Transcript Chapters 1–7 Midterm Mastery Test

Name
Date
Midterm Mastery Test
Period
Page 1
Chapters 1–7 Midterm Mastery Test
Directions Circle the equation that matches the given equation or function.
1. A number divided by 2 plus 3 is 8.
(2 3)
A x
2. Choose any number; divide it by 3, then
subtract 8.
1
A f(x) 3x 8
B f(x) 3x 8
1
C f(x) 3x 8
D f(x) 3x 8
8
B x(2 3) 8
x
C (2) 3 8
(x 3)
D 2 8
Directions Circle the zeros of f(x).
3. f(x) 3x 6
4. f(x) 2x 8
A x3
A x 16
B x2
B x 4
C x 2
C x 16
D x 3
D x4
Directions Circle the term that correctly completes the sentence or
answers the question.
5. Which expression is equal to
4
9 ?
4x2y
4
i
9
2
B 3i
2
C 3i
A 32y
A
D 8. Which expression is in its lowest terms?
4a3b
B a
2
17x3y
C 21a
4
9
6. The turning point of a parabola that spills
water is also its _____.
A maximum value
B root
C radicand
D minimum value
7. The factors of (x3 y3) are ________.
A (x2 y2)(x y)
B (x y)(x2 xy y2)
C (x y)(x2 xy y2)
D (x y)(x2 xy y2)
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3xy
D x6y4
9. 兹3m
苶 兹n
苶 is the conjugate of ________.
A
兹苶
3m 苶
苶
兹n
B 兹3m
苶 兹n
苶
C 兹(3m)(n
苶)苶
D 兹n
苶 兹3m
苶
6
10. To rationalize the denominator of 兹17
苶 , you
can ________.
苶
兹17
A multiply by 兹17
苶
B square the numerator and the denominator
兹17
苶
C multiply by 6
D divide by 兹6
苶
Algebra 2
Name
Date
Midterm Mastery Test
Period
Page 2
Chapters 1–7 Midterm Mastery Test, continued
Directions Solve each inequality and graph it on the number line.
11. |2x 3| 15
1
12. |2x 8| 18
_________________________
_________________________
Directions Find the solution for each equation. Check your answer.
13. 4x 2 18
____________________
16. 8x 6 4x 3 ____________________
2
14. 3x 15 25
____________________
17. 5x 6 12x 5 ____________________
15. 3x 6 2x 5
____________________
18. 6x 42 x
5
____________________
Directions Write the domain and range for each function below.
19. (1, 3), (4, 25), (5, 2), (7, 6)
_______________________________
20. (21, 7), (22, 6), (23, 5), (24, 4)
_______________________________
Directions Calculate f(x) for the given domain values.
21. f(x) 3x; x 0, 2, 1, 4, 2
_______________________________
1
22. f(x) 3x; x 3, 3, 300, 180, 99
_______________________________
Directions Graph each linear function and label the y-intercept.
(Use graph paper. Label the x- and y-axes first.)
23. f(x) 3x 12
____________________
1
24. f(x) 4x
____________________
Directions Given m and b, write the equation of the line.
25. m 7; b 4
__________________
2
26. m 3; b 5
__________________
Directions Write the equation of the line passing through the two points.
27. (3, 0) and (6, 2)
__________________
28. (5, 2) and (3, 3)
__________________
Directions Multiply, using the distributive law. Simplify by adding like terms.
29. (a b)(5a 7b)
________________
30. (4x y)(3x 2y xy) ________________
Directions Solve for x by factoring.
31. 3x2 18x 0
__________________
33. 3x2 4x 4 0
__________________
32. x2 6x 16 0
__________________
34. 4x2 2x 6 0
__________________
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Algebra 2
Name
Date
Midterm Mastery Test
Period
Page 3
Chapters 1– 7 Midterm Mastery Test, continued
Directions Solve by completing the square. Check your answers. You
may leave expressions for square roots in your answers.
35. x2 18x 19 0
__________________
36. x2 14x 31 0
__________________
Directions Solve using the quadratic formula. Then write whether the
roots are real or complex.
37. 4x2 2x 5 0
__________________
39. 2x2 8x 18 0
__________________
38. 6x2 10x 22 0
__________________
40. 6x2 5x 12 0
__________________
Directions Find the values of f(x) for x 0, 1, 1, 2, 2, 3, 3.
Then sketch the parabola.
