Download Large File with 120 review problems and answer key at the

REVIEW FOR FINAL 2ND SEMESTER
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the given expression. Assume that no variable equals 0.
____
1.
a.
c.
b.
d.
Simplify the given expression.
____
____
____
____
____
2.
a.
b.
c.
d.
a.
b.
c.
d.
a.
c.
b.
d.
a.
c.
b.
d.
a.
c.
3.
4.
5.
6.
b.
d.
Simplify the expression using long division.
____
____
____
7.
a. quotient
b. quotient
and remainder 16
and remainder 0
c. quotient
d. quotient
and remainder –32
and remainder 32
a. quotient
b. quotient
and remainder –26
and remainder 4
c. quotient
d. quotient
and remainder –14
and remainder 14
8.
9. Find
and
a. –6,555; 12,255
b. –6,585; 12,279
for the function
.
c. –6,584; 12,280
d. –185; –221
For the given graph,
a. describe the end behavior,
b. determine whether it represents an odd-degree or even-degree polynomial function, and
c. state the number of real zeros.
____ 10.
f( x)
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has three real zeros.
b. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has three real zeros.
c. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has four real zeros.
d. The end behavior of the graph is
It is an even-degree polynomial function.
The function has three real zeros.
as
and
as
.
as
and
as
.
as
and
as
.
as
and
as
.
____ 11.
f( x)
10
8
6
4
2
–5
–4
–3
–2
–1
–2
1
2
3
4
5
x
–4
–6
–8
–10
a. The end behavior of the graph is
It is an even-degree polynomial function.
The function has two real zeros.
b. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has two real zeros.
c. The end behavior of the graph is
It is an even-degree polynomial function.
The function has three real zeros.
d. The end behavior of the graph is
It is an even-degree polynomial function.
The function has two real zeros.
as
and
as
.
as
and
as
.
as
and
as
.
as
and
as
.
as
and
as
.
as
and
as
.
____ 12.
f( x)
30
25
20
15
10
5
–6
–5
–4
–3
–2
–1
–5
1
2
3
4
5
6
x
–10
–15
–20
–25
–30
a. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has three real zeros.
b. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has four real zeros.
c. The end behavior of the graph is
It is an even-degree polynomial function.
The function has three real zeros.
d. The end behavior of the graph is
It is an odd-degree polynomial function.
The function has three real zeros.
____ 13. Graph the function
a.
–3
–2
.
as
and
as
.
f( x)
100
100
50
50
–1
1
2
3
–3
x
–2
–1
–50
–50
–100
–100
100
50
50
1
2
3
x
1
2
3
x
1
2
3
x
f( x)
d.
100
–1
____ 14. Graph the function
as
c.
f( x)
–2
and
by making a table of values.
f( x)
b.
–3
as
–3
–2
–1
–50
–50
–100
–100
by making a table of values.
f( x)
a.
–3
–2
100
50
50
–1
1
2
3
x
–2
–1
–50
–100
–100
f( x)
–2
–3
–50
b.
–3
f( x)
c.
100
100
50
50
1
2
3
x
2
3
x
1
2
3
x
f( x)
d.
100
–1
1
–3
–2
–1
–50
–50
–100
–100
For the given function, determine consecutive values of x between which each real zero is located.
____ 15.
a.
b.
c.
d.
There is a zero between x = 0 and x = 1.
There is a zero between x = 0 and x = –1.
There are zeros between x = 1 and x = 0, x = 0 and x = –1.
There are zeros between x = 2 and x = 3, x = 1 and x = 2, x = –1 and x = –2, x = –1 and x =
–2, x = –2 and x = –3.
Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.
____ 16.
a.
b.
c.
d.
The relative maximum is at
The relative maximum is at
The relative maximum is at
The relative maximum is at
Factor the polynomial completely.
____ 17.
, and the relative minimum is at
, and the relative minimum is at
, and the relative minimum is at
, and the relative minimum is at
.
.
.
.
a.
b.
c.
d.
a.
b.
c.
d.
____ 18.
Solve the given equation. State the number and type of roots.
____ 19.
a.
b.
c.
d.
The equation has two real roots, and 4.
The equation has two real roots, and –4.
The equation has two real roots, –2 and –4.
The equation has two real roots, –2 and 4.
a.
b.
c.
d.
The equation has two real roots, and –10.
The equation has two real roots, –1 and –10.
The equation has two real roots, –1 and 10.
The equation has two real roots, and 10.
____ 20.
____ 21. Find all the rational zeros of the function
a.
,
b.
____ 22. Find
, 0,
d.
,
for the following functions.
a.
b.
____ 23. Find
c.
d.
for the following functions.
a.
b.
____ 24. Find
c.
d.
for the following functions.
a.
b.
____ 25. Find
.(calculator)
c.
c.
d.
for the following functions.
, 0,
,0
,
a.
c.
,
b.
,
d.
,
____ 26. Find
,
for the following functions.
a.
c.
,
,
b.
d.
,
,
Find the inverse of the given relation.
____ 27.
a.
b.
c.
d.
____ 28.
a.
c.
b.
d.
____ 29. Determine whether each pair of functions are inverse functions.
1)
2)
a.
b.
c.
d.
Only 2 is an inverse function.
Only 1 is an inverse function.
Neither 1 nor 2 is an inverse function.
Both 1 and 2 are inverse functions.
____ 30. Simplify
a.
.
c.
b.
____ 31. Simplify
a.
d.
.
c.
b.
d.
Simplify.
____ 32.
a.
b.
c.
d.
a.
b.
c.
d.
a.
c.
b.
d.
a.
c.
b.
d.
____ 33.
____ 34.
____ 35.
Write the given radical using rational exponents.
____ 36.
a.
c.
b.
d.
Simplify each expression.
____ 37.
a.
c.
b.
d.
____ 38.
a.
c.
b.
d.
Solve the given equation.
____ 39.
a.
b.
c.
104
9
34
9
109
9
d. 14
9
____ 40.
a. 2.24
b. 0.21
c. 0.24
d. 0.19
a. 0.31
b. 0.67
c. 0.1
d. 10
a.
c.
____ 41.
____ 42.
7
9
b.
5
n=
3
n=
8
9
d. n = 7
n=
Solve the given inequality.
____ 43.
a.
b.
312
−4
c.
d.
96
6
____ 44.
a. n < 3
b.
9
n<
5
c. n < 9
d.
27
n<
5
Simplify the given expression.
____ 45.
+
a.
c.
b.
d.
____ 46. 17 +
a.
c.
b.
d.
a.
c.
b.
d.
____ 47.
Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of the rational
function.
____ 48.
a.
b.
c.
d.
asymptotes:
asymptotes:
asymptotes:
asymptotes:
; hole:
; hole:
; hole:
; hole:
Graph the rational function.
____ 49. f(x) =
y
a.
–24 –20 –16 –12 –8
y
c.
24
24
20
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
24
x
–24 –20 –16 –12 –8
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
–24
–24
4
8
12
16
20
24 x
y
b.
–24 –20 –16 –12 –8
y
d.
24
24
20
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
–24 –20 –16 –12 –8
24 x
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
–24
–24
4
8
12
16
20
24
x
____ 50. If y varies directly as x and
when
, find y when
.
a. 168
c. –168
b. 16,800
d. –16,800
____ 51. If y varies directly as x and
when
, find y when
.
a. 1,400
c. 2.86
b. 2,240
d. 140
____ 52. Suppose y varies jointly as x and z. Find y when x = 2 and z = 11, if y = 160 when x = 3 and z = 8. Round your
answer to the nearest hundredth, if necessary.
a. 1,173.33
c. 13.33
b. 146.67
d. 174.55
____ 53. Suppose y varies jointly as x and z. Find y when
and
, if
when
and
.
Round your answer to the nearest hundredth, if necessary.
a. 3,433.33
c. 312.12
b. –312.12
d. –135.96
____ 54. If y varies inversely as x and
when
, find y when
. Round your answer to the nearest
hundredth, if necessary.
a. –746.15
c. 50.44
b. 746.15
d. –50.44
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
____ 55. Write an equation to represent the amount of meat needed m to sustain x Siberian tigers for d days.
a.
c.
b.
d.
____ 56. How much meat would seven Siberian tigers need for the month of April?
a. 750 pounds
c. 5425 pounds
b. 175 pounds
d. 5250 pounds
It has been found that the average number of daily phone calls C between two cities is directly proportional to
the product of the populations
and
of the two cities and inversely proportional to the square of the
distance d between the cities. That is,
.
____ 57. The distance between Albany, New York, and Cleveland, Ohio, is about 480 miles. If the average number of
daily phone calls between the cities is 250,000, find the value of k and write the equation of variation. Round to
the nearest thousandth. The population of Albany and Cleveland is 95,000 and 2,900,000 respectively.
a. 0.021
c. 0.209
b. 0.040
d. 4.780
The average American drinks about eight servings of hydrated beverages everyday.
