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College Algebra, 3rd Edition Test Bank

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    Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor using u -substitution. 1) 36 + x 4 - 13 x 2 1) Answer: ( x + 2)( x - 2)( x + 3)( x - 3) Explanation: Graph the elements of the set on a number line. 2) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 2) Answer: Explanation: Rewrite the expression using the associative property of multiplication and simplify, if possible. 3) -8  - 3 8 x 3) Answer: -8 - 3 8 x = 3 x Explanation: The cost C , in millions of dollars, for a government to find and seize P % of an illegal drug is modeled by the rational equation C = 350 P 100 - P (0 ” P < 100). 4) Why does the cost increase dramatically the closer you get to 100%? 4) Answer: It would require many resources. Explanation: Find the indicated sum. 5) ( 7 d 2 + 2 d - 4 ) + ( -10 d 2 - 10 d - 3 ) 5) Answer: -3 d 2 - 8 d - 7 Explanation: 1

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    Factor out the common binomial factor. 6) Factor out the common binomial factor. 5 x ( x - 6 ) - 7 ( x - 6 ) 6) Answer: ( 5 x - 7 )( x - 6 ) Explanation: Identify as either true or false. If false, state why. 7) R 2 N 7) Answer: False. Not all real numbers are natural numbers. Explanation: Factor the trinomial completely. 8) 5 x 2 + 48 x + 64 8) Answer: ( 5 x + 8 )( x + 8 ) Explanation: Translate the phrase into an algebraic expression. 9) nine times the sum of a number and five , decreased by one 9) Answer: 9 ( n + 5 ) - 1 Explanation: The cost C , in millions of dollars, for a government to find and seize P % of an illegal drug is modeled by the rational equation C = 350 P 100 - P (0 ” P < 100). 10) Will 100% of the drugs ever be seized? 10) Answer: No Explanation: List all the numbers in the set that are elements of Z. 11) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 11) Answer: { 36 } Explanation: Compute the product. 12) ( x + 2 )( x + 3 )( x + 4 ) 12) Answer: x 3 + 9 x 2 + 26 x + 24 Explanation: Factor the perfect square trinomial completely. 13) x 2 - 18 x + 81 13) Answer: ( x - 9 ) 2 Explanation: 2

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    Evaluate without a calculator, using the order of operations. 14) 5 4 2 ÷ 25 16 - 4 9 14) Answer: 1 3 Explanation: Simplify and add (if possible). 15) 2 12 + 4 27 15) Answer: 16 3 Explanation: Simplify using the quotient property of exponents. Write the answer using positive exponents only. 16) 7 m -10 16) Answer: 7 m 10 Explanation: Simplify the expression. Assume the variable represents a nonnegative real number. 17) 45 n 2 17) Answer: 3 n 5 Explanation: Perform the operation indicated. Write final result in lowest terms. 18) 11 2 s - 9 8 s 2 18) Answer: 44 s - 9 8 s 2 Explanation: List all the numbers in the set that are elements of W. 19) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 19) Answer: { 36 } Explanation: Translate the phrase into an algebraic expression. 20) the difference between a number and six is squared 20) Answer: ( n – 6 ) 2 Explanation: 3

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    Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” if needed) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.” 21) x 3 - 4 x 2 - 9 x + 36 21) Answer: ( x - 4 )( x + 3 )( x - 3 ) Explanation: List all the numbers in the set that are elements of R. 22) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 22) Answer: -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 Explanation: Reduce to lowest terms. 23) b - 5 -2 b + 10 23) Answer: - 1 2 Explanation: Rewrite the expression as a compound fraction. Then simplify using either method. 24) 1 + 6 x -1 1 - 6 x -1 24) Answer: 1 + 6 x 1 - 6 x ; x + 6 x - 6 Explanation: Factor by grouping. 25) Factor by grouping. x 5 + 2 x 3 - 4 x 2 - 8 25) Answer: ( x 2 + 2 )( x 3 - 4 ) Explanation: Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” if needed) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.” 26) -21 x 2 + 6 x + 15 x 3 26) Answer: 3 x (5 x - 2)( x - 1) Explanation: 4