41. f(x) 3x2
__________________
42. f(x) x2 7x 6
__________________
Directions Sketch the graphs, using the function and three points: two
roots and the turning point. Write whether the roots are real
or complex.
43. f(x) x2 2x 8
__________________
Directions Find the common solution(s).
44. y 5x 8
__________________
y 3x 1
Directions Divide by factoring.
45. (64a3 8b3) ÷ (4a 2b)
_________________________
46. (3x 16)3 ÷ (3x 16)
_________________________
47. (2x y)3 ÷ (4x2 4xy y2)
_________________________
Directions Find each sum or difference.
48. (7x4 3x3 x2 6) (13x4 6x 3)
_________________________
49. (6x3y2 4x2y3 2xy4 3) (2x2y3 3x3y 2xy4 4)
_________________________
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Algebra 2
Name
Date
Midterm Mastery Test
Period
Page 4
Chapters 1– 7 Midterm Mastery Test, continued
Directions Find the products.
50. (2x 5y)3
________________
51. (3x y)(x2 6x 2)
________________
Directions Simplify the complex fractions.
14x
5
52.
2xy
35
____________________
4y3
x2
53.
16x2y4
3x
____________________
Directions Simplify each expression.
xy(x2 y2)
54. x3y2(x y)
____________________
6(a2 2ab b2)
55. 2(a2 b2)
____________________
Directions Add or subtract the expressions. Express your answer in
lowest terms.
(3x2 y)
(x2 y2)
(x2 9)
(6x 18)
56. (x y)
(x y)
57. (x 3)
3(x 3)
(a2 1)
(a2 2a 1)
________________
58. (a 1)
(a 1)2
________________
59. a2b
ab
12abc
________________
9abc
________________
Directions Find the products or quotients. Give your answer in
lowest terms.
3xy
4y
8a3b
5b2
• 60. a2b2 ab
61. c
2 • 80a
(x y)
(x2 2xy y2)
______________
62. (x y)2
(x y)
______________
63. (a2 4)
(a2 a 2)
(a 1)
(a2 1)
______________
______________
Directions Complete each operation. Write your answer in
simplest terms.
64. x4 x8
__________________
(x 2y)6
65. (x 2y)5
__________________
(4mn)
2
(9a b2)
__________________
Directions Rewrite using fractional exponents.
4
4
66. 2(兹x
苶) 3(兹x苶)
__________________
67.
Directions Rationalize the denominator and simplify.
(4 兹3苶)
68. __________________
兹b苶
2兹x苶
69. (3x 2兹y苶)
__________________
Directions Solve for the unknown.
70. 11 (4兹y苶) 1
________________
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Algebra 2
Name
Date
Period
Final Mastery Test
Page 1
Chapters 1–13 Final Mastery Test
Directions Circle the function or expression that matches the given
statement.
(AB)
3. logx[ᎏCᎏ]
1. Choose any number; multiply it by 4,
A logxA ⫹ logxB ⫹ logxC
then add 6.
1
A f(x) ⫽ ᎏ4ᎏx ⫺ 6
B f(x) ⫽ 4x ⫺ 6
1
C f(x) ⫽ ᎏ4ᎏx ⫹ 6
D f(x) ⫽ 4x ⫹ 6
B logxA ⫹ logxB ⫺ logxC
C C logxAB
(log A • log B)
x
x
ᎏ
D ᎏ
logxC
4
4. logx 兹苶
Ab
2. (2 ⫻ 10⫺4) ⫼ (8 ⫻ 10⫺9)
(b log A)
A 0.25 ⫻ 10⫺5
x
A ᎏ4ᎏ
B 2.5 ⫻ 105
C 2.5 ⫻
106
D 2.5 ⫻
104
B 4b logxA
4
ᎏ
C ᎏ
(b logxA)
D 4 logxAb
Directions Circle the selection that correctly answers the question or
completes the statement.
1
5. What is the zero of f(x) ⫽ ᎏ3ᎏx ⫺ 8?
8. What is the sum of the geometric sequence
1, 4, 16, 64, . . . , a10?
