Download Second Semester MC Review

Name ________________________________________ Date ___________________ Class __________________
Chapter
x
4
Exponential and Logarithmic Functions
Chapter Test Form B
Select the best answer.
7. Which of the following is the inverse of
f(x) 2(3x)?
1. Which of the following functions is an
example of exponential decay?
A a(x) 0.5(1.2)x C c(x) 0.5(x)0.9
B b(x) 2.4(0.86)x D d(x) log0.5 x
A f 1(x)
2. Which expression shows the value of a
rare postage stamp, originally purchased
for $5000, that has been increasing in
value by 11% for 10 years?
F 5000(0.11)10
6. Which is the inverse of f x
G b x
H c(x)
J d x
x
2
x
log3 x
2
log6 x
6
6
729
J log3 6
729
H log 3
6
3
729?
2x
3
A
1
2
C 0.0625
B
1
8
D 8
2log4 3 as a single
F log4 3
H log4 12
G log4 6
J log4 18
11. Which of the following is the largest?
A log0.5 840
C log3 2712
B log2 328
D log4 260
12. Simplify log 1036
2(10log 12).
F 108
H 1.5
G 0.25
J 12
13. Simplify log5 4
A
2?
log5 250.
3
log 5
C
B log5 254
4x
14. Solve 4
1
log5 1000
log 5
D log25 1000
2x
32
1
.
7
12
5
G x
4
3
H x
2
J There is no solution.
3
2
1
10. Express log4 27
logarithm.
2
x2 1
2
(2x 3)2
C f
9. Evaluate log0.25 2.
5. Which of the statement is ALWAYS true?
A The inverse of a linear function is a
function.
B The inverse of a quadratic function is
a function.
C The inverse of a cubic function is a
function.
D The inverse of a logarithmic function
is a function.
2
log3
G log3 729
4. If g(x) is the inverse of f(x) xx, which of
the following is on g(x)?
F ( 1, 1)
H (27, 3)
G (2, 4)
J (64, 4)
F a x
x
F log3 729
D 24(.99)8
2
1
8. Which is the logarithmic form of 36
3. A balloon with a small leak loses 1% of its
volume each day. If it originally contained
24 liters of gas, what is the volume of the
gas after one week?
A 24(.01)7
C 24(.01)8
x
x
2
B f
D f 1(x)
G 5000(1.11)10
H 5000(11)10
J 5000(1.11)(10)
B 24(.99)7
2log3 x
F x
2
3
2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
69
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
x
4
Exponential and Logarithmic Functions
Chapter Test Form B continued
15. Solve 3x
A
B
1
100.
2
log 3
log 3
C
2
log 3
log 3
D
2
ln 3
ln 3
2
ln 3
ln 3
19. What could be the function shown in the
graph?
16. What is the sum of the solutions of the
equation log2(x 1) log2(4x 2) 2?
1
3
F
G
H
1
2
J
3
2
1
3
17. Simplify e2ln x
ln ex.
C 2x2
A 3x
B x2
log2(x
B b(x)
2log2(x
C c(x)
log2(x
D d(x)
2log2(x
4)
4)
3)
2
3)
2
20. If the data below is from an exponential
function, what is the value of a?
D x3
x
A a(x)
18. What could be the function shown in the
graph?
x
3
5
7
y
4
a
10
F 6
H 6.3
G 2 10
J 7
21. What is the x-intercept of the function
f(x) ln x?
A 0
B 1
C e
x
F f(x)
e
G g(x)
e2
H h(x)
2
J h(x)
22
D does not exist
2
22. The data below is from an exponential
function. What is the value of the
constant ratio?
x
x
2
x
x
2
0
2
4
6
y
1
4
1
4
16
64
F 4
1
G
2
H 2
J 4
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
70
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
x
6
Properties and Attributes of Functions
Chapter Test Form B
Select the best answer.
3. Which function could represent the data
in the table below?
1. The graph below shows how far Lisa
was from her home in miles from 1 P.M.
to 5 P.M. Based on the graph, which
statement is true?
s
10
4
0
7
t
200 80
0
140
A s(t) 20s
B s(t) 20t
C t(s) 20s
D t(s) 20t
2x
4. Evaluate f x x
2
if x 0
if 0 x 1
x 2 if x 1
at x 11.
F f(11) 1
G f(11) 3
H f(11) 6
J f(11) 9
5. A car is driven 30 mph for 2 hours,
55 mph for the next 5 hours, and
20 mph for the next hour. Which function
best represents the distance the car
traveled?
A At 2 P.M., Lisa was getting closer to
home.
