chapter 5
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A protozoan called a euglena is
a. 0.00001
b. 0.0000001
____
2. Simplify
a. - 1
8
m long. Simplify
c. 0.000001
d. 1000000
.
c. 8
b. –6
____
____
3. Simplify
a. 1
b.
4. Evaluate
a. - 1
3
d.
5. Evaluate
a. 0
b.
____
c. –4
d. 0
for
and
.
c. 0
____
for
and
d.
1
9
c.
1
2
.
d. –4
1
4
6. Simplify
1
8
.
b. –9
____
.
.
a.
c.
b.
d.
7. Complete the table of values. Then, graph the ordered pairs and describe the shape of the graph.
x
a. 1, 3, 9, 27, 81
0
1
2
3
4
?
?
?
?
?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
The shape of the graph is a curve where y increases more rapidly as x increases.
b.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
The shape of the graph is a curve where y increases less rapidly as x increases.
c.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
The shape of the graph is a line where y increases as x decreases.
d. 1, 3, 9, 27, 81
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
The shape of the graph is a line where y increases as x increases.
____
8. Find the value of the power
.
a. 1000000
b. 0.0000001
____ 9. Write 10,000 as a power of 10.
a.
b.
____ 10. Write 0.01 as a power of 10.
a.
b.
____ 11. Find the value of the expression
a. 10,700
b. 1,070,000
c. 70
d. 10000000
c.
d.
c.
d.
.
c. 107,000
d. 3,210
____ 12. Find the value of the expression
.
a. 1.33
c. –3,990
b. 0.133
d. 0.0133
____ 13. The planet Mars has an average distance from the sun of about 141,600,000 miles. Write this number in
scientific notation.
a. 14.16 ´ 10
c. 1.416 ´ 10 8
7
b. 1.416 ´ 10
d. 0.1416 ´ 10
____ 14. The table shows estimates of astronomical distances. The distance from Earth to the moon is 383,000 km. The
distance from Earth to the sun is 1 AU. Estimate how many times farther Earth is from the sun than Earth is
from the moon. Explain.
Astronomical Distances
1 kilometer (km)
m
1 astronomical unit (AU)
m
1 parsec (Mpc)
m
a.
About 2500 times; 383,000 km is about
m, so
2500.
b.
About 250,000 times; 383,000 km is about
m, so
250,000.
c.
About 2.5 times; 383,000 km is about
m, so
2.5.
d.
About 250 million times; 383,000 km is about
km, so
____ 15. Simplify
.
a. –18
b. Cannot simplify
c. –216
d. - 1
216
____ 16. Simplify
a.
c.
.
.
b.
d.
____ 17. There are
atoms in 1 gram of oxygen. How many atoms are there in 600 grams of oxygen? Write
your answer in scientific notation. If necessary, round your answer to two decimal places.
a.
c.
b.
d.
____ 18. Simplify
a.
.
c.
b.
d.
____ 19. Simplify
a.
b.
.
c. –
d.
-
____ 20. The edge of a cube measures
a.
cm
b.
cm
____ 21. Simplify
a.
b.
____ 23. Simplify
a.
b. 98
m. What is the volume of the cube in cubic centimeters?
c.
cm
d.
cm
.
a. 3
b. 36
____ 22. Simplify
-
c. 1,296
d. Cannot simplify
.
c. Cannot simplify
d.
and write the answer in scientific notation.
c.
d.
____ 24. The area of Australia/Oceania is approximately
square kilometers. Its population is approximately
people. What is the approximate population density (people per square kilometer) of
Australia/Oceania? Write your answer in standard form. If necessary, round your answer to the nearest
hundredth.
a. 4.04 people/km2
c.
people/km2
b.
d. 24.73 people/km2
people/km2
____ 25. Simplify
.
a.
c.
b.
d.
____ 26. Simplify
.
a. - 3
4
c. - 16
3
b. 8
d.
____ 27. The volume of the cone is
an expression for the cone’s height.
. The height is h and the radius of the base is
a.
c.
b.
d.
____ 28. Find the degree of the monomial
a. 7
b. 11
1
8
. Write and simplify
.
c. –5
d. 4
____ 29. Find the degree of the polynomial
.
a. 6
c. 9
b. 12
d. 14
2
5
3
4
____ 30. Write the polynomial 3x – 8x – 12x – 5x + 2x – 6 in standard form. Then give the leading coefficient.
a.