____ 58. Each member of a household of four members drinks the same amount of hydrated beverages each day as the
average American. How many servings of hydrated beverages (w) would the members of the household
consume in a week?
a. 28
c. 224
b. 32
d. 992
____ 59. Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs
the same distance at a speed of 8 miles per hour, what is the average time taken?
a. 13.25 minutes
c. 16 minutes
b. 14.06 minutes
d. 140.60 minutes
____ 60. Many areas of Northern California depend on the snowpack of the Sierra Nevada Mountains for their water
supply. If 300 cubic centimeters of snow will melt to 33 cubic centimeters of water, how much water does 600
cubic centimeters of snow produce?
a. 16.5 cubic centimeters
c. 72.6 cubic centimeters
b. 66 cubic centimeters
d. 5454 cubic centimeters
Identify the type of function represented by the graph.
y
____ 61.
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
a. absolute value function
b. constant function
c. square root function
d. direct variation function
y
____ 62.
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
a. square root function
b. quadratic function
c. constant function
d. identity function
____ 63.
8
y
7
6
5
4
3
2
1
–13 –12 –11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
x
–2
–3
–4
a. absolute value function
c. rational function
b. quadratic function
d. inverse variation function
____ 64. Identify the type of function represented by the equation y = x.
a. inverse variation function
c. identity function
b. constant function
d. absolute value function
Identify the type of function represented by the equation.
____ 65.
a. absolute value function
b. direct variation function
____ 66. y = | 8x |
a. absolute value function
c. inverse variation function
d. identity function
c. constant function
b. identity function
d. direct variation function
a. absolute value function
b. inverse variation function
c. constant function
d. direct variation function
a. quadratic function
b. identity function
c. rational function
d. absolute value function
a. absolute value function
b. direct variation function
c. identity function
d. constant function
a. absolute value function
b. inverse variation function
c. direct variation function
d. identity function
____ 67.
____ 68.
____ 69.
____ 70.
Solve the inequality. Check your solution.
____ 71.
a.
b.
c.
d.
a.
b.
c.
d.
____ 72.
or
or
Sketch the graph of the given function. Then state the function’s domain and range.
____ 73. y = –1.2(3)x
a.
–5
–4
y
–3
–2
y
c.
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
The domain is all real numbers and the
range is all negative numbers.
1
2
3
4
5
The domain is all real numbers and the
range is all positive numbers.
x
y
b.
–5
–4
–3
–2
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–6
–4
–5
–2
–1
–1
–3
–4
–4
–5
–5
60
50
50
40
40
30
30
20
20
10
10
2
4
6
8
10
x
–5
–4
–3
–2
–1
–10
–20
–20
–30
–30
–40
–40
60
50
50
40
40
30
30
20
20
10
10
2
3
4
5
4
5
x
1
2
3
4
5
x
y
d.
1
3
The domain is all real numbers and the
range is all positive numbers.
60
–1
–10
2
y
c.
60
–2
–10
1
The domain is all real numbers and the
range is all positive numbers.
y
–3
–2
–3
b.
–4
–3
–2
The domain is all real numbers and the
range is all real numbers.
–5
–4
–2
The domain is all real numbers and the
range is all negative numbers.
____ 74. y = 2(4)x
y
a.
–10 –8
y
d.
5
x
–10 –8
–6
–4
–2
–10
–20
–20
–30
–30
–40
–40
2
4
6
8
10
The domain is all real numbers and the
The domain is all real numbers and the
range is all positive numbers.
range is all positive numbers.
____ 75. Use
and
to approximate the value of the expression
.
x
a. 2.079
b. 2,304
c. 8
d. 11.170
Solve the given equation. If necessary, round to four decimal places.
____ 76.
a. 26
b. 1.4444
c. 0.69
d. 4
a. 18.8519
b. 0.2083
c. 1.1870
d. 3.0445
____ 77.
Solve the given inequality. If necessary, round to four decimal places.
____ 78.
a.
b.
c.
d.
a. a < 2.1972
b. a < 1.7918
c. a < 0.2149
d. a < 2.9692
____ 79.
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
____ 80.
a.
b.
c.
; –0.0300
d.
; 0.0300
; 1.0400
; 0.9615
____ 81.
a.
b.
c.
; –0.0669
d.
; 0.0669
____ 82. Evaluate the expression
a. e
b.
; 0.9416
; 1.0620
.
c.
d. 2
Solve the given equation. Round to the nearest ten-thousandth, if necessary.
____ 83.
a. 1.7918
b. 0.4055
c. 1.5
d. 0
a. 1.4
b. 0.6592
c. 0.5666
d. 0.1682
____ 84.
Solve the given inequality. Round to the nearest ten-thousandth, if necessary.
____ 85.
____ 86.
____ 87.
____ 88.
____ 89.
____ 90.
____ 91.
a.
c.
b.
d.
Eros Industries bought a laser printer for $3400. It is expected to depreciate at a rate of 12% per year. What will
the value of the printer be in 3 years? Round to the nearest dollar.
a. $2317
c. $4777
b. $2992
d. $5128
Kronos Industries bought a desktop for $3000. It is expected to depreciate at a rate of 10% per year. What will
the value of the desktop be in 4 years? Round to the nearest dollar.
a. $1968
c. $2700
b. $2057
d. $4391
Ray Industries bought a touch screen monitor for $1200. It is expected to depreciate at a rate of 25% per year.
What will the value of the monitor be in 3 years? Round to the nearest dollar.
a. $142
c. $900
b. $506
d. $2340
Merlin Industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the
value of the laptop be in 5 years? Round to the nearest dollar.
a. $912
c. $1806
b. $988
d. $4043
An anthropologist finds there is so little Carbon-14 remaining in a prehistoric bone that instruments cannot
measure it. This means there is less than 0.2% of the amount of Carbon-14 the bones would have contained
when the person was alive. How long ago did the person die? (The constant for Carbon-14 is 0.00012.)
a. 13,411 years
c. 45,020 years
b. 22,491 years
d. 51,788 years
A paleontologist finds a bone that might be a sauropod’s bone. In the laboratory, she finds that the Carbon-14
found in the bone is
of that found in a living bone tissue. Could this bone have belonged to a sauropod?
Explain your reasoning. (Hint: The sauropods lived from 200 million years ago to 145 million years ago. The
constant for Carbon-14 is 0.00012.)
a. No, because the amount of Carbon-14 found indicates a period before the sauropods even
came into existence.
b. No, because the amount of Carbon-14 found indicates a period after the sauropods became
extinct.
c. Yes, because the number of years calculated is in the range of 200 million years and 145
million years ago.
d. Yes, because the amount of Carbon-14 found in the bone is one-tenth of that found in a
living bone tissue.
____ 92. Radioactive iodine is used to determine the health of thyroid gland. It decays according to the equation
, where t is in days. Find the one-fourth life of this substance. Round to the nearest integer.
a. 2
c. 16
b. 7
d. 69
____ 93. The Freeman family bought a new apartment five years ago for $80,000. The apartment is now worth $199,200.
Assuming a steady rate of growth, what was the yearly rate of appreciation?
a. 19.1%
c. 23%
b. 20%
d. 24.9%
The Gross National Product (GNP) is the value of all the goods and services produced in an economy, plus the
value of the goods and services imported, less the goods and services exported. During the period 1994-2004,
the GNP of Canada grew about 4.8% per year, measured in 2003 dollars. In 1994, the GNP was $5.9 billion.
____ 94. Assuming this rate of growth continues, in what year will the GNP reach $10 trillion?
a. 2103
c. 2164
b. 2153
d. 2168
National Income (NI) is the sum of the incomes that all individuals in an economy earn in the forms of wages,
interest, rents, and profits. It excludes government transfer payments and is calculated before any deductions
are taken for income taxes. During the period 1994-2004, the NI of Australia grew about 5.2% per year,
measured in 2003 U.S. dollars. In 1994, the NI was $4 billion.
____ 95. Assuming this rate of growth continues, what will the NI of Australia be (in billions) in the year 2015?
a. $52.48
c. $11.60
b. $33.88
d. $1.28
____ 96. Assuming this rate of growth continues, in what year will the NI reach $15 trillion?
a. 2020
c. 2162
b. 2156
d. 2211
Bacteria usually reproduce by a process called binary fission. In this type of reproduction, one bacterium
divides to form two bacteria. Under ideal conditions, some bacteria reproduce every 15 minutes.
____ 97. Find the constant k for this type of bacteria under ideal conditions.
a. 0.693
c. 0.0462
b. –0.954
d. 0.133
____ 98. Solve
by using the measurements
,
sides to the nearest tenth and measures of angles to the nearest degree.
, and
. Round measures of
P
r
q
Q
p
R
a.
c.
,
,
,
,
b.
d.
,
,
,
,
____ 99. The upper part of a tree, broken by wind, makes an angle of 38º with the ground. The horizontal distance from
the root of the tree to the point where the top of the tree meets the ground is 20 meters. Find the height of the tree
before it was broken.
____ 100.
____ 101.
____ 102.
____ 103.
____ 104.
a. 9.754 m
c. 25.380 m
b. 15.626 m
d. 41.006 m
Two boys are on opposite sides of a tower. They sight the top of the tower at 33º and 24º angles of elevation
respectively. If the height of the tower is 100 m, find the distance between the two boys.
a. 378.59 m
c. 153.99 m
b. 224.60 m
d. 70.61 m
In a tourist bus near the base of Eiffel Tower at Paris, a passenger estimates the angle of elevation to the top of
the tower to be 60°. If the height of Eiffel Tower is about 984 feet, what is the distance from the bus to the base
of the tower?
a. 492 feet
c. 586.13 feet
b. 568.11 feet
d. 1704.28 feet
A kite at a height of 75 meters from the ground is attached to a string inclined at
to the horizontal. Find the
length of the string to the nearest meter.
a. 43 m
c. 130 m
b. 87 m
d. 150 m
A preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. A
1% incline means 10 units of vertical rise for every 100 units of horizontal run. If the treadmill bed is 32 inches
long, what is the vertical rise when set at a 4% incline?
a. 1.28 in.
c. 12.8 in.
b. 5 in.
d. 80 in.
A preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. A
2% incline means 2 units of vertical rise for every 100 units of horizontal run. At what angle, with respect to the
horizontal, is the treadmill bed when set to a 20% incline? Round to the nearest degree.
a. 4°
c. 11°
b. 6°
d. 20°
Find the value of the given trigonometric function.
____ 105.
a.
c.
b.
d.
a.
c.
b.
d. 2
____ 106.
Find the exact values of the remaining five trigonometric functions of θ.
____ 107. Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and
a.
b.
,
,
,
,
,
,
, and
, and
.
c.
,
d.
,
,
,
,
, and
,
, and
____ 108. Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and csc
a.
,
,
,
.
, and
b.
c.
d.
,
,
,
,
,
,
,
,
, and
, and
,
, and
____ 109. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and
a.
,
,
,
,
.
b.
,
,
,
,
c.
,
,
,
,
d.
,
,
,
,
____ 110. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and
a.
,
b.
,
c.
d.
,
,
,
,
,
,
,
,
,
,
,
,
,
,
____ 111. Suppose θ is an angle in the standard position whose terminal side is in Quadrant II and
a.
b.
,
,
,
,
,
.
,
,
,
.
c.
,
d.
,
,
,
,
,
,
,
Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest
degree.
____ 112.
R
p
q
Q
,
a.
b.
P
r
,
,
,
,
,
c.
d.
The given point P is located on the unit circle. Find
,
,
,
,
and
.
____ 113.
a.
b.
;
;
c.
d.
;
;
____ 114.
a.
b.
c.
;
d.
;
____ 115. Find the exact value of the function
;
;
.
a. 1
c.
b.
d. 0
1
by finding the value of x to the nearest degree.
3
a. 72°
c. 0.35°
b. 0.05°
d. 18°
1
____ 117. Solve x = Sin
by finding the value of x to the nearest degree.
2
a. 60°
c. 0.48°
b. 30°
d. 0.03°
2
____ 118. Find the value of cot (Cos
). Round to the nearest hundredth.
3
a. 0.87
c. 1.12
b. 0.89
d. 1.00
7
____ 119. Find the value of cos (Sin
). Round to the nearest hundredth.
20
a. 0.36
c. 0.94
b. 0.60
d. 1.21
____ 116. Solve x = Arctan
REVIEW FOR FINAL 2AD SEMESTER
Answer Section
MULTIPLE CHOICE
1. ANS: B
Multiply the constants and then multiply the powers using the Power of a Product Property.
Feedback
A
B
C
D
Multiply the powers of the same variable using the Power of a Product Property.
Correct!
Multiply the constants.
A simplified expression cannot contain negative exponents.
PTS: 1
DIF: Basic
REF: Lesson 6-1
OBJ: 6-1.1 Use properties of exponents to multiply monomials.
NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Use properties of exponents to multiply monomials.
KEY: Monomials | Multiply Monomials
2. ANS: A
Use the Distributive Property and then multiply the monomials using the Product of Powers Property.
Feedback
A
B
C
D
Correct!
Did you use the Distributive Property?
Did you multiply the monomials correctly?
Did you calculate the product of powers correctly?
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.3 Multiply polynomials.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Multiply polynomials.
KEY: Polynomials | Multiply Polynomials
3. ANS: A
Use the Distributive Property and then multiply the monomials using the Product of Powers Property.
Feedback
A
B
C
D
Correct!
Did you multiply the monomials correctly?
Did you distribute the terms correctly?
Did you use the Product of Powers Property?
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.3 Multiply polynomials.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Multiply polynomials.
KEY: Polynomials | Multiply Polynomials
4. ANS: C
First, multiply the values and then divide the numerator and the denominator by the common factors.
Feedback
A
B
C
Divide the denominator by x, not x2.
Divide the numerator also with y.
Correct!
D
Did you multiply accurately?
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.1 Simplify rational expressions with multiplication.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Simplify rational expressions with multiplication.
KEY: Rational Expressions | Multiply Rational Expressions
5. ANS: C
To divide two rational expressions, multiply by the reciprocal of the divisor.
Feedback
A
B
C
D
Did you perform all the mathematical actions?
Did you divide correctly?
Correct!
To simplify the values, divide the denominator by b3, not by b4.
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.2 Simplify rational expressions with division.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Simplify rational expressions with division.
KEY: Rational Expressions | Divide Rational Expressions
6. ANS: B
Express the question as a division expression, and then multiply by the reciprocal of the divisor.
Feedback
A
B
C
D
The numerator and the denominator are interchanged.
Correct!
Did you eliminate all the common factors?
Did you simplify correctly?
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.3 Simplify complex fractions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Simplify complex fractions.
KEY: Complex Fractions
7. ANS: B
Use the division algorithm. When dividing, you can add or subtract only similar terms.
Feedback
A
B
C
D
Did you consider both the terms of the divisor?
Correct!
Change the signs of the product terms only.
Did you use the correct signs of the terms?
PTS: 1
DIF: Advanced
REF: Lesson 6-3
OBJ: 6-3.1 Divide polynomials using long division.
NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2
STA: IL J 6B.2 | IL J 8A.7 | IL J 6B
TOP: Divide polynomials using long division.
KEY: Polynomials | Divide Polynomials | Long Division
8. ANS: A
Use the division algorithm. When dividing, you can add or subtract only similar terms.
Feedback
A
Correct!
B
C
D
Did you consider both the terms of the divisor?
Change the signs of the product terms only.
Did you multiply the divisor with the correct term?
PTS: 1
DIF: Advanced
REF: Lesson 6-3
OBJ: 6-3.1 Divide polynomials using long division.
NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2
STA: IL J 6B.2 | IL J 8A.7 | IL J 6B
TOP: Divide polynomials using long division.
KEY: Polynomials | Divide Polynomials | Long Division
9. ANS: B
Replace the values of p(x) and simplify.
Feedback
A
B
C
D
Did you substitute the correct values in the function?
Correct!
Add the value of the constant.
The exponent value of the first term is 5, not 4.
PTS: 1
DIF: Average
REF: Lesson 6-4
OBJ: 6-4.1 Evaluate polynomial functions.
NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA: IL J 8B
TOP: Evaluate polynomial functions.
KEY: Polynomial Functions
10. ANS: B
The end behavior is the behavior of the graph as x approaches positive infinity
or negative infinity
. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function.
Feedback
A
B
C
D
What is the end behavior of the graph?
Correct!
Did you verify the number of real zeros?
Check the degree of the polynomial function.
PTS: 1
DIF: Basic
REF: Lesson 6-4
OBJ: 6-4.2 Identify general shapes of graphs of polynomial functions.
NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Identify general shapes of graphs of polynomial functions.
KEY: Polynomial Functions | Graph Polynomial Functions
11. ANS: D
The end behavior is the behavior of the graph as x approaches positive infinity
or negative infinity
. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function.
Feedback
A
B
C
D
What is the end behavior of the graph?
Check the degree of the polynomial function.
Did you verify the number of real zeros?
Correct!
PTS:
OBJ:
NAT:
TOP:
1
DIF: Basic
REF: Lesson 6-4
6-4.2 Identify general shapes of graphs of polynomial functions.
NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
Identify general shapes of graphs of polynomial functions.
KEY: Polynomial Functions | Graph Polynomial Functions
12. ANS: A
The end behavior is the behavior of the graph as x approaches positive infinity
or negative infinity
. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function.
Feedback
A
B
C
D
Correct!
Did you verify the number of real zeros?
Check the degree of the polynomial function.
What is the end behavior of the graph?
PTS: 1
DIF: Basic
REF: Lesson 6-4
OBJ: 6-4.2 Identify general shapes of graphs of polynomial functions.
NAT: NA 1 | NA 7 | NA 8 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Identify general shapes of graphs of polynomial functions.
KEY: Polynomial Functions | Graph Polynomial Functions
13. ANS: A
Make a table of values and plot the graph.
Feedback
A
B
C
D
Correct!
Did you use the correct equation to plot the graph?
Did you plot the correct graph?
The degree of the polynomial is 5, not 4.
PTS: 1
DIF: Average
REF: Lesson 6-5
OBJ: 6-5.1 Graph polynomial functions.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Graph polynomial functions.
KEY: Polynomial Functions | Graph Polynomial Functions
14. ANS: C
Make a table of values and plot the graph.
Feedback
A
B
C
D
Did you plot the graph correctly?
The degree of the polynomial is 4, not 3.
Correct!
Did you use the correct equation to plot the graph?
PTS: 1
DIF: Average
REF: Lesson 6-5
OBJ: 6-5.1 Graph polynomial functions.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Graph polynomial functions.
KEY: Polynomial Functions | Graph Polynomial Functions
15. ANS: C
Make a table of values to obtain the required answer.
Feedback
A
B
C
D
Did you locate all the real zeros?
You have obtained only some of the real zeros.
Correct!
Does the sign of the polynomial change between these consecutive values?
PTS: 1
DIF: Advanced
REF: Lesson 6-5
OBJ: 6-5.2 Locate real zeros of polynomial functions.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8B.4 | IL J 8B
TOP: Locate real zeros of polynomial functions.
KEY: Polynomial Functions | Zeroes of Polynomial Functions
16. ANS: D
Make a table of values and graph the equation.
Feedback
A
B
C
D
A relative minimum is a point that has no nearby points with a lesser y-coordinate.
Did you obtain the correct value of the relative maximum?
