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Math Problems
Algebra 1
Interpret parts of quadratic expressions: word problems
Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least
3300
3300
3300
calories per week from jogging and playing soccer. He can burn
700
700
700
calories each hour he spends jogging and
600
600
600
calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most
3
3
3
hours per week playing soccer and at most
5
5
5
total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
hours playing soccer and
1
1
1
hour jogging
\newline
(B)
1
1
1
hour playing soccer and
5
5
5
hours jogging
\newline
(C)
3
3
3
hours playing soccer and
2
2
2
hours jogging
\newline
(D)
2
2
2
hours playing soccer and
3
3
3
hours jogging
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17
T
+
6
C
≤
150
34
T
+
27
C
≤
330
\begin{array}{r} 17 T+6 C \leq 150 \\ 34 T+27 C \leq 330 \end{array}
17
T
+
6
C
≤
150
34
T
+
27
C
≤
330
\newline
Fleur wants to make tables and chairs. Each chair or table is made with the same number of wooden boards and nails. She has a total of
150
150
150
wooden boards and
330
330
330
nails. The system of inequalities shown represents the number of tables
(
T
)
(T)
(
T
)
and chairs
(
C
)
(C)
(
C
)
she can make in this situation. Does Fleur have enough boards and nails to make
3
3
3
tables and
9
9
9
chairs?
\newline
Choose
1
1
1
answer:
\newline
(A) Fleur has enough boards and nails.
\newline
(B) Fleur has enough boards but not enough nails.
\newline
(C) Fleur has enough nails but not enough boards.
\newline
(D) Fleur has neither enough boards nor enough nails.
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Some zoo monkeys are on a diet of fruit and nuts. Fruit has about
13
13
13
.
3
3
3
grams
(
g
)
(\mathrm{g})
(
g
)
of sugar per cup and
1.36
g
1.36 \mathrm{~g}
1.36
g
of protein per cup. Nuts have about
4.04
g
4.04 \mathrm{~g}
4.04
g
of sugar per cup and
15.56
g
15.56 \mathrm{~g}
15.56
g
of protein per cup. Each monkey must get between
70
g
70 \mathrm{~g}
70
g
and
90
g
90 \mathrm{~g}
90
g
of sugar per day and at least
85
g
85 \mathrm{~g}
85
g
of protein per day. Which of the following daily diets fits the monkeys' needs?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
cups of fruit and
16
16
16
cups of nuts
\newline
(B)
4
4
4
cups of fruit and
8
8
8
cups of nuts
\newline
(C)
8
8
8
cups of fruit and
4
4
4
cups of nuts
\newline
(D)
16
16
16
cups of fruit and
0
0
0
cups of nuts
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At the beginning of January
2002
2002
2002
, the price of ground beef was
$
1.70
\$ 1.70
$1.70
per pound and the price of tuna fish was
$
2.20
\$ 2.20
$2.20
per pound. For the following
15
15
15
months, the price of ground beef increased at the rate of
$
0.03
\$ 0.03
$0.03
per month and the price of tuna fish decreased at
$
0.02
\$ 0.02
$0.02
per month. In approximately how many months after the beginning of January
2002
2002
2002
was the price of ground beef and tuna fish the same, and what was the price?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
.
5
5
5
months and
$
1.90
\$ 1.90
$1.90
\newline
(B)
7
7
7
.
5
5
5
months and
$
2.00
\$ 2.00
$2.00
\newline
(C)
10
\mathbf{1 0}
10
months and
$
1.90
\$ 1.90
$1.90
\newline
(D)
10
10
10
months and
$
2.00
\$ 2.00
$2.00
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The equations
x
+
y
=
3
x+y=3
x
+
y
=
3
and
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
are graphed in the
x
y
x y
x
y
-plane. Which of the following must be true of the graphs of the two equations?
\newline
Choose
1
1
1
answer:
\newline
(A) The slope of the graph of
x
+
y
=
3
x+y=3
x
+
y
=
3
is
1
1
1
and the slope of the graph of
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
is
−
1
-1
−
1
.
\newline
(B) The graphs of the two equations are perpendicular lines.
\newline
(C) The
y
y
y
-intercept of the graph of
−
5
x
−
5
y
=
−
15
-5 x-5 y=-15
−
5
x
−
5
y
=
−
15
is
−
15
-15
−
15
.
\newline
(D) The graphs of the two equations are the same line.
