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Test Bank for College Algebra, 5th Edition

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    T ESTING M ANUAL L AURIE H URLEY C OLLEGE A LGEBRA F IFTH E DITION Judith A. Beecher Judith A. Penna Marvin L. Bittinger Indiana University Purdue University Indianapolis

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    iii CONTENTS I. ALTERNATE TESTS, FORMS A, B, C, D, E, and F .......................................................... 1 There are six alternate test forms for each chapter and the final examination. Alternate Test Forms A, B, C, and D are equivalent in length and difficulty. Synthesis questions occur at the end of the Test Forms, and are separated from the rest of the test by a solid line. Synthesis questions are meant to be more challenging than the previous test questions, like those problems found in the last part of each exercise set in the text. The synthesis questions have been placed at the end to make it easy to omit them if the instructor wishes to do so. All questions on Test Forms E and F are multiple choice. Effort was made to make the wrong answers as logically wrong as possible. In most cases answers were constructed to avoid students doing backward reasoning. This Instructor’s Testing Manual is designed to accompany College Algebra, 5e, by Beecher/ Penna/Bittinger, 5e . Chapter 1 ................................................................................................................................ 1 Chapter 2 .............................................................................................................................. 37 Chapter 3 .............................................................................................................................. 61 Chapter 4 .............................................................................................................................. 81 Chapter 5 ............................................................................................................................ 105 Chapter 6 ............................................................................................................................ 133 Chapter 7 ............................................................................................................................ 161 Chapter 8 ............................................................................................................................ 185 II. FINAL EXAMINATIONS................................................................................................. 213 III. ANSWER KEYS FOR ALTERNATE TESTS, FORMS A, B, C, D, E, and F ................ 265 IV. ANSWER KEYS FOR FINAL EXAMINATIONS........................................................... 296 Thanks are extended to Janis Cimperman for checking the accuracy of the manuscript, to Mike Penna for producing the graphs, and to Kelly Barber for typing the manuscript.

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    1 CHAPTER 1 NAME_____________________________ TEST FORM A CLASS_____SCORE_____GRADE_____ ____________________________________________________________________________ 1. Determine whether the ordered pair       − 4 3 , 5 is a solution of the equation 3 x – 8 y = 21. 2. Find the intercepts of 6 2 3 = − y x and graph the line. 3. Find the distance between   4, 8 and   –7, 6 . 4. Find the midpoint of the segment with endpoints   1, 0 and   5, – 8 . 5. Find the center and the radius of the circle   2 2 6 9 x y    . 6. Find an equation of the circle with center   –2, 3 and radius 11 . 7. a) Determine whether the relation           5, 5 , 4, 4 , 3, 3 , 1, 1    is a function. Answer yes or no. b) Find the domain of the relation. c) Find the range of the relation. 8. Given that   2 6 2 f x x x    , find each of the following. a)   1 f  b)   3 f a  9. Given that   3 4 x f x x    , find each of the following. a) ( ) 4 − f b) ( ) 3 − f ANSWERS 1. 2. See graph. 3. 4. 5. 6. 7. a) b) c) 8. a) b) 9. a) b)

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    2 CHAPTER 1 NAME_____________________________ TEST FORM A ____________________________________________________________________________ ANSWERS 10. 11. a) b) 12. 13. 14. 15. a) See graph. b) c) 10. Using the graph of f at the right, find   3 . f 11. Determine whether each graph is that of a function. Answer yes or no. a) b) Find the domain of the function. 12.   2 4 x f x x    13.   3 4 g x x   14.   2 9 h x x   15. a) Graph: ( ) 4 1 + − = x x f . b) Visually estimate the domain of ( ) x f . c) Visually estimate the range of ( ) x f .