Did you find the correct coordinates of the function?
Correct!
PTS: 1
DIF: Average
REF: Lesson 6-5
OBJ: 6-5.3 Find the maxima and minima of polynomial functions.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8B.4 | IL J 8B
TOP: Find the maxima and minima of polynomial functions.
KEY: Maxima of Polynomial Functions | Minima of Polynomial Functions
17. ANS: A
Group the monomials to find the GCF (greatest common factor), factor the GCF of each binomial, and then use
the Distributive Property to obtain the factors.
Feedback
A
B
C
D
Correct!
Group the polynomial into binomials to find the GCF.
Factor the GCF of each binomial.
Use the Distributive Property.
PTS: 1
DIF: Average
REF: Lesson 6-6
OBJ: 6-6.2 Factor polynomials by grouping.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 8A.7 | IL J 6B
TOP: Factor polynomials by grouping.
KEY: Polynomials | Factor Polynomials
18. ANS: D
To find the coefficient of the x terms, find two numbers whose product is
or 36 and whose sum is 13.
Feedback
A
B
C
D
Factor the GCF of each group.
The product of the coefficient of the x terms should be equal to the product of the
coefficient of the x2 term and the constant term.
Use the Distributive Property to obtain two binomial factors.
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 6-6
OBJ: 6-6.3 Factor polynomials with addition recognizing the FOIL method.
NAT: NA 1 | NA 3 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 8A.7 | IL J 6B
TOP: Factor polynomials with addition by recognizing the FOIL method.
KEY: Polynomials | Factor Polynomials | FOIL Method
19. ANS: B
Factor the equation and find the roots.
Feedback
A
B
C
D
Did you factor correctly?
Correct!
You have calculated the incorrect roots.
Did you calculate correctly?
PTS: 1
DIF: Average
REF: Lesson 6-8
OBJ: 6-8.1 Determine the number and types of roots for a polynomial equation.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8D
TOP: Determine the number and types of roots for a polynomial equation.
KEY: Polynomial Equations | Roots | Real Roots
20. ANS: A
Factor the equation and find the roots.
Feedback
A
B
C
D
Correct!
You have obtained the incorrect roots.
Did you calculate correctly?
Did you factor correctly?
PTS: 1
DIF: Average
REF: Lesson 6-8
OBJ: 6-8.1 Determine the number and types of roots for a polynomial equation.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8D
TOP: Determine the number and types of roots for a polynomial equation.
KEY: Polynomial Equations | Roots | Real Roots
21. ANS: C
Use the Rational Zero Theorem.
Feedback
A
B
C
D
You must also include the positive rational zeros in the answer.
Did you apply the Rational Zero Theorem correctly?
Correct!
You must also include the negative rational zeros in the answer.
PTS: 1
DIF: Average
REF: Lesson 6-9
OBJ: 6-9.2 Find all the rational zeros of a polynomial function.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8B.4 | IL J 8D | IL J 8B
TOP: Find all the rational zeros of a polynomial function.
KEY: Polynomial Functions | Zeroes of Polynomial Functions
22. ANS: B
Subtract g(x) from f(x) to obtain the required answer.
Feedback
A
B
C
D
Did you find the value of the correct function?
Correct!
Check the calculation.
Did you subtract the functions correctly?
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.2 Find the difference of functions.
STA: IL J 8B.6
TOP: Find the difference of functions.
23. ANS: D
Multiply f(x) and g(x) to obtain the required answer.
NAT: NA 1 | NA 6 | NA 7 | NA 10 | NA 2
KEY: Functions | Difference of Functions
Feedback
A
B
C
D
The answer has an incorrect operator.
You have multiplied the two functions incorrectly.
Did you check the calculations?
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.3 Find the product of functions.
NAT: NA 1 | NA 6 | NA 7 | NA 10 | NA 2
STA: IL J 8B.6
TOP: Find the product of functions.
KEY: Functions | Product of Functions
24. ANS: D
Multiply f(x) and g(x) to obtain the required answer.
Feedback
A
B
C
D
Did you check the calculations?
You have multiplied the two functions incorrectly.
The answer has an incorrect operator.
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.3 Find the product of functions.
NAT: NA 1 | NA 6 | NA 7 | NA 10 | NA 2
STA: IL J 8B.6
TOP: Find the product of functions.
KEY: Functions | Product of Functions
25. ANS: D
Divide f(x) by g(x) to obtain the required answer.
Feedback
A
B
C
D
What is the solution of the function?
Did you include the correct sign in the answer?
Did you calculate correctly?
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.4 Find the quotient of functions.
NAT: NA 1 | NA 6 | NA 7 | NA 10 | NA 2
STA: IL J 8B.6
TOP: Find the quotient of functions.
KEY: Functions | Quotient of Functions
26. ANS: C
Divide f(x) by g(x) to obtain the required answer.
Feedback
A
B
C
D
What is the solution of the function?
Did you include the correct sign in the answer?
Correct!
Did you calculate correctly?
PTS: 1
DIF: Average
REF: Lesson 7-1
NAT: NA 1 | NA 6 | NA 7 | NA 10 | NA 2
OBJ: 7-1.4 Find the quotient of functions.
STA: IL J 8B.6
TOP: Find the quotient of functions.
KEY: Functions | Quotient of Functions
27. ANS: C
The inverse relation is the set of ordered pairs obtained by reversing the coordinates of each original ordered
pair.
Feedback
A
B
C
D
Write the inverse of all the ordered pairs in the relation.
Did you write all the values with the correct sign?
Correct!
Did you check the sign of all the values?
PTS: 1
DIF: Basic
REF: Lesson 7-2
OBJ: 7-2.1 Find the inverse of a relation.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8B.6 | IL J 8B
TOP: Find the inverse of a relation.
KEY: Relations | Inverses of Relations
28. ANS: D
The inverse relation is the set of ordered pairs obtained by reversing the coordinates of each original ordered
pair.
Feedback
A
B
C
D
Write the inverse of all the ordered pairs in the relation.
Did you write all the values with the correct sign?
Did you check the sign of all the values?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 7-2
OBJ: 7-2.1 Find the inverse of a relation.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8B.6 | IL J 8B
TOP: Find the inverse of a relation.
KEY: Relations | Inverses of Relations
29. ANS: B
Two functions f and g are inverse functions if and only if both of their compositions are the identity function.
Feedback
A
B
C
D
Did you find both compositions in each pair?
Correct!
How will you determine whether a pair of functions are inverse functions?
The composition of the second pair of functions is not an identity function.
PTS: 1
DIF: Average
REF: Lesson 7-2
OBJ: 7-2.3 Determine whether two functions or relations are inverses.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 8B.6 | IL J 8B
TOP: Determine whether two functions or relations are inverses.
KEY: Functions | Inverses of Functions
30. ANS: D
Factor into squares where possible. Use the Product Property of Radicals to simplify.
Feedback
A
B
C
Did you use the Product Property of Radicals?
Factor terms in the radicand into squares if possible and then use the Product Property of
Radicals.
Write all the terms left in the radicand also.
D
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.1 Simplify radical expressions with multiplication.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Simplify radical expressions with multiplication.
KEY: Radical Expressions | Simplify Radical Expressions
31. ANS: D
Factor into squares where possible. Use the Product Property of Radicals to simplify.
Feedback
A
B
C
D
Did you use the Product Property of Radicals?
Write all the terms left in the radicand also.
Factor terms in the radicand into squares if possible and then use the Product Property of
Radicals.
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.1 Simplify radical expressions with multiplication.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Simplify radical expressions with multiplication.
KEY: Radical Expressions | Simplify Radical Expressions
32. ANS: A
Find the principal square root of each term of the radicand and simplify the expression.
Feedback
A
B
C
D
Correct!
Check the sign between the two radicals.
Check for the interchanged digits before the radicals.
Compute again and check the sign.
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.3 Add and subtract radical expressions.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
TOP: Add and subtract radical expressions.
KEY: Radical Expressions
33. ANS: A
Find the square of the expression and simplify for the same radicands and numbers.
Feedback
A
B
C
D
Correct!
Check the sign between the first number and the radical.
You have to add the square of the radicals.
You have not computed the square correctly.
PTS:
NAT:
TOP:
34. ANS:
1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.4 Multiply radical expressions.
NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
Multiply radical expressions.
KEY: Radical Expressions
A
Multiply the numerator and denominator by the conjugate of the denominator and simplify.
Feedback
A
B
C
D
Correct!
The radical multiplication is not correct.
You have not multiplied the numerator by the conjugate of the denominator.
Check your work and try again.
PTS:
NAT:
TOP:
35. ANS:
1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.5 Divide radical expressions.
NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
Divide radical expressions.
KEY: Radical Expressions
A
Multiply the numerator and denominator by the conjugate of the denominator and simplify.
Feedback
A
B
C
D
Correct!
You have not multiplied the denominator by its conjugate.
You have not multiplied the numerator by the conjugate of the denominator.
Check your work and try again.
PTS:
NAT:
TOP:
36. ANS:
1
REF: Lesson 7-5
OBJ: 7-5.5 Divide radical expressions.
NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: IL J 6B.2 | IL J 6B
Divide radical expressions.
KEY: Radical Expressions
D
For any real number b and any positive integer n,
.
Feedback
A
B
C
D
Did you use the Property of Powers correctly?
Use the definition of
on each term of the radicand.
Did you apply the Property of Powers to each term of the radicand?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
37. ANS:
1
DIF: Average
REF: Lesson 7-6
7-6.2 Write radical expressions as expressions with rational exponents.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6A
Write radical expressions as expressions with rational exponents.
