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Algebra 2B Review Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
2x 2 − 10
=
x 2 − 25
2
a.
5
8
b.
25
ÊÁ
ÁÁ −2y 3m
2. Simplify ÁÁÁ 2m 3
ÁÁ y w
Ë
4m
16y
a.
w 12
−8y 7m
b.
y 2m w 3
1.
3.
(5a 3 ) 2
8c 4 d 3
⋅
(4cd) 2
−45a 3 b 7
10a 3
a.
9b 7 c 2 d 3
2a 3
b. − 7 2 3
9b c d
y − 2 4y − 3
−
=
4.
6y
4y 2
a.
b.
−3y + 1
24y 2
y 2 − 8y + 9
6y 2
c.
d.
2x
x+5
2x
x−5
ˆ˜ 4
˜˜
˜˜ .
˜˜
˜
¯
c.
d.
16y 10m
w3
−8y 10m
w 12
=
c.
d.
c.
d.
10a 3
9b 7 c 2 d 3
10a 6
− 7 2 3
9b c d
−
2y 2 − 16y − 9
12y 2
2y 2 − 16y + 9
12y 2
1
5. Which rational function best represents the graph below?
x+1
x−1
c. f(x) =
x−2
x−2
x+1
x−1
b. f(x) =
d. f(x) =
x+2
x+2
6. What are the equations of the vertical and horizontal asymptotes for?
a.
f(x) =
f(x) =
3
(x + 2)(x − 3)
a. x = 2, y = 0, x = –2
c. x = –2, y = 0, x = 3
b. x = 2, y = 0, x = –3
d. x = –2, y = 0, x = –3
7. Which of the following is the best solution for the equation?
y+3
8
= 2−
y+1
y − 2y − 3
2
a.
no solution
7
b. y = , y = –2
2
8. What is the solution to the inequality?
c.
y = 5, y = –1
d.
y=5
x<–
x
3x − 2
+
>4
x+1
x
2
3
2
x>–
3
a.
x>2
c.
b.
x<2
d.
8
=
x+4
x 2 + 3x − 4
x+4
2
x − 3x − 4
x−4
c.
x 2 + 3x + 4
x+4
d.
x+3
9. x – 1 +
a.
b.
2
10. Pilar is graphing a parabola with a vertex of (–3, 2) and x-intercepts of –4 and –2. Which of the following might be
the equation of the parabola she is graphing?
c. y = –3(x + 3)2 – 3
a. y = –2(x – 3)2 + 2
2
b. y = –2(x + 3) + 2
d. y = –(2x + 3)2 – 2
11. What is the equation of the circle graphed below?
a. (x – 1)2 + (y + 1)2 = 2
c. (x + 1)2 + (y – 1)2 = 2
2
2
b. (x – 1) + (y + 1) = 1
d. (x + 1)2 + (y – 1)2 = 1
12. Which of the following is the graph of y = –3x2 + 12x – 9?
a.
c.
b.
d.
13. What are the foci of 4(x + 1)2 + 8(y – 3)2 = 32?
a. (–1, 0) and (3, 0)
c. (–1, 5) and (–1, 1)
b. (0, –1) and (0, 3)
d. (1, 3) and (–3, 3)
2
2
14.
–3x + 2y – 12x + 8y + 2 = 0
What is the standard form of the equation of the conic given above?
(x + 2) 2 (y + 2) 2
(y + 2) 2 (x + 2) 2
−
=1
−
=1
a.
c.
2
3
2
3
b.
(x − 2) 2 (y + 2) 2
−
=1
2
3
d.
(y + 2) 2 (x + 2) 2
−
=1
3
2
3
15. Which of the following is the graph of
a.
b.
(x − 2) 2 (y + 1) 2
+
= 1?
25
9
c.
d.