30 if 0 t 2
A d t 55 if 2 t 7
20 if 7 t 8
B Between 4 and 5 P.M., Lisa was
getting closer to home.
C Lisa was at home at 1 P.M.
30t if 0 t 2
B d t 55t if 2 t 7
20t if 7 t 8
D Lisa was at home at 3 P.M.
2. Which words could be represented by the
function h(t) 100 20t?
C d t F John has $20 in his bank account. He
plans to deposit $20 each month.
30t
if 0 t 2
55t 50 if 2 t 7
if 0 t 2
if 2 t 7
20t 195 if 7 t 8
30t
G John has $20 in his bank account. He
plans to deposit $100 each month.
D d t 55t 50
H John has $100 in his bank account.
He plans to deposit $20 each month.
x 5 if x 0
, which is
3 x 5 if x 0
the rule for g(x), a horizontal translation
of f(x) 3 units left?
6. Given f (x ) J John has $100 in his bank account.
He plans to withdraw $20 each
month.
F g (x ) G g (x ) H g (x ) J g (x ) x2
if x 3
3 x 4 if x 3
x 8 if x 3
3 x 8 if x 3
x8
if x 3
3 x 14 if x 3
x8
if x 0
3 x 14 if x 0
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
109
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
x
6
Properties and Attributes of Functions
Chapter Test Form B continued
7. f(x) 12x 6 and g(x) 2f(x). What
is the y-intercept of g(x)?
A (0, 12)
C (0, 12)
1
B (0, 6)
D
,0
2
8. Compare the end behavior for the pair of
functions.
and g x log x
4x 3
4x
H
J
13. Which is the inverse of
x 7
?
6
2
G As x , f (x) and g (x) and
D y 6(x 7)2
as x , f (x) 0as x 0,g (x) 6
14. What are the domain and range of the
1
1?
inverse of y x
H As x , f (x) and g (x) and
as x , f (x) 0as x 0,g (x) J As x , f (x) and g (x) and
as x , f (x) 0 and g (x) 0
B As x , f (x) and g (x) and
2
B y 7 6 x
C y A As x , f (x) and g (x) and
as x , f (x) and g (x) x 7
f (x ) A y 7 6 x
F As x , f (x) and g (x) and
as x 0, f (x) 0 and g (x) 9 Compare the end behavior for the pair of
functions.
f x 4 x 5 and g x log4 x
4 x 2 13 x 13
4x
F D:
; R: y 0
G D:
; R: y 0
H D: x 0; R:
J D: x 1; R: y 0
Use constant differences or ratios to
determine which parent function would
best model the given data set.
15.
as x , f (x) and g (x) C As x , f (x) and g (x) and
as x , f (x) and g (x) D As x , f (x) and g (x) and
as x , f (x) and g (x) x
3
7
11
15
19
23
y
64
96 144 216
324
486
A exponential
2
10. Given f(x) 3x x 1 and g(x) 4x 5, find (gf)(x).
F 3x2 5x 4
G 12x3 4x2 4x
H 12x3 19x2 x 5
J 12x3 19x2 9x 5
B linear
C quadratic
D square root
16.
11. Given f(x) 5x 3 and g(x) x2, find g(f(2)).
A 7
C 32
B 17
D 49
1
12. Given f(x) 4x 3 and g (x ) ,
4x
find g(f(x)).
1
3 x 16
F
G
1 4x
4x
x
0
5
10
15
y
3.4
4.1
6.0
9.1
20
25
13.4 18.9
F exponential
G linear
H quadratic
J square root
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
110
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
x
9
Sequences and Series
Chapter Test Level B
Select the best answer.
6. Jin-Woo is making a series of
sculptures. Each one takes 5 days
longer to complete than the one before
it. The first sculpture takes 27 days.
How many days does it take Jin-Woo to
complete the first four sculptures?
1. What are the first 5 terms of the
sequence where a1 6 and
an 2 2an1?
A 6, 4, 2, 0, 2
B 6, 8, 6, 8, 6, 8
F 47
H 135
C 6, 14, 26, 54, 106
G 96
J 138
D 6, 10, 18, 34, 66
7. Evaluate
2. A city is tracking reports of identity theft.
During the first 4 weeks of their study,
they find the following number of reports:
11, 22, 44, and 88. Which is a possible
explicit rule for the number of reports in
the nth week?
H an 11 (2)n
G an 2 (11)n
J an 2 (11)n
3. Wayne buys a motorcycle for $8000.
Each year, the cycle loses 20% of its
re-sale value from the previous year.
How much is the motorcycle worth after 3
years?
