Math 1201 Unit 2 Powers and Exponents Final Review
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1 Math 1201 Unit 2 Powers and Exponents Final Review Multiple Choice 1. Write the prime factorization of Write the prime factorization of Determine the greatest common factor of 56 and 88. a. 77 b. 616 c. 7 d Determine the greatest common factor of 84, 210, and 336. a. 14 b c. 21 d Determine the least common multiple of 10 and 22. a. 2 b. 55 c. 220 d Determine the least common multiple of 78 and 102. a b. 6 c d Determine the least common multiple of 48, 72, and 108. a. 432 b. 216 c d 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 a. 100 b. 63 c. 500 d Determine the cube root of a b c d A cube has volume cm 3. What is the surface area of the cube? a cm 2 b cm 2 c. 25 cm 2 d cm Determine the perfect square whole number closest to a b c d Determine the side length of this square. Area = 3969 cm 2 a. 63 cm b cm c cm d. 441 cm June
2 17. Determine the edge length of this cube. Volume = cm 3 a cm b. 45 cm c cm d cm 18. A cube has surface area 3750 square feet. What is its volume? a cubic feet c cubic feet b. 25 cubic feet d cubic feet 19. Identify the index of. a. b. 3 c. 7 d Identify the radicand of. a. 4 b. c. 6 d Evaluate. a. 2 b. 2.6 c. 16 d Evaluate. a. 4 b. impossible c d Evaluate. a. 0.7 b c d 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 b c d Which of these numbers is rational?,,, 30. Which of these numbers is irrational?,,, June
3 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 Which of these numbers is a natural number? 9, 0, 1, a. 9 b. 0 c. d 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 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 Evaluate without using a calculator. a b c. 0.5 d Evaluate without using a calculator. a. 3 b. 3 c. 9 d. does not exist 47. Evaluate without using a calculator. June
4 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 b. 32 d 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 Evaluate a. b. c. d Evaluate a without using a calculator. b c d Evaluate a without using a calculator. b. 1 6 c d Evaluate without using a calculator. 59. Given that, what is? a. 6 b. 1 6 c. d. June
5 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 b. 3 2 c. d Simplify June
6 71. Simplify 72. Simplify 73. Evaluate for and. a. b. c d. 74. Evaluate for and. a. b. 72 c. d. Short Answer 75. Write the prime factorization of Determine the greatest common factor of 735 and Determine the least common multiple of 450 and 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 Determine the perfect square whole number closest to A cube has volume 9261 cubic inches. Determine the area of one face of the cube. 83. Determine the square root of 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
7 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 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
8 103. Here is a student s solution for evaluating a power: Identify any errors in the solution. Write a correct solution Use exponent laws to simplify. Explain your strategy. June
9 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
10 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: ANS: ANS: a) 3 ft. b) ANS: 56 days 80. ANS: ANS: ANS: 441 square inches 83. ANS: ANS: 85. ANS: 86. ANS:, 4 7, 2.4, and ANS: 88. ANS: ANS:,, and June
11 90. ANS: or 91. ANS: or 92. ANS: ANS: 94. ANS: ANS: ANS: ANS: 98. ANS: 99. ANS: or 100. ANS: 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
12 The surface area of a person with mass 75 kg is approximately 2.0 m 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
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