Math O 3
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
Tell whether the function is quadratic. Explain.
x
y
a.
2.
21
1
2
9
4
37
No, the function is not quadratic. The second differences are not
constant.
Yes, the function is quadratic. The second differences are
constant.
b.
____
0
Tell whether the function is quadratic. Explain.
x
y
a.
b.
0
0
1
1
2
8
Yes, the function is quadratic. The second differences are
constant.
No, the function is not quadratic. The second differences are not
constant.
____
3.
Tell whether the function
is quadratic. Explain.
a. This is not a quadratic function because the x-term is missing.
b. This is a quadratic function because it can be written in standard
form as
.
c. This is not a quadratic function because it is not written in
standard form.
d.
This is a quadratic function because it has an
term.
____
4.
Use a table with values x = {–2, –1, 0, 1, 2} to graph the quadratic function y =
−x2.
y
a.
–8
16
16
12
12
8
8
4
4
–4
4
8 x
–8
–4
–4
–4
–8
–8
–12
–12
–16
–16
y
b.
–8
y
c.
16
12
12
8
8
4
4
4
8 x
8 x
4
8 x
y
d.
16
–4
4
–8
–4
–4
–4
–8
–8
–12
–12
–16
–16
____
5.
Tell whether the graph of the quadratic function
upward or downward. Explain.
a. Because
, the parabola opens downward.
b. Because
, the parabola opens downward.
c. Because
, the parabola opens upward.
d. Because
, the parabola opens upward.
opens
____
6.
Identify the vertex of the parabola. Then give the minimum or maximum value
of the function.
y
10
8
(3, 6)
6
4
2
–10 –8
–6
–4
–2
2
–2
4
6
8
10
x
–4
–6
–8
–10
a.
b.
c.
d.
____
7.
The vertex is
The vertex is
The vertex is
The vertex is
, and the minimum is 6.
, and the maximum is 6.
, and the maximum is 3.
, and the minimum is 3.
Find the domain and range.
y
10
(–6, 8)
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a.
b.
____
8.
D:
R: all real numbers
D: all real numbers
R:
c.
d.
D: all real numbers
R:
D:
R:
A rectangular picture measuring 5 in. by 9 in. is surrounded by a frame with
uniform width x. Write a quadratic function in standard form to show the
combined area of the picture and frame.
a.
c.
b.
____
9.
d.
Find the zeros of the quadratic function
from the graph.
y
10
8
6
4
2
–10 –8
–6
–4
–2
2
–2
4
6
8
10
x
–4
–6
–8
–10
a.
b.
____ 10.
c.
d.
1.5
4 and –1
–8
2 and –8
Find the axis of symmetry of the parabola.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a.
b.
____ 11.
c.
d.
Find the axis of symmetry of the graph of
a.
b.
c.
d.
.
____ 12.
____ 13.
Find the vertex of the parabola
.
a.
(–3, 2)
c.
(–2, 0) and (–4, 0)
b.
(2, –3)
d.
(3, –70)
The trajectory of a potato launched from a potato cannon on the ground at an
angle of 45 degrees with an initial speed of 65 meters per second can be
x – 0.0023x2, where the x-axis is the ground.
modeled by the parabola:
Find the height of the highest point of the trajectory and the horizontal
distance the potato travels before hitting the ground.
a.
b.
c.
d.
height: 109 m; distance: 435 m
height: 21 m; distance: 218 m
height: 218 m; distance: 21 m
height: 435 m; distance: 109 m
____ 14.
The height of a curved support beam can be modeled by
.
Find the height and width of the beam.
height
width
a.
b.
c.
d.
____ 15.
height = 25 units; width = 60 units
height = 12 units; width = 60 units
height = 25 units; width = 120 units
height = 12 units; width = 120 units
Graph y = –x2 – 4x – 3.
y
a.
–10 –8
–6
–4
–2
10
8
8
6
6
4
4
2
2
2
–2
4
6
8
x
–6
–4
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
y
–10 –8
y
c.
10
b.
____ 16.
x.
–2
10
8
8
6
6
4
4
2
2
2
4
6
8
x
4
6
8
x
2
4
6
8
x
y
d.
10
–2
2
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
Order the functions from narrowest graph to widest graph.
,
a.
, and
,
,
b.
,
,
c.
,
,
d.
,
,
____ 17.
Solve the equation x2 + 4x + 3 = 0 by graphing the related function.
a. The solutions are 3 and 1.
b. The solutions are 4 and 3.
c. The solutions are –3 and –1.
d. The solutions are –2 and –1.
____ 18.
Solve the equation
a.
b.
by graphing the related function.
c.
d.
____ 19.
A golfer hits the golf ball. The quadratic function
gives the
time x seconds when the golf ball is at height 0 feet. How long does it take for
the golf ball to return to the ground?
a. 16 sec
c. 10 sec
b. 5 sec
d. 80 sec
____ 20.
A kicker starts a football game by “kicking off”. The quadratic function
models the football’s height after x seconds. How long is the
football in the air?
a. 1.94 sec
c. 15 sec
b. 6.63 sec
d. 3.75 sec
____ 21.
Use the Zero Product Property to solve the equation
a. The solutions are –2 and 1.
b. The solutions are 4 and –3.
c. The solutions are –4 and 3.
d. The solutions are 2 and –1.
____ 22.
Solve the quadratic equation
a. –4 and 2
b. 4 and 2
c. –4 and –2
by factoring.
.
d.
____ 23.
4 and –2
Solve the quadratic equation
a. −4
c.
1
3
b.
d.
–1
1
by factoring.
____ 24.
The height of an arrow that is shot upward at an initial velocity of 40 meters
, where h is the height in meters
per second can be modeled by
and t is the time in seconds. Find the time it takes for the arrow to reach the
ground.
a. 6 sec
c. 8 sec
b. 4 sec
d. 2 sec
____ 25.
Write a polynomial to represent the area of the shaded region. Then solve for
x given that the area of the shaded region is 24 square units.
a.
c.
b.
d.
____ 26.
Solve
by using square roots.
a. The solutions are 2 and –2.
b. The solution is 2.
c. There is no solution.
d. The solution is –2.
____ 27.
Solve 4x2 – 121 = 0 by using square roots.
a. ± 11
c. ± 4
2
121
b. No solution
d. ± 2
11
____ 28.
Solve
. If necessary, round to the nearest hundredth.
a.
b.
c.
d.
3.16
100
20
There is no solution as you cannot take the square root of a
negative number.
____ 29.
Marianna is making a piñata that has a ball-like shape. The piñata has a
surface area of 60 square feet. Use the formula for the surface area of a
) to find the radius of the piñata.
sphere (
a. About 22.80 ft
c. About 2.19 ft
b. About 3.87 ft
d. About 4.78 ft
____ 30.
Complete the square for
to form a perfect square trinomial.
a.
c.
b.
d.
____ 31.
Solve
a. 3 and –2
b. 6 and –2
by completing the square.
c. 3 and 0
d. 6 and 3
____ 32.
Solve
by completing the square.
a. The solution is –5.
c. The solutions are –1 and 5.
b. There is no solution.
d. The solutions are –1 and –5.
____ 33.
A gardener wants to create a rectangular vegetable garden in a backyard. She
wants it to have a total area of 120 square feet, and it should be 12 feet longer
than it is wide. What dimensions should she use for the vegetable garden?
Round to the nearest hundredth of a foot.
a. 10.95 feet by 22.95 feet
c. 12.49 feet by 24.49 feet
b. 6.49 feet by 18.49 feet
d. 4.95 feet by 16.95 feet
____ 34.
Solve
by using the Quadratic Formula.
a. x = 9 or x = −1
c. x = 54 or x = −46
b. x = 1 or x = −9
d. x = 18 or x = −2
____ 35.
Solve 3x2 – 5x – 1 = 0 by using the Quadratic Formula. If necessary, round to
the nearest hundredth.
a. x ≈ 11.08 or x ≈ –1.08
c. x ≈ 1.85 or x ≈ –0.18
b. x ≈ 6.01 or x ≈ 3.99
d. There are no solutions.
____ 36.
Find the number of solutions of the equation
discriminant.
by using the
a.
b.
c.
d.
Cannot determine the number of solutions. The discriminant can
only be used for a quadratic equation, and
is
not a quadratic equation.
There are no real solutions.
There is one solution.
There are two solutions.
____ 37.
Workers preparing for the city’s Fourth of July celebration shoot an object
straight up with an initial velocity of 210 ft/s2 from a height of 3 feet above the
ground. Will the object reach a height of 670 feet 0, 1, or 2 times? Use the
where v is the initial velocity in feet per second and
equation
c is the initial height in feet of the object above the ground. Use the
discriminant to explain your answer.
a. 0 times; The discriminant is negative, so the equation has no
solutions.
b. 2 times; The discriminant is positive, so the equation has two
solutions.
c. Cannot determine. There is no discriminant in the equation.
d. 1 time; The discriminant is zero, so the equation has one
solution.
____ 38.
Solve
a.
b.
.
or
or
c.
d.
or
or
____ 39.
A farmer has 120 yards of fencing to build around a rectangular orchard. Let w
be the width of the orchard. Write an equation giving the area of the orchard.
Find the dimensions of the orchard when the area is 900 square yards.
a.
; The width is 50 yd, and the length is 18 yd.
b.
; The width is 30 yd, and the length is 30 yd.
c.
; The width is 58 yd, and the length is 62 yd.
d.
; The width is 72 yd, and the length is 48 yd.
____ 40.
Find the next three terms in the geometric sequence
a. –1, 6, –36
c.
,
,
b.
____ 41.
,
,
d.
,
, 6,
,
, ...
,
The first term of a geometric sequence is 512, and the common ratio is 0.5.
What is the 8th term of the sequence?
a.
b.
c.
d.
22.63
2
4
8
____ 42.
A computer is worth $4000 when it is new. After each year it is worth half what
it was the previous year. What will its worth be after 4 years? Round your
answer to the nearest dollar.
a. $1000
c. $125
b. $250
d. $500
____ 43.
The function
, where x is the time in years, models a
declining lemming population. How many lemmings will there be in 3 years?
a. About 91 lemmings
c. About 273 lemmings
b. About 253 lemmings
d. About 74 lemmings
____ 44.
Tell whether the function
is exponential. Explain your answer.
a. Exponential function.
As the x-values are increased by a constant amount, the
y-values increase by the same amount.
b. Exponential function.
As the x-values are increased by a constant amount, the
y-values are multiplied by a constant amount.
c. Not an exponential function.
As the x-values are increased by a constant amount, the
y-values are not multiplied by a constant amount.
d. Not an exponential function.
As the x-values are increased by a constant amount, the
y-values increase by the same amount.
____ 45.
Graph
a.
.
c.
b.
____ 46.
d.
Graph y = –(4)x.
y
a.
y
c.
5
15
–4
10
–3
–2
–1
1
2
3
4
x
1
2
3
4
x
–5
5
–10
–4
–3
–2
–1
1
2
3
4
x
–15
–5
y
b.
y
d.
5
20
15
–4
–3
–2
–1
1
2
3
4
10
x
5
–5
–4
–3
–2
–1
–5
–10
–10
–15
–15
–20
____ 47.
Graph
.
a.
c.
b.
d.
____ 48.
In the year 2000, the population of Mexico was about 100 million, and it was
growing by 1.53% per year. At this growth rate, the function
gives the population, in millions, x years after 2000. Using
this model, in what year would the population reach 111 million? Round your
answer to the nearest year.
a. 2009
c. 539
b. 2008
d. 2007
____ 49.
The value of a gold coin picturing the head of the Roman Emperor Vespasian
is increasing at the rate of 5% per year. If the coin is worth $105 now, what will
it be worth in 11 years?
a. $169.79
c. $179.59
b. $160.00
d. $162.75
____ 50.
Write a compound interest function to model the following situation. Then, find
the balance after the given number of years.
$2,100 invested at a rate of 2% compounded annually; 3 years
a.
; $56,700
b.
; $2,229
c.
; $16,800
d.
; $2,510
____ 51.
The fish population of Lake Collins is decreasing at a rate of 4% per year. In
2002 there were about 1,100 fish. Write an exponential decay function to
model this situation. Then find the population in 2007.
a.
The population in 2007 will be about 896.91 fish.
b.
The population in 2007 will be about 86 fish.
c.
The population in 2007 will be about 220 fish.
d.
The population in 2007 will be about 897 fish.
____ 52.
A radioactive isotope has a half-life of 13 hours. Find the amount of the
isotope left from a 400-milligram sample after 52 hours. If necessary, round
your answer to the nearest thousandth.
a. 25 mg
c. 0.049 mg
b. 12.5 mg
d. 7.692 mg
____ 53.
Graph the data set {(–1, 0.5), (0, 1), (1, 2), (3, 8), (5, 32)}. Which kind of model
best describes the data?
a. linear
c. quadratic
b. exponential
d. cubic
____ 54.
Look for a pattern in the data set. Which kind of model best describes the
data?
Population Growth of
Bacteria
Time
Number of
(hours)
Bacteria
0
2,000
1
5,000
2
12,500
3
4
a.
b.
____ 55.
31,250
78,125
c.
d.
exponential
cubic
quadratic
linear
Use the information in the table to predict the number of termites in the termite
colony after one year.
Termite Colony Population
Time
Number of
(months)
Termites
0
80
1
320
2
1,280
3
5,120
a.
b.
20,480 termites
1,342,177,280 termites
c.
d.
