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Test Bank for College Algebra, 13th Edition

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    T ESTING M ANUAL D AVID A TWOOD Rochester Community and Technical College C OLLEGE A LGEBRA T HIRTEENTH E DITION Margaret L. Lial American River College John Hornsby University of New Orleans David I. Schneider University of Maryland Callie J. Daniels St. Charles Community College

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    CONTENTS CHAPTER TEST FORMS 1 ANSWERS TO CHAPTER TEST FORMS 191 DIAGNOSTIC PRETESTS AND ANSWERS 235 FINAL EXAMS AND ANSWERS 245

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    1 CHAPTER R, FORM A COLLEGE ALGEBRA NAME DATE 1. Let 54 16 9.6, , 6 , 0, 13, 2.15, , 49 . 7 5 A π ì ü ï ï ï ï = - í ý ï ï ï ï î þ List the elements of A that belong to the given set. a. Natural numbers 1. a. ____________ b. Rational numbers b. ____________ c. Irrational numbers c. ____________ 2. Evaluate the expression if 2 x = - , 4 y = - , and 1 z = : 2. ______________ ( ) 2 2 2 3 y x y z - - 3. Identify the property illustrated. Let a , b , and c represent any real numbers. a. ( ) a b c ac bc + = + 3. a. ____________ b. ( ) 0 a b b a é ù + + - = + ë û b. ____________ c. 1 2 3 1 2 3 2 3 4 2 3 4 æ ö æ ö ÷ ÷ ç ç = ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø ⋅ ⋅ ⋅ ⋅ c. ____________ d. 1 1 ( 3) ( 3) 2 2 p p + = + ⋅ d. ____________ Perform the indicated operations. 4. ( ) 2 3 2 a b é ù + - ë û 4. ______________ 5. ( ) ( ) ( ) 2 3 2 3 2 5 2 7 2 3 x x x x x x - - - + - + - 5. ______________ 6. ( )( ) 2 2 2 3 x x x - + - 6. ______________ 7. ( ) ( ) 7 7 x y x y é ù é ù - - - + ë û ë û 7. ______________ 8. ( ) 3 2 5 x + 8. ______________ 9. 4 3 2 2 3 5 14 10 2 y y y y y - - + - 9. ______________ 10. 2 2 2 9 1 3 x x x x x x - - - - ⋅ 10. ______________ 11. 2 3 3 1 4 4 16 x x x x x x + - - - + - 11. ______________

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    2 CHAPTER R, FORM A 12. 3 4 4 9 7 5 5 7 a b a b a b b a + - - - - 12 . ______________ 13. 11 11 x y x y + 13. ______________ 14. ( ) 2 2 3 4 3 2 5 ⋅ − − + 14. ______________ Factor completely. 15. 3 2 3 2 4 8 32 x y x y - + - 15. ______________ 16. 3 3 8 64 a b + 16. ______________ 17. 4 3 2 6 11 35 x x x - - 17. ______________ 18. 2 28 4 9 x x + - 18. ______________ 19. Evaluate 2 3 125 27 - æ ö ÷ ç ÷ ç ÷ ç è ø . 19. ______________ 20. Simplify 6 2 3 3 4 1 2 1 4 1 6 x y z x z - - - - æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø so that there are no 20. ______________ negative exponents. Assume that all variables represent positive real numbers. Simplify. Assume that all variables represent positive real numbers. 21. 5 3 4 3 8 x y z 21. ______________ 22. 3 112 4 175 x x x + 22. ______________ 23. ( ) ( ) 3 3 3 4 2 5 4 + - 23. ______________ 24. Rationalize the denominator of 12 5 2 7 - and simplify. 24. ______________ 25 . Write the fraction 4 5 as a decimal and a percent. 25. ______________

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    3 CHAPTER R, FORM A 26. The wind chill factor w is given by the equation 26. ______________ 0.16 0.16 35.74 0.6215 35.75 0.4275 w T V TV = + - + where T represents the temperature in degrees Fahrenheit and V represents the wind velocity. Find the wind chill factor when the temperature is –40°F and the wind velocity is 15 mph. (Round to the nearest tenth.)