A 349,525
B 262,144
C 87,381
D 19,683
3
A x ⫽ ᎏ8ᎏ
B x ⫽ 24
C x ⫽ ⫺24
D x⫽2
6. Which function best describes the graph?
A f(x) ⫽ ax
1 x
B f(x) ⫽ [⫺(ᎏaᎏ)]
1 x
C f(x) ⫽ (ᎏaᎏ)
y
D f(x) ⫽ ax
9. In f(x) ⫽ ⫺ax2 ⫺ 2, x is the _______.
A maximum value
B independent variable
x
7. What is the 5th term of (2x ⫺ 1)7 ?
C dependent variable
D radicand
10. In 6x⫺2, x⫺2 equals _______.
A
280x3
A (⫺x)(⫺x)
B
168x3
B ᎏxᎏ2
C ⫺168x3
D ⫺280x3
©AGS Publishing. Permission is granted to reproduce for classroom use only.
1
C x(⫺2)
x
D ⫺(ᎏ2ᎏ)
Algebra 2
Name
Date
Final Mastery Test
Period
Page 2
Chapters 1–13 Final Mastery Test, continued
11. 兹2a
苶 ⫹ 兹b苶 is the conjugate of _______.
13. For any right triangle, sec θ ⫽ __________
1
hypotenuse
A ᎏᎏ
B
A ᎏᎏ
兹苶
(2a ⫹ 苶
兹b苶)
hypotenuse
B ᎏᎏ
C 兹2a
苶 ⫺ 兹b苶
opposite side
C ᎏᎏ
D 兹(2a)(b
苶)苶
adjacent side
D ᎏᎏ
12. (ab)⫺n equals ________.
14. sin 2θ ⫽ __________
n
A 兹ab
苶
A 2sin θ cos θ
B ⫺n(ab)
B cos2 θ ⫺ sin2 θ
C ⫺(ab)n
C 1 ⫺ cos2 θ
1
ᎏ
D ᎏ
(ab)n
D 2sin θ
Directions Graph each inequality on the number line.
15. 6x ⫺ 18 ⬎ 0
2
16. 3x ⫺ ᎏ3ᎏ ⱕ 0
Directions Solve each inequality.
17. |6x ⫺ 3| ⬍ 9
_____________________
18. |3x ⫺ 6| ⱖ 12
_____________________
Directions Find the solution for each equation. Check your answer.
19. 3x ⫹ 2 ⫽ 17
__________________
21. 8x ⫺ 6 ⫽ ⫺4x ⫹ 3
__________________
2
20. ᎏ3ᎏx ⫹ 15 ⫽ 21
__________________
22. 12x ⫽ ⫺6x ⫺ 3
__________________
Directions Graph each linear function and label the y-intercept.
(Use graph paper. Label the x- and y-axes first.)
23. f(x) ⫽ ⫺3x ⫺ 5
__________________
2
24. f(x) ⫽ ᎏ5ᎏx ⫹ 3
__________________
Directions Write the equation of the line passing through the two points.
25. (0, 3) and (2, 6)
__________________
26. (⫺3, 5) and (3, 3)
__________________
Directions Multiply, using the distributive law. Simplify by adding like terms.
27. (x ⫺ y)(7x ⫹ 3y ⫹ xy)
________________
28. (3x ⫹ y)(4x ⫹ 2y ⫹ xy) ________________
Directions Solve for x by factoring.
29. x2 ⫹ 6x ⫺ 16 ⫽ 0
________________
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30. 4x2 ⫹ 4x ⫺ 15 ⫽ 0
________________
Algebra 2
Name
Date
Final Mastery Test
Period
Page 3
Chapters 1–13 Final Mastery Test, continued
Directions Solve by completing the square. Check your answers. You
may leave expressions for square roots in your answers.
31. x2 ⫹ 10x ⫺ 24 ⫽ 0
________________
32. x2 ⫹ 24x ⫺ 52 ⫽ 0
________________
34. 8x2 ⫺ 10x ⫺ 12 ⫽ 0
________________
Directions Solve using the quadratic formula.
33. x2 ⫹ 5x ⫹ 6 ⫽ 0
________________
Directions Sketch each parabola and answer the question.
35. Sketch a narrow parabola that spills water and has a turning point of (0, 3).
________________
Will this parabola have real or complex roots?
36. Sketch a parabola with real roots and a turning point of (0, ⫺7).
________________
Is the turning point a minimum or maximum value for f(x)?
Directions Sketch the graphs, using the function and three points: two
roots and the turning point.
37. f(x) ⫽ x2 ⫺ 2x ⫺ 8
38. f(x) ⫽ x2 ⫺ 2x ⫺ 15
Directions Sketch the graphs, using the roots to find the function and
the turning point.