Rational Exponents | Radical Expressions
A
Use
and simplify the results.
Feedback
A
B
C
D
Correct!
Did you subtract the powers correctly?
Find a common denominator and subtract the powers.
You have to subtract the powers.
PTS:
OBJ:
STA:
KEY:
38. ANS:
1
DIF: Average
REF: Lesson 7-6
7-6.3 Simplify expressions in exponential form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
IL J 6A
TOP: Simplify expressions in exponential form.
Exponential Form
A
For any real number b and any positive integer n,
.
Feedback
A
B
C
D
Correct!
You have not calculated the nth root correctly.
Look at the nth root.
Remember
.
PTS: 1
DIF: Average
REF: Lesson 7-6
OBJ: 7-6.4 Simplify expressions in radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA: IL J 6A
TOP: Simplify expressions in radical form.
KEY: Radical Form
39. ANS: B
Isolate the radical in the original equation, and raise each side of the equation to the power equal to the index of
the radical to eliminate the radical. Check the solution obtained by substituting the value of x in the original
equation.
Feedback
A
B
C
D
Did you isolate the radical?
Correct!
Isolate the radical by adding or subtracting the term without the radical from both the
sides.
Raise each side of the equation to the power equal to the index of the radical.
PTS: 1
DIF: Average
REF: Lesson 7-7
OBJ: 7-7.1 Solve equations containing radicals.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8D
TOP: Solve equations containing radicals.
KEY: Radical Equations | Solve Radical Equations
40. ANS: C
Find the least common denominator and multiply both sides by it.
Feedback
A
B
C
D
Did you substitute the values correctly?
Did you solve the equation correctly?
Correct!
Did you perform the correct arithmetic operation?
PTS: 1
DIF: Advanced
REF: Lesson 8-6
OBJ: 8-6.1 Solve rational equations.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8D.5 | IL J 8D
TOP: Solve rational equations.
KEY: Rational Equations | Solve Rational Equations
41. ANS: A
Find the least common denominator and multiply both the sides by it.
Feedback
A
B
C
D
Correct!
Did you multiply correctly?
Did you calculate correctly?
Did you include the correct values in the formula?
PTS: 1
DIF: Advanced
REF: Lesson 8-6
OBJ: 8-6.1 Solve rational equations.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8D.5 | IL J 8D
TOP: Solve rational equations.
KEY: Rational Equations | Solve Rational Equations
42. ANS: A
Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation.
Feedback
A
B
C
D
Correct!
Did you check the exponent of the base on the right side of the equation?
Did you write the right side of the equation in the correct exponential form?
Did you check the exponent of the base on the left side of the equation?
PTS: 1
DIF: Average
REF: Lesson 9-1
OBJ: 9-1.2 Solve exponential equations.
NAT: NA 1 | NA 3 | NA 4 | NA 10 | NA 2
STA: IL J 8D | IL J 6B.6
TOP: Solve exponential equations.
KEY: Solve Equations | Exponential Equations
43. ANS: C
Isolate the radical in the original inequality, and raise each side of the inequality to the power equal to the index
of the radical to eliminate the radical. Check the solution obtained by substituting the value of x in the original
equation.
Feedback
A
B
C
D
Did you isolate the radical?
Did you check the values in the interval that satisfies the inequality?
Correct!
Raise each side of the inequality to the power equal to the index of the radical.
PTS: 1
DIF: Advanced
REF: Lesson 7-7
OBJ: 7-7.2 Solve inequalities containing radicals.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8D
TOP: Solve inequalities containing radicals.
KEY: Radical Inequalities | Solve Radical Inequalities
44. ANS: D
Eliminate the bases. Then, use the Property of Inequality for Exponential Functions and the Distributive
Property.
Feedback
A
B
C
D
Did you check the exponential form of the right side of the inequality?
Use the Distributive Property while simplifying exponents.
Rewrite each side of the inequality with the same base.
Correct!
PTS: 1
DIF: Average
REF: Lesson 9-1
OBJ: 9-1.3 Solve exponential inequalities.
NAT: NA 1 | NA 3 | NA 4 | NA 10 | NA 2
STA: IL J 8D | IL J 6B.6
TOP: Solve exponential inequalities.
KEY: Solve Inequalities | Exponential Inequalities
45. ANS: C
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator
and add the numerators.
Feedback
A
B
C
D
Did you calculate the numerator correctly?
Add the numerators and simplify.
Correct!
Find the common denominator and then add the numerators.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Add rational expressions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Add rational expressions.
KEY: Rational Expressions | Add Rational Expressions
46. ANS: B
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator
and add the numerators.
Feedback
A
B
C
D
Before adding numerators, find equivalent fractions that have common denominators.
Correct!
Did you multiply correctly?
Multiply the first fraction with the common denominator.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Add rational expressions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Add rational expressions.
KEY: Rational Expressions | Add Rational Expressions
47. ANS: A
Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator
and subtract the numerators.
Feedback
A
B
C
D
Correct!
Find the common denominator and then subtract the numerators.
Before subtracting the numerators, find equivalent fractions that have common
denominators.
Did you use the correct arithmetic action?
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.3 Subtract rational expressions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8A.7
TOP: Subtract rational expressions.
KEY: Rational Expressions | Subtract Rational Expressions
48. ANS: A
If the rational expression of a function is written in the simplest form and the function is undefined for x = a,
then x = a is a vertical asymptote. If the function is defined for x = a, then there is a hole in the graph at x = a.
Feedback
A
B
Correct!
Did you factor correctly?
C
D
Did you calculate properly?
Did you find the correct asymptotes?
PTS: 1
DIF: Advanced
REF: Lesson 8-3
OBJ: 8-3.1 Determine the limitations of domains and ranges of the graphs of rational functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8B.4 | IL J 8B
TOP: Determine the limitations of domains and ranges of the graphs of rational functions.
KEY: Graph Rational Functions | Vertical Asymptotes | Point Discontinuity
49. ANS: A
Draw the vertical asymptote, make a table of values, plot the points, and draw the graph.
Feedback
A
B
C
D
Correct!
You have taken the negative value for plotting the graph.
Where is teh vertical asymptote?
Graph the equation, not the inverse of the equation.
PTS: 1
DIF: Advanced
REF: Lesson 8-3
OBJ: 8-3.2 Graph rational functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8B
TOP: Graph rational functions.
KEY: Graph Rational Functions
50. ANS: C
Use direct proportion to relate the values.
Feedback
A
B
C
D
Did you use the negative sign?
Did you substitute the values correctly?
Correct!
Did you use the correct equation for direct variation?
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.1 Recognize and solve direct variation problems.
STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Recognize and solve direct variation problems.
51. ANS: D
Use direct proportion to relate the values.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
KEY: Direct Variation
Feedback
A
B
C
D
Did you multiply correctly?
Did you use the correct equation for direct variation?
Have you used the correct equation to relate the values?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.1 Recognize and solve direct variation problems.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Recognize and solve direct variation problems.
52. ANS: B
KEY: Direct Variation
Use one set of proportions to find the other set of corresponding values in the equation
.
Feedback
A
B
C
D
Did you substitute the values of all the variables?
Correct!
Have you used all the values of the variables?
Did you use the correct equation for joint variation?
PTS:
OBJ:
STA:
TOP:
53. ANS:
1
DIF: Advanced
REF: Lesson 8-4
8-4.2 Recognize and solve joint variation problems.
IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
Recognize and solve joint variation problems.
B
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
KEY: Joint Variation
Use one set of proportions to find the other set of corresponding values in the equation
.
Feedback
A
B
C
D
Did you substitute the values of all the variables?
Correct!
Did you include the correct sign in the answer?
Did you use the correct equation for joint variation?
PTS: 1
DIF: Advanced
REF: Lesson 8-4
OBJ: 8-4.2 Recognize and solve joint variation problems.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Recognize and solve joint variation problems.
KEY: Joint Variation
54. ANS: D
Use inverse proportion to relate values in the following equation.
Feedback
A
B
C
D
Did you substitute the values correctly?
Did you use the correct equation for inverse variation?
Did you forget to include the negative sign in the answer?
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.3 Recognize and solve inverse variation problems.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Recognize and solve inverse variation problems.
KEY: Inverse Variation
55. ANS: C
The total amount of meat needed can be represented by the product of meat required per day, the number of
tigers, and the number of days.
Feedback
A
B
C
D
This is the meat required for x Siberian tigers for one day.
Did you use all the values?
Correct!
This is the meat required for one Siberian tiger for d days.
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Solve real-world problems with direct, joint, and inverse variation.
KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
56. ANS: D
The correct equation to represent the amount of meat needed is m = 25xd.
Feedback
A
B
C
D
Did you multiply the number of tigers?
Did you multiply the number of days?
What is the number of days in the month of April?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
57. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
Solve real-world problems with direct, joint, and inverse variation.
Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
C
Use the equation
and substitute the values.
Feedback
A
B
C
D
Did you use the correct values for calculation?
The number of daily phone calls is inversely proportional to the square of the distance d
between the cities.
Correct!
Did you use the correct equation?
PTS: 1
DIF: Advanced
REF: Lesson 8-4
OBJ: 8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Solve real-world problems with direct, joint, and inverse variation.
KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
58. ANS: C
The correct equation to represent the total servings of hydrated beverages drunk by the household members is
, where d is the total number of days and m is the total household members.
Feedback
A
B
Did you include the daily servings drunk by an average American?