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    3 CHAPTER 1 NAME_____________________________ TEST FORM A ______________________________________________________________________________ ANSWERS 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. Find the slope of the line containing the given points. 16.   4, – 2 and   –4, 6 17.   4, 1 and ( –7, 1) 18.   –0.5, 8 and   –0.5, 3 19. The number of clients served by Scott’s Small Motor Repairs was 260 in 2010. It grew to 320 in 2014. Find the average rate of change in number of clients from 2010 to 2014. 20. Find the slope and the y -intercept of the graph of 5 x – 2 y = –10. 21. Total Cost . Kelly’s Deli charges $1.95 for a bagel with plain cream cheese plus $0.30 for each additional topping. Write an equation that can be used to determine the total cost, C ( t ), for a bagel with plain cream cheese and t additional toppings. Then find the total cost of a bagel with plain cream cheese and four additional toppings. 22. Write an equation for a line with m = –3 and y -intercept       5 3 , 0 . 23. Write an equation for the line that passes through   3, – 2 and   7, 6 . 24. Write an equation of the horizontal line that passes through   –8, 5 . 25. Determine whether the lines are parallel, perpendicular, or neither. y x y x 2 3 5 8 5 2 = + − = +

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    4 CHAPTER 1 NAME_____________________________ TEST FORM A ____________________________________________________________________________ ANSWERS 26. 27. 28. 29. 30. 31. 32. 26. Find an equation of the line containing the point   –2, – 5 and parallel to the line 4 x – 5 y = 13. 27. Find an equation of the line containing the point   –2, – 5 and perpendicular to the line 4 x – 5 y = 13. 28. The table below shows the average price, in dollars, of a desktop PC at Johnson Office Supply in several recent years. Year, x Average Price, P 2006, 0 725 2008, 2 690 2010, 4 600 2012, 6 500 2014, 8 415 Model the data with a linear function using years 2 and 8 and predict the average price in 2018 using this function. Round to the nearest dollar. Solve. 29. 15 2 3 = + − x 30. x x 12 14 5 12 + = − 31. 2 4 6 2 3 5 n n + = − 32. ( ) ( ) 9 2 8 3 4 y y − = − +

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    5 CHAPTER 1 NAME_____________________________ TEST FORM A ____________________________________________________________________________ ANSWERS 33. 34. 35. 36. See graph. 37. See graph. 38. See graph. 39. 33. Parking lot dimensions . A parking lot has a perimeter of 500 ft. The width is 20 ft less than the length. Find the dimensions. 34. Pricing . The Book Barn prices its paperbacks by raising the wholesale price 60% and then adding 50¢. What is the wholesale price of a paperback that sells for $7.96? 35. Find the zero(s) of the function   f x = 3 x + 1. Solve and write interval notation for the solution set. Then graph the solution set. 36. 6 10 12 8 x x − + > − 37. 2 3 5 7 x − < − ≤ 38. 3 2 5 4 1 9 x or x − ≤ − + ≥ 39. Country Plumbing charges a $25 transportation fee plus $50 per hour for a service call. Tip Top Plumbing charges $62.50 per hour for a service call. For how long a service call is Country Plumbing the less expensive option?

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    6 CHAPTER 1 NAME_____________________________ TEST FORM A ANSWERS 40. 41. 40. Which of the following represents the graph of ( ) 1 4 ? 2 g x x = − A. B. C. D. 41. Find the domain of   4 2 x f x x    .

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    7 CHAPTER 1 NAME_____________________________ TEST FORM B CLASS_____SCORE_____GRADE_____ ____________________________________________________________________________ 1. Determine whether the ordered pair       − 2 3 , 2 is a solution of the equation 4 y – 3 x = 12. 2. Find the intercepts of 4 4 = − y x and graph the line. 3. Find the distance between   4, – 3 and   6, 1 . 4. Find the midpoint of the segment with endpoints   4, – 6 and (– 3, – 12) . 5. Find the center and the radius of the circle     2 2 5 2 100 x y     . 6. Find an equation of the circle with center   8, – 1 and radius 3 . 7. a) Determine whether the relation ( ) ( ) ( ) ( ) { } 3 , 1 , 4 , 2 , 1 , 1 , 0 , 2 − − − is a function. Answer yes or no. b) Find the domain of the relation. c) Find the range of the relation. 8. Given that ( ) 1 2 + + = x x x f , find each of the following. a) ( ) 2 − f b) ( ) 3 f a − 9. Given that   4 2 x f x x   , find each of the following. a) ( ) 2 − f b) ( ) 0 f ANSWERS 1. 2. See graph. 3. 4. 5. 6. 7. a) b) c) 8. a) b) 9. a) b)

