Math 2201
Chapter 4
Final Review
Multiple Choice
____
1. Which of these equations are true?
I.
a.
b.
c.
d.
____
II.
III.
II only
I only
I and II
I, II, and III
2. Which of these equations are true?
I.
II.
a.
b.
c.
d.
____
neither I nor II
II only
I and II
I only
3. Which of these equations are true?
I.
a.
b.
c.
d.
____
II.
I and II
I only
II only
I, II, and III
4. Which of these equations are true?
I.
a.
b.
c.
d.
____
III.
II.
III.
I only
II only
I and II
I, II, and III
5. Which number is not an entire radical?
a.
b.
c.
d.
____
6. Which number is not a mixed radical?
a.
b.
c.
d.
____
7. Which number is not expressed in the simplest form?
a.
b.
c.
d.
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Math 2201
____
Chapter 4
8. Which choice expresses each of these numbers in simplest form?
,
,
,
a.
,
,
b.
, 7, 36,
c.
, 7,
,
d. 4.5, 7, 36, 13.4
____
Final Review
,
9. Which choice expresses each of these numbers as an entire radical?
,
,
,
a. 7.3, 32.4, 6.6, 12
b.
,
,
,
c.
,
,
,
d.
,
,
,
____ 10. Which choice expresses these numbers as the product of two radicals?
,
,
,
a.
,
,
b.
,
c.
,
,
,
d. 3 • 11, 6 • 7, 3 • 5, 4 • 8
,
,
,
____ 11. Which choice expresses these numbers as mixed radicals?
,
a.
b.
c.
d.
3
,
,
,2
,5
,9
13
, 17
, 19
,6
9
,4
, 25
, 81
10.8, 8.2, 21.8, 12.7
____ 12. Which choice lists these numbers in increasing order?
4
,2
a. 2
b. 3
c.
d.
,
,3
,
,4
,2
,4
,2
,
,3
,3
,3
,4
,2
,4
____ 13. Which choice lists these numbers in decreasing order?
,4
a. 4
b.
c. 2
d.
,
,
,2
,4
,
,2
,2
,
,
,2
, _120
,4
,
,4
____ 14. Which set contains like radicals?
a. 14
,5
,–
, 21
b. 6
,
, –2
,
c.
, –9
,5
,3
d. 17(
), 10
,7
,–
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Math 2201
Chapter 4
____ 15. Which is the simplest form of 2
+5
+6
?
+4
–9
+ 12
+
+
Final Review
a.
b.
c.
d.
____ 16. Which is the simplest form of 3
a.
b.
c.
d.
–14
4
10
28
____ 17. Which is the simplest form of
a.
b.
c.
d.
?
?
12
5
6
6
____ 18. Which is the simplest form of 7
–2
–
?
a. 0
b. –3
c. 21
d. –9
____ 19. Which is the simplest form of
a.
b.
c.
d.
–7
–8
25
–3
+9
– 14
?
+ 45
____ 20. Which expression is the simplest form of
?
a.
b. 7.9
c.
d.
____ 21. Which expression is the simplest form of
?
a.
b.
c.
d.
____ 22. Which expression is the simplest form of
?
a.
b.
c.
d.
June 2014
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Math 2201
Chapter 4
Final Review
in simplest form and entire form?
____ 23. Which expressions are equivalent to
a.
b.
c.
d.
____ 24. Which expression is the rationalized form of
?
a.
b.
c.
d.
____ 25. Which expression is the rationalized form of
?
a.
b.
c.
d.
____ 26. Which restrictions apply to the variable in
I.
a.
b.
c.
d.
II.
?
III. x > 0 IV. x ∈ R V. x ∈ N
I, IV, and V
II and IV
I and IV
III and V
____ 27. Which restrictions apply to the variable in
I.
II.
a.
b.
c.
d.
V
III and V
IV
I and IV
III. x > 0 IV. x ∈ R V. x ∈ N
____ 28. Which restrictions apply to the variable in
I.
a.
b.
c.
d.
II.
?
?