Did you multiply the number of days in the week?
C
D
Correct!
Did you include the correct number of days?
PTS:
OBJ:
NAT:
TOP:
KEY:
59. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
Solve real-world problems with direct, joint, and inverse variation.
Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
B
Use the formula,
.
Feedback
A
B
C
D
Did you use the correct values while multiplying?
Correct!
Have you used the correct formula for calculating distance?
Did you place the decimal point correctly?
PTS:
OBJ:
NAT:
TOP:
KEY:
60. ANS:
1
DIF: Advanced
REF: Lesson 8-4
8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
Solve real-world problems with direct, joint, and inverse variation.
Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
B
Use the equation of direct variation
to find the other set of corresponding values.
Feedback
A
B
C
D
Did you use the correct values?
Correct!
Did you check the calculation.
Did you use the correct equation?
PTS: 1
DIF: Advanced
REF: Lesson 8-4
OBJ: 8-4.4 Solve real-world problems with direct, joint, and inverse variation.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 6D.2 | IL J 8D | IL J 8D.3 | IL J 6D
TOP: Solve real-world problems with direct, joint, and inverse variation.
KEY: Direct Variation | Joint Variation | Inverse Variation | Real-World Problems
61. ANS: D
Identify the general function represented by the graph.
Feedback
A
B
C
D
The graph of an absolute value function is in the shape of a V.
The graph of a constant function is a horizontal line that crosses the y-axis at a.
The graph of a square root function is a curve that starts at a point and continues in only
one direction.
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.1 Identify graphs as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify graphs as different types of functions.
KEY: Graphs | Types of Functions | Functions
62. ANS: A
Identify the general function represented by the graph.
Feedback
A
B
C
D
Correct!
The graph of a quadratic function is a parabola.
The graph of a constant function is a horizontal line that crosses the y-axis at a.
The graph of an identity function passes through all points with coordinates (a, a).
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.1 Identify graphs as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify graphs as different types of functions.
KEY: Graphs | Types of Functions | Functions
63. ANS: B
Identify the general function represented by the graph.
Feedback
A
B
C
D
The graph of an absolute value function is in the shape of a V.
Correct!
Is the equation of a rational function applicable to this graph?
Does the equation of an inverse variation function apply to this graph?
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.1 Identify graphs as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify graphs as different types of functions.
KEY: Graphs | Types of Functions | Functions
64. ANS: C
The identity function y = x is a special case of a direct variation function in which the constant is 1.
Feedback
A
B
C
D
The equation of an inverse variation function is
The equation of a constant function is y = a.
Correct!
The equation of an absolute value function is y = | x |.
PTS:
OBJ:
STA:
KEY:
65. ANS:
1
DIF: Basic
REF: Lesson 8-5
8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
Equations | Types of Functions | Functions
C
The general equation of an inverse variation function is
Feedback
A
.
The equation of an absolute value function is y = | x |.
.
B
C
D
The equation of a rational function is
.
Correct!
The equation of an identity function is y = x.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
KEY: Equations | Types of Functions | Functions
66. ANS: A
The general equation of an absolute value function is y = | x |.
Feedback
A
B
C
D
Correct!
The equation of an identity function is y = x.
The equation of a constant function is y = a.
The equation of a direct variation function is y = ax.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
KEY: Equations | Types of Functions | Functions
67. ANS: C
The general equation of a constant function is
.
Feedback
A
B
The equation of an absolute value function is y = | x |.
C
D
Correct!
The equation of a direct variation function is y = ax.
The equation of an inverse variation function is
.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
KEY: Equations | Types of Functions | Functions
68. ANS: A
The general equation of a quadratic function is
.
Feedback
A
B
C
Correct!
The equation of an identity function is y = x.
D
The equation of an absolute value function is y = | x |.
The equation of a rational function is
.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
KEY: Equations | Types of Functions | Functions
69. ANS: B
The general equation of a direct variation function is
.
Feedback
A
B
C
D
The equation of an absolute value function is y = | x |.
Correct!
The equation of an identity function is y = x.
The equation of a constant function is y = a.
PTS:
OBJ:
STA:
KEY:
70. ANS:
1
DIF: Basic
REF: Lesson 8-5
8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
Equations | Types of Functions | Functions
B
The general equation of an inverse variation function is
.
Feedback
A
B
C
The equation of an absolute value function is y = | x |.
Correct!
D
The equation of an identity function is y = x.
The equation of a rational function is
.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.2 Identify equations as different types of functions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8C.1 | IL J 8C
TOP: Identify equations as different types of functions.
KEY: Equations | Types of Functions | Functions
71. ANS: B
Solve the inequality using the “ = ” sign. Find the solution of the equation and the values of the variable that
would make the denominator zero. Use test values to determine the solution of the inequality.
Feedback
A
B
C
D
Did you solve the inequality correctly?
Correct!
Did you find the correct range?
Did you perform the verification steps correctly?
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.2 Solve rational inequalities.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8D.5 | IL J 8D
TOP: Solve rational inequalities.
KEY: Rational Inequalities | Solve Rational Inequalities
72. ANS: D
Solve the inequality using the “ = ” sign. Find the solution of the equation and the values of the variable that
would make the denominator zero. Use test values to determine the solution of the inequality.
Feedback
A
B
Did you solve the inequality correctly?
Did you find the correct range of p?
C
D
Did you perform the verification steps correctly?
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 8-6
OBJ: 8-6.2 Solve rational inequalities.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: IL J 8D.5 | IL J 8D
TOP: Solve rational inequalities.
KEY: Rational Inequalities | Solve Rational Inequalities
73. ANS: A
Make a table of values. Connect the points to sketch a smooth curve.
Feedback
A
B
C
D
Correct!
Multiply the constant with the value of the exponential function.
Did you check the sign of the constant in the function?
What is the effect of multiplying a function by a constant?
PTS: 1
DIF: Average
REF: Lesson 9-1
OBJ: 9-1.1 Graph exponential functions.
NAT: NA 1 | NA 3 | NA 4 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Graph exponential functions.
KEY: Exponential Functions | Graphs | Graph Exponential Functions
74. ANS: B
Make a table of values. Connect the points to sketch a smooth curve.
Feedback
A
B
C
D
Did you use a linear function instead of an exponential function?
Correct!
Multiply the constant with the value of the exponential function.
What is the effect of multiplying a function by a constant?
PTS: 1
DIF: Average
REF: Lesson 9-1
OBJ: 9-1.1 Graph exponential functions.
NAT: NA 1 | NA 3 | NA 4 | NA 10 | NA 2
STA: IL J 8B.2 | IL J 8B
TOP: Graph exponential functions.
KEY: Exponential Functions | Graphs | Graph Exponential Functions
75. ANS: D
Use the Product Property and the Inverse Property of Exponents and Logarithms.
Feedback
A
B
C
D
Did you calculate the logarithm correctly?
Did you substitute the given logarithmic values for solving the expression?
Did you use the Quotient Property of Logarithms?
Correct!
PTS: 1
DIF: Average
REF: Lesson 9-3
OBJ: 9-3.1 Simplify and evaluate expressions using the properties of logarithms.
NAT: NA 1 | NA 4 | NA 6 | NA 7 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Simplify and evaluate expressions using the properties of logarithms.
KEY: Simplify Expressions | Evaluate Expressions | Logarithmic Properties
76. ANS: B
Use the Product Property and the definition of logarithm.
Feedback
A
B
C
D
Did you substitute the values correctly?
Correct!
Have you used the Quotient Property of Logarithms?
Did you use the properties of logarithms?
PTS: 1
DIF: Average
REF: Lesson 9-3
OBJ: 9-3.2 Solve logarithmic equations using the properties of logarithms.
NAT: NA 1 | NA 4 | NA 6 | NA 7 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve logarithmic equations.
KEY: Solve Equations | Logarithmic Equations
77. ANS: C
Use the Property of Inequality for Logarithmic Functions and the Power Property of Logarithms to solve the
equation.
Feedback
A
B
C
D
Take the logarithms of both the sides of the equation.
Did you use the Quotient Property of Logarithms?
Correct!
Did you substitute the values of the equation according to the Power Property of
Logarithms?
PTS: 1
DIF: Average
REF: Lesson 9-4
OBJ: 9-4.1 Solve exponential equations using common logarithms.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve exponential equations using common logarithms.
KEY: Solve Equations | Exponential Equations | Common Logarithms
78. ANS: B
Use the Property of Inequality for Logarithmic Functions and the Power Property of Logarithms to solve the
inequality.
Feedback
A
B
C
D
How do you solve an exponential inequality?
Correct!
Take the logarithm of both sides of the inequality.
Did you use the Quotient Property of Logarithms?
PTS: 1
DIF: Average
REF: Lesson 9-4
OBJ: 9-4.2 Solve exponential inequalities using common logarithms.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve exponential inequalities using common logarithms.
KEY: Solve Inequalities | Exponential Inequalities | Common Logarithms
79. ANS: C
Use the Property of Inequality for Logarithmic Functions and the Power Property of Logarithms to solve the
inequality.
Feedback
A
B
C
Did you use the Power Property to calculate the logarithmic expression?
How do you solve an exponential inequality?
Correct!
D
Take the logarithm of both sides of the inequality.
PTS: 1
DIF: Average
REF: Lesson 9-4
OBJ: 9-4.2 Solve exponential inequalities using common logarithms.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve exponential inequalities using common logarithms.
KEY: Solve Inequalities | Exponential Inequalities | Common Logarithms
80. ANS: D
Use the Change of Base Formula to express the logarithm in terms of common logarithms.