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    4 CHAPTER R, FORM B COLLEGE ALGEBRA NAME DATE 1. Let 2 12 17, , 0, , , 3, 4.2, 25 5 3 A π ì ü ï ï ï ï = - - - í ý ï ï ï ï î þ List the elements of A that belong to the given set. a. Natural numbers 1. a. ____________ b. Integers b. ____________ c. Irrational numbers c. ____________ 2. Evaluate the expression if 1 x = , 2 y = - , and 3 z = : 2. ______________ 2 4 2 3 2 x y y z - + - 3. Identify the property illustrated. Let a , b , and c represent any real numbers. a. 1 1 1 1 2 2 2 2 b b é ù æ ö æ ö ÷ ÷ ç ç ê ú + - + = + - + ÷ ÷ ç ç ÷ ÷ ç ç ê ú è ø è ø ë û 3. a. ____________ b. ( ) ( ) a b c c a b + = + b. ____________ c. 2 0 2 a a + = c. ____________ d. 3 4 1 4 3 = ⋅ d. ____________ Perform the indicated operations. 4. ( ) 2 3 1 x y é ù - - ë û 4. ______________ 5. ( )( ) 2 2 2 2 x y x y + - 5. ______________ 6. 2 2 ( 1) ( 2) (2 2) x x x x x x - - + - - 6. ______________ 7. ( ) ( ) 3 3 x y x y é ù é ù - + - - ë û ë û 7. ______________ 8. ( ) 3 2 3 x y - 8. ______________ 9. 4 3 2 6 7 5 11 3 2 x x x x x - + - - 9. ______________ 10. 2 2 2 2 3 7 2 2 3 x x x x x x x x + + - + + ⋅ 10. ____________ 11. 2 2 2 1 25 5 x x x x x + - - + 11. ____________

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    5 CHAPTER R, FORM B 12. 9 21 3 7 7 3 x x x + - - 12. ____________ 13. 2 2 1 3 2 1 x x x x x x - + - + + - 13. ____________ 14. ( ) 3 7 8 2 3 2 1 − − ⋅ + 14. ______________ Factor completely. 15. 2 8 53 21 x x - - 15. ____________ 16. 3 2 3 3 27 27 x x x + - - 16. ____________ 17. 3 3 3 3 16 16 x y x y y y - - + 17. ____________ 18. 3 2 12 3 ab abc - 18. ____________ 19. Evaluate 2 3 27 64 - æ ö ÷ ç- ÷ ç ÷ ç è ø . 19. ____________ 20. Simplify 10 2 3 3 4 1 5 1/ 2 1/ 4 a b c a b - - æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø so that there are no 20. ____________ negative exponents. Assume that all variables represent positive real numbers. Simplify. Assume that all variables represent positive real numbers. 21. 16 7 10 75 x y z 21. ____________ 22. 2 24 5 54 8 6 x x x - + 22. ____________ 23. ( ) ( ) 3 3 3 4 25 2 3 5 + - 23. ____________ 24. Rationalize the denominator of 3 3 1 1 2 16 + and simplify. 24. ____________ 25 . Write the fraction 3 1 5 as a decimal and a percent. 25. ______________

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    6 CHAPTER R, FORM B 26. Police sometimes use the following procedure to 26. ____________ estimate the speed at which a car was traveling at the time of an accident: A police officer drives a car that is the same type as the one involved in the accident under conditions similar to those during which the accident took place and then skids to a stop. If the car is driven at 30 mph, then the speed at the time of the accident is given by 30 , a s p = where a is the length of the skid marks left at the time of the accident and p is the length of the skid marks in the police test. Find s , the speed, when a is 325 ft and p is 102 ft. (Round to the nearest tenth.)

