1. No category

Name:: ________________________ Period:________ Grp #:_______ Date: __________________
Form A
Algebra 2B Review for the Final Exam, 2015
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
c.
This is an exponential decay function.
d.
This is an exponential growth function.
x
Tell whether the function y = 2 (5) shows growth
or decay. Then graph the function.
a. This is an exponential growth function.
b.
This is an exponential growth function.
2. Use inverse operations to write the inverse of
1
f (x ) = x − 7 .
1
a. f −1 (x ) = x −
1
7
b. f −1 (x ) = x +
6
7
c. f −1 (x ) = x −
6
7
d. f −1 (x ) = x +
1
7
Form A
3. Write the exponential equation 2 3 = 8 in
logarithmic form.
a. log3 8 = 2 b. log2 8 = 3 c. log2 3 = 8
d. log8 2 = 3
9. f (x ) = 0.1 x is transformed 9 units right, compressed
1
vertically by a factor of 2 , and reflected across the
x-axis. Write the transformed function g (x ) .
Ê 1ˆ
2 (x − 9 )
a. g (x ) = −0.1
b. g (x ) = ÁÁÁ − 2 ˜˜˜ 0.1 x + 9
Ë ¯
Ê 1 ˜ˆ −x + 9
Ê 1ˆ
Á
c. g (x ) = ÁÁ 2 ˜˜ 0.1
d. g (x ) = ÁÁÁ − 2 ˜˜˜ 0.1 x − 9
Ë ¯
Ë ¯
4. Express log 2 64 − log 2 4 as a single logarithm.
Simplify, if possible.
a. log2 4 b. 8 c. 4 d. log 2 60
10 − x 2 − 3x
. Identify any x-values for
x 2 + 2x − 8
which the expression is undefined.
−x − 5
a.
x+4
The expression is undefined at x = −4.
−x − 5
b.
x+4
The expression is undefined at x = 2 and
x = −4.
x+5
c.
x+4
The expression is undefined at x = 2 and
x = −4.
x+5
d.
x+4
The expression is undefined at x = −4.
10. Simplify
5. Express log 3 27 −3 as a product. Simplify, if
possible.
1
a. –9 b. 3 c. 27 d. 9
6. Simplify log 7 x 3 − log 7 x .
a. log 7 (x 3 − x) b. 2log 7 x c. log 7 2x
d. 2(x 3 − x)
7. Solve 25 x − 2 = 125 x .
a. x = –4 b. x = 4 c. x = 5 d. x = –5
5x 3
25
÷
. Assume that all expressions
3x 2 y 3y 9
are defined.
xy 8
125x
x
5
a.
b.
c.
d.
10
8
5
9y
5y
xy 8
11. Divide
8. Nadav invests $6,000 in an account that earns 5%
interest compounded continuously. What is the
total amount of her investment after 8 years?
Round your answer to the nearest cent.
a. $8950.95 b. $327,588.90 c. $9850.95
d. $14,950.95
2
Form A
−6x 2 + x − 3 −2x − 4
− 2
. Identify any x-values for which the expression is undefined.
x +9
x2 + 9
−6x 2 − x − 7
−6x 2 − x − 7
a.
;
The
expression
is
always
defined.
b.
; The expression is undefined at x = ±3.
x2 + 9
x2 + 9
−6x 2 + 3x + 1
−6x 2 + 3x + 1
c.
;
The
expression
is
undefined
at
x
=
±3.
d.
; The expression is always defined.
x2 + 9
x2 + 9
12. Subtract
13. Identify the asymptotes, domain, and range of the
1
function g(x) =
+ 3.
x+7
a. Vertical asymptote: x = −7
Domain: {x |x ≠ −7 }
Horizontal asymptote: y = −3
Range: {y || y ≠ −3 }
b. Vertical asymptote: x = 7
Domain: {x |x ≠ 7 }
Horizontal asymptote: y = 3
Range: {y || y ≠ 3 }
c. Vertical asymptote: x = 7
Domain: {x |x ≠ 7 }
Horizontal asymptote: y = −3
Range: {y || y ≠ −3 }
d. Vertical asymptote: x = −7
Domain: {x |x ≠ −7 }
Horizontal asymptote: y = 3
Range: {y || y ≠ 3 }
14. Identify the zeros and asymptotes of
2x 2 − 18
f(x) = 2
.
x − 16
a. Zeros: −4 and 4
Vertical asymptotes: x = −3, x = 3
Horizontal asymptote: y = 2
b.
Zeros: −3 and 3
Vertical asymptotes: x = −4, x = 4
Horizontal asymptote: y = 1
c.
Zeros: −3 and 3
Vertical asymptotes: x = −4, x = 4
Horizontal asymptote: y = 2
d.