16. What is the common difference of the series below?
8 + 15 + 22 + 29 + 36 + …
a. 1.875
c. 8
b. 7
d. 14
17. What is the nth term in the arithmetic series below?
5 + 11 + 17 + 23 + 29 + …
a. 5 + 6n
c. 6n + 1
b. 6n – 1
d. 5(n + 1) + 6
18. What is the sum of the first 23 terms of the arithmetic series 1 + 9 + 17 + 25 + 33 + …?
a. 451
c. 2027
b. 475
d. 2047
19. What is the 71st term of the arithmetic sequence whose first term is 7 and whose common difference is 11?
a. 788
c. 766
b. 777
d. none of the above
20. Which of the following series is neither arithmetic nor geometric?
a. 1 + 3 + 6 + 10 + 15 + …
b. 1 + 1 + 1 + 1 + 1 + …
c. 1 – 3 – 7 – 11 – 15 – …
20 10 5 5
5
d.
+
+ +
+
+…
7
7
7 14 28
4
21. What is the kth term of the following geometric series?
5
5
+ + 5 + 40 + 320 + …
64 8
ÁÊ 5 ˜ˆ (k − 2)
ÁÊ 5 ˜ˆ˜ k
˜˜ 8
a. ÁÁÁÁ ˜˜˜˜ 8
c. ÁÁÁÁ
˜
Ë 64 ¯
Ë 512 ¯
ÊÁ 5 ˆ˜ (k − 3)
(k − 3)
b. (40)8
d. ÁÁÁÁ ˜˜˜˜ 8
Ë 64 ¯
22. What is the common ratio of the following series?
1 + 9 + 81 + 729 + …
1
c. 3
9
1
b.
d. 9
3
What is the 8th term of the geometric sequence whose first term is 5 and whose common ratio is 2?
a. 5(27)
c. 2(58)
8
b. 5(2 )
d. 2(57)
What is the sum of the first 14 terms of 6 + 18 + 54 + 162 + 486 + …?
a. 86,093,436
c. 28 697,808
b. 43,046,718
d. 14,348,904
What is the sum of the first 50 terms of the geometric sequence 12 + 3 + 0.75 + 0.1875 + …?
ÈÍ
˘
ÍÍ
ÊÁ 1 ˆ˜ 50 ˙˙˙˙
Í
Á
˜
a. 12[1 – (0.25)50]
c. 16 ÍÍÍ 1 − ÁÁÁ ˜˜˜ ˙˙˙
ÍÍ
Ë 4 ¯ ˙˙˙˚
ÍÎ
ÈÍ
˘
ÍÍ
ÊÁ 1 ˆ˜ 51 ˙˙˙˙
ÍÍ
b. 12 ÍÍ 1 − ÁÁÁÁ ˜˜˜˜ ˙˙˙
d. 12[1 – (0.25)49]
ÍÍ
˙
4
˙
Ë ¯ ˙˚
ÍÎ
11 11 11
11
What is the sum of the infinite geometric series
+
+
+
+ …?
8
72 648 5832
64
11
a.
c.
99
9
8
99
b.
d.
11
64
An ice cream shop serves vanilla, strawberry, or chocolate ice cream. The ice cream can be served in a cup, sugar
cone, or waffle cone. How many different combinations of flavor and serving method are possible?
a. 6
c. 12
b. 9
d. 27
Abigail rolled a pair of six-sided number cubes numbered 1–6 on each side. What is the probability that the sum of
the digits will be 7?
1
1
a.
c.
3
6
1
1
b.
d.
4
12
a.
23.
24.
25.
26.
27.
28.
5
29. Justine’s local flower shop sells small bouquets of roses, violets, lilies, tulips, daisies, carnations, and
chrysanthemums. How many different large bouquets can she make using 3 different small bouquets from the
flower shop?
a. 35
c. 32
b. 33
d. 30
30. Linda has 5 children. How many different ways can she seat her children on the back seat of her minivan? The
seat has 3 seat belts.
a. 5
c. 20
b. 15
d. 60
31. A bag contains 5 small yellow marbles, 8 large yellow marbles, 2 small green marbles, and 13 large green marbles.
What is the probability of selecting a small marble from the bag?