Feedback
A
B
C
D
Did you use the Change of Base Formula correctly?
What is the Change of Base Formula?
Did you interchange the original base and exponent?
Correct!
PTS: 1
DIF: Average
REF: Lesson 9-4
OBJ: 9-4.3 Evaluate logarithmic expressions using the Change of Base Formula.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.5 | IL J 6B.6 | IL J 6B
TOP: Evaluate logarithmic expressions using the Change of Base Formula.
KEY: Evaluate Expressions | Logarithmic Expressions | Change of Base Formula
81. ANS: D
Use the Change of Base Formula to express the logarithm in terms of common logarithms.
Feedback
A
B
C
D
Did you use the Change of Base Formula correctly?
What is the Change of Base Formula?
Did you interchange the original base and exponent values?
Correct!
PTS: 1
DIF: Average
REF: Lesson 9-4
OBJ: 9-4.3 Evaluate logarithmic expressions using the Change of Base Formula.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.5 | IL J 6B.6 | IL J 6B
TOP: Evaluate logarithmic expressions using the Change of Base Formula.
KEY: Evaluate Expressions | Logarithmic Expressions | Change of Base Formula
82. ANS: D
Use the Inverse Property of Base e and Natural Logarithms to evaluate the expression.
Feedback
A
B
C
D
You have used an incorrect base value.
Did you apply the Inverse Property of Base e and Natural Logarithms correctly?
The exponential and logarithmic functions are inverses.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 9-5
9-5.1 Evaluate expressions involving the natural base and natural logarithms.
NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 6B.5 | IL J 6B.6 | IL J 6B
Evaluate expressions involving the natural base and natural logarithms.
Evaluate Expressions | Natural Logarithms
83. ANS: B
Use natural logarithms to solve the equation.
Feedback
A
B
C
D
Did you verify the solution in the original equation?
Correct!
Apply the Inverse Property of Exponents and Logarithms.
Did you substitute all the logarithm values correctly?
PTS: 1
DIF: Average
REF: Lesson 9-5
OBJ: 9-5.2 Solve exponential equations using natural logarithms.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve exponential equations using natural logarithms.
KEY: Solve Equations | Exponential Equations | Natural Logarithms
84. ANS: D
Use natural logarithms to solve the equation.
Feedback
A
B
C
D
Apply the Inverse Property of Exponents and Logarithms.
Did you verify the solution in the original equation?
Did you check the constant in the original equation?
Correct!
PTS: 1
DIF: Average
REF: Lesson 9-5
OBJ: 9-5.2 Solve exponential equations using natural logarithms.
NAT: NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 6B.6 | IL J 6B
TOP: Solve exponential equations using natural logarithms.
KEY: Solve Equations | Exponential Equations | Natural Logarithms
85. ANS: D
Use natural logarithms to solve the equation.
Feedback
A
B
C
D
Did you calculate the logarithm for the base value?
Did you calculate the natural logarithm for the value in the expression?
Did you calculate according to the Inverse Property of Exponents and the Property of
Equality for Logarithms?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
86. ANS:
1
DIF: Average
REF: Lesson 9-5
9-5.3 Solve exponential inequalities using natural logarithms.
NA 1 | NA 3 | NA 4 | NA 7 | NA 2 STA: IL J 6B.6 | IL J 6B
Solve exponential inequalities using natural logarithms.
Solve Inequalities | Exponential Inequalities | Natural Logarithms
A
Apply the formula y = a
to calculate the exponential decay.
Feedback
A
B
Correct!
This is the value of the printer after one year.
C
D
Did you use the correct formula?
Did you calculate correctly?
PTS:
OBJ:
NAT:
TOP:
KEY:
87. ANS:
1
DIF: Average
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
A
Apply the formula y = a
to calculate the exponential decay.
Feedback
A
B
C
D
Correct!
Did you calculate correctly?
This is the value of the desktop after one year.
Did you use the correct formula?
PTS:
OBJ:
NAT:
TOP:
KEY:
88. ANS:
1
DIF: Average
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
B
Apply the formula y = a
to calculate the exponential decay.
Feedback
A
B
C
D
Did you calculate correctly?
Correct!
This is the value of the touch screen monitor after one year.
Did you use the correct formula?
PTS:
OBJ:
NAT:
TOP:
KEY:
89. ANS:
1
DIF: Average
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
B
Apply the formula y = a
to calculate the exponential decay.
Feedback
A
B
C
D
Did you calculate correctly?
Correct!
This is the value of the laptop after one year.
Did you use the correct formula?
PTS: 1
DIF: Average
REF: Lesson 9-6
OBJ: 9-6.1 Use logarithms to solve problems involving exponential decay.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
TOP: Use logarithms to solve problems involving exponential decay.
KEY: Solve Problems | Logarithms | Exponential Decay
90. ANS: D
Apply the formula
to calculate the exponential decay.
Feedback
A
B
C
D
Write the rate of change as a decimal before using it in the formula.
Use natural logarithms for calculation, not common logarithms.
Did you substitute the correct values in the formula?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
91. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
B
Apply the formula
to calculate the exponential decay.
Feedback
A
B
C
D
When did the sauropods exist?
Correct!
Did you substitute the values correctly?
Did you use the correct formula?
PTS:
OBJ:
NAT:
TOP:
KEY:
92. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
C
Apply the formula
to calculate the exponential decay.
Feedback
A
B
C
D
Check the value of the constant.
Use natural logarithm for calculation, not common logarithm.
Correct!
Is the rate of decay given in percent?
PTS:
OBJ:
NAT:
TOP:
KEY:
93. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.1 Use logarithms to solve problems involving exponential decay.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential decay.
Solve Problems | Logarithms | Exponential Decay
B
Apply the formula y = a
Feedback
to calculate the exponential growth.
A
B
C
D
Incorrect logarithm values are used in calculation.
Correct!
Did you calculate correctly?
Did you use the Power Property of Logarithms?
PTS:
OBJ:
NAT:
TOP:
KEY:
94. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.2 Use logarithms to solve problems involving exponential growth.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential growth.
Solve Problems | Logarithms | Exponential Growth
B
Apply the formula y = a
to calculate the exponential growth.
Feedback
A
B
C
D
Did you convert trillion to billion correctly?
Correct!
Did you use the correct logarithm values?
Did you calculate correctly?
PTS:
OBJ:
NAT:
TOP:
KEY:
95. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.2 Use logarithms to solve problems involving exponential growth.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential growth.
Solve Problems | Logarithms | Exponential Growth
C
Apply the formula y = a
to calculate the exponential growth.
Feedback
A
B
C
D
The growth rate is in percent.
Use the Product Property of Logarithms.
Correct!
Use the formula for exponential growth, not exponential decay.
PTS:
OBJ:
NAT:
TOP:
KEY:
96. ANS:
1
DIF: Advanced
REF: Lesson 9-6
9-6.2 Use logarithms to solve problems involving exponential growth.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential growth.
Solve Problems | Logarithms | Exponential Growth
B
Apply the formula y = a
to calculate the exponential growth.
Feedback
A
B
C
D
Did you convert trillions to billions correctly?
Correct!
Did you use the correct percentage of growth?
Did you calculate correctly?
PTS: 1
DIF: Advanced
REF: Lesson 9-6
OBJ:
NAT:
TOP:
KEY:
97. ANS:
9-6.2 Use logarithms to solve problems involving exponential growth.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
Use logarithms to solve problems involving exponential growth.
Solve Problems | Logarithms | Exponential Growth
C
Apply the formula
to calculate the exponential growth.
Feedback
A
B
C
D
Did you use the time in which the bacteria reproduce?
Have you used the correct formula for exponential growth?
Correct!
Have you used the Inverse Property of Logarithms?
PTS: 1
DIF: Average
REF: Lesson 9-6
OBJ: 9-6.2 Use logarithms to solve problems involving exponential growth.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 STA: IL J 6B.6 | IL J 8D | IL J 8D.2 | IL J 8D.6 | IL J 6B
TOP: Use logarithms to solve problems involving exponential growth.
KEY: Solve Problems | Logarithms | Exponential Growth
98. ANS: A
If the measures of one side and one acute angle are known, you can determine the measures of all sides and
angles of the triangle by using trigonometric functions.
Feedback
A
B
C
D
Correct!
Did you interchange the values of p and q?
Use the measures of the side and acute angle to find the missing measures.
Did you use the trigonometric functions to find the missing measures?
PTS: 1
DIF: Advanced
REF: Page 707
OBJ: 13-1.2 Solve right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve right triangles.
KEY: Solve Triangles | Right Triangles
99. ANS: D
Write an equation using a trigonometric function that involves the ratio of l and 20.
Feedback
A
B
C
D
Did you use the correct trigonometric function?
Did you write an equation using a trigonometric function?
Use the tan function to find the height of the lower part of the tree.
Correct!
PTS: 1
DIF: Average
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
100. ANS: A
Write an equation using a trigonometric function.
Feedback
A
B
C
D
Correct!
Did you write an equation using a trigonometric function?
Use the tan function to find the distance between the two boys.
Did you use the correct trigonometric function?
PTS: 1
DIF: Advanced
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
101. ANS: B
Write an equation using a trigonometric function that involves the ratio of the height of Eiffel Tower and the
distance of the bus from the tower.
Feedback
A
B
C
D
Did you write an equation using a trigonometric function?
Correct!
Use tan 60 to find the distance between the bus and the tower.