39,680 termites
16,777,216 termites
____ 56.
The function
gives the speed in feet per second (ft/s) of a
free-falling object after it has fallen x feet (ignoring air resistance). Find the
speed of the object after it has fallen 31 feet. If necessary, round your answer
to the nearest tenth.
a. 15.7 ft/s
c. 44.5 ft/s
b. 248 ft/s
d. 5.6 ft/s
____ 57.
Find the domain of the square-root function
a.
c.
–8
−1
9
b.
d.
–8
−8
____ 58.
Graph
.
.
y
a.
–9
–6
21
21
18
18
15
15
12
12
9
9
6
6
3
3
–3
–3
3
6
9
12
15
18
x
–9
–3
–3
–6
–9
–9
y
–6
–6
–6
b.
–9
y
c.
21
18
18
15
15
12
12
9
9
6
6
3
3
3
6
9
12
15
18
x
6
9
12
15
18
x
3
6
9
12
15
18
x
y
d.
21
–3
–3
3
–9
–6
–3
–3
–6
–6
–9
–9
____ 59.
Marguerite is given the function
and
3, 4, and 8. She
notices that two of these values are not in the function’s domain. Which two
values are not in the domain? What are the values of y for the two x-values in
the domain?
a. out of the domain: 4 and 8
values of y: 3 and 5
b. out of the domain: 4 and 8
values of y: 7 and 9
c. out of the domain: 2 and 8
values of y: 5 and 7
d. out of the domain: 2 and 3
values of y: 7 and 9
____ 60.
Simplify the expression
a.
4
7
.
c.
16
49
b.
____ 61.
d.
Simplify the expression
numbers.
. All variables represent nonnegative
a.
b.
c.
d.
____ 63.
____ 64.
Simplify
. The variable represents a nonnegative number.
a.
c.
b.
d.
Simplify
.
a.
c.
b.
d.
A community is building a square park with sides that measure 120 meters. To
separate the picnic area from the play area, the park is split by a diagonal line
from opposite corners. Determine the approximate length of the diagonal line
that splits the square. If necessary, round your answer to the nearest meter.
Picnic area
120 m
____ 62.
Play area
120 m
a.
b.
____ 65.
____ 66.
c.
d.
28,800 meters
170 meters
Simplify
240 meters
120 meters
. The variable represents a nonnegative number.
a.
c.
b.
d.
Subtract.
a.
b.
c.
d.
____ 67.
Simplify the expression
.
a.
c.
b.
d.
____ 68.
Find the perimeter of a triangle whose side lengths are 7 cm,
cm, and
cm. Give the answer as a radical expression in simplest form.
a.
(
) cm
b.
(
) cm
c.
(
) cm
d.
cm
____ 69.
Multiply. Write the product in simplest form.
____ 70.
a.
c.
b.
d.
Multiply. Write the product in simplest form.
a.
3 3
b. 3 3
+ 3 6
c.
d.
3 + 3 2
____ 71.
Multiply
. Write the product in simplest form.
a.
b.
____ 72.
____ 73.
c.
d.
–71
Simplify the quotient
a.
c.
b.
d.
Simplify
.
a.
c.
b.
d.
____ 74.
Solve the equation
a. c =
b. c = 40
____ 75.
Solve the equation
a. z = 26
b. z = 676
____ 76.
Solve the equation
a.
4096
b.
9
8
____ 77.
Solve the equation
a. z = –5
b. z = –3
c. z = –1
d. No solution.
____ 78.
Solve
a. z =
1
4
8
. Check your answer.
c. c = 400
d. c =
. Check your answer.
c. z = 6
d. z =
. Check your answer.
c.
81
d.
9
. Check your answer.
. Check your answer.
c. z = –4
b.
d.
z=5
No solution.
____ 79.
The area of a rectangle is 112. The length is 7, and the width is
. What is
the value of x? What is the width of the rectangle? (Hint: The area of a
rectangle is equal to length times width.)
a. The value of x is 256. The width is 16.
b. The value of x is 16. The width is 4.
c. The value of x is 16. The width is 256.
d. The value of x is 256. The width is 16 or –16.
____ 80.
Solve the equation. Check your answer.
a.
b.
____ 81.
____ 82.
____ 83.
____ 84.
c.
d.
16
7
Simplify the expression
a. 8
b. 4
Simplify the expression
a. 81
b. 9
Simplify the expression
a. 9
b. 3
15
17
.
c.
d.
16
192
c.
d.
53
3
c.
d.
920483
27
.
.
Tell whether the relationship is an inverse variation. Explain.
x
2
3
4
a.
b.
c.
y
409
240
194
The product xy is constant, so the relationship is not an inverse
variation.
The product xy is not constant, so the relationship is an inverse
variation.
The product xy is constant, so the relationship is an inverse
variation.
d.
____ 85.
____ 86.
Write and graph the inverse variation in which y = 4 when x = 2.
a.
c.
b.
d.
Let
a.
b.
____ 87.
The product xy is not constant, so the relationship is not an
inverse variation.
,
=0
= 36
, and
. Let y vary inversely as x. Find
c.
=1
d.
= 16
.
The frequency of a radio wave varies inversely as its wavelength. If a
1,000-meter wave has a frequency of 300 kilohertz, what is the wavelength of
a wave that has a frequency of 600 kilohertz? Round your answer to the
nearest meter.
a. 1,000 m
c. 500 m
b. 2,000 m
d. 180 m
____ 88.
Identify the excluded value for the rational function
a. 5
c. –1
b. 1
d. –5
____ 89.
Identify the asymptotes of
a.
b.
c.
d.
____ 90.
.
Vertical asymptote: x = 1 . Horizontal asymptote: y = 3.
Vertical asymptote: x = 3. Horizontal asymptote: y = 1 .
Vertical asymptote: x = 14 . Horizontal asymptote: y = –3.
Vertical asymptote: x = −1 . Horizontal asymptote: y = –3.
Graph the function
.
y
a.
–10 –8
–6
–4
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–6
–4
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
y
–10 –8
y
c.
10
b.
____ 91.
.
10
8
8
6
6
4
4
2
2
2
4
6
8
10
x
4
6
8
x
10
y
d.
10
–2
–2
2
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
2
4
6
8
x
Which rational function has a graph with the horizontal asymptote
a.
c.
?
b.
____ 92.
Find the excluded values of the rational expression
a.
b.
c.
d.
____ 93.
____ 95.
____ 96.
____ 97.
.
The excluded values are –4 and –1.
The excluded values are 3 and –5.
The excluded values are –5 and 4.
The excluded values are 4 and 1.
Simplify the rational expression
a.
b.
c.
d.
____ 94.
d.
. Identify any excluded values.
3r; r 3
3r; r 3 or 0
3r; no excluded values
;r 3
Simplify the rational expression
.
a.
c.
b.
d.
Simplify the rational expression
.
a.
c.
b.
d.
Multiply. Simplify your answer.
a.
c.
b.
d.
Multiply. Simplify your answer.
____ 98.
a.
c.
b.
d.
Multiply. Simplify your answer.
.
____ 99.
____ 100.
____ 101.
a.
c.
b.
d.
Divide. Simplify your answer.
a.
c.
b.
d.
Simplify
.
a.
c.
b.
d.
Add. Simplify your answer.
a.
c.
b.
____ 102.
____ 103.
d.
Subtract. Simplify your answer.
a.
c.
b.
d.
Find the LCM of
and
a.
b.
____ 104.
____ 105.
.
c.
d.
Add. Simplify your answer.
a.
c.
b.
d.
Subtract and simplify. Find the excluded values.
a.
;
b.
;
and
c.
;
,
and
d.
;
____ 106.
and
Divide. Simplify your answer.
____ 107.
a.
c.
b.
d.
Divide.
a.
b.
____ 108.
c.
d.
Divide by using long division.
a.
b.
____ 109.
____ 110.
____ 111.
____ 112.
c.
d.
Divide.
(
)
(
)
a.
c.
b.
d.
Divide.
a.
c.
b.
d.
Solve
. Check your answer.
6
13
a.
m=
b.
m = − 136
c.
m=
d.
m = − 176
6
17
Solve
a.
b.
z = 103
z = −2
. Check your answer.
c.
z= 2
d.
z = − 54
____ 113.
Marukh can wash the car in 50 minutes. Steven can wash the car in 40
minutes. If Marukh and Steven work together, how long will it take them to
wash the car? Round your answer to the nearest minute.
a. 90 minutes
c. 22 minutes
b. 5 minutes
d. 45 minutes
____ 114.
Solve
a.
b.
. Check for extraneous solutions.
c.
d.
x = –1 or x = 1
x=1
x = –1
x = 3 or x = –4
____ 115.
Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30
minutes if they work together. Working alone, it takes Rita 1 less hour to
complete the jigsaw puzzle than it takes Brittany, and Brittany completes the
jigsaw puzzle three times as fast as Maria. How much time would it take each
to complete the jigsaw puzzle working alone?
a. Rita takes 5 hours, Brittany takes 6 hours, and Maria takes 18
hours.
b. Rita takes 2 hours, Brittany takes 3 hours, and Maria takes 9
hours.
c. Rita takes 4 hours, Brittany takes 5 hours, and Maria takes 15
hours.
d. Rita takes 3 hours, Brittany takes 4 hours, and Maria takes 12
hours.
____ 116.
Find the tangent of
to the nearest thousandth.
A
5
C
a.
b.
2.400
0.417
13
12
B
c.
d.
0.923
0.385
____ 117.
A camera is mounted at a point 4,400 ft from the base of a rocket launching
pad. Assuming the rocket rises vertically, what is the height of the rocket from
its base when the camera angle is 30º? Round your answer to the nearest
foot.
a. 3,811 ft
c. 2,200 ft
b. 7,621 ft
d. 2,540 ft
Numeric Response
118.
For what value of c will
have one zero?
119.
Find the number of solutions of
.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
120.
The formula for finding the approximate volume of a cylinder is
,
where r is the radius and h is the height. The height of a cylinder is 18.09 cm
and the approximate volume is 9500 cm3. Find the radius of the cylinder to the
nearest hundredth of a centimeter.
121.
The hypotenuse of a right triangle is 13 cm. One of the legs is 7 cm longer
than the other leg. Find the area of the triangle. (Hint: Use the Pythagorean
Theorem.)
x
13
x+7
122.
The 7th term of a geometric sequence is 31.45728. The common ratio is –0.8.
Find the first term of the sequence.
123.
Solve the equation.
124.
Technetium-99 has a half life of approximately 6 hours. The original
measurement for the mass of a sample was lost. After 24 hours, 20 grams of
Technetium-99 remain. How many grams was the original sample?
125.
Find the area of the trapezoid if
.
the formula
,
, and
. Use
C
B
A
D
126.
At the grocery store, the numbers of rolls of paper towels Joyce can buy is
inversely proportional to the price of the rolls. She can afford 8 rolls of paper
towels that cost $0.50 each. How many rolls can Joyce buy if each costs
$2.00?
127.
What is the excluded value for
128.
The base of a triangle is
m and the area is
longer is the base than the height?
?
m . How much
Matching
Match each vocabulary term with its definition.
a. linear equation
b. minimum
c. parabola
d. quadratic equation
e. quadratic function
f. linear function
g. maximum
____ 129.
the y-value of the highest point on the graph of the function
____ 130.
a function that can be written in the form
are real numbers and
____ 131.
the y-value of the lowest point on the graph of the function
____ 132.
the shape of the graph of a quadratic function
____ 133.
an equation that can be written in the form
are real numbers and
, where a, b, and c
, where a, b, and c
Match each vocabulary term with its definition.
a. axis of symmetry
b. completing the square
c. discriminant
d. vertex
e. maximum
f. zero of a function
g. minimum
____ 134.
for the function f, any number x such that
____ 135.
the highest or lowest point on a parabola
____ 136.
in the quadratic equation
____ 137.
a process used to form a perfect-square trinomial
____ 138.
the line that divides the parabola into two symmetrical halves
Match each vocabulary term with its definition.
a.
b.
c.
d.
e.
f.
g.
h.
i.
common ratio
geometric sequence
arithmetic sequence
exponential decay
exponential function
exponential growth
half-life
compound interest
two-lives
____ 139.
the interest earned or paid on both the principal and previously earned interest
____ 140.
an exponential function of the form
____ 141.
a function of the form
> 0, and
____ 142.
an exponential function of the form
____ 143.
the time it takes for one-half of the substance to decay into another substance
____ 144.
a sequence in which the ratio of successive terms is a constant r, called the
common ratio, where
and
____ 145.
in a geometric sequence, the constant ratio of any term and the previous term
in which b > 1
, where a and b are real numbers with
,b
in which 0 < b < 1
Match each vocabulary term with its definition.
a. extraneous solution
b. exponential equation
c. radical equation
d. radical expression
e. radicand
f. square-root function
g. exponential expression
h. like radicals
____ 146.
radical terms having the same radicand and index
____ 147.
a solution of a derived equation that is not a solution of the original equation
____ 148.
a function whose rule contains a variable under a square-root sign
____ 149.
the number or expression under a radical sign
____ 150.
an expression that contains a radical sign
____ 151.
an equation that contains a variable within a radical
Match each vocabulary term with its definition
a. inverse variation
b. discontinuous function
c. asymptote
d. excluded value
e. direct variation
f. rational function
g. rational expression
h. rational equation
i. continuous function
____ 152.
a function whose rule can be written as a rational expression
____ 153.
a line that a graph gets closer to as the value of a variable becomes extremely
large or small
____ 154.
an equation that contains one or more rational expressions
____ 155.
a relationship between two variables, x and y, that can be written in the form
, where k is a nonzero constant and
____ 156.
an algebraic expression whose numerator and denominator are polynomials
and whose denominator has a degree greater than or equal to 1
____ 157.
a function whose graph has one or more jumps, breaks, or holes
____ 158.
value of x for which a function or expression is not defined
Math O 3
Answer Section
MULTIPLE CHOICE
1. ANS: B
If the first differences of the x-terms are constant, check the differences of the
y-terms.