The leading coefficient is –12.
b.
The leading coefficient is –6.
c.
The leading coefficient is –12.
d.
The leading coefficient is –6.
____ 31. Classify the polynomial according to its degree and number of terms.
a. The polynomial is a seventh degree monomial.
b. The polynomial is a linear monomial.
c. The polynomial is a seventh degree binomial.
d. The polynomial is a quadratic binomial.
____ 32. A toy rocket is launched from a platform 34 feet above the ground at a speed of 90 feet per second. The height
of the rocket in feet is given by the polynomial
, where t is the time in seconds. How high will
the rocket be after 3 seconds?
a. 160 feet
c. 2608 feet
b. 126 feet
d. 256 feet
____ 33. Add or subtract.
a.
b.
____ 34. Add.
c.
d.
a.
b.
____ 35. Subtract.
c.
d.
a.
b.
c.
d.
____ 36. A company distributes its product by train and by truck. The cost of distributing by train can be modeled as
, and the cost of distributing by trucks can be modeled as
, where x is
the number of tons of product distributed. Write a polynomial that represents the difference between the cost
of distributing by train and the cost of distributing by trucks.
a.
c.
b.
d.
____ 37. The legs of an isosceles triangle measure
units. The perimeter of the triangle is
units. Write a polynomial that represents the measure of the base of the triangle.
a.
c.
b.
d.
____ 38. Multiply.
a.
c. 6 2
3
b. 6 2
3
d.
____ 39. Multiply.
a.
b.
c.
d.
____ 40. Multiply.
a.
b.
____ 41. Multiply.
c.
d.
a.
c.
b.
d.
____ 42. A builder uses parallelogram-shaped stones as decoration around a building’s windows. The stones come in
many different sizes. Each stone has a base length of x inches and a height of
inches. Write a
polynomial to describe the area of a stone. Then find the area of a stone that has a length of 6 units.
a.
b.
; Area = 139 in2
; Area = 19 in.
c.
d.
; Area = 114 in2
; Area = 114 in2
____ 43. Multiply.
a.
b.
c.
d.
____ 44. Multiply.
a.
b.
c.
d.
____ 45. Multiply.
a.
b.
c.
d.
____ 46. A circular pool is surrounded by a circular walkway. The radius of the pool is
walkway is
. Write a polynomial that represents the area of the walkway.
(Area of a circle is given by
a.
b.
, where r represents the radius of the circle.)
c. 8
d.
and the radius of the
____ 47. Weldon installed a square hot tub in his backyard and wants to enclose it with a fence. The fence will enclose
an area that is 4 feet longer and 2 feet wider than the hot tub. If Weldon bought a total of 44 feet of fencing,
what are the dimensions of the hot tub?
a. The hot tub is 8 feet long and 8 feet wide.
b. The hot tub is 13 feet long and 9 feet wide.
c. The hot tub is 16 feet long and 12 feet wide.
d. The hot tub is 5 feet long and 5 feet wide.
chapter 5
Answer Section
MULTIPLE CHOICE
1. ANS: C
Feedback
A
B
C
D
Check the exponent.
Check the exponent.
Correct!
The exponent is negative.
PTS: 1
NAT: 12.1.1.d
2. ANS: D
=
=
1
8
DIF: Basic
STA: A.11.A
The reciprocal of 2 is
REF: Page 447
OBJ: 7-1.1 Application
TOP: 7-1 Integer Exponents
.
= 8.
Feedback
A
B
C
D
Check the sign of your answer. A negative exponent does not affect the sign of the
answer.
A nonzero number raised to a negative exponent is equal to 1 divided by that number
raised to the opposite (positive) exponent.
A nonzero number raised to a negative exponent is equal to 1 divided by that number
raised to the opposite (positive) exponent.
Correct!
PTS: 1
DIF: Average
REF: Page 447
OBJ: 7-1.2 Zero and Negative Exponents
NAT: 12.1.1.d
STA: A.11.A
TOP: 7-1 Integer Exponents
KEY: negative exponent | evaluate | power | exponent
3. ANS: A
Any nonzero base to the zero power is equal to 1.
=1
Feedback
A
B
C
D
Correct!
A nonzero number raised to the zero power is equal to 1.
A nonzero number raised to the zero power is equal to 1.
A nonzero number raised to the zero power is equal to 1.