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    Simplify using the quotient property of exponents. Write the answer using positive exponents only. 27) -16 w 24 -4 w 8 27) Answer: 4 w 16 Explanation: Create a mathematical model using descriptive variables. 28) The speed of the truck was two miles per hour more than the speed of the car. 28) Answer: Let c represent the speed of the car. Then c + 2 represents 2 mph more than the speed of the car. Explanation: Simplify by combining like terms. 29) -2 b - 9 b - 6 b 29) Answer: -17 b Explanation: Simplify the expression by building a perfect square root factor for the denominator. 30) 36 22 30) Answer: 18 22 11 Explanation: List all the numbers in the set that are elements of N. 31) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 31) Answer: { 36 } Explanation: Use the properties of exponents to simplify the expression. Write the answer using positive exponents only. 32) 3 m 2 n 5 6 m n 5 32) Answer: m 2 Explanation: 5

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    Evaluate the expression for the given value(s). 33) 2 x 2 y given x = -3 and y = 5 . 33) Answer: 90 Explanation: 34) 3 x - 5 y given x = 2 and y = -2 . 34) Answer: 16 Explanation: Simplify by removing all grouping symbols and combining like terms. 35) 10 a + ( -3 a ) 35) Answer: 7 a Explanation: Convert to decimal form and graph by estimating the number's location between two integers. 36) 8 3 36) Answer: 2. 6 Explanation: Compute the product and simplify the result. 37) ( 8 + 5 )( 8 - 5 ) 37) Answer: 59 Explanation: Evaluate the expression for the given value(s). 38) 8 Â -20 y given y = -5. 38) Answer: 80 Explanation: Convert the following number to decimal notation. 39) The maximum distance from Pluto to the Sun is 7.3 × 10 12 meters. 39) Answer: 7,300,000,000,000 meters Explanation: 6

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    Perform the operation indicated. Write final result in lowest terms. 40) 1 x + 1 + x x 2 - 4 x - 5 40) Answer: 2 x - 5 ( x - 5 ) ( x + 1 ) Explanation: Perform the operation indicated without the aid of a calculator. 41) 3 7 ÷ (-12) 41) Answer: - 1 28 Explanation: Simplify the expression, assuming that the variable can represent any real number. 42) 3 p 3 27 42) Answer: p 3 Explanation: Rewrite the expression using the commutative property of addition and simplify if possible. 43) -3 + 1 43) Answer: 1 + ( -3 ) = -2 Explanation: Write the polynomial in standard form and name the lead coefficient. 44) 9 x 2 + 5 x 3 - 1 + (-3 x ) 44) Answer: 5 x 3 + 9 x 2 - 3 x - 1 ; 5 Explanation: 7

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    The cost C , in millions of dollars, for a government to find and seize P % of an illegal drug is modeled by the rational equation C = 350 P 100 - P (0 ” P < 100). 45) Complete the table. Round to the nearest dollar. P 350 P 100 - P 40 60 80 90 92 95 97 100 45) Answer: P 350 P 100 - P 40 233 60 525 80 1400 90 3150 92 4025 95 6650 97 11317 100 ERROR Explanation: Find the binomial square. 46) ( x + 6 ) 2 46) Answer: x 2 + 12 x + 36 Explanation: Evaluate/Simplify the expression. 47) | -6.8 | 47) Answer: 6.8 Explanation: Factor the trinomial completely. 48) x 2 - 5 x - 14 48) Answer: ( x + 2 )( x - 7 ) Explanation: 8

