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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
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|
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a. 63 cm
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b. 15.83 cm
c. 992.25 cm
d. 441 cm
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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.
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,
,
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.
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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
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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.
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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,
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,
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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.
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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.
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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.
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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.
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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
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Math 1201
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
ANS:
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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:
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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:
...
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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
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