1. Use inverse operations to write the
inverse of .
2. Use inverse operations to write the
inverse of .
3. Write the exponential equation in logarithmic form. 4. Write the logarithmic equation
in exponential form. 5. Write the logarithmic equation
in exponential form.
6. Evaluate by using mental math.
7. Evaluate 0.0001 by using mental math.
8. Express as a single logarithm. Simplify, if possible.
9. Express as a
single logarithm. Simplify, if possible.
10. Express as a single logarithm. Simplify, if possible.
11. Express as a product. Simplify, if possible.
12. Express as a product. Simplify, if possible.
13. Simplify the expression . 14. Simplify the expression .
15. Simplify .
16. Solve .
17. Solve .
18. Solve .
19. Simplify .
20. Simplify .
21. Distance varies directly as time because as time increases, the distance traveled increases
proportionally. The speed of sound in air is about 335 feet per
second. How long would it take for sound to travel 11,725 feet?
22. The volume V of a cylinder varies jointly with the height h and the radius squared r2, and
cm3 when cm and
cm2. Find V when cm and cm2. Round your answer to the nearest hundredth.
23. The number of lawns l that a volunteer can mow in a day varies inversely with the number of shrubs s that need to be pruned that day. If the volunteer can prune 6 shrubs and mow 8 lawns in one day, then how many lawns can be mowed if there are only 3 shrubs to be pruned?
24. Multiply .
Assume that all expressions are defined.
25. Divide . Assume that all expressions are defined.
1 7
5 8
1 1 6
Algebra 2
26. The area of a rectangle is equal to square units. If the length of the rectangle is equal to
units, what expression represents its width?
27. Simplify the expression . Assume that all variables are
positive.
28. Simplify the expression . Assume that all variables are positive.
29. Write the expression in radical form, and simplify. Round to the nearest whole number if necessary.
30. Write the expression by using rational exponents.
31. Simplify the expression
.
32. Simplify the expression
.
33. Evaluate the piecewise function
for
and .
34. Graph the piecewise function .
35. Given and
, find .
36. Given and
, find .
37. Given and ,
find .
38. Given and
, write the composite function and state its domain.
39. Given and
, write the composite function and state its domain.
40. Find the center and radius of a circle that has a diameter with
endpoints and .
41. Graph the equation .
42. Write the equation of a circle with center and radius . 43. Write the equation of a circle with
center and radius . 44. Write the equation of the circle
with center and containing the point .
45. Write the equation of the circle with center and
containing the point . 46. Write the equation of the line that
is tangent to the circle
at the point . 47. Write an equation in standard
48. Graph the ellipse
.
49. Graph the ellipse
.
50. Find the constant difference for a hyperbola with foci and
and the point on the hyperbola .
51. Find the constant difference for a hyperbola with foci and
and the point on the hyperbola .
52. Write an equation in standard form for the hyperbola with center , vertex , and focus . 53. Find the vertices and asymptotes of
the hyperbola , and then graph.
54. Find the vertices, co-vertices, and asymptotes of the hyperbola
, and then graph.
55. Use the Distance Formula to find the equation of a parabola with focus
and directrix .
56. Write the equation in standard form for the parabola with vertex
and the directrix . 57. Write the equation in standard
form for the parabola with vertex and the directrix . 58. Find the vertex, value of p, axis of
symmetry, focus, and directrix of
the parabola .
Then, graph the parabola. 59. Identify the conic section the
equation represents.
60. Identify the conic section the equation
represents.
61. Identify the conic section that the equation
represents.
62. Find the standard form of the equation
by completing the square. Then, identify and graph the conic section.
63. Find the standard form of the equation
by completing the square. Then, identify and graph the conic section.
1 2 3 4 5 6 7 8 9
–1 x
5
64. Find the standard form of the equation
by completing the square. Then,
identify and graph the conic section. 65. Louise wears an outfit everyday that consists of one top (shirt, T-shirt, or blouse), one bottom (pants or skirt) and one scarf. Her wardrobe consists of a tan skirt, a pair of black pants, 2 T-shirts, one silk blouse, 1 button-down shirt, and a set of 3 scarves. How many different outfits can Louise put together?
66. There are 7 singers competing at a talent show. In how many different ways can the singers appear? 67. Joel owns 12 shirts and is selecting
the ones he will wear to school next week. How many different ways can Joel choose a group of 5 shirts? (Note that he will not wear the same shirt more than once during the week.)
68. An experiment consists of rolling a number cube. What is the probability of rolling a number greater than 4? Express your answer as a fraction in simplest form.
69. An experiment consists of spinning a spinner. The table shows the results. Find the experimental probability that the spinner does not land on red. Express your answer as a fraction in simplest form.
Outcome Frequency
red 10
purple 11
yellow 13
70. A grab bag contains 3 football cards and 7 basketball cards. An experiment consists of taking one card out of the bag, replacing it, and then selecting another card. What is the probability of selecting a football card and then a
basketball card? Express your answer as a decimal.
71. A grab bag contains 7 football cards and 3 basketball cards. An experiment consists of taking one card out of the bag, replacing it, and then selecting another card. What is the probability of selecting a football card and then a
basketball card? Express your answer as a decimal.
