Math 1201 Unit 2 Powers and Exponents Final Review Multiple Choice 1. Write the prime factorization of 630. 2. Write the prime factorization of 4116. 3. Determine the greatest common factor of 56 and 88. a. 77 b. 616 c. 7 d. 8 4. Determine the greatest common factor of 84, 210, and 336. a. 14 b. 1680 c. 21 d. 42 5. Determine the least common multiple of 10 and 22. a. 2 b. 55 c. 220 d. 110 6. Determine the least common multiple of 78 and 102. a. 1326 b. 6 c. 2652 d. 7956 7. Determine the least common multiple of 48, 72, and 108. a. 432 b. 216 c. 31 104 d. 12 8. A developer wants to subdivide a rectangular plot of land measuring 600 m by 750 m into congruent square lots. What is the side length of the largest possible square? a. 75 m b. 30 m c. 150 m d. 50 m 9. What is the side length of the smallest square that could be tiled using a 6-cm by 15-cm tile? Assume the tiles cannot be cut. a. 10 cm b. 90 cm c. 30 cm d. 3 cm 10. One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every 10 days. Suppose both neighbours cut their lawns today. How many days will pass before both neighbours cut their lawns on the same day again? a. 80 days b. 60 days c. 2 days d. 40 days 11. What is the side length of the largest square that could be used to tile a rectangle that measures 6 ft. by 34 ft.? Assume the squares cannot be cut. a. 6 ft. b. 2 ft. c. 102 ft. d. 4 ft. 12. Determine the square root of 250 000. a. 100 b. 63 c. 500 d. 200 13. Determine the cube root of 42 875. a. 1225 b. 4763.9 c. 207.1 d. 35 14. A cube has volume 15 625 cm 3. What is the surface area of the cube? a. 132 893.3 cm 2 b. 3750 cm 2 c. 25 cm 2 d. 10 416.7 cm 2 15. Determine the perfect square whole number closest to 7293. a. 7292 b. 7225 c. 6859 d. 7396 16. Determine the side length of this square. Area = 3969 cm 2 a. 63 cm b. 15.83 cm c. 992.25 cm d. 441 cm June 2014 1
17. Determine the edge length of this cube. Volume = 91 125 cm 3 a. 301.87 cm b. 45 cm c. 6.71 cm d. 3375 cm 18. A cube has surface area 3750 square feet. What is its volume? a. 5625 cubic feet c. 1448 cubic feet b. 25 cubic feet d. 15 625 cubic feet 19. Identify the index of. a. b. 3 c. 7 d. 2 20. Identify the radicand of. a. 4 b. c. 6 d. 8 21. Evaluate. a. 2 b. 2.6 c. 16 d. 1.41 22. Evaluate. a. 4 b. impossible c. 12.8 d. 4 23. Evaluate. a. 0.7 b. 0.007 c. 0.1143 d. 0.49 24. Evaluate. 25. Write an equivalent form of 0.4 as a fourth root. 26. Write an equivalent form of as a square root. 27. Which of these roots lies between 3 and 4?,,, 28. Evaluate. a. 0.0085 b. 0.0042 c. 0.13 d. 0.013 29. Which of these numbers is rational?,,, 30. Which of these numbers is irrational?,,, June 2014 2
31. Order these numbers from greatest to least:,,,, a.,,,, c.,,,, b.,,,, d.,,,, 32. Which of these numbers is an integer, but not a whole number? 9, 0, 1, a. 0 b. 9 c. d. 1 33. Which of these numbers is a natural number? 9, 0, 1, a. 9 b. 0 c. d. 1 34. Which irrational number could be used to represent the hypotenuse of a right triangle with legs 7 cm and 8 cm? a. cm b. cm c. cm d. cm 35. Which of these numbers is a whole number, but not a natural number? 0, 3, 1, a. b. 1 c. 0 d. 3 36. Write in simplest form. a. b. 6 3 c. d. 37. Write in simplest form. 38. Write in simplest form. 39. Write 6 5 as an entire radical. 40. Write as an entire radical. 41. Write as an entire radical. 42. Write in simplest form. 43. Write 7 14 as an entire radical. 44. Evaluate without using a calculator. a. 8 b. 4 c. 4 d. 21 1 3 45. Evaluate without using a calculator. a. 0.05 b. 0.125 c. 0.5 d. 0.29 46. Evaluate without using a calculator. a. 3 b. 3 c. 9 d. does not exist 47. Evaluate without using a calculator. June 2014 3
48. Write as a radical. 49. Write as a power. 50. Write a., or as a radical. c., or b., or d., or 51. Evaluate a. 18 c. 1.741 101... b. 32 d. 40 52. Evaluate a. c. b.... d. 53. Evaluate a. b. does not exist c. d. 54. Evaluate without using a calculator. a. 3 b. 1 6 c. 1 9 d. 9 55. Evaluate a. b. c. d. 1 6 56. Evaluate a. 1 256 without using a calculator. b. 3 256 c. 1 256 d. 256 57. Evaluate a. 1 36 without using a calculator. b. 1 6 c. 1 36 d. 1 6 58. Evaluate without using a calculator. 59. Given that, what is? a. 6 b. 1 6 c. d. June 2014 4