The set of ordered pairs satisfies a quadratic function.
Feedback
A
B
Check the second y-differences.
Correct!
PTS:
OBJ:
TOP:
2. ANS:
1
DIF: Basic
REF: Page 590
9-1.1 Identifying Quadratic Functions
9-1 Identifying Quadratic Functions
B
NAT: 12.5.2.b
If the first differences of the x-terms are constant, check the differences of the
y-terms.
The set of ordered pairs does not satisfy a quadratic function.
Feedback
A
B
Check the second y-differences.
Correct!
PTS:
OBJ:
TOP:
3. ANS:
1
DIF: Basic
REF: Page 590
9-1.1 Identifying Quadratic Functions
9-1 Identifying Quadratic Functions
B
NAT: 12.5.2.b
is a quadratic function if it can be written in standard form ax2 +
is solved for y, it is in
bx + c, where a is not equal to 0. When
, b = 0, and c = –2
standard form, with a =
Feedback
A
B
C
D
The coefficient of the x-term in a quadratic function can be
equal to 0.
Correct!
You can rewrite the function in standard form.
This is a quadratic function, but not for this reason. The
presence of an x-squared term is not enough to determine that
a function is quadratic.
PTS:
OBJ:
TOP:
4. ANS:
1
DIF: Basic
REF: Page 590
9-1.1 Identifying Quadratic Functions
9-1 Identifying Quadratic Functions
D
Make a table with values x = {–2, –1,
0, 1, 2}.
x
y = −x2
NAT: 12.5.2.b
Graph the points and
connect with a smooth
curve.
y
(x, y)
16
–2
–1
0
1
2
y=
y=
y=
y=
y=
−(–2)2 = −(4) = –4
−(–1)2 = −(1) = –1
−(0)2 = −(0) = 0
−(1)2 = −(1) = –1
−(2)2 = −(4) = –4
(–2, –4)
(–1, –1)
(0, 0)
(1, –1)
(2, –4)
Feedback
A
B
C
D
First, make a table of values. Then, graph the points and
connect the points with a smooth curve.
Square the x-value.
First, make a table of values. Then, graph the points and
connect the points with a smooth curve.
Correct!
PTS:
OBJ:
NAT:
5. ANS:
1
DIF: Average
REF: Page 591
9-1.2 Graphing Quadratic Functions by Using a Table of Values
12.5.4.c
TOP: 9-1 Identifying Quadratic Functions
B
Since
Check that the function is in standard form.
Identify the value of a.
, the parabola opens downward.
Feedback
A
B
C
D
To determine the direction the parabola opens, find the value
of a in the standard form of the equation.
Correct!
If a > 0, the parabola opens upward. If a < 0, the parabola
opens downward.
If a > 0, the parabola opens upward. If a < 0, the parabola
opens downward.
PTS:
OBJ:
TOP:
6. ANS:
1
DIF: Average
REF: Page 592
9-1.3 Identifying the Direction of a ParabolaNAT:
9-1 Identifying Quadratic Functions
B
12.5.1.e
The vertex is the highest or lowest point on the parabola. If a parabola opens
upward, the vertex is the lowest point. If a parabola opens downward, the
vertex is the highest point. The maximum or minimum value is the y-value of
the vertex.
Feedback
A
B
C
D
The maximum or minimum value is the y-value of the vertex.
Correct!
The maximum or minimum value is the y-value of the vertex.
If a parabola opens upward, then there is a minimum value. If
a parabola opens downward, then there is a maximum value.
PTS:
OBJ:
NAT:
7. ANS:
1
DIF: Average
REF: Page 592
9-1.4 Identifying the Vertex and the Minimum or Maximum
12.5.4.c
TOP: 9-1 Identifying Quadratic Functions
B
The graph opens upward. The vertex is
range begins at the minimum value.
, so the minimum is 8. The
Feedback
A
B
C
D
The domain is all the x-values. The range is all the y-values.
Correct!
The range begins at the minimum or maximum value.
You may not be able to see the entire graph, but that does not
mean the graph stops.
PTS: 1
NAT: 12.5.1.g
8. ANS: D
DIF: Average
REF: Page 593
OBJ: 9-1.5 Finding Domain and Range
TOP: 9-1 Identifying Quadratic Functions
Step 1 Draw a picture.
5 + 2x
5
9
9 + 2x
Step 2 Find the dimensions of the frame.
Since the frame has uniform width x, the length of the picture and frame is an
additional 2x. The width of the picture and frame is also an additional 2x.
Step 3 Find the combined area of the picture and frame.
The area of the picture and frame is
Feedback
.
A
B
C
D
The frame extends on each side of the length and width of the
picture.
Find the combined area, not the perimeter.
Find the combined area, not the perimeter.
Correct!
PTS: 1
9. ANS: B
DIF: Advanced
NAT: 12.5.4.c
TOP: 9-1 Identifying Quadratic Functions
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
A zero of a function is the x-value that makes the function equal to 0. The
x-intercept is the same as the zero of a function because it is the value of x
when y = 0. Look at the graph and find the x-intercepts.
Feedback
A
B
C
D
A zero of a function is an x-value that makes the function equal
to 0. A zero of a function is the same as an x-intercept of a
function.
Correct!
The two x-intercepts are the zeros of the function.
Look at the graph and find where it intersects the x-axis.
PTS:
OBJ:
NAT:
10. ANS:
1
DIF: Basic
REF: Page 599
9-2.1 Finding Zeros of Quadratic Functions From Graphs
12.5.1.e
TOP: 9-2 Characteristics of Quadratic Functions
B
If a function has one zero, use the x-coordinate of the vertex to find the axis of
symmetry.
If a function has two zeros, use the average of the two zeros to find the axis of
symmetry.
Feedback
A
B
C
D
The axis of symmetry of a parabola is a vertical line. All the
points it contains have the same x-value, so the variable in the
equation should be x and not y.
Correct!
The axis of symmetry of a parabola is a vertical line. All the
points it contains have the same x-value, so the variable in the
equation should be x and not y.
Look at the graph. Does the line you found divide the parabola
into two symmetrical halves?
PTS:
OBJ:
TOP:
11. ANS:
1
DIF: Average
REF: Page 600
9-2.2 Finding the Axis of Symmetry by Using Zeros
9-2 Characteristics of Quadratic Functions
B
For a quadratic function
.
line
,
NAT: 12.5.1.e
, the axis of symmetry is the vertical
Find the values of a and b.
Substitute the values into the formula.
Feedback
A
B
C
D
The axis of symmetry of a parabola is a vertical line. All the
points it contains have the same x-value, so the variable in the
equation should be x and not y.
Correct!
Use the formula x = -b/2a to find the axis of symmetry.
Use the formula x = -b/2a to find the axis of symmetry.
PTS:
OBJ:
NAT:
12. ANS:
1
DIF: Average
REF: Page 601
9-2.3 Finding the Axis of Symmetry by Using the Formula
12.5.1.e
TOP: 9-2 Characteristics of Quadratic Functions
A
The zeros of
are –2 and –4. The axis of symmetry is at x
.
When
Feedback
,
. The vertex of the parabola is (–3, 2).
A
B
C
D
Correct!
You switched the x- and y-coordinates.
These are the zeros of the function. The vertex is the point on
the parabola that intersects the axis of symmetry.
When using the formula to find the vertex, -b/2a, remember to
include the negative sign.
PTS:
OBJ:
TOP:
13. ANS:
1
DIF: Average
REF: Page 601
9-2.4 Finding the Vertex of a Parabola
9-2 Characteristics of Quadratic Functions
A
NAT: 12.5.1.e
Find the zeros of the function. One zero will be at x = 0, the starting point, and
the other will be where the projectile hits the ground and so will give the
horizontal distance traveled. Because the trajectory is a parabola, the highest
point will be the vertex (halfway between the zeros). Find the vertex on the
graph.
Feedback
A
B
C
D
Correct!
Find the zeros of the parabola to find the distance.
Find the zeros of the parabola to find the distance.
Check which is the height and which is the distance.
PTS: 1
NAT: 12.5.1.e
14. ANS: D
DIF: Average
REF: Page 602
OBJ: 9-2.5 Application
TOP: 9-2 Characteristics of Quadratic Functions
To find the height, find
.
Substitute 0 for x in the function.
Solve.
To find the width, find the distance between the zeros.
Substitute 0 for
width = 120 units
in the function.
Solve for x.
Distance between the zeros
Feedback
A
To find the height, find f(0). To find the width, find the distance
between the zeros.
B
C
D
The width is the distance between the zeros.
To find the height, find f(0).
Correct!
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: 9-2 Characteristics of Quadratic Functions
15. ANS: B
Step 1 Find the axis of symmetry.
Use
, with a = –1 and b = –4.
= −2
Step 2 Find the vertex.
The x-value of the vertex is −2 . To find the y-value, substitute −2 for x.
y = –(−2 )2 – 4(−2 ) – 3 = 1 . So, the vertex is at (−2 , 1 ).
Step 3 Find the y-intercept.
This is the c-value in the equation, or –3.
Step 4 Graph the axis of symmetry, vertex, y-intercept, and two other points.
Then use the axis of symmetry to find other points. Connect the points with a
smooth curve.
Feedback
A
B
C
D
First, find the axis of symmetry, vertex, and y-intercept. Then,
graph the axis of symmetry, vertex, y-intercept, and two other
points.
Correct!
Check that you graphed the y-intercept correctly.
Check that you applied the signs correctly when finding points.
PTS:
OBJ:
TOP:
16. ANS:
1
DIF: Basic
REF: Page 606
9-3.1 Graphing a Quadratic Function
NAT: 12.5.4.c
9-3 Graphing Quadratic Functions KEY: quadratic function | graph
C
In the standard form of a quadratic function, f(x) = ax2 + bx + c, the coefficient
a determines the width of the graph. The function with the largest value of
will be the narrowest.
Feedback
A
Compare the absolute value of the coefficients, not just the
coefficients.
Put the graphs of the functions in order from narrowest to
widest.
Correct!
Compare the coefficients. The function with the narrowest
graph has the greatest absolute value coefficient.
B
C
D
PTS:
OBJ:
TOP:
17. ANS:
1
DIF: Average
REF: Page 614
9-4.1 Comparing Widths of Parabolas
9-4 Transforming Quadratic Functions
C
NAT: 12.5.2.d
Step 1 Graph the related function x2 + 4x + 3 = y.
Locate the axis of symmetry. The axis of symmetry is x =
=
= –2.
The x-coordinate of the vertex is –2. The y-coordinate of the vertex is (–2)2 +
4(–2) + 3 = –1. So, the vertex is (–2, –1).
Find points on the graph near the vertex.
x
y
–4
3
–3
0
–2
–1
–1
0
0
3
Graph the points and connect with a smooth curve.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
(–2, –1)
2
4
6
8
10
x
–4
–6
–8
–10
Step 2 Locate the zeros or x-intercepts on the graph.
x = –3 and x = –1 where y = 0.
Check the values in x2 + 4x + 3.
x = –3
x = –1
2
2
(–3) + 4(–3) + (–1) + 4(–1) +3
3=0
=0
9 – 12 + 3 = 0
1–4+3=0
0=0
0=0
The solutions are –3 and –1.
Feedback
A
B
C
D
These are the factors of the constant in the equation. Locate
values of x on the graph where y = 0.
These are the coefficients in the equation. Locate the values of
x on the graph where y = 0.
Correct!
These are the coordinates of the vertex. Locate the values of x
on the graph where y = 0.
PTS:
OBJ:
TOP:
18. ANS:
1
DIF: Average
REF: Page 622
9-5.1 Solving Quadratic Equations by Graphing
9-5 Solving Quadratic Equations by Graphing
C
NAT: 12.5.4.c
Check that the equation is in standard form.
Write the related function.
Find the axis of symmetry and the vertex.
The vertex is at
.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
2
4
6
8
10
x
. The solution is
Find where
.
Feedback
A
First, write the related function. Then, graph the related
function and find the zeros.
Check the signs.
Correct!
First, write the related function. Then, graph the related
function and find the zeros.
B
C
D
PTS:
OBJ:
TOP:
19. ANS:
1
DIF: Average
REF: Page 622
9-5.1 Solving Quadratic Equations by Graphing
9-5 Solving Quadratic Equations by Graphing
B
NAT: 12.5.4.c
Step 1 Write the related function.
Step 2 Graph the function.
y
100
90
80
70
60
50
40
30
20
10
1
2
3
4
5
6
7
8
9
x
Step 3 Find the zeros of the function.
. The zeros appear to
The golf ball leaves the ground and returns when
be at 0 and 5. So the golf ball leaves the ground when
and returns to
. The golf ball is above the ground for 5 seconds.
the ground at
Feedback
A
B
C
Graph the function and find the zeros of the function.
Correct!
To find out how long the ball is above the ground, find the time
when it leaves the ground and the time when it returns to the
ground.
To find out how long the ball is above the ground, find the time
when it leaves the ground and the time when it returns to the
ground.