III. x > 0 IV. x ∈ R V. x ∈ N
III and IV
I and IV
III and V
II and IV
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Math 2201
Chapter 4
____ 29. Which restrictions apply to the variable in
I. x ≠ 0 II.
a.
b.
c.
d.
?
III. x > 0 IV. x ∈ R V. x ∈ N
I, III, and V
V
I, II, and IV
IV
____ 30. Which restrictions apply to the variable in
I.
a.
b.
c.
d.
II.
III.
?
IV. x ∈ N V. x ∈ R
II and V
I, III, and IV
III and V
I, II, and V
____ 31. Which restrictions apply to the variable in
II. x > 0 III.
I.
a.
b.
c.
d.
I, III, and IV
I and V
III and V
II and V
I. x > 0 II.
III.
?
IV. x ∈ R V. y ∈ R
III and IV
II and V
II and IV
I and IV
____ 33. Which restrictions apply to the variable in
I.
a.
b.
c.
d.
?
IV. x ∈ N V. x ∈ R
____ 32. Which restrictions apply to the variable in
a.
b.
c.
d.
Final Review
?
IV. y > 0 V. y ∈ R
II. 6 – y > 0 III.
III, IV, and V
I, III, and IV
II, IV, and V
I, II, and V
____ 34. What is the value of x in
?
a. 12
b. 54
c.
d. 9
____ 35. What is the value of x in
a.
b.
c.
d.
?
1
–11
11
–1
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Math 2201
Chapter 4
Final Review
?
____ 36. What is the value of x in
a. 3
b.
c.
d. 24
____ 37. What is the value of x in
a.
b.
c.
d.
?
–65
35
215
115
____ 38. What is the value of x in
a.
b.
c.
d.
?
–7
1
45
–4
____ 39. What is the value of x in
?
a.
b. 25
c. 5
d. 10
____ 40. What is the value of x in
a.
b.
c.
d.
8
2
4
1
____ 41. What is the value of x in
a.
b.
c.
d.
?
5
7
27
15
____ 42. What is the value of x in
a.
b.
c.
d.
?
?
95
155
–15
5
____ 43. What is the value of x in
?
a. 8
b.
c. 21
d.
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Math 2201
Chapter 4
____ 44. What is the value of x in
Final Review
?
a.
b.
c. 0
d. 6
____ 45. How many solutions are there for
a.
b.
c.
d.
none
two: 3, –3
one: 13
one: –3
____ 46. How many solutions are there for
a.
b.
c.
d.
?
none
two: 3, –3
one: 3
one: 33
____ 47. How many solutions are there for
a.
b.
c.
d.
?
?
none
one: –6
one: 44
two: –6, 6
____ 48. How many solutions are there for
a.
b.
c.
d.
?
one: –1
none
two: 1, –1
one: 6
____ 49. How many solutions are there for
a.
b.
c.
d.
one: 2
none
two: 3, –3
one: 3
____ 50. How many solutions are there for
a.
b.
c.
d.
?
?
one: 21
none
two: 9, –9
one: 9
Short Answer
51. Express
52. Express
53. Express
54. Express
as a mixed radical in simplest form.
as a mixed radical in simplest form.
as a mixed radical in simplest form.
as a mixed radical in simplest form.
55. Express
as a product of two radicals.
56. Express
as a product of two radicals.
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Math 2201
Chapter 4
57. Express 7
as an entire radical.
58. Express 3
as an entire radical.
59. Convert
–
–
+3
+5
60. Add
into mixed radical form. Then simplify.
.
61. Subtract 8
–2
–3
62. Express 2
+7
+3
.
–4
in simplest form.
63. Express
in mixed radical form and entire form.
64. Express
in mixed radical form and entire form.
65. Expand the expression
66. Expand the expression
.
.
67. A small rectangular glass tile has a length of
68. Write
69. Write
Final Review
cm and a width of
cm. Determine the area of the tile.
in simplest form.
in simplest form.