39. x ⫽ ⫺8, x ⫽ 4
40. x ⫽ ⫺3, x ⫽ 3
Directions Find the common solution(s).
41. y ⫽ 3x2
__________________
y ⫽ 3x ⫹ 6
42. 4y ⫹ 3x ⫽ 12
__________________
2x ⫹ 3y ⫽ 1
Directions Simplify the complex fractions.
x5
3x
43.
(ᎏ4ᎏ)
__________________
44.
(ᎏ9ᎏ)
__________________
2
(ᎏxᎏ2 )
6x
(ᎏ1ᎏ2 )
Directions Simplify each expression.
(x2 ⫹ 2xy ⫹ y2)
ᎏ
45. ᎏ
(x2 ⫺ y2)
__________________
4(a2 ⫺ 2ab ⫹ b2)
ᎏ
46. ᎏ
2(a2 ⫺ b2)
__________________
Directions Add or subtract the expressions. Express your answer in lowest terms.
47. (3x4 ⫹ 5x3 ⫺ 2x2 ⫹ 6) ⫹ (⫺4x4 ⫺ 8x ⫺ 3)
_________________________
48. (7x3y2 ⫺ 4x2y3 ⫹ xy4 ⫺ 3) ⫺ (⫺x2y3 ⫹ 3x3y ⫺ 2xy4 ⫹ 4)
_________________________
(4x2
⫹ y)
(x2
⫺
y2)
ᎏ ⫹ ᎏᎏ
49. ᎏ
(x ⫹ y)
(x ⫹ y)
_________________________
ᎏ ⫺ ᎏᎏ
50. ᎏ
(a ⫹ 1)
(a ⫹ 1)
_________________________
(a2 ⫺ 1)
(a2 ⫺ 2a ⫹ 1)
©AGS Publishing. Permission is granted to reproduce for classroom use only.
Algebra 2
Name
Date
Final Mastery Test
Period
Page 4
Chapters 1–13 Final Mastery Test, continued
Directions Find the products or quotients. Give your answer in lowest terms.
51. (12x3y2 ⫹ 8x2y ⫹ 4xy2) ÷ 4xy
_________________________
52. (100x2 ⫺ 9y2) ⫼ (10x ⫹ 3y)
_________________________
53. (5x ⫺ 2y)3
_________________________
9a3b2
6b2
ᎏ
54. ᎏᎏ
•ᎏ
2
35a
c
(a ⫺ 4)
ᎏ
55. ᎏ
(a2 ⫺ 4)
_________________________
(a2 ⫺ 1)
ᎏ
⫼ᎏ
(a2 ⫺ a ⫺ 2)
_________________________
Directions Rewrite using fractional exponents.
4
4
56. 兹x
苶 ⫹ 3(兹x苶)
__________________
4mn
ᎏ2ᎏ
a b2
57.
__________________
Directions Rationalize the denominator and simplify.
(3 ⫹ 兹2苶)
58. ᎏᎏ
兹b苶
__________________
4兹x苶
59. ᎏᎏ
__________________
61. 46 ⫺ 2兹a
苶 ⫽ 50
__________________
(x ⫹ 2兹y苶)
Directions Solve for the unknown.
60. 兹x
苶
⫺7⫽1
__________________
Directions Write the equations in logarithmic form.
62. 48 ⫽ 65,536
__________________
63. 104 ⫽ 10,000
__________________
Directions Write the equations in exponential form.
64. log3243 ⫽ 5
__________________
65. ln 5 ⫽ 1.609
__________________
Directions Solve each equation for x.
66. 82x ⫽ 8(3x ⫺ 1)
__________________
3
(6x ⫺ 4)苶
67. 兹苶
53x ⫽ 兹5苶
__________________
Directions Use your calculator to solve for x. If necessary, rewrite as
logarithmic equations first. Round your answers to the
nearest thousandth.
68. 10x ⫽ 15
____________________
69. 6(x ⫹ 2) ⫽ 42
____________________
71. f(x) ⫽ x2 ⫹ 1
____________________
Directions Find the equation for f ⫺1(x).
70. f(x) ⫽ x ⫺ 7
____________________
Directions Sketch the circles. Identify the center and radius of each.