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    Identify the number of terms in the expression and the coefficient of each term. 49) -5 x 2 + x - 9 49) Answer: three terms; coefficients: -5 , 1, -9 Explanation: Simplify the expression. Write your answer using positive exponents only. 50) -20 a 8 b 3 10 a 4 b -2 50) Answer: -2 a 4 b 5 Explanation: Solve the problem. 51) For the binomial 7 x - 5 a. Determine its conjugate. b. Find the product of the binomial with its conjugate. 51) Answer: a. 7 x + 5 b. 49 x 2 - 25 Explanation: Factor the difference of perfect squares completely. 52) 49 x 2 - 9 52) Answer: ( 7 x + 3 )( 7 x - 3 ) Explanation: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. 53) -64 53) A) -8 B) 8 C) -32 D) not a real number Answer: D Explanation: A) B) C) D) 54) 18 + 63 3 54) A) 6 + 21 B) 6 + 3 7 C) 6 + 7 D) 6 + 63 Answer: C Explanation: A) B) C) D) 9

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    Find the binomial square. 55) ( 3 x - 7 ) 2 55) A) 3 x 2 - 21 x + 49 B) 9 x 2 + 49 C) 9 x 2 - 42 x + 49 D) 9 x 2 - 21 x + 49 Answer: C Explanation: A) B) C) D) Evaluate the expression for the given value(s). 56) 3 y 2 + 4 y - 5 given y = -2 . 56) A) -1 B) 15 C) -9 D) -25 Answer: A Explanation: A) B) C) D) Perform the operation indicated. Write final result in lowest terms. 57) x 2 + 2 x - 3 x 2 - 3 x - 10 ÷ x 2 - 9 x 2 - 25 Â x - 3 x - 1 57) A) x + 2 x + 5 B) ( x + 5) ( x - 1) 2 ( x + 2) ( x - 3) 2 C) ( x + 2) ( x - 3) 2 ( x + 5) ( x - 1) 2 D) x + 5 x + 2 Answer: D Explanation: A) B) C) D) Perform the operation indicated without the aid of a calculator. 58) - 6 - (- 44 ) 58) A) -50 B) -38 C) 38 D) 50 Answer: C Explanation: A) B) C) D) 10

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    Translate the key phrase into an algebraic expression. Use descriptive variables. 59) The length of a rectangular lawn is 6 ft less than three times the width of the lawn. Express the length of the lawn in terms of the width. 59) A) 3 w - 6 B) 3 + w - 6 C) 6 w - 3 D) 3 ( w - 6 ) Answer: A Explanation: A) B) C) D) Perform the operation indicated. Write final result in lowest terms. 60) a + 3 a 2 - 4 - a + 5 a 2 - 4 a + 4 60) A) -6 a + 4 ( a + 2) 2 ( a - 2) B) -6 a - 16 ( a + 2) 2 ( a - 2) C) -6 a + 4 ( a + 2) ( a - 2) 2 D) -6 a - 16 ( a + 2) ( a - 2) 2 Answer: D Explanation: A) B) C) D) Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” if needed) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.” 61) x 2 + 2 x + 3 61) A) ( x + 2)( x + 1) B) ( x + 3)( x + 1) C) ( x – 3)( x – 1) D) prime Answer: D Explanation: A) B) C) D) Simplify the expression using the product to a power property. 62) ( -2 ab 10 ) 2 62) A) 4 a 2 b 20 B) -4 ab 20 C) -4 a 2 b 20 D) 4 ab 20 Answer: A Explanation: A) B) C) D) 11

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    Evaluate/Simplify the expression. 63) 1 6 63) A) -6 B) - 1 6 C) 6 D) 1 6 Answer: D Explanation: A) B) C) D) Simplify the expression. 64) - 9 4 3 2 64) A) 27 8 B) 27 2 C) - 27 8 D) not a real number Answer: D Explanation: A) B) C) D) Use the properties of exponents to simplify the expression. Write the answer using positive exponents only. 65) -7 x 0 + ( -7 x ) 0 65) A) -14 B) -2 C) -6 D) 0 Answer: C Explanation: A) B) C) D) Factor the difference of perfect cubes completely. 66) 27 a 3 - 1000 66) A) (3 a + 10)(9 a 2 - 30 a + 100) B) (3 a - 10)(9 a 2 + 30 a + 100) C) (3 a + 10)(9 a 2 - 100) D) (3 a - 10)(9 a 2 + 100) Answer: B Explanation: A) B) C) D) 12