PTS: 1
DIF: Average
REF: Page 447
OBJ: 7-1.2 Zero and Negative Exponents
NAT: 12.1.1.d
STA: A.11.A
TOP: 7-1 Integer Exponents
KEY: zero exponent | zero power | evaluate | power | exponent
4. ANS: D
Substitute –3 for a and –3 for b.
1
( 9 )(1)
Evaluate expressions with exponents.
1
9
Simplify.
Feedback
A
B
Any nonzero number raised to the zero power is 1.
A nonzero number raised to a negative exponent is equal to 1 divided by that number
raised to the opposite (positive) exponent.
Any nonzero number raised to the zero power is 1.
Correct!
C
D
PTS:
OBJ:
NAT:
5. ANS:
1
DIF: Average
REF: Page 447
7-1.3 Evaluating Expressions with Zero and Negative Exponents
12.1.1.d
STA: A.11.A
TOP: 7-1 Integer Exponents
B
Substitute 2 for a and –2 for b.
1
(1)( 4 )
Evaluate expressions with exponents.
1
4
Simplify.
Feedback
A
B
C
D
Any nonzero number raised to the zero power is 1.
Correct!
Any nonzero number raised to the zero power is 1.
A nonzero number raised to a negative exponent is equal to 1 divided by that number
raised to the opposite (positive) exponent.
PTS:
OBJ:
NAT:
6. ANS:
1
DIF: Average
REF: Page 447
7-1.3 Evaluating Expressions with Zero and Negative Exponents
12.1.1.d
STA: A.11.A
TOP: 7-1 Integer Exponents
B
Rewrite
=
without negative or zero
exponents.
Simplify each part of the expression.
=
.
=
.
=
Feedback
A
Any number to the zero power is equal to 1. A negative exponent in the numerator
becomes positive in the denominator.
Correct!
Any number to the zero power is equal to 1. A negative exponent in the numerator
becomes positive in the denominator.
A negative exponent in the denominator becomes positive in the numerator.
B
C
D
PTS:
OBJ:
NAT:
7. ANS:
x
1
DIF: Advanced
REF: Page 448
7-1.4 Simplify Expressions with Zero and Negative Exponents
12.5.3.d
STA: A.11.A
TOP: 7-1 Integer Exponents
A
0
1
2
3
4
The function
is exponential with a base greater than 1. The shape of the graph is a curve where y
increases more rapidly as x increases.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
Feedback
A
B
C
D
Correct!
Check for algebra mistakes when creating the table.
Check for algebra mistakes when creating the table.
Sketch the graph to determine how the behavior of x affects y.
PTS: 1
DIF: Advanced
TOP: 7-1 Integer Exponents
NAT: 12.5.2.c
STA: A.1.D
8. ANS: D
Start with 1 and move the decimal point seven places to the right.
= 10000000
Feedback
A
B
C
D
Count the number of places to move the decimal point.
If the exponent is positive, move the decimal point to the right. If the exponent is
negative, move the decimal point to the left.
Start with 1 and move the decimal point.
Correct!
PTS: 1
DIF: Basic
REF: Page 452
OBJ: 7-2.1 Evaluating Powers of 10
NAT: 12.1.1.f
TOP: 7-2 Powers of 10 and Scientific Notation
9. ANS: C
The decimal point is 4 places to the right of 1, so the exponent is 4.
10,000 =
Feedback
A
B
C
D
Count the number of decimal places to the right of 1.
Count the number of decimal places to the right of 1.
Correct!
The number is greater than 1, so the exponent is positive.
PTS: 1
DIF: Basic
REF: Page 453
OBJ: 7-2.2 Writing Powers of 10
NAT: 12.1.1.f
TOP: 7-2 Powers of 10 and Scientific Notation
KEY: write | exponents | power | powers of 10
10. ANS: D
The decimal point is 2 places to the left of 1, so the exponent is –2.
0.01 =
Feedback
A
B
C
D
Count the number of decimal places to the left of 1. The exponent is the opposite of that
number.
Count the number of decimal places to the left of 1. The exponent is the opposite of that
number.
The number is less than one, so the exponent is negative.
Correct!
PTS: 1
DIF: Basic
REF: Page 453
OBJ: 7-2.2 Writing Powers of 10
NAT: 12.1.1.f
TOP: 7-2 Powers of 10 and Scientific Notation
KEY: write | exponents | power | powers of 10
11. ANS: C
Move the decimal point 3 places to the right.
