+2)A) 6x2+2x+7B) 6x2+2x+11C) 4x2+2x+7D) 4x2+2x+11Page 22

Algebra and Trigonometry, 6th Edition Test Bank - Page 24 preview image

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3Multiply PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x+2)(x2-2x+4)A) x3+8B) x3-8C) x3+4x2+4x+8D) x3-4x2-4x+82) (x-12)(x2+2x-7)A) x3-10x2-31x+84B) x3+14x2+17x-84C) x3-10x2-17x-84D) x3+14x2+31x+843) (x+6)(x2+8x-5)A) x3+14x2+43x-30B) x4+6x3+8x2+43x-30C) x3+14x2+53x-30D) x3+14x2+53x+304) (x+4)(2x2+5x+9)A) 2x3+13x2+29x+36B) 2x3+8x2+20x+36C) 10x3+25x2+45xD) 40x4+2x3+180x2+365) (7x-1)(x2-4x+1)A) 7x3-29x2+11x-1B) 7x3-27x2+3x-1C) 7x3-28x2+7x+1D) 7x3+29x2-11x+14Use FOIL in Polynomial MultiplicationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x+9)(x-5)A) x2+4x-45B) x2-45x+4C) x2+3x-45D) x2+4x+42) (2x-7)(x+6)A) 2x2+5x-42B) x2-42x+5C) 2x2+4x-42D) x2+5x+43) (2x-7)(5x-1)A) 10x2-37x+7B) 7x2-37x+7C) 10x2-37x-37D) 7x2-37x-374) (7x2-2)(9x2-1)A) 63x4-25x2+2B) 16x4-25x2+2C) 63x4-25x2-25D) 63x2-25x+25) (5x3-2)(x2+1)A) 5x5+5x3-2x2-2B) 5x5+3x3-2C) 5x5+3x2-2D) 5x6+5x3-2x2-2Page 23

Algebra and Trigonometry, 6th Edition Test Bank - Page 25 preview image

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Solve the problem.6) Write a polynomial in standard form that represents the volume of the open box.x11-6x9-6xA) 36x3-120x2+99xB) 36x3+120x2+99xC) 36x2-120x+99D) 6x3-120x2+99x7) Write a polynomial in standard form that represents the area of the shaded region.x+7x+5x+3x+2A) 3x+11B) 17x+31C) x2+14x+11D)-3x-115Use Special Products in Polynomial MultiplicationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x+7)(x-7)A) x2-49B) x2-14C) x2-14x-49D) x2+14x-492) (9x+5)(9x-5)A) 81x2-25B) x2-25C) 81x2-90x-25D) 81x2+90x-253) (3+11x)(3-11x)A) 9-121x2B) 9-66x-121x2C) 121x2-9D) 9+66x-121x24) (5x2+7x)(5x2-7x)A) 25x4-49x2B) 25x4-70x3-49x2C) 10x4-14x2D) 25x4+70x3-49x25) (1+x3)(1-x3)A) 1-x6B) 2-x6C) 2-x9D) 1-x9Page 24

Algebra and Trigonometry, 6th Edition Test Bank - Page 26 preview image

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6) (12-y3)(12+y3)A) 144-y6B) 144-y9C) 144-y3D) y6-1447) (x+3)2A) x2+6x+9B) x2+9C) 9x2+6x+9D) x+98) (x-12)2A) x2-24x+144B) x2+144C) 144x2-24x+144D) x+1449) (7x+9)2A) 49x2+126x+81B) 49x2+81C) 7x2+126x+81D) 7x2+8110) (6x-1)2A) 36x2-12x+1B) 36x2+1C) 6x2-12x+1D) 6x2+111) (3x2+4)2A) 9x4+24x2+16B) 9x2+24x+16C) 3x4+24x2+16D) 9x4+1612) (9x2-2)2A) 81x4-36x2+4B) 81x4+36x2+4C) 81x4-36x2-4D) 81x2-36x+413) (5+3x)2A) 25+30x+9x2B) 25+9x2C) 25x2+30x+9D) 25+30x+3x214) (9-5x)2A) 81-90x+25x2B) 81+25x2C) 81x2-90x+25D) 81-90x-25x215) (x-3)3A) x3-9x2+27x-27B) x3-3x2+15x-27C) x3-9x2+15x-27D) x3-9x2+9x-2716) (3x+5)3A) 27x3+135x2+225x+125B) 27x3+135x2+135x+125C) 9x6+15x3+15,625D) 9x2+30x+2517) (4x-5)3A) 64x3-240x2+300x-125B) 64x3-240x2+240x-125C) 64x3+240x2+300x+125D) 16x2-40x+256Perform Operations with Polynomials in Several VariablesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Perform the indicated operations.1) (-6x2y-xy)+(9x2y+3xy)A) 3x2y+2xyB) 15x2y+4xyC) 3x2y+4xyD) 15x2y+2xyPage 25