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    7 CHAPTER R, FORM C COLLEGE ALGEBRA NAME DATE 1. Let 70 1 , , 2 , 0, 64, 19, 1.23, 4, 2.76 . 10 8 A π ì ü ï ï ï ï = - - - í ý ï ï ï ï î þ List the elements of A that belong to the given set. a. Rational numbers 1. a. ____________ b. Real numbers b. ____________ c. Whole numbers c. ____________ 2. Evaluate the expression if 2 x = - , 1 y = - , and 3 z = : 2. ______________ ( ) 2 3 2 x y x y z - + + 3. Identify the property illustrated. Let a , b , and c represent any real numbers. a. ( ) ( ) 1 1 3 3 a b b a + = + 3. a. ____________ b. 1 1 0 2 2 æ ö ÷ ç + - = ÷ ç ÷ ç è ø b. ____________ c. ( ) 9 9 9 a b a b + = + c. ____________ d. ( ) ( ) 2 9 2 9 a a = ⋅ d. ____________ Perform the indicated operations. 4. ( ) 2 4 2 x y é ù - + ë û 4. ______________ 5. 3 2 3 3( ) 2( ) 3( 2 ) x x x x x x - - + + + - 5. ______________ 6. 2 2 (3 2 )(2 3 4 ) x y x xy y + - + 6. ______________ 7. ( ) ( ) 5 2 5 2 a b a b é ù é ù + - + + ë û ë û 7. ______________ 8. ( ) 3 4 3 b c - 8. ______________ 9. 5 3 2 3 2 3 9 2 x x x x - - + - 9. ______________ 10. 2 2 2 6 5 6 2 3 2 4 x x x x x - - - ¸ + - 10. ______________ 11. 2 2 2 20 25 5 16 x x x x x + - - ⋅ - - 11. ______________

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    8 CHAPTER R, FORM C 12. 3 4 10 7 5 5 7 a b a b a b b a + - + - - 12. ______________ 13. 2 2 1 4 1 x x - - 13. ______________ 14. ( ) 2 3 2 3 4 1 3 2 + − − 14. ______________ Factor completely. 15. 2 2 10 19 6 x xy y - + 15. ______________ 16. 4 16 x - 16. ______________ 17. 3 2 2 3 2 4 8 a a b ab b + - - 17. ______________ 18. 4 2 2 2 18 x x y - 18. ______________ 19. Evaluate 4 3 27 64 - æ ö ÷ ç ÷ ç ÷ ç è ø . 19. ______________ 20. Simplify 12 3 8 1 6 5 4 2 3 3 4 a b a b c - - - - - æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø so that there are no 20. ______________ negative exponents. Assume that all variables represent positive real numbers. Simplify. Assume that all variables represent positive real numbers. 21. 5 13 80 a b 21. ______________ 22. 4 4 3 3 3 16 2 54 x y y xy xy + - 22. ______________ 23. ( ) ( ) 3 2 3 2 x y x y + - 23. ______________ 24. Rationalize the denominator of 12 3 7 + and simplify. 24. ______________ 25 . Write the fraction 12 5 as a decimal and a percent. 25. ______________

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    9 CHAPTER R, FORM C 26. Police sometimes use the following procedure to 26. ______________ estimate the speed at which a car was traveling at the time of an accident: A police officer drives a car that is the same type as the one involved in the accident under conditions similar to those during which the accident took place and then skids to a stop. If the car is driven at 30 mph, then the speed at the time of the accident is given by 30 , a s p = where a is the length of the skid marks left at the time of the accident and p is the length of the skid marks in the police test. Find s , the speed, when a is 375 ft and p is 185 ft. (Round to the nearest tenth).

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    10 CHAPTER R, FORM D COLLEGE ALGEBRA NAME DATE 1. Let 10 5 5, 17.8, 3.6, 0, , 49, 3 , , 8 . 2 3 A π ì ü ï ï ï ï = - - - í ý ï ï ï ï î þ List the elements of A that belong to the given set. a. Natural numbers 1. a. ____________ b. Rational numbers b. ____________ c. Integers c. ____________ 2. Evaluate the expression if 3 x = - , 4 y = - , and 1 z = : 2. ______________ ( ) 2 2 5 2 x z x y + - 3. Identify the property illustrated. Let a , b and c represent any real numbers. a. ( ) ( ) a b c b c a + = + 3. a. ____________ b. 2 1 2 1 7 5 7 5 b b æ ö æ ö ÷ ÷ ç ç = ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø ⋅ ⋅ b. ____________ c. 1 1 1 4 4 = ⋅ c. ____________ d. ( ) ( ) 4 4 4 a a a a é ù + - = + - ë û d. ____________ Perform the indicated operations. 4. ( ) 2 2 3 2 x y é ù - - ë û 4. ______________ 5. ( )( ) 2 2 2 3 1 2 x x x x - + + - 5. ______________ 6. ( ) ( ) 3 2 4 3 2 3 4 7 2 3 5 x x x x x x - + - + - + + 6. ______________ 7. ( ) ( ) 2 4 2 4 r s r s é ù é ù + - + + ë û ë û 7. ______________ 8. ( ) 3 2 a b + 8. ______________ 9. 4 3 2 2 2 2 11 6 3 y y y y y - - + - 9. ______________ 10. 2 2 2 2 3 10 15 3 7 4 3 4 x x x x x x x + - + ¸ - + - - 10. ______________ 11. 2 2 4 1 10 16 5 14 x x x x x x - + - - + + - 11. ______________