D
PTS: 1
NAT: 12.5.4.c
20. ANS: D
DIF: Average
REF: Page 624
OBJ: 9-5.2 Application
TOP: 9-5 Solving Quadratic Equations by Graphing
When the football is kicked, its height is 0, and when the football returns to the
ground, its height is also 0.
Solve
by graphing the related function
and
finding the zeros.
y
100
90
80
Height (ft)
70
60
50
40
30
20
10
1
2
3
4
5
x
Time (sec)
The zeros appear to be at 0 and 3.75. The football is in the air for 3.75
seconds.
Feedback
A
B
C
D
Graph the function. The difference between the zeros is the
amount of time the football is in the air.
Graph the function. The difference between the zeros is the
amount of time the football is in the air.
Graph the function. The difference between the zeros is the
amount of time the football is in the air.
Correct!
PTS:
NAT:
KEY:
21. ANS:
1
DIF: Average
REF: Page 624
OBJ: 9-5.2 Application
12.5.4.c
TOP: 9-5 Solving Quadratic Equations by Graphing
quadratic function | height
A
Multiply the binomials on the left side, and subtract the number on the right
side to write the equation in standard form. Now that one side of the equation
is zero, factor the new trinomial and use the Zero Product Property to solve
the equation. The Zero Product Property says: For any real numbers a and b,
if ab = 0, then a = 0 or b = 0. After you have factored the equation, you get
or
.
Feedback
A
B
C
D
Correct!
To use the Zero Product Property, one side of the equation
must be zero.
To use the Zero Product Property, one side of the equation
must be zero.
When x + a = 0, x = –a.
PTS:
OBJ:
TOP:
22. ANS:
1
DIF: Basic
REF: Page 630
9-6.1 Using the Zero-Product Property
9-6 Solving Quadratic Equations by Factoring
A
NAT: 12.5.4.a
Factor the trinomial.
or
Use the Zero Product Property.
or
Solve each equation.
The solutions are –4 and 2.
Feedback
A
B
C
D
Correct!
Check your factorization by multiplying the factors together.
Substitute the solutions into the original equation to check your
answer.
Check your factorization by multiplying the factors together.
PTS:
OBJ:
NAT:
23. ANS:
1
DIF: Average
REF: Page 631
9-6.2 Solving Quadratic Equations that Have Two Solutions
12.5.4.a
TOP: 9-6 Solving Quadratic Equations by Factoring
D
Factor the polynomial, first factoring out a GCF if it is helpful. Set each factor
equal to zero and solve for w. Since the two factors containing w are identical,
there is only one solution.
Feedback
A
Substitute the solution into the original equation to check your
B
C
D
answer.
Check the sign.
Substitute the solution into the original equation to check your
answer.
Correct!
PTS:
OBJ:
TOP:
24. ANS:
1
DIF: Average
REF: Page 631
9-6.2 Solving Quadratic Equations by Factoring
9-6 Solving Quadratic Equations by Factoring
C
NAT: 12.5.4.a
The arrow reaches the ground when
Factor out the GCF, .
Use the Zero Product Property.
Solve each equation.
or
or
.
It takes the arrow 8 seconds to reach the ground.
Feedback
A
B
C
D
The arrow reaches the ground when h = 0.
First, set h equal to zero. Then, factor and solve.
Correct!
The arrow reaches the ground when h = 0.
PTS: 1
NAT: 12.5.4.c
25. ANS: A
DIF: Average
REF: Page 632
OBJ: 9-6.3 Application
TOP: 9-6 Solving Quadratic Equations by Factoring
Step 1 The area of the shaded region is equal to the area of the large
rectangle minus the area of the small rectangle.
Write an equation.
Use FOIL.
Simplify.
Step 2
or
or
Rewrite the equation in standard form.
Factor.
Use the Zero Product Property.
Solve each equation.
A negative number is not reasonable
for distance.
Feedback
A
B
C
D
Correct!
The area of the shaded region is 24 square units.
Subtract the area of the smaller rectangle from the area of the
larger rectangle.
The area of the shaded region is 24 square units.
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: 9-6 Solving Quadratic Equations by Factoring
26. ANS: C
KEY: multi-step
Take the square root of both sides of the equation. There is no number whose
square is negative, so there is no solution.
Feedback
A
B
C
D
Check your answers by substituting into the original equation.
Every positive number has two square roots, and negative
numbers have no square roots that are real numbers.
Correct!
Every positive number has two square roots, and negative
numbers have no square roots that are real numbers.
PTS:
OBJ:
TOP:
27. ANS:
1
DIF: Basic
REF: Page 636
9-7.1 Using Square Roots to Solve x^2 = a
9-7 Solving Quadratic Equations by Using Square Roots
A
4x2 – 121 = 0
+ 121 = + 121
=
x2 =
x = ± 112
Feedback
A
Correct!
NAT: 12.5.4.a
Add 121 to both sides.
Divide both sides by 4.
Take the square root of both sides.
Use the plus/minus sign to show positive and
negative roots.
The solutions are 112 and – 112 .
B
C
D
Check your positive and negative signs.
If possible, take the square root to find x.
Check your solution.
PTS:
OBJ:
TOP:
28. ANS:
1
DIF: Average
REF: Page 637
9-7.2 Using Square Roots to Solve Quadratic Equations
9-7 Solving Quadratic Equations by Using Square Roots
A
NAT: 12.5.4.a
Add 10 to both sides and simplify.
Take the square root of both sides.
Evaluate
on the calculator.
The approximate solutions are 3.16 and
.
Feedback
A
B
C
D
Correct!
First, add to undo the subtraction. Then, take the square root
of both sides.
First, add to undo the subtraction. Then, take the square root
of both sides.
There is a solution. First, add to undo the subtraction. Then,
take the square root of both sides.
PTS: 1
NAT: 12.1.2.d
29. ANS: C
DIF: Average
REF: Page 637
OBJ: 9-7.3 Approximating Solutions
TOP: 9-7 Solving Quadratic Equations by Using Square Roots
Use the formula for the surface area of a
sphere.
Substitute 60 for the surface area.
Divide both sides by
.
Simplify.
Take the square root of both sides.
Feedback
A
B
C
D
Take the square root, not the square.
Before taking the square root, divide by pi.
Correct!
After dividing by pi, take the square root.
PTS: 1
NAT: 12.5.4.c
30. ANS: B
DIF: Average
REF: Page 638
OBJ: 9-7.4 Application
TOP: 9-7 Solving Quadratic Equations by Using Square Roots
Divide the coefficient of the x-term by 2, and then square it to get the constant
term,
.
Add the result to the expression to form a perfect square trinomial.
Feedback
A
B
C
D
Divide the coefficient of the x-term by 2, and then square it to
get the constant term.
Correct!
Divide the coefficient of the x-term by 2, and then square it to
get the constant term.
The final term of a perfect square trinomial must be added, not
subtracted.
PTS: 1
NAT: 12.5.3.b
31. ANS: B
DIF: Basic
REF: Page 645
TOP: 9-8 Completing the Square
OBJ: 9-8.1 Completing the Square
The equation is in the form
Add
or
to both sides of the equation.
Factor the perfect square trinomial.
Take the square root of both sides of the
equation.
Solve.
The solutions are 6 and –2.
Feedback
A
B
C
D
Add (b/2)^2 to both sides of the equation and factor the perfect
square trinomial.
Correct!
Add (b/2)^2 to both sides of the equation and factor the perfect
square trinomial.
Add (b/2)^2 to both sides of the equation and factor the perfect
square trinomial.
PTS: 1
DIF: Average
REF: Page 646
OBJ: 9-8.2 Solving x^2+bx=c by Completing the Square
TOP: 9-8 Completing the Square
32. ANS: D
NAT: 12.5.4.a
Divide by 2 to make the leading coefficient
1.
. Complete the square by adding
9 to both sides.
Factor the perfect-square trinomial.
Take the square root of both sides. Use
the symbol.
Solve each equation.
Feedback
A
B
C
D
There is more than one solution.
First, divide by 2 to make the leading coefficient 1. Then,
complete the square.
Substitute into the original equation to check your answer.
Correct!
PTS:
OBJ:
TOP:
33. ANS:
1
DIF: Average
REF: Page 647
9-8.3 Solving ax^2 + bx = c by Completing the Square
9-8 Completing the Square
B
NAT: 12.5.4.a
Set up an equation where length times width is equal to area: x(x + 12) = 120.
Multiply the factors on the left side, and then add 36 to both sides to make the
left side a perfect square trinomial:
.
.
Factor the trinomial, and take the square root of both sides:
or
Solve the two resulting equations for x:
.
Only the positive solution, 6.49, makes sense for the width.
Add 12 to calculate the length: 6.49 + 12 = 18.49.
Feedback
A
B
Anything you add to the left side of an equation must also be
added to the right side.
Correct!
C
D
After you take the square root, solve for the width.
Anything you add to the left side of an equation must also be
added to the right side.
PTS: 1
NAT: 12.5.4.c
34. ANS: A
DIF: Average
REF: Page 647
TOP: 9-8 Completing the Square
Write the equation in standard form:
and –9 for c in the Quadratic Formula,
OBJ: 9-8.4 Application
. Substitute for a, –8 for b,
. Write as two
equations, one adding the square root and one subtracting it. Simplify each
equation to find the values of x.
Feedback
A
B
C
D
Correct!
Use the opposite of b, the coefficient of the x-term in the
equation.
For the numerator in the Quadratic Formula, find the square
root before adding it to or subtracting it from –b.
The denominator of the Quadratic Formula is 2 times a.
PTS: 1
NAT: 12.5.4.a
35. ANS: C
DIF: Average
REF: Page 653
OBJ: 9-9.1 Using the Quadratic Formula
TOP: 9-9 The Quadratic Formula and the Discriminant
3x2 – 5x – 1= 0
The equation is in standard
form, ax2 +bx – c= 0.
Use the Quadratic Formula.
x =
Substitute 3 for a, –5 for b, and
–1 for c.
x =
Simplify.
x =
x =
x=
or x =
x ≈ 1.85 or x ≈ –0.18
There are two solutions.
Use a calculator to approximate
x.
Feedback
A
B
C
D
Check your calculations.
First, identify a, b, and c. Then, substitute a, b, and c in the
Quadratic Formula and solve.
Correct!
There are solutions to this equation.
PTS:
OBJ:
TOP:
36. ANS:
1
DIF: Average
REF: Page 653
9-9.2 Using the Quadratic Formula to Estimate Solutions NAT: 12.5.4.a
9-9 The Quadratic Formula and the Discriminant
B
Discriminant of the quadratic equation
,
, and
Substitute for a, b, and c in the
discriminant.
Simplify.
is negative.
, then the equation has two real solutions.
, then the equation has one real solution.
, then the equation has no real solutions.
If
If
If
Therefore, the equation
has no real solutions.
Feedback
A
B
C
D
The equation is quadratic. Use the discriminant to help you
find the number of solutions.
Correct!
If the discriminant is greater than 0, then the equation has two
real solutions. If the discriminant is less than 0, then the
equation has no real solutions.
If the discriminant is greater than 0, then the equation has two
real solutions. If the discriminant is less than 0, then the
equation has no real solutions.
PTS: 1
NAT: 12.5.4.a
37. ANS: B
DIF: Average
REF: Page 654
OBJ: 9-9.3 Using the Discriminant
TOP: 9-9 The Quadratic Formula and the Discriminant
Substitute 670 for h, 210 for v, and 3
for c.
Write the equation in standard form.
Evaluate the discriminant.
Substitute
for a, 210 for b, and
for c.
The discriminant is positive, so the equation has two solutions. The object will
reach a height of 670 feet twice.
Feedback
A
B
C
D
First, substitute 670 for h, 210 for v, and 3 for c in the equation.
Then, evaluate the discriminant.
Correct!
First, substitute 670 for h, 210 for v, and 3 for c in the equation.
Then, evaluate the discriminant.
If the discriminant is positive, then there are two solutions. If
the discriminant is negative, then there are no solutions. If the
discriminant is equal to 0, then there is one solution.
PTS: 1
NAT: 12.5.4.c
38. ANS: C
or
or
DIF: Average
REF: Page 655
OBJ: 9-9.4 Application
TOP: 9-9 The Quadratic Formula and the Discriminant
Factor.
Use the Zero Product
Property.
Solve each equation.
Feedback
A
B
C
D
Check the signs.
Factor, and then solve each equation.
Correct!
Factor, and then solve each equation.
PTS: 1
DIF: Average
REF: Page 655
OBJ: 9-9.5 Solving Using Different Methods
NAT: 12.5.4.a
TOP: 9-9 The Quadratic Formula and the Discriminant
39. ANS: B
Step 1 Find the length of the orchard in terms of w.
Let w represent the width of the orchard.
Step 2 Write an equation for the area of the orchard.
Step 3 Find the dimensions of the orchard when the area is 900 square yards.
Substitute 900 for the area of
the orchard.
The equation is in standard
form:
,
, and
.
Substitute 1 for a, –60 for b,
and 900 for c.
Simplify.
Substitute 30
for w and
simplify.
The width and length of the orchard are each 30 yd.
Feedback
A
B
C
D
Substitute 900 for the area of the orchard and solve the
equation.
Correct!
If the width is w, then the length is 60 – w.
Check your equation to verify that it shows the correct area.
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: 9-9 The Quadratic Formula and the Discriminant
40. ANS: D
KEY: multi-step
Find the value of the common ratio by dividing each term by the one before it.
Then, multiply each term by the common ratio to get the next term.