107,000
Feedback
A
B
C
Move the decimal point the correct number of places.
Move the decimal point the correct number of places.
Correct!
D
For powers of 10, the exponent tells the number of places to move the decimal point.
PTS: 1
DIF: Average
REF: Page 453
OBJ: 7-2.3 Multiplying by Powers of 10
NAT: 12.1.1.f
TOP: 7-2 Powers of 10 and Scientific Notation
KEY: exponents | multiplication | power | powers of 10
12. ANS: B
Move the decimal point 3 places to the left.
0.133
Feedback
A
B
C
D
Move the decimal point the correct number of places.
Correct!
For powers of 10, the exponent tells the number of places to move the decimal point.
Move the decimal point the correct number of places.
PTS: 1
DIF: Average
REF: Page 453
OBJ: 7-2.3 Multiplying by Powers of 10
NAT: 12.1.1.f
TOP: 7-2 Powers of 10 and Scientific Notation
KEY: exponents | multiplication | power | powers of 10
13. ANS: C
To write 141,600,000 in scientific notation, count the number of places to move the decimal point to get a
number between 1 and 10. The number of places to move the decimal point is the exponent. If you move the
decimal point to the left, the exponent is positive.
To move the decimal point between the 1 and the 4, move the decimal point 8 places to the left.
141,600,000 = 1.416 ´ 10 8
Feedback
A
B
C
D
The number that multiplies the power of 10 should be greater than or equal to 1 and less
than 10.
The exponent should be equal to the number of places the decimal point is moved.
Correct!
The number that multiplies the power of 10 should be greater than or equal to 1 and less
than 10.
PTS:
NAT:
KEY:
14. ANS:
1 AU
1
DIF: Average
REF: Page 454
OBJ: 7-2.4 Application
12.1.1.f
STA: A.11.A
TOP: 7-2 Powers of 10 and Scientific Notation
exponents | scientific notation | standard notation
A
Distance from Earth to the sun
m
Distance from Earth to the moon
To find how many times farther Earth is from the sun than Earth is from the moon, divide the distance from
Earth to the sun by the distance from Earth to the moon.
2500
From the sun to Earth is about 2500 times farther than from the moon to Earth.
Feedback
A
B
C
D
Correct!
To find how many times farther Earth is from the sun than Earth is from the moon,
divide the distance from Earth to the sun by the distance from Earth to the moon.
Convert each number to scientific notation, and then divide using the laws of exponents.
Convert each number to scientific notation, and then divide using the laws of exponents.
PTS: 1
DIF: Advanced
NAT: 12.1.2.b
TOP: 7-2 Powers of 10 and Scientific Notation
15. ANS: C
To multiply powers with the same base, keep the same base and add the exponents. Then, evaluate the power.
= –216
=
Feedback
A
B
C
D
The exponent tells how many times to multiply the base number by itself.
If the bases are the same, add the exponents. Then evaluate the power.
Correct!
Check the sign of the exponent.
PTS: 1
DIF: Basic
REF: Page 461
OBJ: 7-3.1 Finding Products of Powers
NAT: 12.5.3.c
TOP: 7-3 Multiplication Properties of Exponents
KEY: evaluate | product | multiply | power | exponent
16. ANS: A
To multiply powers with the same base, keep the same base and add the exponents.
=
=
Feedback
A
B
C
D
Correct!
Rewrite only powers with the same base. Do not combine powers with different bases.
To multiply powers with the same base, add the exponents, not subtract.
To multiply powers with the same base, add the exponents, not multiply.
PTS: 1
DIF: Average
REF: Page 461
OBJ: 7-3.1 Finding Products of Powers
NAT: 12.5.3.c
TOP: 7-3 Multiplication Properties of Exponents
KEY: evaluate | product | multiply | power | exponent
17. ANS: B
number of atoms = number of atoms in 1 gram number of grams
=(
=(
=(
=
=
=
)
)(
)(
)
)
Write 600 in scientific notation.
Use the Commutative and Associative Properties
to group.
Multiply within each group.
Write 22.56 in scientific notation. Round if
necessary.
Feedback
A
B
C
D
The first term of a scientific notation must be a number that is greater than or equal to 1
and less than 10.
Correct!
Add the exponents when multiplying powers with the same base.