C $4096
B $3904
D $6400
H 256, 512
G 32, 64
J 256, 65, 536
4
4 1.5 k 1
C
4
k 1
D
1.5 4 k 1
k 1.5 4
4
k 1
F $48.80
H $58.80
G $51.20
J $60.00
6
1
k 1
.
A 1
C 1
B 0
D 2
F $500
H $515
G $505
J $525
11. Novinha sells 6 boxes of daisies at the
first day of a flower show. If every day
she sells 8 more than the day before and
the show lasts for two weeks, how many
boxes of daisies does she sell in all?
k 1
k 1
B
4
D 819
10. Maurice’s landlord raises his rent by
the same amount each year. During
his second year in his apartment, he
paid $530 each month. During his sixth
year he paid $590 each month. How
much did Maurice pay during his first
year in the apartment?
5. Which is summation notation for the
series 4 6 9 13.5?
1.5 k B 91
k 3
F 25, 36
4
C 169
9. Evaluate
4. How many dots are in the next two
iterations of the sequence shown below?
A
A 13
8. Jim owes his brother $100. He has
agreed to pay 20% of the remaining
balance each month. How much will Jim
pay towards his debt in the first
3 months?
1
A $2200
k.
k 1
1
F an 11 (2)n
13
A 48
C 702
B 110
D 812
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
169
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
x
9
Sequences and Series
Chapter Test Level B continued
19. Chiqua hikes for 6 hours during the first
day of a 4 day camping trip. Each day,
she hikes 70% as long as the day
before. How many hours does she hike
in all?
12. What is the common difference of the
sequence 8, 12, 16, 20, …?
F 1.5
H 4
G 2.5
J 8
13. What is S31 for the arithmetic series
9 8.5 8 7.5 7 …?
A 6
C 46.5
B 38.75
D 511.5
B 15
D 20
20. Which of the following series converges?
F
14. A population of sea monkeys starts out
numbering 86. Their numbers increase
by 10% each month. If no sea monkeys
die, what is the approximate total
population after one year?
F 189
H 1135
G 270
J 1323
C 20
B 10
D 64
1 3 9 27
2 2 2
2
G 40 20 10 5 …
H 10 15 22.5 33.75 …
J 100 110 121 133.1 …
21. A printer is making a design for a client
of nested squares. Each square is
drawn inside another square as shown.
15. What is the geometric mean of 4 and
16?
A 8
C 17
A 13
16. What is the common ratio of the
3 3
geometric sequence , , 3, 6, ….
4 2
F
1
3
H 2
G
1
2
J 3
If he continues this pattern, what is the
total perimeter of all the squares?
C 88
B 77
D 95
22. Evaluate
geometric series
m 1
3 0.9 m 1
F 15.7
H 21.6
G 17.12
J 27.0
q 1 3
F 6
6
q 1
.
H 12
G 9
J 18
23. Which is a counterexample that
disproves 4n 4n ?
A n 1
18. What is the approximate sum of the
8
D 80 in.
B 32 in.
17. Tella volunteers 10 hours at a local
shelter during one month. If she
increases her hours by 10% each
month, approximately how many hours
total will she volunteer in 7 months?
A 70
C 64 in.
A 16 in.
C n1
D n2
B n0
24. An infinite geometric series has a sum
of 200 and a common ratio of 0.4.
What is the first term of the series?
?
F 80
H 333
G 120
J 500
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
170
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
10
x
Trigonometric Functions
Chapter Test Form B
Select the best answer.
6. When viewed from the side, a nail is
located at 85 on a tire. The tire turns
counterclockwise through 7.25 complete
rotations. What is the new position of the
nail in the tire?
1. The sides of right ABC have lengths
12 ft, 16 ft, and 20 ft. Which could be the
cosine of angle C?
3
4
C
A
5
3
5
5
D
B
4
3
2. A camper creates a make-shift tent by
leaning a branch against a tree and
draping a tarp over it. The roof is
constructed from a 15 ft branch that
makes a 15 angle with the ground.
Approximately how tall is the tent at its
highest point?
F 3.89 ft
H 14.49 ft
G 4.02 ft
J 15.56 ft
3. What is the value of csc ? (Picture is
not to scale.)
F 175
H 5
G 5
J 175
7. What is the reference angle for
210?
A 30
C 120
B 60
D 150
8. A Ferris wheel has a diameter of
100 ft. The passengers ride in cars that
make 5 revolutions in 7.5 minutes.
Approximately how far does a car on
the Ferris wheel travel in 1 minute?
F 209 ft
H 471 ft
G 418 ft
J 942 ft
9. Which angle measure is closest to 4.7
radians?