Feedback
A
B
C
D
First, find the value of the common ratio by dividing each term
by the one before it. Then, multiply each term by the common
ratio to get the next term.
Check the signs of the terms.
Check the order of the terms.
Correct!
PTS:
OBJ:
TOP:
41. ANS:
1
DIF: Basic
REF: Page 766
11-1.1 Extending Geometric Sequences
11-1 Geometric Sequences
C
NAT: 12.5.1.a
Find a specific term from a given sequence by using the formula.
, where:
an = your result
a1 = the initial term of the sequence
n = the number in the sequence you want to calculate
r = the common ratio between the terms
Feedback
A
B
C
D
This is the first term raised to the power of the common ratio.
Use the formula for the nth term in a sequence.
The power used in the formula is (n – 1), not (n – 2).
Correct!
The power used in the formula is (n – 1), not (n – 2).
PTS:
OBJ:
TOP:
42. ANS:
1
DIF: Average
REF: Page 767
11-1.2 Finding the nth Term of a Geometric Sequence
NAT: 12.5.1.a
11-1 Geometric Sequences
KEY: geometric sequence | nth term
B
Use the equation an = a1 • r n – 1 to solve the problem.
The variables represent the following values:
an = value of the computer after n years
a1 = the initial value of the computer
r = rate of depreciation, 0.5
n = the number of years
Feedback
A
B
C
D
Check that you found the value after the correct number of
years.
Correct!
Check that you found the value after the correct number of
years.
Check that you found the value after the correct number of
years.
PTS: 1
NAT: 12.5.1.a
43. ANS: D
f(x) =
f(3) =
f(3) ≈
DIF: Average
REF: Page 768
TOP: 11-1 Geometric Sequences
OBJ: 11-1.3 Application
KEY: geometric sequence | depreciation
90(0.937)x
90(0.937)3
74.03913
Write the function.
Substitute 3 for x.
Use a calculator to evaluate.
Round your answer to the nearest
f(3) ≈
74
whole number since the number of
lemmings must be a whole number.
There will be about 74 lemmings in 3 years.
Feedback
A
B
C
D
Check your calculation. Use order of operations to determine
which operation to do first.
Check your calculation. Use order of operations to determine
which operation to do first.
Check your calculation. Use order of operations to determine
which operation to do first.
Correct!
PTS:
OBJ:
TOP:
44. ANS:
1
DIF: Average
REF: Page 772
11-2.1 Evaluating an Exponential Function
11-2 Exponential Functions
C
NAT: 12.5.1.e
In an exponential function, as the x-values are increased by a constant
amount, the y-values are multiplied by a constant amount. Make a table of
values to test the function.
x
–1
y = 6(x)5
?
+1
0
?
×?
+1
1
?
×?
+1
2
?
×?
If the y-values are multiplied by a constant amount as the x-values increase by
1, then the function is exponential.
Feedback
A
B
C
D
In an exponential function, a constant increase in the x-values
causes the y-values to be multiplied by a constant number.
Make a table of values to see what happens to the y-values as
the x-values are increased by a constant amount.
Correct!
In an exponential function, a constant increase in the x-values
causes the y-values to be multiplied by a constant number.
PTS:
OBJ:
TOP:
45. ANS:
1
DIF: Average
REF: Page 773
11-2.2 Identifying an Exponential Function
11-2 Exponential Functions
B
NAT: 12.5.1.e
Choose several values of x and generate ordered pairs. Then, graph the
ordered pairs and connect with a smooth curve.
Feedback
A
B
C
D
Check that you have identified the base correctly.
Correct!
The coefficient multiplies the power, it is not added to the
power.
Be sure you are using the sign of the exponent correctly.
PTS:
OBJ:
TOP:
46. ANS:
1
DIF: Basic
REF: Page 773
11-2.3 Graphing y = ab^x with a > 0 and b > 1
NAT: 12.5.1.h
11-2 Exponential Functions
KEY: exponential function | graph
B
Make a table. Choose several values of x and generate ordered pairs.
x y = –(4)x
(x, y)
–1
–1 –(4) = –(0.25) =
(–1,
–0.25
–0.25)
0
0 –(4) = –(1) = –1
(0, –1)
1
1 –(4) = –(4) = –4
(1, –4)
2
2 –(4) = –(16) = –16
(2, –16)
Graph the ordered pairs and connect them with a smooth curve.
y
5
–4
–3
–2
–1
1
2
3
4
x
–5
–10
–15
Feedback
A
B
C
D
Make a table. Substitute values for x into the equation to
generate ordered pairs.
Correct!
Make a table. Substitute values for x into the equation to
generate ordered pairs.
Make a table. Substitute values for x into the equation to
generate ordered pairs.
PTS:
OBJ:
TOP:
47. ANS:
1
DIF: Basic
REF: Page 774
11-2.4 Graphing y = ab^x with a < 0 and b > 1
11-2 Exponential Functions
D
NAT: 12.5.1.h
Choose some values of x and generate ordered pairs.
x
0
1
2
Then graph the points and connect with a smooth curve.
Feedback
A
B
C
D
The values you found are the opposite of the correct values.
You did not multiply by the value of a after raising b to the
power of x.
Connect the ordered pairs you found with a smooth curve.
Correct!
PTS: 1
NAT: 12.5.1.h
48. ANS: D
DIF: Average
OBJ: 11-2.5 Graphing y = abx with 0 < b < 1
TOP: 11-2 Exponential Functions
Use the equation
to calculate the final population.
You can use a table on a calculator or spreadsheet to find the answer.
Year
x
Population
(millions)
=
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
0
1
2
3
4
5
6
7
8
9
10
11
100
101.5
103.1
104.7
106.3
107.9
109.5
111.2
112.9
114.6
116.4
118.2
Feedback
A
B
C
Check your answer by substituting into the equation
100(1.0153)^x.
To find the answer, add 2000 to the number of years needed
to reach the final population.
You may have used the final population as the exponent x in
the expression 100(1.0153)^x. Instead, make a table of values
to find the year when 100(1.0153)^x will equal the final
population.
D
Correct!
PTS:
NAT:
KEY:
49. ANS:
1
DIF: Average
REF: Page 775
12.5.1.h
TOP: 11-2 Exponential Functions
exponential function | graph | growth
C
OBJ: 11-2.6 Application
Use the exponential growth equation.
Substitute 105 for a, 0.05 for r, and 11 for
t.
Simplify.
Feedback
A
B
C
D
Use the exponential growth equation. Each year the painting is
worth (1+ rate) times its value the previous year.
Convert the rate to a decimal and use the exponential growth
equation. Each year the painting is worth (1+ rate) times its
value the previous year.
Correct!
Use the exponential growth equation. Each year the painting is
worth (1+ rate) times its value the previous year.
PTS: 1
NAT: 12.5.1.h
50. ANS: B
DIF: Average
REF: Page 781
OBJ: 11-3.1 Exponential Growth
TOP: 11-3 Exponential Growth and Decay
Use the compound interest formula
. Here, P is 2,100; r is 2%
expressed as the decimal 0.02; and n is 1 because annually means 1 time per
year.
Feedback
A
B
C
D
Express the interest rate in decimal form.
Correct!
The formula has (1+ n/t). Remember to add the 1.
The term n in the exponent should be the number of times per
year interest is added.
PTS: 1
NAT: 12.5.1.h
51. ANS: D
DIF: Average
REF: Page 782
OBJ: 11-3.2 Application
TOP: 11-3 Exponential Growth and Decay
Step 1 Write the exponential decay function for this situation.
Use the formula.
Substitute 1,100 for a, and
for r.
Simplify inside the parentheses. This is
the exponential decay function.
Step 2 Find the population in 2007.
Substitute 5 for t.
Use a calculator and round to the nearest
whole number.
The population in 2007 will be approximately 897 fish.
Feedback
A
B
C
D
Round your answer to the nearest whole number because
there can only be a whole number of fish.
An exponential decay function should have a variable t for the
time. Also, remember that one percent is one hundredth.
An exponential decay function should have (1 – r) to the power
of t.
Correct!
PTS: 1
NAT: 12.5.1.h
52. ANS: A
DIF: Average
REF: Page 783
OBJ: 11-3.3 Exponential Decay
TOP: 11-3 Exponential Growth and Decay
First calculate t:
.
Write the half-life formula. A represents the final
amount, P represents the original amount, and t
represents the number of half-lives in a given
time period.
Substitute 400 for P and 4 for t.
Use a calculator.
Feedback
A
B
C
Correct!
Be sure you correctly calculated the number of times the
amount is halved.
To find how many times the amount divides in two, divide the
number of hours by the half-life.
D
Use an exponential equation. The final amount is not the
beginning amount divided by the number of hours.
PTS:
NAT:
KEY:
53. ANS:
1
DIF: Average
REF: Page 784
OBJ: 11-3.4 Application
12.5.1.h
TOP: 11-3 Exponential Growth and Decay
exponential function | decay | half-life
B
Plot the data points and connect them. See whether a line, a parabola, or an
exponential curve is the best fit.
This function is exponential.
y
40
30
20
10
–10 –8
–6
–4
–2
–10
2
4
6
8
10
x
–20
–30
–40
Feedback
A
B
C
D
Graph the points. Does a line, a parabola, or an exponential
curve best fit the data?
Correct!
Graph the points. Does a line, a parabola, or an exponential
curve best fit the data?
Graph the points. Does a line, a parabola, or an exponential
curve best fit the data?
PTS:
OBJ:
TOP:
KEY:
54. ANS:
1
DIF: Basic
REF: Page 789
11-4.1 Graphing Data to Choose a Model
11-4 Linear Quadratic and Exponential Models
model | data | linear | exponential | quadratic
A
NAT: 12.5.2.g
Check for a pattern in the differences and the ratios of the y-terms.
A linear function has constant first differences.
A quadratic function has constant second differences.
A cubic function has constant third differences.
An exponential function has constant ratios.
Population Growth
of Bacteria
Change Time
Number
First
in Time (hours)
of
Difference
Bacteria
0
2,000
1
1
5,000
3,000
1
2
12,500
7,500
1
3
31,250
18,750
1
4
78,125
46,875
Second
Difference
4,500
11,250
28,125
Ratio
2.5
2.5
2.5
2.5
For each change in time of 1 hour, only the ratios of the y-terms remain
constant.
The best model for the data is an exponential function.
Feedback
A
Correct!
Check the differences and the ratios. Cubic functions have
constant third differences.
Check the differences and the ratios. Quadratic functions have
constant second differences.
Check the differences and the ratios. Linear functions have
constant first differences.
B
C
D
PTS:
OBJ:
TOP:
55. ANS:
1
DIF: Average
REF: Page 790
11-4.2 Using Patterns to Choose a Model
11-4 Linear Quadratic and Exponential Models
B
NAT: 12.5.2.g
Step 1 Find a function.
Use the table to check for a common sum, difference, or ratio.
+1
+2
Termite Colony Population
Time (months)
Number of
Termites
0
80
1
320
2
1,280
×4
×4
+3
3
5,120
×4
There is a constant ratio of 4. The data can be modeled with an exponential
function.
y = abx
80 = a(40)
80 = a(1)
80 = a
y = 80(4)x
Use the general form of an exponential function to
find the constant value.
Choose an ordered pair from the table and substitute
for x and y.
Use (0, 80). The common ratio, b, is 4.
Simplify. 40 = 1
Solve for a.
Use a = 80 and b = 4 to write an exponential equation
that models the data.
Step 2 Evaluate the function for time of 1 year.
y = 80(4)x
y = 80(4)12
y=
1,342,177,280
One year equals 12 months. Substitute 12 for x.
Simplify.
There will be 1,342,177,280 termites after 1 year.
Feedback
A
B
C
D
Find the population in month 12, not month 4.
Correct!
The termite population grows by multiplication, not addition.
Use the common difference or ratio to find a formula to predict
the number of termites. Use 12 months for 1 year.
PTS:
OBJ:
TOP:
56. ANS:
1
DIF: Average
REF: Page 791
11-4.3 Problem-Solving Application
11-4 Linear Quadratic and Exponential Models
C
NAT: 12.5.2.g
Substitute 31 for x.
Use a calculator to approximate the square root of
31.
After it has fallen 31 feet, the object’s speed is about 44.5 ft/s.
Feedback
A
B
C
D
Find the square root of the number before you multiply by the
number outside the radical.
Find the square root of the number before you multiply by the
number outside the radical.
Correct!
Multiply the square root by the number outside the radical.
PTS: 1
DIF: Basic
REF: Page 798
OBJ: 11-5.1 Evaluating Square-Root Functions
57. ANS: A
TOP: 11-5 Square-Root Functions
The expression under the radical sign must be greater than or equal to 0, so
. Solve the inequality for x to find the domain of the function.
Feedback
A
B
C
D
Correct!
The expression under the radical must be greater than or
equal to zero.
The expression under the radical must be greater than or
equal to zero.
The expression under the radical must be greater than or
equal to zero.
PTS: 1
DIF: Advanced
REF: Page 799
OBJ: 11-5.2 Finding the Domain of Square Root Functions
58. ANS: C
TOP: 11-5 Square-Root Functions
Step 1 Find the domain of the function.
The expression under the radical sign,
greater than or equal to 0.
, must be
Step 2 Choose several x-values from the domain and generate ordered pairs.
x
0
2
0.5
3.4
3
5.5
6
6.9
9
8.0
Step 3 Plot the points and connect them with a smooth curve.
y
21
18
15
12
9
6
3
–9
–6
–3
–3
3
6
9
12
15
18
21
x
–6
–9
Feedback
A
B
C
D
x is also under the radical sign. The graph of a square root
function is not linear.