72. x2 ⫹ (y ⫺ 4)2 ⫽ 64
_____________
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73. (x ⫹ 3)2 ⫹ (y ⫹ 6)2 ⫽ 49
_____________
Algebra 2
Name
Date
Final Mastery Test
Period
Page 5
Chapters 1–13 Final Mastery Test, continued
Directions Sketch the ellipses. Identify the center, vertices, and foci.
74. 9(x ⫹ 4)2 ⫹ (y ⫹ 7)2 ⫽ 81
____________
(x ⫺ 3)2
(y ⫹ 3)2
75. ᎏ9ᎏ ⫹ ᎏ16ᎏ ⫽ 1
____________
Directions Sketch the hyperbolas. Identify the center, asymptotes,
vertices, and foci.
y2
x2
76. ᎏ16ᎏ ⫺ ᎏ9ᎏ ⫽ 1
_______________
(x ⫺ 3)2
(y ⫹ 5)2
77. ᎏ9ᎏ ⫺ ᎏ16ᎏ ⫽ 1
_______________
Directions Sketch the parabolas. Identify the vertex, focus, and directrix.
78. 12x ⫽ y2
_______________
79. (y ⫺ 2)2 ⫽ (x ⫺ 3)
_______________
Directions Change radians to degrees.
3␲
80. ᎏ2ᎏ
_______________
␲
81. ᎏ6ᎏ
_______________
Directions Use the Law of Sines to find the indicated value.
82.
D
e
118°
_______________
83.
M
c⫽?
n
l⫽?
24°
7°
N
_______________
m ⫽ 13 in.
32°
C
d⫽4m
L
E
Directions Sketch the triangle and use the Law of Cosines to find the indicated
value. Round your answer to the nearest hundredth.
84. Find the third side of a triangle with sides of 19 m and 16 m and an included angle of 43°.
85. Find the third side of a triangle with sides of 120 cm and 100 cm and an included angle of 47°.
Directions Evaluate each expression. Do NOT use your calculator.
86. 5P5
______________________
88. 8P3
87. 6C6
______________________
89.
10C6
______________________
______________________
Directions Use the data set below to complete items 90–93.
{36, 48, 31, 52, 65, 39, 36, 42, 49, 55, 60, 54}
90. What is the range of the data set?
_____________________
91. What is the mean of the data set?
_____________________
92. What is the median of the data set?
_____________________
93. What is the mode of the data set?
_____________________
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Algebra 2
Name
Date
Final Mastery Test
Period
Page 6
Chapters 1–13 Final Mastery Test, continued
Directions Tell whether each sequence is convergent or divergent. If it is
convergent, find its sum.
94.
⬁
n
∑ (⫺ᎏ14ᎏ1 )
n⫽0
__________________
95.
⬁
(5k ⫹ 1)
ᎏ
∑ᎏ
3k
__________________
n⫽0
Directions Solve each problem.
96. A spinner is divided in 10 equal parts. The parts are labeled with the letters
A, B, C, D, E, F, G, H, I, and J. What is the probability of spinning a vowel?
_________________
97. If repetition is allowed, how many six-digit codes can be formed using the
_________________
digits 0, 2, 4, 6, and 8?
Directions Given f(x) ⫽ x2 ⫺ 1 and g(x) ⫽ 2x ⫹ 1, complete items
98–103.
98. f(x) ⫹ g(x)
________________
99. g(x) ⫺ f(x)
________________
100. f(x)g(x)
f(x)
________________
101. ᎏ
g(x)
________________
102. f(g(x))
________________
103. g(f(x))
________________
Directions Use conversion rules to complete each item.
104. 6.8 L ⫽ _______ mL
105. 265.3 mg ⫽ _______ g
Directions Solve.
106. Gasoline weighs 0.69 g/cm3. If a car has a 41 L gas tank, how much
_____________________
extra weight, in kilograms, is the car pulling when the gas tank is full?
Directions Use the data in the tables to complete items 107–110.
107. Display the data in the
“Miles Driven” data set in
a frequency table.
108. Display the “Miles Driven”
data in a stem-and-leaf plot.
109. Display the “Miles Driven”
data in a histogram.
110. Display the data about the
Miles Driven per day
28
42
18
35
47
30
25
31
51
36
22
36
17
15
26
28
29
26
66
54
Ski Trip Budget
Item
Percent of Total
Lodging
40%
Equipment Rental 26%
Food
16%
Gasoline
8%
Misc.
10%
ski trip budget in a circle graph.
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Algebra 2