13
5
A
C
12
13
13
12
B
D
5
13
4. What is the angle of rotation shown
below?
A 90
C 180
B 135
D 270
10. The tangent of is 1 and the cosine
2
. Which is the cosecant of
of is 2
?
F 2
H
2
2
2
2
J
2
G 11. The point (4, 6) is on the terminal side
of in standard position. Which is the
cosine of ?
F 30
H 240
G 120
J 330
5. Which two angles are both coterminal
with 50?
A 2 13
13
C
2
13
B 2
13
D
2 13
13
A 230 and 130C 130 and 310
B 230 and 410 D 410 and 310
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
189
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
10
x
Trigonometric Functions
Chapter Test Form B continued
12. Charles is trying to get his kite out of a
tree. The kite is 12 feet above him and
he’s standing 10 feet from the tree. If he
can throw a ball in a straight line, at what
angle should he throw it in order to hit the
kite?
H 50.2
F 33.6
J 56.4
G 39.8
13. Which value of makes the equation
2
(sin ) 1 true?
3
C 300
A 150
D 330
B 225
14. Which set of expressions, where n is an
integer, gives all possible values of
3
cos1 ?
2
7
5
(2 )n,
(2 )n
6
6
5
4
(2 )n,
(2 )n
G
3
3
11
(2 )n,
(2 )n
H
6
6
2
J
(2 )n,
(2 )n
3
3
17. Given the information in the diagram
below, what are the measures of sides t
and r rounded to the nearest tenth?
(Picture is not to scale.)
A t 3.8, r 9.2 C t 2.1, r 6.1
B t 9.2, r 3.8 D t 6.1, r 2.1
18. Nemili is making a stained glass window.
She wants to make a triangular pane
having side lengths a 2.15 in. and
b 4.5 in. If mA 40, how many
different panes can Nemili make?
F
F 0
H 2
G 1
J 3
19. The Ford family wants to carpet a
section of their basement with the
dimensions shown below. The carpet
they want to use costs $1.50 per
square foot. What is the approximate
cost of carpeting this area? (Picture is
not to scale.)
15. The footprint of a tent is shown below.
What is the area of the floor of the tent to
the nearest tenth of a square foot?
(Picture is not to scale.)
A $15.78
C $26.98
B $17.99
D $29.68
20. For KMH with side lengths k, m, and
h, which equation can be used to
determine k ?
A 3.05 ft2
B 4.80 ft2
C 5.75 ft2
D 8.95 ft2
F k h 2 m 2 2hmcosK
G k h 2 m 2 2hm sinK
16. Given that mC 35, a 12, and
b 15, which is the length of side c in
ABC to the nearest tenth?
F 8.6
H 14.9
G 12.7
J 16.3
H k h 2 m 2 2hmcosK
J k h 2 m 2 2hm sinK
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
190
Holt McDougal Algebra 2
Name ________________________________________ Date ___________________ Class __________________
Chapter
11
x
Trigonometric Graphs and Identities
Chapter Test Form B
Select the best answer.
6. What is the period of g(x) 2cot(2x)?
H F
1. Which function has a period of 2?
A
C
4
G
2
J 2
7. Which could be the equation of the graph
below?
B
D
2. Which function has an amplitude of 3
and a period of
2
?
C y 2cotx
A y tan2x
B y 2tanx
D y cot2x
8. Vail places her ring on a glass table
top before the table is moved. The
coefficient of friction, , between the
ring and glass is 0.65. Using the
equation mg sin
mgcos
, which
is the angle at which the ring begins
to slide off the table?
H 40.5
F 28.8
G 33.0
J 49.5
9. Which expression is equivalent to
sec ?
cot 1
F f (x) 3cos4x H f ( x ) 3 cos x
2
1
G f (x) 4cos3x J f ( x ) cos 3 x
2
3. At 20C, the speed of sound is
approximately 344 m/s. The lower limit
of sound waves audible to the human
ear is about 0.0172 m. What is the
frequency of these sound waves?
A 0.00005 Hz
C 5.9168 Hz
B 0.16901 Hz
D 20,000 Hz
4. Consider the function
g ( x ) sin x . Which expression
4
gives the values of the x-intercepts,
where n is an integer?
n
F
H
n
4
4
4
n
G J n
4
4
5. Which is NOT in the domain of the
function y tanx?
A B 0
C
A
1
cos C
1
sin B
sin tan D
cos sin 10. Which of the following is a trigonometric
identity?
F cot2 1 csc2
G cos( ) cos
H sec2 1 tan2
2
D 2
J cos2( ) 1 sin2
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
209
Holt McDougal Algebra 2