Add the exponents when multiplying powers with the same base.
PTS: 1
NAT: 12.5.3.c
18. ANS: B
DIF: Average
STA: A.11.A
REF: Page 461
OBJ: 7-3.2 Application
TOP: 7-3 Multiplication Properties of Exponents
Use the Power of a Power Property.
Simplify the exponent of the first term.
Add the exponents since the powers have the same base.
Write with a positive exponent.
Feedback
A
B
C
D
Multiply the exponents when a power is raised to another power.
Correct!
Continue simplifying to a fraction with a positive exponent.
Multiply the exponents when a power is raised to another power. Add the exponents
when a power is multiplied by another power.
PTS: 1
NAT: 12.5.3.c
19. ANS: A
DIF: Advanced
REF: Page 462
OBJ: 7-3.3 Finding Powers of Powers
TOP: 7-3 Multiplication Properties of Exponents
Use the Power of a Power Property.
Use the Associative and Commutative Properties.
Add the exponents.
-
Write with a positive exponent.
Feedback
A
B
C
D
Correct!
To find the product of two powers with the same base, add the exponents.
A power raised to a power is equal to the base raised to the product of the exponents.
A power raised to a power is equal to the base raised to the product of the exponents. To
find the product of two powers with the same base, add the exponents.
PTS: 1
DIF: Advanced
REF: Page 463
OBJ: 7-3.4 Finding Powers of Products
NAT: 12.5.3.c
TOP: 7-3 Multiplication Properties of Exponents
20. ANS: D
The edge is
cm.
The volume of a cube is the measure of a side, cubed.
cm
Feedback
A
B
C
D
Convert to centimeters first.
The volume of a cube is the measure of the edge raised to the power of 3.
To find the volume of the cube, raise the measure of the edge to the power of 3.
Correct!
PTS: 1
DIF: Advanced
NAT: 12.1.3.g
TOP: 7-3 Multiplication Properties of Exponents
21. ANS: B
To divide powers with the same base, keep the same base and subtract the exponents.
Feedback
A
B
C
D
To divide powers with the same base, subtract the exponents.
Correct!
To divide powers with the same base, subtract the exponents.
The bases are the same, so the expression can be simplified.
PTS: 1
DIF: Basic
REF: Page 467
OBJ: 7-4.1 Finding Quotients of Powers
TOP: 7-4 Division Properties of Exponents
KEY:
exponent | power | division | base
22. ANS: B
First, use the Power of a Product Property to rewrite the denominator. Then, for each power with the same
base, keep the base and subtract the exponents.
Feedback
A
B
C
D
To divide powers with the same base, subtract the exponents, not divide.
Correct!
The bases are the same, so the expression can be simplified.
The exponent in the denominator applies to both bases. Use the Power of a Product
Property.
PTS:
NAT:
KEY:
23. ANS:
1
DIF: Average
REF: Page 467
OBJ: 7-4.1 Finding Quotients of Powers
12.5.3.c
TOP: 7-4 Division Properties of Exponents
exponent | power | division | base
C
Write as a product of quotients:
.
Simplify each quotient to get
. If necessary, adjust the result so it is in scientific notation with
exactly one digit to the left of the decimal point.
Feedback
A
B
Check the exponent.
Write your answer in scientific notation.
C
D
Correct!
Check the exponent.
PTS:
OBJ:
TOP:
24. ANS:
1
DIF: Average
REF: Page 468
7-4.2 Dividing Numbers in Scientific Notation
7-4 Division Properties of Exponents
A
Population of
Australia/Oceania
Area of
Australia/Oceania
NAT: 12.1.1.f
Write as a product of quotients.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The population density of Australia/Oceania is about 4.04 people/km2.
Feedback
A
B
C
D
Correct!
Write your answer in standard form, not in scientific notation. Multiply the two terms.
Subtract the exponents when dividing nonzero powers with the same base. Also, write
the answer in a standard form, not in scientific notation.
To find the population density, divide the population by the area, instead of dividing the
area by the population.
PTS: 1
NAT: 12.1.1.f
25. ANS: B
DIF: Average
STA: A.11.A
REF: Page 468
OBJ: 7-4.3 Application
TOP: 7-4 Division Properties of Exponents
=
Simplify exponents with like bases:
.
=
Use the Power of a Quotient Property.
=
Use the Power of a Product Property.