1
%
c. 25%
a.
4
b. 7%
d. 28%
32. A total of 5 freshmen, 13 sophomores, and 9 seniors entered the school raffle. What is the probability that either a
freshman or senior will win the raffle?
1
1
c.
a.
7
4
4
14
b.
d.
27
27
33. Yumiko recorded the number of hours she watched television each day for a week in the chart below.
What is the variance of her data?
20
c. 3
7
20
d. 20
b.
7
Which expression represents f(g(x)) if f(x) = x2 + x – 1 and g(x) = x + 3?
a. x2 + x + 2
c. x2 + 7x + 11
2
b. x + 2x + 2
d. x3 + 4x2 + 2x – 3
Which expression represents g(f(x)) if f(x) = 5x3 – 2x and g(x) = 3x3?
a. 3(5x3 – 2x)3
c. 8x3 – 2x
3
3
3
b. 5(3x ) – 2(3x )
d. 15x6 – 6x4
If f(x) = 4x2 – x and g(x) = 3x2, which is an equivalent form of g(x) – f(x)?
a. –x2 – x
c. x2 – x
2
b. –x + x
d. x2 + x
Which function is the inverse of f(x) = 3x – 1?
x−1
a. f 1(x) = 3x + 1
c. f 1(x) =
3
x−1
b. f 1(x) = –3x – 1
d. f 1(x) =
3
a.
34.
35.
36.
37.
6
38. Which function is the inverse of f(x) = 7x – 10?
1
a. f 1(x) = x + 10
c.
7
1
10
b. f 1(x) = x +
d.
7
7
39. Mrs. Jacobs wrote the equation
f 1(x) = –7x – 10
f 1(x) = –7x + 10
x 2 − 10x + 25
= 1 on the board. Which of the following statements is correct
x−5
about the equation she wrote?
a. The equation is true only when x = 6.
b. The equation is always true.
c. The equation is never true.
d. The equation is always true, except when x = 5.
t
ÊÁ 1 ˆ˜ 300
, where A = the number of
40. A certain radioactive element decays over time according to the equation y = A ÁÁÁÁ ˜˜˜˜
Ë 2¯
grams present initially and t = time in years. If 100 grams were initially present, how many grams will remain after
600 years?
a. 0.8 gram
c. 50 grams
b. 25 grams
d. 5000 grams
41. Which function represents exponential growth?
x
ÁÊ 3 ˆ˜
1
a. f(x) = (4) x
c. f(x) = 3 ÁÁÁÁ ˜˜˜˜
2
Ë 4¯
b.
f(x) = 25(0.25)x
d.
ÊÁ 1 ˆ˜ x
f(x) = −2 ÁÁÁÁ ˜˜˜˜
Ë 2¯
3
2
42. What is the value of 16 ?
a. 10
c. 24
b. 12
d. 64
43. The student enrollment, S, of a university was 1475 students in 1999. The enrollment has increased by exactly
10% per year. Which of the following equations expresses the university’s student enrollment in terms of t, where
t is the number of years since 1999?
a. S = 1475(0.1)t
c. S = 0.1(1475)t
t
b. S = 1475(1.1)
d. S = 1.1(1475)t
7
44. Given: y varies inversely as x, and y = 4 when x = –4. Write and graph the inverse variation function.
4
a. y = −x
c. y = x
b.
1
y = −x
d.
y=−
10 − x 2 − 3x
. Identify any x-values for which the expression is undefined.
x 2 + 2x − 8
−x − 5
x+4
The expression is undefined at x = −4.
−x − 5
x+4
The expression is undefined at x = 2 and x = −4.
x+5
x+4
The expression is undefined at x = 2 and x = −4.
x+5
x+4
The expression is undefined at x = −4.