60. Simplify by writing as a single power. 61. Simplify. Write using powers with positive exponents. 62. Simplify. Write using powers with positive exponents. 63. Simplify. 64. Simplify. 65. Simplify 66. A sphere has volume 350 cubic inches. Determine the radius of the sphere to the nearest inch. a. 7 in. b. 4 in. c. 5 in. d. 825 in. 67. Evaluate 68. Evaluate a. 5 6 b. c. 6 5 d. 69. Evaluate a. 125 64 b. 3 2 c. d. 64 125 70. Simplify June 2014 5
71. Simplify 72. Simplify 73. Evaluate for and. a. b. c. 531 441 d. 74. Evaluate for and. a. b. 72 c. d. Short Answer 75. Write the prime factorization of 35 700. 76. Determine the greatest common factor of 735 and 1715. 77. Determine the least common multiple of 450 and 180. 78. A builder wants to cover a wall measuring 9 ft. by 15 ft. with square pieces of plywood. a) What is the side length of the largest square that could be used to cover the wall? Assume the squares cannot be cut. b) How many square pieces of plywood would be needed? 79. Bill and Betty do chores at home. Bill mows the lawn every 8 days, and Betty bathes the dog every 14 days. Suppose Bill and Betty do their chores today. How many days will pass before they both do their chores on the same day again? 80. Determine the cube root of 551 368. 81. Determine the perfect square whole number closest to 54 362. 82. A cube has volume 9261 cubic inches. Determine the area of one face of the cube. 83. Determine the square root of 308 025. 84. Evaluate. 85. Evaluate. 86. Which of these numbers are rational numbers, but not integers? 3.12, 4,, 4 7, 2.4,, 0, 51 2, 87. Which of these numbers are irrational?,,, 6.314,, 12.8,, June 2014 6
88. Write in simplest form. 89. Write 8 19 as an entire radical. 90. Write as a radical. 91. Write as a power. 92. Evaluate. 93. Evaluate without using a calculator. 94. Evaluate without using a calculator. 95. Evaluate without using a calculator. 96. Evaluate without using a calculator. 97. Simplify Write using powers with positive exponents. 98. Simplify 99. Evaluate 100. Evaluate Problem 101. Harish simplified as shown: Identify the error Harish made, then write a correct solution. 102. A formula for the approximate surface area, SA square metres, of a person s body is, where m is the person s mass, in kilograms. Calculate the surface area of a person with mass 75 kg. June 2014 7
103. Here is a student s solution for evaluating a power: Identify any errors in the solution. Write a correct solution. 104. Use exponent laws to simplify. Explain your strategy. June 2014 8
MULTIPLE CHOICE 1. ANS: C 2. ANS: B 3. ANS: D 4. ANS: D 5. ANS: D 6. ANS: A 7. ANS: A 8. ANS: C 9. ANS: C 10. ANS: D 11. ANS: B 12. ANS: C 13. ANS: D 14. ANS: B 15. ANS: B 16. ANS: A 17. ANS: B 18. ANS: D 19. ANS: B 20. ANS: B 21. ANS: A 22. ANS: A 23. ANS: A 24. ANS: A 25. ANS: A 26. ANS: D 27. ANS: C 28. ANS: C 29. ANS: D 30. ANS: B 31. ANS: C 32. ANS: B 33. ANS: A 34. ANS: A 35. ANS: C 36. ANS: B 37. ANS: B 38. ANS: A 39. ANS: C 40. ANS: A 41. ANS: C 42. ANS: A 43. ANS: C 44. ANS: B 45. ANS: C 46. ANS: A 47. ANS: C 48. ANS: B 49. ANS: B 50. ANS: D 51. ANS: B 52. ANS: C 53. ANS: C 54. ANS: C 55. ANS: C 56. ANS: A 57. ANS: D 58. ANS: D 59. ANS: D 60. ANS: A June 2014 9
61. ANS: B 62. ANS: D 63. ANS: A 64. ANS: A 65. ANS: B 66. ANS: B 67. ANS: B 68. ANS: A 69. ANS: A 70. ANS: B 71. ANS: B 72. ANS: D 73. ANS: A 74. ANS: A SHORT ANSWER 75. ANS:, or 76. ANS: 245 77. ANS: 900 78. ANS: a) 3 ft. b) 15 79. ANS: 56 days 80. ANS: 82 81. ANS: 54 289 82. ANS: 441 square inches 83. ANS: 555 84. ANS: 85. ANS: 86. ANS:, 4 7, 2.4, and 51 2 87. ANS: 88. ANS: 11 14 89. ANS:,, and June 2014 10
90. ANS: or 91. ANS: or 92. ANS: 16 93. ANS: 94. ANS: 9 4 95. ANS: 10 3 96. ANS: 1 27 97. ANS: 98. ANS: 99. ANS: 0.064 or 100. ANS: 1 8 125 PROBLEM 101. ANS: Harish made an error in the second line, when he wrote as the product of and. Correct solution: 102. ANS: Substitute m = 75 in the formula:... June 2014 11
The surface area of a person with mass 75 kg is approximately 2.0 m 2. 103. ANS: In the first line of the solution, to write the power with a positive exponent, the student wrote the fraction inside the brackets as a negative fraction instead of taking the reciprocal of the original fraction. In the second line, the student wrote the index of the radical as 2 instead of 3. The radicand should have been positive and should have been written as the reciprocal of the fraction. A correct solution is: 104. ANS: Write each radical as a power. Use the product of powers law: Write equivalent fractions with a common denominator, 40. I can write this power as a radical: or June 2014 12