=
Simplify:
=
Use the Power of a Power Property to simplify the
exponents.
.
Feedback
A
Use the Power of a Power Property to raise the constant to the power outside the
parenthesis.
Correct!
Use the Power of a Power Property to raise every term in the problem to the exponent
outside the parenthesis.
Check to see if the terms are correctly placed in the numerator and denominator.
B
C
D
PTS:
OBJ:
TOP:
26. ANS:
1
DIF: Average
REF: Page 469
7-4.4 Finding Positive Powers of Quotients
7-4 Division Properties of Exponents
B
Rewrite with a positive exponent.
=
=8
=
NAT: 12.5.3.c
Use the Power of a Quotient Property, and simplify.
Feedback
A
B
C
D
Raising a fraction to an exponent is different from multiplying the fraction.
Correct!
First, rewrite the fraction with a positive exponent. Then, use the Power of a Quotient
Property and simplify.
When you rewrite the fraction with a positive exponent, the numerator and the
denominator switch places.
PTS:
OBJ:
TOP:
27. ANS:
1
DIF: Basic
REF: Page 470
7-4.5 Finding Negative Powers of Quotients
7-4 Division Properties of Exponents
C
Formula for volume of a cone
NAT: 12.5.3.c
Substitute the given values.
Divide both sides by
.
Simplify.
Feedback
A
B
C
D
The volume of a cone is one third times the area of its circular base times its height.
When dividing like bases, subtract exponents.
Correct!
To divide a number by a fraction, multiply the number by the reciprocal of the fraction.
PTS: 1
DIF: Advanced
NAT: 12.5.3.c
TOP: 7-4 Division Properties of Exponents
28. ANS: B
Add the exponents of the variables. 7 + 4 = 11
STA: A.4.A
The degree is 11.
Feedback
A
B
C
D
Add the exponents of the variables.
Correct!
The degree of the monomial is the sum of the exponents of the variables.
Add the exponents of the variables.
PTS:
OBJ:
TOP:
29. ANS:
1
DIF: Basic
REF: Page 476
7-5.1 Finding the Degree of a Monomial
7-5 Polynomials
C
: degree 9,
: degree 2, and : degree 3
The degree of the polynomial is 9.
NAT: 12.5.2.b
Feedback
A
B
C
D
The degree of a monomial is the sum of the exponents of the variables.
The degree of a polynomial is the degree of the monomial or term with the highest
degree.
Correct!
The degree of a polynomial is the degree of the monomial or term with the highest
degree.
PTS: 1
DIF: Average
REF: Page 476
OBJ: 7-5.2 Finding the Degree of a Polynomial
NAT: 12.5.2.b
TOP: 7-5 Polynomials
30. ANS: C
The standard form is written with the terms in order from highest to lowest degree.
Feedback
A
B
C
D
Find the correct coefficient of the x-cubed term.
The standard form is written with the terms in order from highest to lowest degree.
Correct!
The standard form is written with the terms in order from highest to lowest degree.
PTS: 1
DIF: Basic
REF: Page 477
OBJ: 7-5.3 Writing Polynomials in Standard Form
NAT: 12.5.3.d
TOP: 7-5 Polynomials
31. ANS: B
A polynomial that has a highest degree of 1 is called a linear polynomial.
A polynomial with 1 term is called a monomial.
Feedback
A
B
C
D
Check the highest degree.
Correct!
Check the highest degree and the number of terms.
Check the highest degree and the number of terms.
PTS: 1
DIF: Basic
REF: Page 478
OBJ: 7-5.4 Classifying Polynomials
NAT: 12.5.2.b
32. ANS: A
TOP: 7-5 Polynomials
Substitute 3 for t.
Simplify. Begin by raising 3 to the power of 2.
=
=
= 160
The rocket will be 160 feet above the ground after 3 seconds.
Feedback
A
B
C
D
Correct!
Be sure to include the last term of the polynomial.
First, substitute 3 for t. Then, evaluate the polynomial.
Evaluate the polynomial by using the order of operations.
PTS: 1
NAT: 12.5.3.c
33. ANS: A
DIF: Average
STA: A.4.A
REF: Page 478
OBJ: 7-5.5 Application
TOP: 7-5 Polynomials
= –10m + 2m4 – 13m
– 20m4
= –10m – 13m + 2m4
– 20m4
=
Identify like terms.