The points marked are correct but you need to find several
more. The graph of a square root function is not linear.
Correct!
Only the x term is under the radical sign.
PTS: 1
DIF: Average
REF: Page 800
OBJ: 11-5.3 Graphing Square-Root Functions
59. ANS: D
TOP: 11-5 Square-Root Functions
Step 1 Find the two values that are not in the domain.
The domain of the function is all the x-values that make the expression under
the radical sign greater than or equal to 0.
The only x-values given that are not greater than or equal to 3.5 are 2 and 3.
These values are out of the domain.
Step 2 Find the y-values for the two x-values in the domain.
Substitute the other given values into the equation to solve for y.
Substitute 4 for x.
Simplify.
Substitute 8 for x.
Simplify.
Feedback
A
B
C
D
Only x-values that make the expression under the radical sign
positive are part of the domain.
Use values of the domain to find the y-values (range).
The square root of –1 does not simplify to –1.
Correct!
PTS: 1
KEY: multistep
60. ANS: A
DIF: Advanced
TOP: 11-5 Square-Root Functions
Feedback
A
B
C
D
Correct!
First divide out any factors common to the numerator and the
denominator.
Take the square root of the numerator and the denominator.
Factor the numerator and the denominator. Divide out any
common factors and look for perfect square factors.
PTS:
OBJ:
TOP:
61. ANS:
1
DIF: Basic
REF: Page 805
11-6.1 Simplifying Square-Root Expressions
11-6 Radical Expressions
C
NAT: 12.5.3.c
Factor perfect squares out of the radicand. Use the Product Property of
Square Roots to take the square root of each factor separately. Simplify.
Feedback
A
B
C
D
First, factor perfect squares out of the radicand. Then, take the
square roots of the perfect squares.
First, factor perfect squares out of the radicand. Then, take the
square roots of the perfect squares.
Correct!
Take the square root of the factor when removing the radical.
PTS:
OBJ:
TOP:
62. ANS:
1
DIF: Average
REF: Page 806
11-6.2 Using the Product Property of Square Roots
11-6 Radical Expressions
B
NAT: 12.5.3.c
Simplify the radicand.
=
Use the Quotient Property of Square Roots.
=
always indicates a nonnegative square root.
Feedback
A
B
C
D
Simplify the numerator. Find the square root of the radicand
(the expression under the radical sign).
Correct!
Find the square root of the expression.
The radical sign always indicates a nonnegative square root.
PTS:
OBJ:
TOP:
63. ANS:
1
DIF: Average
REF: Page 806
11-6.3 Using the Quotient Property of Square Roots
11-6 Radical Expressions
C
=
NAT: 12.5.3.c
Use the Quotient Property.
=
Find perfect square factors if possible. Write 300 as
100(3).
=
Use the Product Property.
Simplify.
=
Feedback
A
B
Only factors that aren't perfect squares remain beneath the
radical sign.
Check your calculations. A factor from the numerator is
C
D
missing.
Correct!
Factors that aren't perfect squares remain beneath the radical
sign.
PTS:
OBJ:
NAT:
64. ANS:
1
DIF: Basic
REF: Page 807
11-6.4 Using the Product and Quotient Properties Together
12.5.3.c
TOP: 11-6 Radical Expressions
B
Since the park is square and the diagonal line stretches between opposite
corners, the length of the diagonal line is the hypotenuse of a right triangle.
Use the Pythagorean Theorem, a2 + b2 = c2, to solve this problem.
Let c = the length of the diagonal.
The diagonal is about 170 meters long.
Feedback
A
B
C
D
Remember to take the square root after you add the squares
of the leg lengths.
Correct!
Use the Pythagorean Theorem to find the length of the
diagonal.
Use the Pythagorean Theorem to find the length of the
diagonal.
PTS:
NAT:
KEY:
65. ANS:
1
DIF: Average
REF: Page 807
12.5.3.c
TOP: 11-6 Radical Expressions
Pythagorean Theorem | right triangle | diagonal
B
OBJ: 11-6.5 Application
Factor the radicand.
Use the Product Property of Square Roots.
Simplify.
Feedback
A
The square root of 9 is 3.
B
C
D
Correct!
Only combine like terms.
Factor the radicand completely.
PTS: 1
66. ANS: A
DIF: Advanced
NAT: 12.5.1.g
TOP: 11-6 Radical Expressions
Combine the like radicals.
=
Feedback
A
B
C
D
Correct!
The terms are like radicals, so keep the same radical.
Use the correct operation.
Combine the like radicals, and keep the same radical.
PTS:
OBJ:
TOP:
67. ANS:
1
DIF: Basic
REF: Page 811
11-7.1 Adding and Subtracting Square-Root Expressions
11-7 Adding and Subtracting Radical Expressions
A
NAT: 12.5.3.c
Factor the radicands using
perfect-square factors.
Use the Product Property of
Square Roots.
=
=
=
=
Combine like radicals.
Feedback
A
B
C
D
Correct!
The answer should have the radical sign with at least the
variable as the radicand. You cannot square the radical
expression without changing its value.
Factor the radicands using perfect-square factors.
Use the Product Property of Square Roots.
PTS:
OBJ:
TOP:
68. ANS:
1
DIF: Average
REF: Page 812
11-7.2 Simplifying Before Adding or Subtracting
11-7 Adding and Subtracting Radical Expressions
B
NAT: 12.5.3.c
Write 12 using a perfect-square factor. Then, use the Product Property of
Square Roots, and combine the like radicals.
Feedback
A
B
C
D
Write one of the radicands using a perfect-square factor. Then,
use the Product Property of Square Roots, and combine the
like radicals.
Correct!
Simplify the radical by taking the square root of the
perfect-square factor. Then, combine the like radicals.
Two of the terms you combined are not like radicals.
PTS: 1
NAT: 12.5.3.c
69. ANS: C
DIF: Average
REF: Page 812
OBJ: 11-7.3 Application
TOP: 11-7 Adding and Subtracting Radical Expressions
Product Property of Square
Roots.
Factor 60 using a perfect-square
factor.
Product Property of Square
Roots.
Simplify.
Feedback
A
B
C
D
Take the square root of the perfect-square factor.
Use the Product Property of Square Roots. Then factor the
number using a perfect-square factor.
Correct!
Factor the number using a perfect-square factor.
PTS: 1
NAT: 12.5.3.c
70. ANS: C
DIF: Advanced
REF: Page 816
OBJ: 11-8.1 Multiplying Square Roots
TOP: 11-8 Multiplying and Dividing Radical Expressions
Distribute
. Use the Product Property of Square Roots to multiply the
factors in each term. If the radicand in either term contains any perfect square
factors, factor the radicand(s) and simplify. Combine like terms if applicable.
Feedback
A
B
C
D
Combine only like terms.
Use the Distributive Property, then simplify.
Correct!
Simplify your answer.
PTS:
OBJ:
TOP:
71. ANS:
1
DIF: Basic
REF: Page 817
11-8.2 Using the Distributive Property
11-8 Multiplying and Dividing Radical Expressions
A
Expand the expression to get
NAT: 12.1.5.e
. Use the FOIL method to
, and then combine like terms.
get
Feedback
A
B
C
D
Correct!
Expand the expression and then use the FOIL method.
Combine only like terms.
The product of two negative numbers is positive.
PTS:
OBJ:
TOP:
72. ANS:
1
DIF: Average
REF: Page 817
11-8.3 Multiplying Sums and Differences of Radicals
11-8 Multiplying and Dividing Radical Expressions
C
NAT: 12.5.3.c
Multiply by a form of 1 to get a
perfect-square radicand in the
denominator.
Simplify the denominator.
Feedback
A
B
C
D
First, multiply by a form of 1 to get a perfect-square radicand in
the denominator. Then, simplify the denominator.
Rationalize the denominator by finding the appropriate form of
1 to multiply by.
Correct!
A quotient with a square root in the denominator is not
simplified.
PTS:
OBJ:
TOP:
73. ANS:
1
DIF: Basic
REF: Page 818
11-8.4 Rationalizing the Denominator
11-8 Multiplying and Dividing Radical Expressions
A
NAT: 12.5.3.c
Multiply the numerator and
denominator by the conjugate of
.
=
=
=
Simplify.
=
Feedback
A
B
C
D
Correct!
Multiply the numerator and the denominator by the conjugate
of the denominator.
Multiply the numerator and the denominator by the conjugate
of the denominator.
Multiply the numerator and the denominator by the conjugate
of the denominator.
PTS: 1
DIF: Advanced
NAT: 12.1.3.a
TOP: 11-8 Multiplying and Dividing Radical Expressions
74. ANS: C
Square both sides.
Feedback
A
B
C
D
The radical cannot be negative.
Square both sides, not multiply.
Correct!
Square both sides to isolate the variable.
PTS: 1
DIF: Basic
REF: Page 822
OBJ: 11-9.1 Solving Simple Radical Equations
75. ANS: B
TOP: 11-9 Solving Radical Equations
Add 10 to both sides.
Square both sides.
Feedback
A
B
C
D
After isolating the square root, you need to square both sides.
Correct!
Check the signs.
The radical cannot be negative.
PTS:
OBJ:
TOP:
76. ANS:
1
DIF: Basic
REF: Page 823
11-9.2 Solving Radical Equations by Adding or Subtracting
11-9 Solving Radical Equations
C
There are two methods to solve the equation.
Method 1 Divide both sides by 8 and then square both sides.
Method 2 Square both sides and then divide both sides by (8)2 which is 64.
Feedback
A
B
C
D
Divide both sides by the same number; don't subtract.
Square both sides of the equation.
Correct!
Square both sides of the equation.
PTS:
OBJ:
TOP:
77. ANS:
1
DIF: Basic
REF: Page 823
11-9.3 Solving Radical Equations by Multiplying or Dividing
11-9 Solving Radical Equations
B
Add
to both sides.
Square both sides.
z = –3
Simplify.
Solve.
Feedback
A
B
C
D
Subtract one of the radicals from both sides of the equation.
Then square both sides to get rid of the radicals.
Correct!
Subtract one of the radicals from both sides of the equation.
Then square both sides to get rid of the radicals.
Subtract one of the radicals from both sides of the equation.
Then square both sides to get rid of the radicals.
PTS:
OBJ:
TOP:
78. ANS:
1
DIF: Average
REF: Page 824
11-9.4 Solving Equations with Square Roots on Both Sides
11-9 Solving Radical Equations
B
Isolate the radical on one side of the equation.
Square both sides. Write the equation in standard form. Factor.
Solve for z.
Check your answers in the original equation to determine if a solution is
extraneous.
Feedback
A
B
C
D
Square both sides of the equation.
Correct!
Check your answer in the original equation.
Square both sides of the equation.
PTS: 1
DIF: Average
TOP: 11-9 Solving Radical Equations
79. ANS: A
REF: Page 825
OBJ: 11-9.5 Extraneous Solutions
Set up the equation for the area of the rectangle: A = lw. Substitute the values
. Divide both sides of the equation by 7 to
given in the problem:
, then square both sides to find x. The width is the square root of x,
isolate
and it must be positive.
Feedback
A
B
C
D
Correct!
Square both sides of the equation.
The width is the square root of x.
The width of a rectangle cannot be negative.
PTS: 1
DIF: Average
TOP: 11-9 Solving Radical Equations
80. ANS: A
REF: Page 825
OBJ: 11-9.6 Application
Square both sides.
Simplify.
Subtract
and 9 from both sides.
Factor.
or
If
, then
. A square root cannot be negative. So,
is an extraneous solution, and the only solution is
.
Feedback
A
B
C
D
Correct!
Check your answer by substituting the solution in the equation.
First, square both sides and simplify. Then, factor and solve for
x.
First, square both sides and simplify. Then, factor and solve for
x.
PTS: 1
81. ANS: B
DIF: Advanced
TOP: 11-9 Solving Radical Equations
=?
What number multiplied by itself 3 times equals 64?
=4
The number is 4 because
.
Feedback
A
B
C
D
What root raised to the given power equals the given number?
Correct!
What root raised to the given power equals the given number?
What root raised to the given power equals the given number?
PTS: 1
DIF: Advanced
TOP: 11-Ext Rational Exponents
82. ANS: D
3
REF: Page 832
A number raised to the
root of that number.
Think
.
OBJ: 11-Ext.1 Evaluating Roots
power is equal to the 3rd
Feedback
A
First, rewrite the number as a radical. Then, simplify.
First, rewrite the number as a radical. Then, simplify.
A number raised to the 1/n power is equal to the nth root of
that number.
Correct!
B
C
D
PTS: 1
DIF: Average
TOP: 11-Ext Rational Exponents
83. ANS: A
REF: Page 833
OBJ: 11-Ext.2 Evaluating 1/b^n
=
=
Power of a Power Property
=
Definition of
Take the fifth root of 243.
Raise the result to the 2nd power.
=
=9
Feedback
A
Correct!
Take the root, then raise the result to the power in the
numerator of the exponent.
The denominator indicates the root to take. Raise the result to
the power indicated by the numerator of the exponent.
The denominator indicates the root to take. Raise the result to
the power indicated by the numerator of the exponent.
B
C
D
PTS:
OBJ:
TOP:
84. ANS:
1
DIF: Average
REF: Page 834
11-Ext.3 Evaluating Expressions with Rational Exponents
11-Ext Rational Exponents
D
A relationship is an inverse variation if the product of each pair of
corresponding numbers is the same.
x
2
3
4
y
xy
409 818
240 720
194 776
The product xy is not constant, so the relationship is not an inverse variation.