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    The cost C , in millions of dollars, for a government to find and seize P % of an illegal drug is modeled by the rational equation C = 350 P 100 - P (0 ” P < 100). 67) What is the cost of seizing 60% of the drugs? 67) A) $525 B) $350 C) $210 D) $233 Answer: A Explanation: A) B) C) D) List all the numbers in the set that are elements of H. 68) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 68) A) -1 3 4 , - 3 , ʌ , 9 2 , 36 B) - 3 , ʌ , 36 C) - 3 , ʌ D) -1 3 4 , - 3 , ʌ , 9 2 Answer: C Explanation: A) B) C) D) Compute the product. 69) (3 x - 1)(2 x + 5) 69) A) 6 x 2 + 13 x - 5 B) 6 x 2 + 17 x - 5 C) 6 x 2 - 13 x - 5 D) 6 x 2 - 17 x - 5 Answer: A Explanation: A) B) C) D) Use a descriptive variable and an inequality symbol (<, >, • , ” ) to write a model for the statement. 70) The Ellis family will spend at least $9500 on home improvements. 70) A) Let a represent the amount. a • $9500 . B) Let a represent the amount. a ” $9500 . C) Let a represent the amount. a < $9500 . D) Let a represent the amount. a > $9500 . Answer: A Explanation: A) B) C) D) 13

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    Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” if needed) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.” 71) x 2 - 14 x + 40 71) A) ( x - 4 )( x + 10 ) B) ( x + 1)( x + 40 ) C) ( x - 4 )( x - 10 ) D) ( x + 4 )( x + 10 ) Answer: C Explanation: A) B) C) D) Simplify the expression using the quotient to a power property. 72) 2 y 9 z 7 2 72) A) 4 y 18 z 7 B) 2 y 11 z 9 C) 4 y 18 z 14 D) 4 y 11 z 7 Answer: C Explanation: A) B) C) D) Reorder the elements of the set in order from smallest to largest. 73) -3.5, -1 3 4 , 3.25, - 3 , -0.8, ʌ , 9 2 , 36 73) A) -3.5, -1 3 4 , - 3 , -0.8, ʌ , 3.25, 9 2 , 36 B) -3.5, -1 3 4 , - 3 , -0.8, 3.25, ʌ , 9 2 , 36 C) -3.5, - 3 , -1 3 4 , -0.8, 3.25, ʌ , 9 2 , 36 D) -3.5, - 3 , -1 3 4 , -0.8, ʌ , 3.25, 9 2 , 36 Answer: A Explanation: A) B) C) D) 14

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    Perform the operation indicated. Write final result in lowest terms. 74) n 2 - n - 20 n 2 + 8 n + 16 Â n n 2 - 25 74) A) n ( n + 5) ( n + 4) B) n ( n + 4)( n + 5) C) n ( n + 4)( n - 5) D) n ( n + 5) ( n + 4) 2 Answer: B Explanation: A) B) C) D) Convert the following number to scientific notation. 75) The diameter of Jupiter is approximately 143,000,000 meters. 75) A) 1.43 × 10 7 meters B) 1.43 × 10 8 meters C) 14.3 × 10 8 meters D) 14.3 × 10 7 meters Answer: B Explanation: A) B) C) D) Simplify by combining like terms. 76) 4 x + 14 x 2 - 9 x - 5 x 2 76) A) 9 x 2 + 5 x B) -9 x 2 - 5 x C) 9 x 2 - 5 x D) 18 x 2 - 14 x Answer: C Explanation: A) B) C) D) Factor the trinomial completely. 77) 6 x 2 - 5 x - 6 77) A) ( 2 x + 3 )( 3 x - 2 ) B) ( 2 x + 1)( 3 x - 6 C) ( 2 x - 3 )( 3 x + 2 ) D) ( 6 x - 3 )( x + 2 ) Answer: C Explanation: A) B) C) D) 15

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