70. State any restrictions on the variables, then simplify.
71. State any restrictions on the variable, then simplify.
72. State any restrictions on the variables, then multiply.
73. State any restrictions on the variable, then multiply.
74. State any restrictions on the variable, then expand.
75. State any restrictions on the variable, then expand.
76. State any restrictions on the variable, then divide.
77. State any restrictions on the variable, then divide.
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Math 2201
Chapter 4
Final Review
78. Joss has been contracted to water lawns for the summer using circular sprayers. The radius of sprayed water,
r, in metres, is modelled by r =
, where A is the area of grads watered by in square metres. Determine
the area covered for a circle with a radius of 4 m, to the nearest tenth of a metre.
79. State any restrictions on x, then solve
.
80. State any restrictions on x, then solve
.
81. State any restrictions on x, then solve
82. State any restrictions on x, then solve
.
.
83. State any restrictions on x, then solve
.
84. State any restrictions on x, then solve
.
85. State any restrictions on x, then solve
.
86. State any restrictions on x, then solve
.
87. State any restrictions on x, then solve
.
88. State any restrictions on x, then solve
.
Problem
89. Kyle made an error while expressing
as a mixed radical.
Identify his error and correct the solution.
90. Order the numbers in increasing order. Show your work.
3
,7
,2
,9
,8
91. Manny wants to sew a ribbon border around a small triangular cushion with sides of
cm.
a) Determine the exact length of ribbon Manny needs.
b) Determine the length Manny needs to one decimal place.
cm,
92. A rectangle has a width of
cm and a height of
cm. A triangle has a width of
height of
cm Determine which figure covers the greater area. Do not use a calculator.
93. Simplify
94. Simplify
95. Simplify
June 2014
cm, and
cm and a
. Explain each step.
. Explain each step.
. Explain each step.
9
Math 2201
Chapter 4
Final Review
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
B
A
D
B
C
C
B
B
B
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
A
C
C
B
D
C
C
B
B
D
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
B
A
B
D
D
B
C
D
D
C
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
D
A
C
B
D
D
B
D
B
C
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
C
A
A
D
A
C
B
C
C
B
SHORT ANSWER
51. ANS:
2
52. ANS:
50
53. ANS:
4
54. ANS:
6
55. ANS:
e.g.,
56. ANS:
e.g.,
57. ANS:
58. ANS:
59. ANS:
60. ANS:
61. ANS:
62. ANS:
63. ANS:
64. ANS:
65. ANS:
66. ANS:
67. ANS:
68. ANS:
69. ANS:
70. ANS:
x 0; x, y ∈ R
71. ANS:
y 0; y ∈ R
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Math 2201
Chapter 4
Final Review
72. ANS:
x, y 0; x, y ∈ R
73. ANS:
x 0; x ∈ R
74. ANS:
x –3; x ∈ R
75. ANS:
x 1; x ∈ R
76. ANS:
x > 0; x ∈ R
77. ANS:
x > 0; x ∈ R
78. ANS:
A = 32.7 m2
79. ANS:
80. ANS:
81. ANS:
82. ANS:
83. ANS:
no restrictions, x = –7
84. ANS:
85. ANS:
86. ANS:
87. ANS:
88. ANS:
PROBLEM
89. ANS:
He made an error in step 2. He did not take the square root of the factors he took out from under the radical.
The correct solution is:
90. ANS:
From least to greatest, the mixed radicals are 3
June 2014
,8
,2
,9
,7
.
11
Math 2201
Chapter 4
Final Review
91. ANS:
a)
The exact length of ribbon is
b)
cm.
The length of ribbon is 29.4 cm.
92. ANS:
Rectangle:
Triangle:
60 > 54 and
93. ANS:
, so the rectangle covers a greater area.
in the second term.
Step 1: Factor x5 in the first term and
Step 2: Calculate the square root of x4, multiply the first term by the result and remove x4 from the radicand.
Do the same for 4.
94. ANS:
.
Step 1: Multiply both terms in the brackets by
Step 2: Calculate the square roots of the perfect squares.
Step 3: Multiply the powers of x.
95. ANS:
.
Step 1: Divide numerator and denominator by
Step 2: Factor y3.
Step 3: Write any perfect squares in a radical as square roots outside the radical.
Step 4: Divide numerator and denominator by 6.
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