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    8 CHAPTER 1 NAME_____________________________ TEST FORM B ____________________________________________________________________________ ANSWERS 10. 11. a) b) 12. 13. 14. 15. a) See graph. b) c) 10. Using the graph of f at the right, find   0 . f 11. Determine whether each graph is that of a function. Answer yes or no. a) b) Find the domain of the function. 12.   2 6 x f x x   13.   3 5 g x x   14.   2 16 h x x   15. a) Graph: ( ) 4 2 − = x x f . b) Visually estimate the domain of ( ) x f . c) Visually estimate the range of ( ) x f .

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    9 CHAPTER 1 NAME_____________________________ TEST FORM B ____________________________________________________________________________ ANSWERS 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. Find the slope of the line containing the given points. 16.   0, 5 and   0, – 8 17.   –2, 6 and   –9, – 11 18.   0.3, 4 and   –5, 4 19. The enrollment at a school in 2006 was 55. In 2014, the enrollment was 145. Find the average rate of change in enrollment from 2006 to 2014. 20. Find the slope and the y -intercept of the graph of 12 5 6 = − y x . 21. Total Cost . Jackson Park Field Days charges a $5 entrance fee plus $1.25 per ride. Write an equation that can be used to determine the total cost,   , C r of going on r rides at Jackson Park Field Days. Then find the total cost of going on six rides. 22. Write an equation for a line with 2 3 m  and y -intercept   0, – 4 . 23. Write an equation for the line that passes through   –6, 5 and   10, 2 . 24. Write an equation of the vertical line that passes through ( ) 4 . 5 , 6 . 0 − . 25. Determine whether the lines are parallel, perpendicular, or neither. 3 6 1 2 5 x y y x + = = −

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    10 CHAPTER 1 NAME_____________________________ TEST FORM B ____________________________________________________________________________ ANSWERS 26. 27. 28. 29. 30. 31. 32. 26. Find an equation of a line containing the point   –2, 6 and parallel to the line 2 x + y = 5. 27. Find an equation of the line containing the point   –2, 6 and perpendicular to the line 5 2 = + y x . 28. The table below shows the average number of lunches per day, sold for various years. Year, x Lunches Sold, S 2011, 0 50 2012, 1 65 2013, 2 70 2014, 3 88 Model the data with a linear function using years 1 and 3 and estimate the average number of lunches sold per day in 2017 using this function. Round to the nearest whole number of lunches. Solve. 29. 24 3 8 − = + − x 30. 4 3 3 4 − = + − x x 31. 1 2 5 2 2 3 n n − = − + 32. ( ) ( ) 3 4 8 2 7 y y + = − −

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    11 CHAPTER 1 NAME_____________________________ TEST FORM B ____________________________________________________________________________ ANSWERS 33. 34. 35. 36. See graph. 37. See graph. 38. See graph. 39. 33. Room Dimensions . A rectangular room has a perimeter of 54 ft. The width is four-fifths of the length. What are the dimensions of the room? 34. Amount of an Investment . Gary makes an investment at 4.5% simple interest. At the end of one year, the total value of the investment is $3448.50. How much was originally invested? 35. Find the zero(s) of the function   6 3 f x x   . Solve and write interval notation for the solution set. Then graph the solution set. 36. 18 3 6 x x − > + 37. 5 3 1 7 x − ≤ + < 38. 5 3 7 3 5 14 x or x + < − + ≥ 39. Doreen’s Catering charges $150 for set up plus $12 per person for parties under 100 people. Jackson’s Catering charges $18 per person for parties under 100 people. For what size party is Jackson’s a better deal? Assume that the party will be under 100 people.

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    12 CHAPTER 1 NAME_____________________________ TEST FORM B ANSWERS 40. 41. 40. Which of the following represents the graph of ( ) 2 2 ? 3 g x x = − A. B. C. D. _________________________________________________________ 41. Find the domain of ( ) x x x f − = 3 .

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