Zeros: −4 and 4
Vertical asymptotes: x = −3, x = 3
Horizontal asymptote: y = 1
a.
x 2 + 9x + 18
.
x+6
There is a hole in the graph at x = −6.
b.
There is a hole in the graph at x = 6.
c.
There are no holes in the graph.
d.
There is a hole in the graph at x = −3.
15. Identify holes in the graph of f (x ) =
3
Form A
21. Find the probability of rolling a 1 or an odd number
on a number cube. Express your answer as a
fraction in simplest form.
2
1
1
a. 1 b. 3 c. 6 d. 2
18
.
x
a. x = 6 b. x = 3 or x = 6 c. x = −3 or x = −6
d. x = 3
16. Solve the equation x − 9 = −
x
≥ −1 algebraically.
x−6
a. x ≤ 3 or x ≥ 6 b. x ≤ 3 or x > 6 c. 3 ≤ x ≤ 6
d. 3 ≤ x < 6
22. In a survey about a change in public policy, 100
people were asked if they favor the change, oppose
the change, or have no opinion about the change.
Of the 100 people surveyed, 40 are male and 35
oppose the change in policy. Of the 35 who oppose
the change, 15 are female. What is the probability
that a randomly selected respondent to the survey is
a female or opposes the change in policy? Express
your answer as a percent.
a. 80% b. 75% c. 50% d. 100%
17. Solve
18. 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.)
a. 792 ways b. 95,040 ways c. 60 ways
d. 17 ways
23. A group of 4 students went to drink pearl tea and
study at a local tea shop. The shop offers 12
different flavors of pearl tea. What is the
probability that at least 2 students ordered the same
flavor? Express your answer as a decimal, and
round to the nearest ten thousandths.
a. 0.4271 b. 0.3333 c. 0.5729 d. 0.1667
19. A person is selected at random. What is the
probability that the person was not born on a
Monday? Express your answer as a percent. If
necessary, round your answer to the nearest tenth
of a percent.
a. 20.0% b. 80.0% c. 14.3% d. 85.7%
24. The data {0, 2, 3, 7, 7} represent a random sample
of the number of days absent from school for five
students at Monta Vista High. Find the mean and
the standard deviation of the data.
a. The mean is 3.8, and the standard deviation is
about 2.79. b. The mean is 19, and the standard
deviation is about 8.16. c. The mean is 4.2, and
the standard deviation is about 2.86. d. The mean
is 3.8, and the standard deviation is about 7.76.
20. A bag contains hair ribbons for a spirit rally. The
bag contains 8 black ribbons and 7 green ribbons.
Lila selects a ribbon at random, then Jessica selects
a ribbon at random from the remaining ribbons.
What is the probability that Lila selects a black
ribbon and Jessica selects a green ribbon? Express
your answer as a fraction in simplest form.
8
7
56
4
a. 35 b. 30 c. 225 d. 15
4
Form A
25. Use the Binomial Theorem to expand the binomial (4x − 4y) 4 .
a. 256x 4 + 1024x 3 y + 1536x 2 y 2 + 1024xy 3 + 256y 4 b. 256x 4 + 256y 4
c. 256x 4 − 1024x 3 y + 1536x 2 y 2 − 1024xy 3 + 256y 4 d. 256x 4 − 256y 4
26. Students randomly receive 1 of 4 versions (A, B, C,
D) of a math test. What is the probability that at
least 3 of the 5 students tested will get version A of
the test? Express your answer as a percent, and
round to the nearest tenth.
a. 10.4% b. 8.8% c. 1.6% d. 74.7%
30. Write the arithmetic series
5 + 1 − 3 − 7 − 11 − 15 − 19 in summation notation.
7
a.
∑ (5 − 4k )
k=1
7
b.
∑ ÊÁË 9 − 4(k − 1) ˆ˜¯
k=1
7
c.
∑ ÁÊË 5 − 4(k + 1) ˜ˆ¯
k=1
27. Find the first 5 terms of the sequence with a 1 = 6
and a n = 2a n − 1 − 1 for n ≥ 2.
a. 1, 2, 3, 4, 5 b. 6, 11, 21, 41, 81 c. 6, 12, 24,
48, 96 d. 6, 7, 8, 9, 10
7
d.
∑ (9 − 4k )
k=1
31. Find the 7th term of the geometric sequence with
a 3 = 16 and a 5 = 64.
a. 384 b. 112 c. 512 d. 256
6
28. Expand the series
∑ (−1) (7 − k)k and evaluate.
k
32. Determine if the geometric series 14 + 21 +
k=2
189
4
a. 0 b. 56 c. 50 d. 6
+ ... converges or diverges.
a. diverges b. converges
29. Find the 5th term of the arithmetic sequence with
a 7 = 25 and a 13 = 55.
a. 5 b. 20 c. 15 d. –5
5
63
2
+
Form A
33. Use a trigonometric function to find the value of x.
a. x = 50
= 45
3 b. x = 25
1
38. Find all possible values of sin −1 .
2
π
2π
a.