72. Find the first 5 terms of the sequence with and
for . 73. Find the first 5 terms of the
sequence with and for . 74. Find the first 5 terms of the
sequence .
75. Find the first 5 terms of the
sequence .
76. Write a possible explicit rule for
nth term of the sequence 23.1,
20.2, 17.3, 14.4, 11.5, 8.6, ... 77. Write a possible explicit rule for
nth term of the sequence 23.1,
20.2, 17.3, 14.4, 11.5, 8.6, ... 78. Write the series
in summation notation.
79. Write the series
80. Expand the series and evaluate.
81. Evaluate the series .
82. Evaluate the series .
83. Find the missing terms in the
arithmetic sequence 18, ____, ____, ____, 42.
84. Find the missing terms in the
arithmetic sequence 16, ____, ____, ____, 52.
85. Find the missing terms in the
arithmetic sequence 18, ____, ____, ____, –14.
86. Find the 5th term of the arithmetic sequence with and
.
87. Find the sum for the arithmetic
series .
88. Find the sum for the arithmetic
series .
89. Determine whether the sequence 12, 40, 68, 96 could be geometric or arithmetic. If possible, find the common ratio or difference.
90. Find the 7th term of the geometric sequence –4, 12, –36, 108, –324, ... 91. Find the 7th term of the geometric
sequence with and .
92. Find the sum of the geometric series:
3 6 12 ... 384
93. Find the sum of the geometric series with a1 2
,
32
r
, and
n
5
94. Write an equation of the line that is tangent to the circle 2 2
100 x y at the point
6,8
.95. Write an equation of the line that is tangent to the circle 2 2
169 x y at the point
5,12
.96. Find the sum for the infinite geometric series: 12 4 4 4 ...
3 9
97. A piece of machinery costs $50,000. The value of the
machine depreciates 9% per year. What is the machine worth after 1 year? After 2 years? After 5 years? In how many years will the machine be worth $10,000? 98. A ball thrown into the air from a
roof 15 feet above the ground with an initial vertical velocity of 30 ft/sec can be modeled by the
equation: 2
( ) 16 30 15 h t t t . How long will the ball be in the air? What is it’s maximum height?
99. A circle is inscribed in a square with a side measuring 24 inches. If you randomly throw darts at the board, what is the probability of hitting the board but missing the circle?
100. Solve for x:
log
2(𝑥 + 2) +log
2(𝑥) = 3101. Solve for x:
log
(𝑥
2+ 5𝑥 + 6) −log
(𝑥 + 3) = 2102. Solve for x:
Algebra 2 Final Exam Answer Section
SHORT ANSWER
1.
2.
3.
4.
5. 6. –2 7. –4 8. 3 9. 3 10. 4 11. –9 12. –4 13. 3 14. 4 15.
16. x = 12 17. x = 4
18.
19. –5x 20. –6x 21. 35 sec
22. cm3
23. 16 lawns
24.
25.
26.
27.
28.
29. ; 32
30. 31. 27 32. 16
33. ;
34.
35. =
36. =
37. 1
7
5 8
2 4 6 8 10 –2
–4 –6 –8
–10 x
2 4 6 8 10
–2
–4
–6
–8
38. , ,
39. , ,
40. center ; radius 5 41.
42.
43.
44.
45.
46. y = x
47.
48.
49.
50. 2 51. 8
52.
53.
Vertices: and
Asymptotes: and
2 4 6 8 10 –2
–4 –6 –8
–10 x
2 4 6 8 10
–2
–4
–6
–8
–10 y
34 254
(6, –5) 6 12 18 –6
–12
–18 x
6 12 18
–6
–12
–18 y
(1, –4)6 12 18 –6
–12
–18 x
6 12 18
–6
–12
54. Same as #53
55.
56.
57.
58. Vertex , focus , ,
axis of symmetry , and directrix .
59. ellipse 60. ellipse 61. hyperbola 62. ellipse
63. Same as #62
64. ellipse
65. 24 outfits
66. 66. 5,040 ways
67. 792 ways
68.
69.
70. 0.21 71. 0.21
72. 6, 11, 21, 41, 81
73. 7, 23, 87, 343, 1367
74. –3, –1, 3, 11, 27 75. –4, 2, 20, 74, 236 2 4 6 8 10
–2 –4 –6 –8
–10 x
2 4 6 8 10
–2
–4 –6 –8 –10
y
1 2 3 4 5 –1
–2 –3 –4
–5 x
1 2 3 4 5
–1
–2
–3
–4
–5 y
1 2 3 4 5 –1
–2 –3 –4
–5 x
1 2 3 4 5
–1
–2
–3
–4
–5 y
76. 77.
78.
79.
80. 6
81. 253
82. 276
83. 24, 30, 36
84. 25, 34, 43
85. 10, 2, –6 86. 15
87. 1313
88. 630
89. It could be arithmetic with d = 28.
90. –2,916
91. 256
92. 765
93. 211 263 26.375 8 8
94. 8 3
6
4y x x
95. 12 5
5
12y x x
96. 18
97. $45,500; $41,405; $31,201.61; 17.1years
98. 2.3 seconds in the air; max height of 29.1 ft
99.
4 .2146 21.5% 4
100. x = 2
101. x = 98