45. Simplify
a.
b.
c.
d.
16
x
8
46. Using the graph of f (x) =
1
x
as a guide, describe the transformation and graph g (x) =
a.
Translate f (x) right 3 units.
c.
Translate f (x) down 3 units.
b.
Translate f (x) up 3 units.
d.
Translate f (x) left 3 units.
1
+ 3.
x+7
Vertical asymptote: x = 7
Domain: {x |x ≠ 7 }
Horizontal asymptote: y = −3
Range: {y | y ≠ −3 }
Vertical asymptote: x = −7
Domain: {x |x ≠ −7 }
Horizontal asymptote: y = 3
Range: {y | y ≠ 3 }
47. Identify the asymptotes, domain, and range of the function g(x) =
a.
b.
Vertical asymptote: x = −7
Domain: {x |x ≠ −7 }
Horizontal asymptote: y = −3
Range: {y | y ≠ −3 }
Vertical asymptote: x = 7
Domain: {x |x ≠ 7 }
Horizontal asymptote: y = 3
Range: {y | y ≠ 3 }
c.
d.
9
1
x
+ 3.
a.
x 2 + 8x + 12
. Then graph.
x+2
There is a hole in the graph at x = −6.
c. There are no holes in the graph.
b.
There is a hole in the graph at x = −2.
48. Identify holes in the graph of f (x) =
d.
There is a hole in the graph at x = 2.
10
49. Graph the function f(x) = 4 3 x + 5 , and identify its domain and range.
c.
a.
The domain is the set of all real numbers.
The range is also the set of real numbers.
b.
The domain is the set of all real numbers.
The range is also the set of real numbers.
d.
The domain is the set of all real numbers.
The range is also the set of real numbers.
The domain is the set of all real numbers.
The range is also the set of real numbers.
11
50. Using the graph of f (x) =
a.
b.
x as a guide, describe the transformation and graph g (x) = 4 x − 3 .
Stretch f vertically by a factor of 4 and
translate it left 3 units.
c.
Stretch f vertically by a factor of 4 and
translate it right 3 units.
d.
Compress f horizontally by a factor of
1
4
and translate it up 3 units.
Compress f horizontally by a factor of
and translate it down 3 units.
12
1
4
51. Graph the inequality y ≤
a.
x−5
b.
c.
d.
52. Which equation can be used to find x?
a.
sin 32° =
x
7
c.
tan 32° =
x
7
b.
cot 32° =
7
x
d.
cos 32° =
x
7
13
53. Find A to the nearest degree.
a.
55°
c.
35°
b.
30°
d.
60°
54. Rewrite
5π
radians in degree measure.
4
a.
450°
c.
225π °
b.
225°
d.
112.5°
55. Which angle is coterminal with a –400° angle in standard position?
a.
40°
c.
320°
b.
80°
d.
400°
56. Find the exact value of cos θ if the terminal side of θ in standard position contains the point (6, –8).
4
5
a.
–
b.
3
5
c.
4
5
d.
–
3
5
57. Which equation is graphed?
a.
2
y = 3 sin θ
3
c.
3
y = 2 sin θ
2
b.
2
y = 3 cos θ
3
d.
3
y = 2 cos θ
2
14
58. Find the amplitude of y = 6 cos 4θ.
a.
3
2
c.
b.
6
d.
4
π
2
59. Find the period of y = tan 5θ.
a.
10π
c.
b.
2π
5
d.
5π
π
5
60. Which equation is graphed?
π
a.
y = sin (θ – )
4
b.
y = cos (θ –
π
4
)
61. Find the phase shift of y = sin (θ –
a.
3π
4
b.
–
3π
4
c.
y = sin (θ +
d.
y = cos (θ +
c.
4π
3
d.
–
3π
).
4
4π
3
15
π
4
π
4
)
)
ID: A
Algebra 2B Review Final Exam
Answer Section
MULTIPLE CHOICE
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