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    11 CHAPTER R, FORM D 12. 2 2 3 2 5 4 4 x x x x + + + - - 12. ______________ 13. 1 3 2 4 x x x - + - 13. ______________ 14. 4 3 7 1 2 4 5 + ⋅ − − ⋅ 14. ______________ Factor completely. 15. 2 18 27 4 x x - + 15. ______________ 16. 4 2 6 11 10 x x + - 16. ______________ 17. 4 3 3 4 8 2 16 r rs r s s - - + 17. ______________ 18. 3 3 8 64 x y + 18. ______________ 19. Evaluate 3 2 16 49 - æ ö ÷ ç ÷ ç ÷ ç è ø . 19. ______________ 20. Simplify 6 3 2 4 3 5 6 2 3 5 4 1 4 x y z x y z - - æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø so that there are 20. ______________ no negative exponents. Assume that all variables represent positive real numbers. Simplify. Assume that all variables represent positive real numbers. 21. 14 18 5 84 a b c 21. ______________ 22. 4 4 5 5 768 48 x x + 22. ______________ 23. ( ) ( ) 10 2 6 10 6 + - 23. ______________ 24. Rationalize the denominator of 1 1 3 27 - and simplify. 24. ______________ 25 . Write the fraction 3 8 − as a decimal and a percent. 25. ______________

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    12 CHAPTER R, FORM D 26. The length of one leg of a right triangle is 26. ______________ 2 2 a c b = - where c is the length of the hypotenuse and b is the length of the other leg. Find the length of the unknown leg if the length of the hypotenuse is 45 m and the length of the other leg is 28 m. (Round to the nearest tenth.)

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    13 CHAPTER R, FORM E COLLEGE ALGEBRA NAME DATE 1. Let 5 12 , 3.2, , 4, 64, 3, , 0 8 8 2 A π ì ü ï ï ï ï = - - í ý ï ï ï ï î þ . List the elements of A that belong to the given set. A. Rational numbers 1. A. ____________ a. 5 12 , 3.2, 4, 64, 8 2 ì ü ï ï ï ï - - í ý ï ï ï ï î þ b. 12 4, 64, , 0 2 ì ü ï ï ï ï - í ý ï ï ï ï î þ c. 5 12 , 4, 64, , 0 8 2 ì ü ï ï ï ï - í ý ï ï ï ï î þ d. 5 12 , 3.2, 4, 64, , 0 8 2 ì ü ï ï ï ï - - í ý ï ï ï ï î þ B. Real numbers B. ____________ a. , 3 8 π ì ü ï ï ï ï í ý ï ï ï ï î þ b. 12 4, 64, , 0 2 ì ü ï ï ï ï - í ý ï ï ï ï î þ c. 5 12 , 3.2, , 4, 64, 3, , 0 8 8 2 π ì ü ï ï ï ï - - í ý ï ï ï ï î þ d. 3.2, , 3 8 π ì ü ï ï ï ï - í ý ï ï ï ï î þ C. Natural numbers C. ____________ a. 5 12 , 3.2, 4, 64, , 0 8 2 ì ü ï ï ï ï - - í ý ï ï ï ï î þ b. 12 4, 64, , 0 2 ì ü ï ï ï ï - í ý ï ï ï ï î þ c. 12 64, , 0 2 ì ü ï ï ï ï í ý ï ï ï ï î þ d. 12 64, 2 ì ü ï ï ï ï í ý ï ï ï ï î þ 2. Evaluate the expression if 5 x = - and 2 y = - : 2. _____________ 4 2 3 4 x y y x - - - - a. 5 23 b. 5 26 c. 5 14 d. 1 2

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