Did you use the correct tan value?
PTS: 1
DIF: Average
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
102. ANS: B
Write an equation using a trigonometric function that involves the ratio of the height of the kite from the ground
and the length of the string.
Feedback
A
B
C
D
Did you write an equation using a trigonometric function?
Correct!
Use sin 60 to find the length of the string.
Write an equation using trigonometric functions and then find the length.
PTS: 1
DIF: Basic
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
103. ANS: A
Use the tan function to find the measure of the inclined angle to find the vertical rise.
Feedback
A
B
C
D
Correct!
When one of the trigonometric ratios is known, use its inverse to find the measure of the
required angle.
Did you find the inclined angle correctly?
Did you use the correct trigonometric function?
PTS: 1
DIF: Advanced
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
104. ANS: C
Use the
function to find the measure of the required angle.
Feedback
A
B
C
D
Did you use the correct trigonometric function to determine the required angle?
When one of the trigonometric ratios is known, use its inverse to find the measure of the
required angle.
Correct!
Use the inverse of the tan function to find the measure of the required angle.
PTS: 1
DIF: Advanced
REF: Page 707
OBJ: 13-1.3 Solve real-world problems involving right triangles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Solve real-world problems involving right triangles.
KEY: Right Triangles | Real-World Problems
105. ANS: D
First, find the reference angle
. Then, find the value of the trigonometric function for
. Then, using the
quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ.
Feedback
A
B
C
D
Use a reference angle to find the value of the given trigonometric function.
Did you find the reference angle of the given angle?
Find the sine of the given angle, not tan.
Correct!
PTS: 1
DIF: Average
REF: Page 723
OBJ: 13-3.1 Find values of sine and cosine for general angles. NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Find values of sine and cosine for general angles.
KEY: Sine | Cosine
106. ANS: B
First, find the reference angle
. Then, find the value of the trigonometric function for
. Then, using the
quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ.
Feedback
A
B
C
D
Use a reference angle to find the value of the given trigonometric function.
Correct!
Find the csc of the given angle and not cos.
Did you find the reference angle of the given angle?
PTS:
OBJ:
NAT:
TOP:
1
DIF: Average
REF: Page 723
13-3.2 Find values of secant and cosecant for general angles.
NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
Find values of secant and cosecant for general angles.
KEY: Secant | Cosecant
107. ANS: C
If the quadrant that contains the terminal side of θ in the standard position and the exact value of one
trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained
using the function definitions.
Feedback
A
B
C
D
Did you use the correct signs of the trigonometric functions for Quadrant III?
Use the function definitions to find the remaining five trigonometric functions.
Correct!
The angle is in Quadrant III and not in Quadrant I.
PTS: 1
DIF: Advanced
REF: Page 723
OBJ: 13-3.4 Use reference angles to find values of trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Use reference angles to find values of trigonometric functions.
KEY: Reference Angles | Trigonometric Functions
108. ANS: C
If the quadrant that contains the terminal side of θ in the standard position and the exact value of one
trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained
using the function definitions.
Feedback
A
B
C
D
Did you use the correct signs of the trigonometric functions for Quadrant III?
Use function definitions to find the remaining five trigonometric functions.
Correct!
The angle is in Quadrant III and not in Quadrant I.
PTS: 1
DIF: Advanced
REF: Page 723
OBJ: 13-3.4 Use reference angles to find values of trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Use reference angles to find values of trigonometric functions.
KEY: Reference Angles | Trigonometric Functions
109. ANS: A
If the quadrant that contains the terminal side of θ in the standard position and the exact value of one
trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained
using the function definitions.
Feedback
A
B
C
D
Correct!
Did you use the correct signs of the trigonometric functions for Quadrant IV?
The angle is in Quadrant IV and not in Quadrant I.
Use function definitions to find the remaining five trigonometric functions.
PTS:
OBJ:
NAT:
TOP:
KEY:
110. ANS:
1
DIF: Advanced
REF: Page 723
13-3.4 Use reference angles to find values of trigonometric functions.
NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
Use reference angles to find values of trigonometric functions.
Reference Angles | Trigonometric Functions
A
If the quadrant that contains the terminal side of θ in the standard position and the exact value of one
trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained
using the function definitions.
Feedback
A
B
C
D
Correct!
The angle is in Quadrant IV and not in Quadrant I.
Did you use the correct signs of the trigonometric functions for Quadrant IV?
Use function definitions to find the remaining five trigonometric functions.
PTS: 1
DIF: Advanced
REF: Page 723
OBJ: 13-3.4 Use reference angles to find values of trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
TOP: Use reference angles to find values of trigonometric functions.
KEY: Reference Angles | Trigonometric Functions
111. ANS: D
If the quadrant that contains the terminal side of θ in the standard position and the exact value of one
trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained
using the function definitions.
Feedback
A
B
C
D
The angle is in Quadrant II and not in Quadrant I.
Use function definitions to find the remaining five trigonometric functions.
Did you use the correct signs of the trigonometric functions for Quadrant II?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
112. ANS:
Let
1
DIF: Advanced
REF: Page 723
13-3.4 Use reference angles to find values of trigonometric functions.
NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D
Use reference angles to find values of trigonometric functions.
Reference Angles | Trigonometric Functions
A
be any triangle with a, b, and c representing the measures of sides opposite angles with
measurements A, B, and C respectively. Then,
.
Feedback
A
B
C
D
Correct!
Apply the Law of Sines to solve the triangle.
Did you apply the Law of Sines to solve the triangle?
Did you interchange the values of the sides?
PTS: 1
DIF: Average
REF: Page 731
OBJ: 13-4.1 Solve problems by using the Law of Sines.
NAT: NA 1 | NA 4 | NA 6 | NA 10 | NA 3
STA: IL J 9D.1 | IL J 9D
TOP: Solve problems by using the Law of Sines.
KEY: Solve Problems | Law of Sines
113. ANS: B
If the terminal side of an angle θ in the standard position intersects the unit circle at
, then
and
.
Feedback
A
B
C
D
Did you write the answers in the correct order?
Correct!
Did you change the sign of the coordinates?
Check the sign of the coordinates.
PTS: 1
DIF: Basic
REF: Page 743
OBJ: 13-6.1 Define and use the trigonometric functions based on the unit circle.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.4 | IL J 9D
TOP: Define and use the trigonometric functions based on the unit circle.
KEY: Trigonometric Functions | Unit Circle
114. ANS: B
If the terminal side of an angle θ in the standard position intersects the unit circle at
, then
.
Feedback
A
B
C
D
Did you write the answers in the correct order?
Correct!
Did you change the sign of the coordinates?
Check the sign of the coordinates.
PTS: 1
DIF: Basic
REF: Page 743
OBJ: 13-6.1 Define and use the trigonometric functions based on the unit circle.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.4 | IL J 9D
TOP: Define and use the trigonometric functions based on the unit circle.
KEY: Trigonometric Functions | Unit Circle
115. ANS: B
Evaluate the value of the trigonometric function.
Feedback
A
B
C
D
Where is the terminal side of the angle?
Correct!
What is the reference angle?
Is the terminal side of the angle on a quadrant line?
PTS: 1
DIF: Basic
REF: Page 743
OBJ: 13-6.2 Find the exact values of trigonometric functions of angles.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.4 | IL J 9D
TOP: Find the exact values of trigonometric functions of angles.
KEY: Trigonometric Functions
116. ANS: D
Evaluate the inverse trigonometric function to obtain an angle measure.
Feedback
A
B
C
D
Did you use the correct trigonometric function?
Did you calculate the inverse correctly?
Did you find the inverse of the trigonometric function?
Correct!
and
PTS: 1
DIF: Basic
REF: Page 749
OBJ: 13-7.1 Solve equations by using inverse trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.6 | IL J 9D
TOP: Solve equations by using inverse trigonometric functions.
KEY: Inverse Trigonometric Functions
117. ANS: B
Evaluate the inverse trigonometric function to obtain an angle measure.
Feedback
A
B
C
D
Did you use the correct trigonometric function?
Correct!
Did you find the inverse of the trigonometric function?
Did you calculate the inverse correctly?
PTS: 1
DIF: Basic
REF: Page 749
OBJ: 13-7.1 Solve equations by using inverse trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.6 | IL J 9D
TOP: Solve equations by using inverse trigonometric functions.
KEY: Inverse Trigonometric Functions
118. ANS: B
Evaluate the inverse trigonometric function to obtain an angle measure. Find the value of the cotangent of that
angle measure.
Feedback
A
B
C
D
Did you find the cotangent value correctly?
Correct!
Did you find the inverse of the correct trigonometric function?
Did you calculate the answer correctly?
PTS: 1
DIF: Basic
REF: Page 749
OBJ: 13-7.2 Find values of expressions involving trigonometric functions.
NAT: NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.5 | IL J 9D
TOP: Find values of expressions involving trigonometric functions.
KEY: Trigonometric Functions
119. ANS: C
Evaluate the inverse trigonometric function to obtain an angle measure. Find the value of the cosine of that
angle measure.
Feedback
A
B
C
D
Did you find the cosine of the answer?
Did you evaluate the inverse trigonometric function first?
Correct!
Did you evaluate the correct inverse function?
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Basic
REF: Page 749
13-7.2 Find values of expressions involving trigonometric functions.
NA 1 | NA 4 | NA 9 | NA 10 | NA 3
STA: IL J 9D.5 | IL J 9D
Find values of expressions involving trigonometric functions.
Trigonometric Functions