Use the Commutative Property to
move like terms together.
Combine like terms.
Feedback
A
B
C
D
Correct!
When combining like terms, only add or subtract the coefficients. The powers stay the
same.
Check your addition and subtraction.
Only add or subtract coefficients on like terms.
PTS:
OBJ:
STA:
34. ANS:
1
DIF: Advanced
REF: Page 484
7-6.1 Adding and Subtracting Monomials
NAT: 12.5.3.c
A.4.A
TOP: 7-6 Adding and Subtracting Polynomials
D
Identify like terms. Rearrange terms to get like terms
together.
Combine like terms.
=
=
Feedback
A
B
C
D
First, identify the like terms and rearrange these terms so they are together. Then,
combine the like terms.
Check that you have included all the terms.
When adding polynomials, keep the same exponents.
Correct!
PTS: 1
NAT: 12.5.3.c
35. ANS: A
DIF: Basic
STA: A.4.A
REF: Page 485
OBJ: 7-6.2 Adding Polynomials
TOP: 7-6 Adding and Subtracting Polynomials
Rewrite subtraction as addition of the opposite.
Identify like terms. Rearrange terms to get like terms
together.
Combine like terms.
=
=
=
Feedback
A
B
C
D
Correct!
Check that you have included all the terms.
Check the coefficients and the signs.
First, rewrite the subtraction as an addition of the opposite. Then, combine the like
terms.
PTS: 1
DIF: Average
REF: Page 485
OBJ: 7-6.3 Subtracting Polynomials
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-6 Adding and Subtracting Polynomials
36. ANS: C
Subtract and simplify. Subtracting a negative number is the same as adding the opposite.
(
)–(
)
=(
)+(
)
=
Feedback
A
B
C
D
Change all the signs when subtracting.
Subtracting a negative number is the same as adding the opposite.
Correct!
The last term of the polynomial that represents the cost of distributing by truck is
negative. Subtracting a negative number is the same as adding the opposite.
PTS: 1
DIF: Average
REF: Page 486
OBJ: 7-6.4 Application
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-6 Adding and Subtracting Polynomials
37. ANS: D
The perimeter of a triangle is the sum of the measures of its sides. In an isosceles triangle, the legs have equal
lengths.
+ base
Substitute the given values.
Combine like terms.
Subtract
from both sides.
Subtract
from both sides.
Add 2 to both sides.
Feedback
A
B
C
D
When finding the perimeter of a triangle, add the measures of the three sides.
Check the signs.
When finding the perimeter of a triangle, add the measures of the three sides.
Correct!
PTS: 1
DIF: Advanced
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-6 Adding and Subtracting Polynomials
38. ANS: A
Rearrange the terms to group like bases.
To multiply powers, add the exponents.
Feedback
A
B
C
D
Correct!
To find the coefficient, multiply the fraction by the whole number.
To find the coefficient, multiply the fraction by the whole number. To find the product
of two powers with the same base, add the exponents.
To find the product of two powers with the same base, add the exponents.
PTS: 1
DIF: Advanced
REF: Page 492
OBJ: 7-7.1 Multiplying Monomials
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-7 Multiplying Polynomials
39. ANS: D
Use the Distributive Property to multiply the monomial by each term inside the parentheses. Group terms to
get like bases together, and then multiply.
Feedback
A
B
C
D
Don't forget to multiply the coefficients for each term.
When multiplying like bases, add the exponents.
Multiply the coefficients for each term; don't add.
Correct!
PTS:
OBJ:
STA:
40. ANS:
1
DIF: Advanced
REF: Page 492
7-7.2 Multiplying a Polynomial by a Monomial
NAT: 12.5.3.c
A.4.B
TOP: 7-7 Multiplying Polynomials
C
Use FOIL.
Distribute n and –5.
Distribute n and –5 again.
Multiply.
Combine like-terms.
Feedback
A
B
C
D
Distribute again, multiply and combine like-terms.
You did not multiply the outer terms.
Correct!
You did not multiply the inner and outer terms.
PTS: 1
NAT: 12.5.3.c
41. ANS: B
DIF: Basic
STA: A.4.B
REF: Page 494
OBJ: 7-7.3 Multiplying Binomials
TOP: 7-7 Multiplying Polynomials
Distribute
and .
Distribute
and
again.
Multiply.
Combine like terms.
Feedback
A
B
C
D
Check the signs.
