Mid-Chapter Quiz: Lessons 1-1 through 1-3
1. Evaluate 3c – 4(a + b) if a = –1, b = 2 and
SOLUTION: 2. TRAVEL The distance that Maurice traveled in 2.5 hours riding his bicycle can be found by using the formula d =
rt, where d is the distance traveled, r is the rate, and t is the time. How far did Maurice travel if he traveled at a rate
of 16 miles per hour?
SOLUTION: Substitute r = 16, t = 2.5 in the formula d = rt.
Maurice traveled 40 meters.
3. Evaluate
if m = 6 and n = –3.
SOLUTION: 4. GEOMETRY The formula for the surface area of the rectangular prism below is given by the formula S = 2xy +
2yz + 2xz. What is the surface area of the prism if x = 2.2, y = 3.5, and z = 5.1?
SOLUTION: Substitute the values for x, y, and z into the formula for the surface area.
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The surface area of the prism is 73.54 square units.
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Mid-Chapter Quiz: Lessons 1-1 through 1-3
4. GEOMETRY The formula for the surface area of the rectangular prism below is given by the formula S = 2xy +
2yz + 2xz. What is the surface area of the prism if x = 2.2, y = 3.5, and z = 5.1?
SOLUTION: Substitute the values for x, y, and z into the formula for the surface area.
The surface area of the prism is 73.54 square units.
5. MULTIPLE CHOICE What is the value of
if q = –4, r = 3, and t = 8?
A B C
D
SOLUTION: So, the correct choice is B.
Name the sets of numbers to which each number belongs.
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The number
is a real number. Since
can be expressed as a ratio where a and b are integers and b is not 0
it is also a rational number. It is not a part of the set {…–2, –1, 0, 1, 2, …} so it is not an integer. Since it is not a part
of the set {…0, 1, 2, 3, …} it is not a whole number or a natural number.
Mid-Chapter Quiz: Lessons 1-1 through 1-3
So, the correct choice is B.
Name the sets of numbers to which each number belongs.
6. SOLUTION: The number
is a real number. Since
can be expressed as a ratio where a and b are integers and b is not 0
it is also a rational number. It is not a part of the set {…–2, –1, 0, 1, 2, …} so it is not an integer. Since it is not a part
of the set {…0, 1, 2, 3, …} it is not a whole number or a natural number.
Q, R
7. SOLUTION: The number
is a real number. Since
can be expressed as a ratio where a and b are integers and b
is not 0 it is also a rational number. It is part of the set {…–2, –1, 0, 1, 2, …} so it is an integer. It is not part of the
set {…0, 1, 2, 3, …} so it is not a whole number and since it is not a whole number it is not a natural number either.
Z, Q, R
8. SOLUTION: is a real number. Since it is a nonterminating decimal it is irrational.
I, R
9. –32.4
SOLUTION: The number –32.4 is a real number. Since –32.4 can be expressed as a ratio where a and b are integers and b is
not 0 it is also a rational number. It is not a part of the set {…–2, –1, 0, 1, 2, …} so it is not an integer. Since it is not
a part of the set {…0, 1, 2, 3, …} it is not a whole number or a natural number.
Q, R
10. What is the property illustrated by the equation
SOLUTION: Distributive Property; the Distributive Property states that there is no difference between a term multiplied by each
term in a group and the term multiplied by the group.
11. Simplify –3(7a – 4b) + 2(–3a + b).
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Brittany
buying T-shirts
12. CLOTHES
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and jeans for her new job. T-shirts cost $10.50, and jeans cost $26.50. She
buys 3 T-shirts and 3 pairs of jeans. Illustrate the Distributive Property by writing two expressions representing how
much Brittany spent.
Mid-Chapter Quiz: Lessons 1-1 through 1-3
12. CLOTHES Brittany is buying T-shirts and jeans for her new job. T-shirts cost $10.50, and jeans cost $26.50. She
buys 3 T-shirts and 3 pairs of jeans. Illustrate the Distributive Property by writing two expressions representing how
much Brittany spent.
SOLUTION: The cost of a T-shirt is $10.50 and a pair of jeans is $26.50. Brittany buys 3 T-shirts and 3 pairs of jeans. So, the
expression is
3(10.50 + 26.50).
Use the Distributive Property to rewrite the expression.
3(10.50 + 26.50) = 3(10.50) + 3(26.50)
13. MULTIPLE CHOICE Which expression is equivalent to
F G 46m – 47n
H
J SOLUTION: The correct choice is F.
14. Identify the additive inverse and the multiplicative inverse for
SOLUTION: Since
Since
, the additive inverse of
, the multiplicative inverse of
is
.
is .
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15. Write a verbal sentence to represent the equation
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Mid-Chapter Quiz: Lessons 1-1 through 1-3
The correct choice is F.
14. Identify the additive inverse and the multiplicative inverse for
SOLUTION: Since
Since
, the additive inverse of
, the multiplicative inverse of
is
.
is .
15. Write a verbal sentence to represent the equation
SOLUTION: The operation division can be represented verbally as quotient of or divided by. Since the denominator of the
fraction is an expression, the verbal expression should accurately represent this. For example, the quotient of a and
a minus 3 is equal to 1 can be interpreted as
which is inaccurate. The phrase the difference of is
clearer.
The quotient of a number a and the difference of a number a and 3 is equal to 1.
16. Solve 6x + 4y = –1 for x.
SOLUTION: 17. MULTIPLE CHOICE Which algebraic expression represents the verbal expression, the product of 4 and the
difference of a number and 13?
A 4n – 13
B 4(n – 13)
C
D SOLUTION: The product of 4 and the difference of a number and 13 is 4(n − 13).
So, the correct choice is B.
18. Solve –3(6x + 5) + 2(4x) = 20.
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D SOLUTION: The product
of 4Lessons
and the 1-1
difference
a number and 13 is 4(n − 13).
Mid-Chapter
Quiz:
throughof1-3
So, the correct choice is B.
18. Solve –3(6x + 5) + 2(4x) = 20.
SOLUTION: 19. What is the height of the trapezoid below?
SOLUTION: Substitute A = 80.625, a = 15.5, and b = 6 in the formula
.
So, the height of the trapezoid is 7.5 units.
and the formula for the volume of a
20. GEOMETRY The formula for the surface area of a sphere is
sphere is
a. Find the volume and surface area of a sphere with radius 2 inches. Write your answers in terms of
b. Is it possible for a sphere to have the same numerical value for the surface area and volume? If so, find the radius
of such a sphere.
SOLUTION: a. Substitute r = 2 in the formula
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.
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Mid-Chapter Quiz: Lessons 1-1 through 1-3
So, the height of the trapezoid is 7.5 units.
and the formula for the volume of a
20. GEOMETRY The formula for the surface area of a sphere is
sphere is
a. Find the volume and surface area of a sphere with radius 2 inches. Write your answers in terms of
b. Is it possible for a sphere to have the same numerical value for the surface area and volume? If so, find the radius
of such a sphere.
SOLUTION: a. Substitute r = 2 in the formula
The volume of the sphere is
Substitute r = 2 in the formula
.
cubic inches.
.
The surface area of the sphere is 16π square inches.
b. Equate the formulas for the volume of a sphere and the surface area of a sphere.
Yes; when the radius is 3 units, the sphere have the same numerical value for the surface area and volume.
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