+ (2π )n,
+ (2π )n b. 0.0151
3
3
π
5π
π
c.
+ (2π )n,
+ (2π )n d.
+ (2π )n,
6
6
4
3π
+ (2π )n
4
2 c. x = 50 2 d. x
3
39. A triangle has a side with length 4 feet and another
side with length 10 feet. The angle between the
sides measures 61º. Find the area of the triangle.
Round your answer to the nearest tenth.
a. 35.0 ft 2 b. 17.5 ft 2 c. 1220.0 ft 2 d. 9.7 ft 2
34. A surveyor whose eye level is 5 feet above the
ground determines the angle of elevation to the top
of an office building to be 41.7°. If the surveyor is
standing 40 feet from the base of the building, what
is the height of the building to the nearest foot?
a. 41 ft b. 50 ft c. 32 ft d. 36 ft
40. Adolfo surveyed a triangular region of land and
sent the measurements: a = 130 meters, b = 150
meters, m∠A = 49º to the engineer at the office.
The engineer called back asking for more
information. Determine how many, if any, triangles
can be formed using Adolfo’s measurements. If
possible, find the unknown measurements.
a. Two triangles are possible.
c1 = 162.3 m; c2 = 34.6 m;
m∠B 1 = 60.6° ; m∠B 2 = 119.4°
m∠C 1 = 70.4° ; m∠C 2 = 11.6°
b. One triangle is possible.
c = 132.5 m; m∠B = 80.7° ; m∠C = 50.3°
c. Two triangles are possible.
c1 = 127.5 m; c2 = 86.9 m;
m∠B 1 = 80.7° ; m∠B 2 = 99.3°
m∠C 1 = 50.3° ; m∠C 2 = 31.7°
d. No triangles are possible.
35. Find the measures of a positive angle and a
negative angle that are coterminal with −296°.
a. −116° and −476° b. −206° and −386°
c. 656° and 296° d. 64° and −656°
36. Find the measure of the reference angle for
θ = −137°.
a. 133° b. 223° c. 43° d. –43°
5π
from radians to degrees.
6
a. 300º b. 150º c. 126º d. 225º
37. Convert
41. Using f(x) = sin x as a guide, graph g(x) = 2sin 3x .
Identify the amplitude and period.
6
Form A
2
a.
amplitude = 2; period = 3 π
b.
amplitude = 4; period = 3π
d.
amplitude = 4; period = 3π
42. Using f(x) = cos x as a guide, graph
g(x) = cos(x −
π
4
) . Identify the x-intercepts and
phase shift.
a.
c.
2
amplitude = 2; period = 3 π
x-intercepts: x =
phase shift:
7
π
4
π
4
+ nx where n is an integer;
units to the left
Form A
d.
b.
x-intercepts: x =
phase shift:
π
4
π
4
+ nx where n is an integer;
x-intercepts: x =
units down
phase shift:
π
4
π
4
+ nx where n is an integer;
units up
c.
43. Find the period for f(x) = −3sin 5x .
2π
2π
a. 10π b.
c.
d. 6π
3
5
x-intercepts: x =
phase shift:
π
4
π
4
44. A initial investment of $10,000 grows at 11% per
year. What function represents the value of the
investment after t years?
a. f(t) = 10000(0.11) t b. f(t) = 10000(12) t
+ n π where n is an integer;
c. f(t) = 10000(1.11)t d. f(t) = 10000(1.11) t
units to the right
8
Form A
45. Find the inverse of f(x) = 5x − 1 .
a.
(x − 1)
f −1 (x) =
5
b.
(x + 1)
f −1 (x) =
5
c.
f −1 (x) = 5x + 1
d.
x
f −1 (x) = + 1
5
46. Simplify lne 7x .
a. e 7x b. 7x c. 7 d. e 7
1
47. Find the period of f(x) = tan 6 x .
a. 6π b.
1
3
π c. 12π d.
1
6
π
9
ID: A
Algebra 2B Review for the Final Exam, 2015
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
B
D
B
C
A
B
A
A
D
B
A
D
D
C
A
B
B
A
D
D
D
A
A
A
C
A
B
D
C
D
D
A
B
A
D
C
B
A
B
1
ID: A
40.
41.
42.
43.
44.
45.
46.
47.
A
A
C
C
D
B
B
A
2