Feedback
A
If the product of each x – y pair is the same, the relationship is
an inverse variation.
If the product of each x – y pair is the same, the relationship is
an inverse variation.
If the product of each x – y pair is the same, the relationship is
an inverse variation.
Correct!
B
C
D
PTS:
OBJ:
TOP:
85. ANS:
1
DIF: Average
REF: Page 851
12-1.1 Identifying an Inverse Variation
NAT: 12.5.1.e
12-1 Inverse Variation
KEY: inverse variation | relationship
D
First, find the constant of variation.
Substitute the given values.
8=k
Solve for k.
Use a table of values to graph
x
–8
–6
–4
0
4
6
8
. Use both positive and negative values.
y
–1
−1.3
–2
Undefined
2
1.3
1
Feedback
A
B
This equation does not have the correct constant of variation.
To find k, use xy = k and substitute the given x- and y-values.
This equation does not have the correct constant of variation.
To find k, use xy = x and substitute the given x- and y-values.
C
D
This is a direct variation equation, but it should be an inverse
variation equation. Inverse variation equations are in the form
y = k/x.
Correct!
PTS:
OBJ:
TOP:
86. ANS:
1
DIF: Average
REF: Page 852
12-1.2 Graphing an Inverse Variation
NAT: 12.5.1.e
12-1 Inverse Variation
KEY: inverse variation | relationship | graph
C
Write the Product Rule for Inverse Variation.
Substitute 4 for , 6 for , and 24 for .
Simplify and solve for
.
Feedback
A
B
C
D
Divide both sides of the equation by the same number, not
subtract.
The Product Rule for Inverse Variation states that (x1)(y1) =
(x2)(y2).
Correct!
The Product Rule for Inverse Variation states that (x1)(y1) =
(x2)(y2).
PTS: 1
NAT: 12.5.1.e
87. ANS: C
DIF: Basic
REF: Page 853
TOP: 12-1 Inverse Variation
OBJ: 12-1.4 Using the Product Rule
Let w represent the wavelength in meters and let f represent the frequency in
kilohertz.
Product Rule for Inverse Variation.
Substitute for the known quantities.
Simplify.
Divide both sides by 600.
Feedback
A
B
Use the Product Rule for Inverse Variation and solve for the
wavelength.
You solved for the wavelength assuming a direct variation.
Use the Product Rule for Inverse Variation and solve for the
C
D
wavelength.
Correct!
Use the Product Rule for Inverse Variation and solve for the
wavelength.
PTS: 1
NAT: 12.5.1.e
88. ANS: C
DIF: Average
REF: Page 854
TOP: 12-1 Inverse Variation
OBJ: 12-1.5 Application
Set the denominator equal to 0.
Solve for x.
The excluded value is –1.
Feedback
A
B
C
D
Set the denominator equal to 0, and solve for x.
Find the value that makes the denominator equal to 0.
Correct!
Set the denominator equal to 0, and solve for x.
PTS: 1
DIF: Basic
TOP: 12-2 Rational Functions
89. ANS: A
REF: Page 858
OBJ: 12-2.1 Identifying Excluded Values
Find the excluded value by setting the denominator equal to 0 and solving for
x. This is the vertical asymptote. Find the horizontal asymptote by using the
formula, y = c if the original equation is in the form:
.
Feedback
A
B
C
D
Correct!
The vertical asymptote should be an excluded value of x.
Set the denominator equal to 0 to find the vertical asymptote.
Check your signs.
PTS: 1
DIF: Average
TOP: 12-2 Rational Functions
90. ANS: A
REF: Page 859
Step 1 Identify the asymptotes.
Vertical asymptote: Use
–b equals –3.
Horizontal asymptote: Use
OBJ: 12-2.2 Identifying Asymptotes
. The value of b is 3 so
. The value of c is 3.
Step 2 Graph the asymptotes using dashed lines.
Step 3 Make a table of values. Choose x-values on both sides of the vertical
asymptotes.
Step 4 Plot the points and connect them with smooth curves. The curves will
get very close to the asymptotes but will not touch them.
Feedback
A
B
C
D
Correct!
The value of the horizontal asymptote shown is the opposite of
the correct value.
The values of the vertical and horizontal asymptotes shown
are the opposites of the correct values.
The vertical asymptote is at the excluded value x + b = 0, or x
= –b.
PTS: 1
DIF: Average
REF: Page 860
OBJ: 12-2.3 Graphing Rational Functions Using Asymptotes
91. ANS: A
TOP: 12-2 Rational Functions
A horizontal asymptote
is the line at
that the graph gets closer
to as the absolute value of the variable increases.
A rational function in the form of
excluded value, or
has a vertical asymptote at the
, and a horizontal asymptote at
.
Feedback
A
B
C
D
Correct!
This function has a vertical asymptote at x = –3, not a
horizontal asymptote at y = –3.
Check your answer by graphing the function.
Check your answer by graphing the function.
PTS: 1
92. ANS: D
DIF: Advanced
TOP: 12-2 Rational Functions
The excluded values are all values of n that make the denominator equal to
zero.
n2 – 5n + 4 = 0
Set the denominator equal to 0.
(n – 4)(n – 1) = 0
n – 4 =0 or n – 1 =
0
n = 4 or n = 1
Factor.
Use the Zero-Product Property to solve each
factor for n.
4 must be excluded. 1 must be excluded.
The excluded values are 4 and 1.
Feedback
A
B
C
D
The excluded values are numbers that make the denominator
equal to 0.
The excluded values are numbers that make the denominator
equal to 0.
First, set the denominator equal to 0. Then, factor and solve
each factor to see what values must be excluded.
Correct!
PTS: 1
NAT: 12.5.3.c
93. ANS: A
DIF: Average
REF: Page 866
OBJ: 12-3.1 Identifying Excluded Values
TOP: 12-3 Simplifying Rational Expressions
Factor common factors out of the numerator and/or denominator. Divide out
the common factors to simplify the expression. Finally, use the original
denominator to determine excluded factors.
Feedback
A
B
C
D
Correct!
Determine excluded values from the original denominator.
Determine excluded values from the original denominator.
Divide out common factors.
PTS:
OBJ:
TOP:
94. ANS:
1
DIF: Basic
REF: Page 867
12-3.2 Simplifying Rational Expressions
12-3 Simplifying Rational Expressions
C
NAT: 12.5.3.c
Factor the numerator and
denominator.
Divide out the common factors.
Simplify.
Feedback
A
B
C
D
Factor the denominator. Divide out common factors.
Factor the denominator. Divide out common factors.
Correct!
Factor the denominator. Divide out common factors.
PTS:
OBJ:
NAT:
95. ANS:
1
DIF: Basic
REF: Page 867
12-3.3 Simplifying Rational Expressions with Trinomials
12.5.3.c
TOP: 12-3 Simplifying Rational Expressions
B
Factor.
=
Identify the opposite binomials.
=
Divide out the common factors, and
simplify.
=
Feedback
A
B
C
D
Factor the denominator also.
Correct!
Identify the opposite binomials. Then, divide out common
factors and simplify.
Identify the opposite binomials. Then, divide out common
factors and simplify.
PTS:
OBJ:
NAT:
96. ANS:
1
DIF: Average
REF: Page 868
12-3.4 Simplifying Rational Expressions Using Opposite Binomials
12.5.3.c
TOP: 12-3 Simplifying Rational Expressions
C
Arrange the expressions so like terms are together:
.
Multiply the numerators and denominators, remembering to add exponents
when multiplying:
.
Divide, remembering to subtract exponents:
.
Since
, this expression simplifies to
Feedback
A
B
C
D
A variable raised to the 0 power simplifies to 1.
When dividing powers with the same base, subtract the
exponents.
Correct!
Multiply, then simplify.
PTS:
OBJ:
TOP:
97. ANS:
1
DIF: Average
REF: Page 878
12-4.1 Multiplying Rational Expressions
12-4 Multiplying and Dividing Rational Expressions
B
NAT: 12.5.3.c
=
Write the polynomial over 1.
=
Factor the numerator and
denominator.
=
Divide out common factors.
=
Multiply remaining factors.
Feedback
A
B
C
D
Divide out common factors, and multiply the remaining factors.
Correct!
First, rewrite the polynomial as an expression over 1. Then,
multiply and simplify.
Continue simplifying until the answer is in simplest form.
PTS:
OBJ:
NAT:
98. ANS:
=
1
DIF: Average
REF: Page 879
12-4.2 Multiplying a Rational Expression by a Polynomial
12.5.3.c
TOP: 12-4 Multiplying and Dividing Rational Expressions
A
Factor the numerator and
denominator.
=
Simplify.
=
Multiply the remaining factors.
Feedback
A
B
C
D
Correct!
Factor the numerator and denominator and divide out the
common factors.
Factor the numerator and denominator and divide out the
common factors.
Factor the numerator and denominator and divide out the
common factors.
PTS:
OBJ:
NAT:
99. ANS:
1
DIF: Average
REF: Page 879
12-4.3 Multiplying Rational Expressions Containing Polynomials
12.5.3.c
TOP: 12-4 Multiplying and Dividing Rational Expressions
A
Write as multiplication by the reciprocal.
=
Multiply the numerators and the denominators.
=
Divide out common factors. Simplify.
=
Feedback
A
B
C
D
Correct!
Divide out common factors, and simplify.
First, write as multiplication by the reciprocal. Then, multiply
the numerators and the denominators.
Write as multiplication by the reciprocal first.
PTS:
OBJ:
NAT:
100. ANS:
1
DIF: Basic
REF: Page 880
12-4.4 Dividing by Rational Expressions and Polynomials
12.5.3.c
TOP: 12-4 Multiplying and Dividing Rational Expressions
A
=
Factor.
=
Multiply the numerators and the
denominators.
Divide out common factors and
simplify.
=
Feedback
A
B
C
D
Correct!
First, factor, and then multiply the numerators and the
denominators. Next, divide out common factors and simplify.
First, factor, and then multiply the numerators and the
denominators. Next, divide out common factors and simplify.
First, factor, and then multiply the numerators and the
denominators. Next, divide out common factors and simplify.
PTS: 1
DIF: Advanced
NAT: 12.5.3.c
TOP: 12-4 Multiplying and Dividing Rational Expressions
101. ANS: C
Combine like terms in the numerator.
Factor. Divide out common factors.
Simplify.
Feedback
A
B
C
D
Divide out only common factors.
Factor the denominator and continue simplifying your answer.
Correct!
The denominators are the same, so keep the common
denominator.
PTS:
OBJ:
NAT:
102. ANS:
1
DIF: Average
REF: Page 885
12-5.1 Adding Rational Expressions with Like Denominators
12.5.3.c
TOP: 12-5 Adding and Subtracting Rational Expressions
D
=
=
Subtract the numerators.
=
Combine like terms.
=
Factor. Divide out common factors.
=
Simplify.
Feedback
A
B
C
D
Factor the numerator and the denominator. Then, divide out
common factors.
Subtract, not add.
Subtract the numerator. Then, combine like terms.
Correct!
PTS:
OBJ:
NAT:
103. ANS:
1
DIF: Average
REF: Page 886
12-5.2 Subtracting Rational Expressions with Like Denominators
12.5.3.c
TOP: 12-5 Adding and Subtracting Rational Expressions
B
1. Factor each expression.
2. Use every factor of both expressions the greatest number of times it
appears in either expression.
3. If the same factor appears only once in each expression, it should appear
only once in the LCM.
Feedback
A
B
C
The LCM should have one more factor.
Correct!
LCM is the least common multiple, not the common factor of
D
the expressions.
If the same factor appears only once in each expression, it
should appear only once in the LCM.
PTS:
OBJ:
TOP:
104. ANS:
1
DIF: Average
REF: Page 886
12-5.3 Identifying the Least Common Multiple
12-5 Adding and Subtracting Rational Expressions
C
Identify the LCD,
NAT: 12.5.3.c
.
=
=
Rewrite each fraction with a denominator
of
.
=
Add.
=
and
are not like terms, so they
cannot be combined. Factor and divide out
common factors.
=
Simplify.
Feedback
A
B
C
D
To simplify the numerator, factor out 3y.
First find a common denominator. Then add the numerators.
Correct!
To simplify the numerator, factor out 3y.
PTS:
OBJ:
NAT:
105. ANS:
=
1
DIF: Basic
REF: Page 887
12-5.4 Adding and Subtracting with Unlike Denominators
12.5.3.c
TOP: 12-5 Adding and Subtracting Rational Expressions
B
Factor the difference of
squares.
Write each expression using
the LCD.
=
Subtract the numerators.
=
Distribute.
=
Simplify.
=
Excluded values are values that make the denominator equal to 0. If
, then the denominator is 0. Therefore,
and
.
Feedback
A
B
C
D
First, factor the difference of squares. Then, write each
expression using the LCD, subtract, and simplify.
Correct!
Excluded values are values that make the denominator equal
to 0.
Check the step where you used the Distributive Property.
PTS: 1
DIF: Advanced
NAT: 12.5.3.c
TOP: 12-5 Adding and Subtracting Rational Expressions
106. ANS: B
Rewrite as a rational expression.
=
=
Divide each term in the numerator
by the denominator.
=
Simplify by dividing out common
factors.
=
Simplify by using powers of
exponents.
Feedback
A
Write the division of each term by the divisor as a quotient.