Algebra and Trigonometry, 6th Edition Test Bank - Page 27 preview image

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2) (4x2y-12xy+10)+(-3x2y+8xy-5)A) x2y-4xy+5B)-x2y-20xy+15C)-4x3y2+5D) 7x2y+20xy+153) (12x4y2-7x2y2+5xy)+(11x4y2-8x2y2+10xy)A) 23x4y2-15x2y2+15xyB)-15x4y2+23x2y2+15xyC) 23x4y2+15x2y2+15xyD) 15x4y2-23x2y2+15xy4) (x3+9xy-6y2)-(8x3+6xy+y2)A)-7x3+3xy-7y2B) 9x3+3xy-7y2C)-7x3+3xy-5y2D) 7x3-3xy-5y25) (9x4+7xy-y3)-(x4+5xy+7y3)A) 8x4+2xy-8y3B) 10x4+13xy+6y3C) 9x4+2xy-8y3D) 8x4+2xy-6y36) (9x4y2+11x3y+6y)-(2x4y2+8x3y+4y+7x)A) 7x4y2+3x3y+2y-7xB) 11x4y2+19x3y+10y+7xC) 7x4y2-3x3y+2y-7xD) 7x4y2+3x3y+2y+7xFind the product.7) (x-11y)(x-3y)A) x2-14xy+33y2B) x-14xy+33yC) x2-14xy-14y2D) x2-17xy+33y28) (x+3y)(8x-11y)A) 8x2+13xy-33y2B) x2+13xy-33y2C) 8x2+13xy+13y2D) x2+13xy+13y29) (6xy+7)(7xy+3)A) 42x2y2+67xy+21B) 13x2y2+67xy+21C) 42x2y2+67xy+67D) 13x2y2+67xy+6710) (4x+3y)2A) 16x2+24xy+9y2B) 16x2+9y2C) 4x2+24xy+9y2D) 4x2+9y211) (3x-11y)2A) 9x2-66xy+121y2B) 9x2+121y2C) 3x2-66xy+121y2D) 3x2+121y212) (x-y)(x2+xy+y2)A) x3-y3B) x3+y3C) x3-2x2y-2xy2-y3D) x3+2x2y+2xy2-y313) (x2y2+9)2A) x4y4+18x2y2+81B) x2y2+18xy+81C) x4y4+9x2y2+81D) x4y4+8114) (5x+6y)(5x-6y)A) 25x2-36y2B) 5x2-6y2C) 25x2-60xy-36y2D) 25x2+60xy-36y2Page 26

Algebra and Trigonometry, 6th Edition Test Bank - Page 28 preview image

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15) (3xy2-13y)(3xy2+13y)A) 9x2y4-169y2B) 3x2y4-13y2C) 9x2y4-78xy3-169y2D) 9x2y4+78xy3-169y20.5Factoring Polynomials1Factor Out the Greatest Common Factor of a PolynomialMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor out the greatest common factor.1) 2x+12A) 2(x+6)B) 2(x+12)C) 2x(x+6)D) 2x(6)2) 4x2+28xA) 4x(x+7)B) x(4x+28)C) 4(x2+7x)D) 4x(x+7x)3) 21x4-9x3+12x2A) 3x2(7x2-3x+4)B) 3(7x4-3x3+4x2)C) x2(21x2-9x+12)D) 3x(7x3-3x2+4x)4) x(x+13)+5(x+13)A) (x+13)(x+5)B) (x2+13x)+(5x+65)C) 5x(x+13)D) 13x(x+5)5) x(5x+4)-2(5x+4)A) (5x+4)(x-2)B) (5x+4)(x+2)C) (5x-2)(x+4)D)-2x(5x+4)6) x2(x-3)-(x-3)A) (x-3)(x2-1)B) (x-3)(x2+1)C) x2(x-3)D) (x3-3x2)-(x-3)2Factor by GroupingMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor by grouping. Assume any variable exponents represent whole numbers.1) x3-4x2-3x+12A) (x-4)(x2-3)B) (x-3)(x2-4)C) (x+4)(x2+3)D) (x-4)(x-3)2) x3+7x+2x2+14A) (x+2)(x2+7)B) (x-2)(x2+7)C) (x+2)(x2-7)D) (x+2)(x+7)3) 5x3-25x2+8x-40A) (x-5)(5x2+8)B) (x+5)(5x2+8)C) (x-5)(5x2-8)D) (x-5)(5x+8)3Factor TrinomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the trinomial, or state that the trinomial is prime.1) x2+8x+15A) (x+5)(x+3)B) (x-5)(x+3)C) (x-5)(x+1)D) primePage 27