Correct!
Combine only like terms.
Combine only like terms.
PTS: 1
DIF: Average
REF: Page 495
OBJ: 7-7.4 Multiplying Polynomials
NAT: 12.5.3.c
STA: A.4.B
TOP: 7-7 Multiplying Polynomials
42. ANS: C
The area of a parallelogram is given by A = bh.
Substitute x for b and
for h, and then use the Distributive Property to multiply.
To find the area, substitute 6 for x and use the order of operations to simplify.
The area is 114 in2.
Feedback
A
B
C
D
When multiplying, distribute x over both terms in the binomial.
The polynomial is correct. Find the area of the stone, not the height.
Correct!
When multiplying, distribute x over both terms in the binomial.
PTS: 1
DIF: Average
REF: Page 496
OBJ: 7-7.5 Application
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-7 Multiplying Polynomials
KEY: laws of exponents | product of monomials | multiplying monomials
43. ANS: C
Method 1
The factors fit the pattern for squaring a
=
+
binomial to get a perfect square trinomial. Use
the rule for
Identify
.
and
from the given binomial.
Use these values to determine
,
, and
Substitute the terms into the corresponding
places.
Method 2
Use FOIL to multiply the binomials.
Feedback
A
B
C
D
Check your multiplication and addition.
Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule
for squaring a binomial.
Correct!
Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule
for squaring a binomial.
PTS:
OBJ:
STA:
44. ANS:
1
DIF: Average
REF: Page 501
7-8.1 Finding Products in the Form (a + b)^2
A.4.B
TOP: 7-8 Special Products of Binomials
D
NAT: 12.5.3.c
Use the rule for
.
Use the FOIL method, and then combine like terms.
Simplify.
Feedback
A
B
C
D
Check the signs.
Check the signs.
The last term in the product should be the square of the second term in the binomial.
Correct!
PTS:
OBJ:
STA:
45. ANS:
1
DIF: Basic
REF: Page 502
7-8.2 Finding Products in the Form (a – b)2
A.4.B
TOP: 7-8 Special Products of Binomials
A
=
NAT: 12.5.3.c
Use the rule for
.
Use the FOIL method, and then combine like terms.
.
Simplify.
Feedback
A
B
C
D
Correct!
The terms in the product should be squares.
First, use the FOIL method. Then, combine the like terms.
Use the FOIL method.
PTS: 1
DIF: Basic
REF: Page 503
OBJ: 7-8.3 Finding Products in the Form (a + b)(a – b)
NAT: 12.5.3.c
STA: A.4.B
TOP: 7-8 Special Products of Binomials
46. ANS: B
Area of a circle is given by
, where r represent the radius of the circle.
Find the total circular area (pool plus walkway) first. The radius is
get a polynomial for the total area.
Then find the circular pool area. The radius is
for the pool area.
, so the area is
, so the area is
. Simplify to
. Simplify to get a polynomial
Subtract the pool area from the total area to write a polynomial that represents the area of the walkway.
Feedback
A
B
C
D
Subtract the smaller area from the larger area. You subtracted the opposite way.
Correct!
To subtract a polynomial, add the opposite of each term.
To subtract a polynomial, add the opposite of each term.
PTS: 1
DIF: Average
REF: Page 503
OBJ: 7-8.4 Problem-Solving Application
NAT: 12.5.3.c
STA: A.4.A
TOP: 7-8 Special Products of Binomials
47. ANS: D
Step 1 Set up the problem.
Let the square hot tub be x feet long and x feet wide.
The fencing creates a rectangle that is
feet long and
feet wide.
x+ 8
x
x
x+ 4
Step 2 Set up an equation.
A total of 44 feet of fencing represents the perimeter of the large rectangle.
Step 3 Solve the equation and answer the question.
Distribute.
Combine like terms.
Subtract 24 from both sides.
Divide both sides by 5.
The hot tub is 5 feet long and 5 feet wide.
Feedback
A
B
C
D
The fencing is 4 feet longer and 2 feet wider than the hot tub on each side of the hot tub.
Solve for the dimensions of the hot tub instead of the dimensions of the fence.
Solve for the dimensions of the hot tub instead of the dimensions of the fence.
Correct!
PTS: 1
DIF: Advanced
TOP: 7-8 Special Products of Binomials
NAT: 12.5.4.c
KEY: multi-step
STA: A.7.A