Simplify by dividing out common factors and using the rule of
exponents.
or
B
C
D
Correct!
Write the division of each term by the divisor as a quotient.
Simplify by dividing out common factors and using the rule of
exponents.
Write the division of each term by the divisor as a quotient.
Simplify by dividing out common factors and using the rule of
exponents.
PTS:
OBJ:
TOP:
107. ANS:
1
DIF: Average
REF: Page 893
12-6.1 Dividing a Polynomial by a Monomial
12-6 Dividing Polynomials
D
NAT: 12.5.3.c
Factor the numerator.
=
=
Divide out the common factors. Simplify.
Feedback
A
B
C
D
First, factor the numerator. Then, divide out the common
factors and simplify.
First, factor the numerator. Then, divide out the common
factors and simplify.
Check the signs.
Correct!
PTS:
OBJ:
TOP:
108. ANS:
1
DIF: Basic
REF: Page 894
12-6.2 Divide a Polynomial by a Binomial
12-6 Dividing Polynomials
B
Write the problem in long division form.
NAT: 12.5.3.c
To find the first term of the quotient, divide
the first term of the dividend by the first term
of the divisor.
Multiply the divisor by the first term of the
quotient and place it under the dividend.
Subtract. Bring down the next term in the
dividend.
Repeat these steps until you get 0.
Feedback
A
B
C
D
Check the answer by multiplying the quotient by the divisor.
Correct!
Check the answer by multiplying the quotient by the divisor.
Check the answer by multiplying the quotient by the divisor.
PTS: 1
NAT: 12.5.3.c
109. ANS: C
DIF: Average
REF: Page 895
TOP: 12-6 Dividing Polynomials
OBJ: 12-6.3 Polynomial Long Division
Write the problem in long division form. There will be a remainder when you
finish with the long division. Write the remainder as a rational expression using
the divisor as the denominator.
Feedback
A
B
C
D
Use long division.
Write the remainder as a rational expression using the divisor
as a denominator.
Correct!
Use long division.
PTS:
OBJ:
TOP:
110. ANS:
1
DIF: Average
REF: Page 896
12-6.4 Long Division with a Remainder
12-6 Dividing Polynomials
D
NAT: 12.5.3.c
Write the polynomials in
standard form.
Write in long division form.
Use 0x as a placeholder
for the missing x term.
.
Multiply x + 1 by –7x2.
Subtract. Bring down the
next term.
. Multiply x
+ 1 by 10x.
Subtract. Bring down the
next term.
. Multiply x + 1
by 10.
Subtract. Write the
remainder as a fraction in
the answer.
Feedback
A
B
C
D
Subtract the products after you multiply.
Add zeros as placeholders for missing terms.
Write the remainder as a fraction of the divisor.
Correct!
PTS:
OBJ:
NAT:
111. ANS:
1
DIF: Average
REF: Page 896
12-6.5 Dividing Polynomials that Have a Zero Coefficient
12.5.3.c
TOP: 12-6 Dividing Polynomials
B
Use cross products.
Multiply. Distribute 2 on the right side..
m= −
6
13
Subtract 2m from both sides.
Divide both sides by 13.
Feedback
A
B
C
D
First compute the cross products. Then solve for the variable.
Correct!
First compute the cross products. Then solve for the variable.
First compute the cross products. Then solve for the variable.
PTS:
OBJ:
NAT:
112. ANS:
1
DIF: Average
REF: Page 900
12-7.1 Solving Rational Equations by Using Cross Products
12.5.4.a
TOP: 12-7 Solving Rational Equations
B
Multiply both sides of the equation by the LCD: 4z(z + 10).
Divide out common factors, then distribute. This gives the equation:
–8z – 80 + z + 10 = 28z
Combine like terms and simplify. Then solve for z.
Feedback
A
B
C
D
When solving for the variable, perform the same operations on
both sides of the equation.
Correct!
Keep track of signs when multiplying by the LCD and solving
for the variable.
Find the LCD of all the rational expressions in the equation.
PTS:
OBJ:
TOP:
113. ANS:
1
DIF: Average
REF: Page 900
12-7.2 Solving Rational Equations by Using the LCD
12-7 Solving Rational Equations
C
NAT: 12.5.4.a
The answer will be the number of minutes Marukh and Steven need to wash
the car.
Marukh can wash the car in 50 minutes, so she washes 501 of the car in 1
minute.
Steven can wash the car in 40 minutes, so he washes 401 of the car in 1
minute.
Let m represent the number of minutes it takes them both to wash the car.
(Marukh’s rate)m + (Steven’s rate)m = Total time to wash the car
1
1
50 m + 40 m = 1
m) = 200(1) Multiply both sides of the
equation by the LCD, 200.
4m + 5m = 200 Distribute 200 on the left side.
9m = 200 Combine like terms.
m=
Divide.
m = 22 minutes Round to the nearest minute.
200( 501 m +
1
40
Marukh and Steven can wash the car in 22 minutes.
Feedback
A
B
C
D
If two people work together, it will take them less time to finish
the task.
First, find how much of the job can each person do in 1 minute.
Correct!
First, find how much of the job can each person do in 1 minute.
PTS:
OBJ:
TOP:
114. ANS:
1
DIF: Average
REF: Page 901
12-7.3 Problem-Solving Application
12-7 Solving Rational Equations
B
4x2 + 4x = x2 + 4x + 3
(3x – 3)(x + 1) = 0
NAT: 12.5.4.a
Use cross products to solve.
Distribute x on the left side.
Multiply on the right side.
Add and subtract to move
terms to one side of the equal
sign. Then, factor.
3(x – 1)(x + 1) = 0
x–1=0
or x + 1 = 0
Use the Zero-Product
x=1
x = –1 Property.
Solve for x.
Check
Check
Substitute each x-value in the
original equation.
1 is the only solution.
–1 is an extraneous solution.
and
are both
undefined.
–1 is not a
solution.
Feedback
A
B
C
D
Substitute the solution in the original equation to check your
answer.
Correct!
Use cross products and factoring to solve for x.
Cross multiply to solve for x.
PTS: 1
NAT: 12.5.4.a
115. ANS: D
DIF: Average
REF: Page 902
TOP: 12-7 Solving Rational Equations
Rita’s time working alone
Brittany’s time working alone
Maria’s time working alone
hr
Time working together
OBJ: 12-7.4 Extraneous Solutions
hr
hr
hr
The inverse of the time
working together is the
inverse of the sum of
the inverses of the times
working alone.
Substitute.
Find the common
denominator,
Add.
.
Simplify.
Multiply both sides by
the LCD,
.
Distribute.
Subtract
from
both sides.
Factor.
Solve for .
If
, then Rita’s time is negative. Thus
and
.
Rita takes 3 hours, Brittany takes 4 hours, and Maria takes 12 hours.
Feedback
A
B
C
D
The inverse of the time working together is equal to the sum of
the inverses of the times working alone.
The inverse of the time working together is equal to the sum of
the inverses of the times working alone.
The inverse of the time working together is equal to the sum of
the inverses of the times working alone.
Correct!
PTS: 1
116. ANS: A
DIF: Advanced
TOP: 12-7 Solving Rational Equations
Use the appropriate ratio:
sin x =
cos x =
tan x =
Feedback
A
B
C
D
Correct!
Check that you used the correct ratio.
Check that you used the correct ratio.
Check that you used the correct ratio.
PTS:
OBJ:
KEY:
117. ANS:
1
DIF: Average
REF: Page 908
12-Ext.1 Finding the Value of a Trigonometric Ratio
cosine | sine | tangent | trigonometric ratio
D
Rocket
B
Camera's angle
A
C
Launching
Pad
height ≈ 2,540 ft
Draw a diagram to model the
problem.
Definition of tangent
Substitute the given values for
angle A and the distance of the
adjacent side.
Solve for the height.
Substitute the value of the
tangent and simplify.
Feedback
A
B
C
D
The height of the rocket equals the product of the camera's
distance from the rocket launching pad times the tangent of
the angle.
The height of the rocket equals the product of the camera's
distance from the rocket launching pad times the tangent of
the angle.
The height of the rocket equals the product of the camera's
distance from the rocket launching pad times the tangent of
the angle.
Correct!
PTS: 1
DIF: Average
TOP: 12-Ext Trigonometric Ratios
NUMERIC RESPONSE
REF: Page 908
OBJ: 12-Ext.2 Application
118. ANS:
0
PTS: 1
119. ANS:
DIF: Average
TOP: 9-4 Transforming Quadratic Functions
2
PTS: 1
DIF: Average
NAT: 12.5.4.c
TOP: 9-5 Solving Quadratic Equations by Graphing
120. ANS:
12.93
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: 9-7 Solving Quadratic Equations by Using Square Roots
121. ANS:
30
PTS: 1
122. ANS:
TOP: 9-8 Completing the Square
DIF: Advanced
NAT: 12.5.1.a
TOP: 11-1 Geometric Sequences
DIF: Average
TOP: 11-2 Exponential Functions
5
PTS: 1
124. ANS:
NAT: 12.5.4.c
120
PTS: 1
123. ANS:
DIF: Advanced
320
PTS: 1
DIF: Advanced
NAT: 12.5.2.h
TOP: 11-3 Exponential Growth and Decay
125. ANS:
15
PTS: 1
DIF: Advanced
NAT: 12.1.3.a
TOP: 11-7 Adding and Subtracting Radical Expressions
126. ANS:
2
PTS: 1
127. ANS:
TOP: 12-1 Inverse Variation
DIF: Advanced
TOP: 12-3 Simplifying Rational Expressions
DIF: Advanced
TOP: 12-6 Dividing Polynomials
1
PTS: 1
128. ANS:
DIF: Average
5
PTS: 1
MATCHING
129. ANS:
TOP:
130. ANS:
TOP:
131. ANS:
G
PTS: 1
DIF: Basic
9-1 Identifying Quadratic Functions
E
PTS: 1
DIF: Basic
9-1 Identifying Quadratic Functions
B
PTS: 1
DIF: Basic
REF: Page 592
REF: Page 590
REF: Page 592
TOP:
132. ANS:
TOP:
133. ANS:
TOP:
9-1 Identifying Quadratic Functions
C
PTS: 1
DIF: Basic
9-1 Identifying Quadratic Functions
D
PTS: 1
DIF: Basic
9-5 Solving Quadratic Equations by Graphing
134. ANS:
TOP:
135. ANS:
TOP:
136. ANS:
TOP:
137. ANS:
TOP:
138. ANS:
TOP:
F
PTS: 1
DIF: Basic
9-2 Characteristics of Quadratic Functions
D
PTS: 1
DIF: Basic
9-1 Identifying Quadratic Functions
C
PTS: 1
DIF: Basic
9-9 The Quadratic Formula and the Discriminant
B
PTS: 1
DIF: Basic
9-8 Completing the Square
A
PTS: 1
DIF: Basic
9-2 Characteristics of Quadratic Functions
139. ANS:
TOP:
140. ANS:
TOP:
141. ANS:
TOP:
142. ANS:
TOP:
143. ANS:
TOP:
144. ANS:
TOP:
145. ANS:
TOP:
H
PTS: 1
DIF:
11-3 Exponential Growth and Decay
F
PTS: 1
DIF:
11-3 Exponential Growth and Decay
E
PTS: 1
DIF:
11-2 Exponential Functions
D
PTS: 1
DIF:
11-3 Exponential Growth and Decay
G
PTS: 1
DIF:
11-3 Exponential Growth and Decay
B
PTS: 1
DIF:
11-1 Geometric Sequences
A
PTS: 1
DIF:
11-1 Geometric Sequences
REF: Page 591
REF: Page 622
REF: Page 599
REF: Page 592
REF: Page 654
REF: Page 645
REF: Page 600
Basic
REF: Page 782
Basic
REF: Page 783
Basic
REF: Page 772
Basic
REF: Page 783
Basic
REF: Page 783
Basic
REF: Page 766
Basic
REF: Page 766
146. ANS:
TOP:
147. ANS:
TOP:
148. ANS:
TOP:
149. ANS:
TOP:
150. ANS:
TOP:
151. ANS:
TOP:
H
PTS: 1
DIF: Basic
11-7 Adding and Subtracting Radical Expressions
A
PTS: 1
DIF: Basic
11-9 Solving Radical Equations
F
PTS: 1
DIF: Basic
11-5 Square-Root Functions
E
PTS: 1
DIF: Basic
11-6 Radical Expressions
D
PTS: 1
DIF: Basic
11-6 Radical Expressions
C
PTS: 1
DIF: Basic
11-9 Solving Radical Equations
REF: Page 811
152. ANS:
TOP:
153. ANS:
TOP:
F
PTS: 1
12-2 Rational Functions
C
PTS: 1
12-2 Rational Functions
REF: Page 824
REF: Page 798
REF: Page 805
REF: Page 805
REF: Page 822
DIF: Basic
REF: Page 858
DIF: Basic
REF: Page 858
154. ANS:
TOP:
155. ANS:
TOP:
156. ANS:
TOP:
157. ANS:
TOP:
158. ANS:
TOP:
H
PTS: 1
DIF:
12-7 Solving Rational Equations
A
PTS: 1
DIF:
12-1 Inverse Variation
G
PTS: 1
DIF:
12-3 Simplifying Rational Expressions
B
PTS: 1
DIF:
12-2 Rational Functions
D
PTS: 1
DIF:
12-2 Rational Functions
Basic
REF: Page 900
Basic
REF: Page 851
Basic
REF: Page 866
Basic
REF: Page 858
Basic
REF: Page 858