Algebra and Trigonometry, 6th Edition Test Bank - Page 29 preview image

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2) x2-3x-28A) (x+4)(x-7)B) (x-4)(x-7)C) (x-4)(x+1)D) prime3) x2-8x+15A) (x-3)(x-5)B) (x+3)(x-5)C) (x+3)(x+1)D) prime4) x2+10x-24A) (x+12)(x-2)B) (x-12)(x+2)C) (x-12)(x+1)D) prime5) x2-x-6A) (x+2)(x-3)B) (x+3)(x-2)C) (x+1)(x-5)D) prime6) x2-x-35A) (x-35)(x+1)B) (x+5)(x-7)C) (x-5)(x+7)D) prime7) 5x2+18x+16A) (5x+8)(x+2)B) (5x+2)(x+8)C) (5x+8)(5x+2)D) prime8) 7x2-44x+12A) (7x-2)(x-6)B) 7(x-2)(x-6)C) (7x+6)(x-2)D) (7x-2)(7x+6)9) 7x2+2x-5A) (7x-5)(x+1)B) (7x+1)(x-5)C) (7x+5)(x-1)D) prime10) 5x2-3x+2A) (5x+2)(x-1)B) (5x-1)(x+2)C) (5x-2)(x+1)D) prime11) 10x2+21x+9A) (2x+3)(5x+3)B) (2x-3)(5x-3)C) (10x+3)(x+3)D) prime12) 6x2-17x+12A) (2x-3)(3x-4)B) (2x+3)(3x+4)C) (6x+3)(x+4)D) prime13) 20x2+7x-6A) (4x+3)(5x-2)B) (4x-3)(5x+2)C) (20x+3)(x-2)D) prime14) x2-2xy-63y2A) (x+7y)(x-9y)B) (x-7y)(x-9y)C) (x-7y)(x+y)D) prime15) 2x2+3xy+y2A) (2x+y)(x+y)B) (2x-y)(x-y)C) (2x+y)(x+2y)D) prime16) 7x2-55xy-72y2A) (7x+8y)(x-9y)B) (7x+9y)(x-8y)C) y(7x+8)(x-9)D) prime17) 6x2+13xy+6y2A) (3x+2y)(2x+3y)B) (3x-2y)(2x-3y)C) (6x+2y)(x+3y)D) primePage 28

Algebra and Trigonometry, 6th Edition Test Bank - Page 30 preview image

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4Factor the Difference of SquaresMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the difference of two squares.1) x2-9A) (x+3)(x-3)B) (x+3)2C) (x-3)2D) prime2) 16x2-49A) (4x+7)(4x-7)B) (4x-7)2C) (4x+7)2D) prime3) 16x2-121y2A) (4x+11y)(4x-11y)B) (4x-11y)2C) (4x+11y)2D) prime4) x4-256A) (x2+16)(x+4)(x-4)B) (x2+16)(x2+16)C) (x2-16)(x2-16)D) prime5) (16x4-81)A) (4x2+9)(2x+3)(2x-3)B) (4x2+9)(4x2-9)C) (2x+3)2(2x-3)2D) (4x2+9)(4x2+9)5Factor Perfect Square TrinomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the perfect square trinomial.1) x2-10x+25A) (x-5)2B) (x+5)2C) (x-5)(x+5)D) prime2) x2-20x+400A) (x-20)2B) (x+20)2C) (x+20)(x-20)D) prime3) 36x2+12x+1A) (6x+1)2B) (6x+1)(6x-1)C) (x+6)2D) prime6Factor the Sum or Difference of Two CubesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor using the formula for the sum or difference of two cubes.1) x3-125A) (x-5)(x2+5x+25)B) (x+5)(x2-5x+25)C) (x+125)(x2-1)D) prime2) x3+64A) (x+4)(x2-4x+16)B) (x-4)(x2+4x+16)C) (x+4)(x2+16)D) primePage 29

Algebra and Trigonometry, 6th Edition Test Bank - Page 31 preview image

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3) 27x3-1A) (3x-1)(9x2+3x+1)B) (3x-1)(9x2+1)C) (3x+1)(9x2-3x+1)D) prime4) 8x3+1A) (2x+1)(4x2-2x+1)B) (2x-1)(4x2+1)C) (2x-1)(4x2+2x+1)D) prime5) 27x3+64A) (3x+4)(9x2-12x+16)B) (3x-4)(9x2+12x+16)C) (3x+4)(9x2+12x+16)D) (3x+4)(9x2+16)6) 125x3-8A) (5x-2)(25x2+10x+4)B) (5x+2)(25x2-10x+4)C) (5x-2)(25x2-10x+4)D) (5x-2)(25x2+4)7Use a General Strategy for Factoring PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor completely, or state that the polynomial is prime.1) 4x3-16xA) 4x(x+2)(x-2)B) 4(x+2)(x2-2x)C) x(x+2)(4x-8)D) prime2) 50x2-32A) 2(5x+4)(5x-4)B) 2(5x-4)2C) 2(5x+4)2D) prime3) 4x2+16x+12A) 4(x+1)(x+3)B) (4x+4)(x+3)C) (x+1)(4x+12)D) 4(x2+4x+3)4) 6x4-6A) 6(x2+1)(x+1)(x-1)B) 6(x2+1)(x2-1)C) 6(x+1)2(x-1)2D) prime5) x3-2x2-25x+50A) (x-2)(x+5)(x-5)B) (x+2)(x+5)(x-5)C) (x-2)(x-5)2D) prime6) 8x2-8x-48A) 8(x+2)(x-3)B) (8x+16)(x-3)C) primeD) 8(x-2)(x+3)7) x3-36xA) x(x+6)(x-6)B) (x2+6)(x-6)C) x(x-6)2D) prime8) 9x3-9xA) 9x(x+1)(x-1)B) x(x+3)(x-3)C) 9x(x2+1)D) 9x(x2-1)Page 30

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