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Math 1201 Unit 2 – Powers and Exponents Final Review Multiple Choice ____ ____ ____ ____ ____ ____ ____ 1. Write the prime factorization of 630. a. b. c. d. 2. Write the prime factorization of 4116. a. b. c. d. 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 cm3. What is the surface area of the cube? a. 132 893.3 cm2 b. 3750 cm2 c. 25 cm2 d. 10 416.7 cm2 ____ 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 June 2014 b. 15.83 cm c. 992.25 cm d. 441 cm 1 Math 1201 Unit 2 – Powers and Exponents Final Review ____ 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 c. 6 d. 8 b. 2.6 c. 16 d. 1.41 b. impossible c. –12.8 d. 4 b. 0.007 c. 0.1143 d. 0.49 b. c. d. ____ 25. Write an equivalent form of 0.4 as a fourth root. a. b. c. d. ____ 20. Identify the radicand of a. 4 b. ____ 21. Evaluate a. 2 . . ____ 22. Evaluate a. –4 . ____ 23. Evaluate a. 0.7 . ____ 24. Evaluate . a. ____ 26. Write an equivalent form of a. as a square root. b. c. d. ____ 27. Which of these roots lies between 3 and 4? , , , a. b. c. d. ____ 28. Evaluate a. 0.0085 c. 0.13 d. 0.013 c. d. c. d. . b. 0.0042 ____ 29. Which of these numbers is rational? , , , a. b. ____ 30. Which of these numbers is irrational? , a. June 2014 , , b. 2 Math 1201 Unit 2 – Powers and Exponents ____ 31. Order these numbers from greatest to least: a. , , , , b. , , , , , c. d. , , , Final Review , , , , , , , , ____ 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 d. –1 c. ____ 34. Which irrational number could be used to represent the hypotenuse of a right triangle with legs 7 cm and 8 cm? a. b. c. d. cm cm cm 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 a. in simplest form. b. 6 3 c. d. c. d. c. d. ____ 39. Write 6 5 as an entire radical. a. b. c. d. ____ 40. Write a. as an entire radical. b. c. d. ____ 41. Write a. as an entire radical. b. c. d. ____ 42. Write a. in simplest form. b. c. d. ____ 43. Write 7 14 as an entire radical. a. b. c. d. ____ 44. Evaluate a. 8 c. –4 d. c. 0.5 d. 0.29 c. −9 d. does not exist c. d. ____ 37. Write a. ____ 38. Write a. ____ 45. Evaluate a. 0.05 ____ 46. Evaluate a. –3 ____ 47. Evaluate a. June 2014 in simplest form. b. in simplest form. b. without using a calculator. b. 4 without using a calculator. b. 0.125 without using a calculator. b. 3 21 1 3 without using a calculator. b. 3 Math 1201 ____ 48. Write a. Unit 2 – Powers and Exponents as a radical. b. ____ 49. Write c. d. c. d. as a power. a. b. ____ 50. Write a. Final Review as a radical. c. , or , or b. d. , or , or ____ 51. Evaluate a. 18 b. 32 c. 1.741 101... d. 40 ____ 52. Evaluate a. c. b. ... d. ____ 53. Evaluate a. b. does not exist ____ 54. Evaluate a. 3 without using a calculator. b. 1 6 c. c. d. d. 9 1 9 ____ 55. Evaluate a. – ____ 56. Evaluate a. 1 256 b. c. – without using a calculator. b. 3 256 c. d. – 1 256 ____ 57. Evaluate a. 1 36 without using a calculator. b. 1 c. 1 – 36 6 ____ 58. Evaluate a. without using a calculator. b. c. ____ 59. Given that a. –6 June 2014 b. , what is 1 − 6 – 1 6 d. –256 d. – 1 6 d. ? c. d. 4 Math 1201 Unit 2 – Powers and Exponents by writing as a single power. ____ 60. Simplify a. b. ____ 61. Simplify a. ____ 62. Simplify a. c. a. . Write using powers with positive exponents. c. d. c. d. b. c. d. b. c. d. . b. ____ 64. Simplify a. d. . Write using powers with positive exponents. b. c. d. b. ____ 63. Simplify Final Review . ____ 65. Simplify a. ____ 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. b. c. d. b. c. 825 in. ____ 67. Evaluate a. ____ 68. Evaluate a. 5 6 6 5 d. ____ 69. Evaluate a. 125 64 b. 3 2 c. d. c. d. 64 125 ____ 70. Simplify a. June 2014 b. 5 Math 1201 Unit 2 – Powers and Exponents Final Review ____ 71. Simplify a. b. c. d. b. c. d. ____ 72. Simplify a. ____ 73. Evaluate for a. and . b. ____ 74. Evaluate for a. and c. 531 441 d. c. d. . b. 72 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? 1 4 3.12 , –4, , , 2.4, , 0, 5 , 2 7 87. Which of these numbers are irrational? , , , 6.314, , –12.8, June 2014 , 6 Math 1201 88. Write Unit 2 – Powers and Exponents Final Review 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 96. Evaluate without using a calculator. 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 Math 1201 Unit 2 – Powers and Exponents Final Review 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 June 2014 . Explain your strategy. 8 Math 1201 Unit 2 – Powers and Exponents Final Review MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: C B D D D A A C C D B C D B B A B D B B A A A A A D C C D B C B A A C B B A C A C A C B C A C B B D B C C C C A D D D A June 2014 9 Math 1201 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: Unit 2 – Powers and Exponents Final Review B D A A B B B A A B B D A 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: , 1 4 , 2.4, and 5 2 7 87. ANS: , , and 88. ANS: 11 14 89. ANS: June 2014 10 Math 1201 Unit 2 – Powers and Exponents Final Review 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 8 125 100. ANS: 1 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 Math 1201 Unit 2 – Powers and Exponents Final Review The surface area of a person with mass 75 kg is approximately 2.0 m2. 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