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Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than
108
108
108
kilowatts
(
k
W
)
(\mathrm{kW})
(
kW
)
of power. It was determined that the main contributors to power usage, speakers and floodlights, use
1.8
k
W
1.8 \mathrm{~kW}
1.8
kW
and
2.2
k
W
2.2 \mathrm{~kW}
2.2
kW
, respectively. Anouk also must keep within her budget of
$
3
,
300
\$ 3,300
$3
,
300
. The rental company is charging
$
75
\$ 75
$75
for each speaker and
$
42
\$ 42
$42
for each floodlight. Which of the following combinations meets Anouk's requirements?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
40
40
speakers and
30
30
30
floodlights
\newline
(B)
12
12
12
speakers and
54
54
54
floodlights
\newline
(C)
26
26
26
speakers and
13
13
13
floodlights
\newline
(D)
38
38
38
speakers and
22
22
22
floodlights
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Alek went for a walk.
\newline
D
(
t
)
D(t)
D
(
t
)
models the distance Alek walked (in kilometers) after
t
t
t
hours.
\newline
What does the statement
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
D(0.5) < D(1) - D(0.5)
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.
\newline
(B) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.
\newline
(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.
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Copacabana beach in Rio de Janeiro is one of the most popular beaches in the world.
\newline
P
(
t
)
P(t)
P
(
t
)
models the number of people at the beach,
t
t
t
hours past midnight on a specific day.
\newline
What does the statement
P
(
10
)
=
N
P(10)=N
P
(
10
)
=
N
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) There were
10
10
10
people at the beach at
N
N
N
hours past midnight.
\newline
(B) There were
N
N
N
people at the beach at
10
:
00
10:00
10
:
00
a.m.
\newline
(C) There was an equal number of people at the beach at
10
:
00
10:00
10
:
00
a.m. and at
N
N
N
hours past midnight.
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Jayce is a taxi driver.
\newline
M
(
n
)
M(n)
M
(
n
)
models Jayce's fee (in dollars) for his
n
th
n^{\text{th}}
n
th
drive on a certain day.
\newline
What does the statement
M
(
10
)
=
K
M(10)=K
M
(
10
)
=
K
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Jayce's fees for his
K
th
K^{\text{th}}
K
th
drive and his
1
0
th
10^{\text{th}}
1
0
th
drive are equal.
\newline
(B) Jayce's fee for his
1
0
th
10^{\text{th}}
1
0
th
drive is equal to
K
K
K
dollars.
\newline
(C) Jayce's fee for his
K
th
K^{\text{th}}
K
th
drive is equal to
$
10
\$10
$10
.
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Kaori is taking a free-throw.
\newline
H
(
d
)
H(d)
H
(
d
)
models the basketball's height (in meters) at a horizontal distance of
d
d
d
meters from Kaori.
\newline
What does the statement
H
(
R
)
=
4
H(R) = 4
H
(
R
)
=
4
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) At a horizontal distance of
R
R
R
meters from Kaori, the ball's height was equal to
4
4
4
meters.
\newline
(B) At a horizontal distance of
4
4
4
meters from Kaori, the ball's height was equal to
R
R
R
meters.
\newline
(C) The ball was at the same height at the horizontal distances of
4
4
4
meters and
R
R
R
meters.
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Copacabana beach in Rio de Janeiro is one of the most popular beaches in the world.
\newline
P
(
t
)
P(t)
P
(
t
)
models the number of people at the beach,
t
t
t
hours past midnight on a specific day.
\newline
What does the statement
P
(
10
)
=
N
P(10)=N
P
(
10
)
=
N
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) There were
N
N
N
people at the beach at
10
10
10
:
00
00
00
a.m.
\newline
(B) There were
10
10
10
people at the beach at
N
N
N
hours past midnight.
\newline
(C) There was an equal number of people at the beach at
10
10
10
:
00
00
00
a.m. and at
N
N
N
hours past midnight.
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Baby Amelia's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Amelia's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
30
)
=
H
(
25
)
+
5
H(30) = H(25) + 5
H
(
30
)
=
H
(
25
)
+
5
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) It took Amelia
5
5
5
months to grow from a height of
25
25
25
centimeters to a height of
30
30
30
centimeters.
\newline
(B) When Amelia was
30
30
30
months old, she was
5
5
5
centimeters taller than when she was
25
25
25
months old.
\newline
(C) The sum of Amelia's heights at
5
5
5
months and
25
25
25
months old is equal to her height at
30
30
30
months old.
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Baby Kana's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Kana's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
160
)
=
150
H(160)=150
H
(
160
)
=
150
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) When Kana was
150
150
150
months old, her height was equal to
160
160
160
centimeters.
\newline
(B) When Kana was
160
160
160
months old, her height was equal to
150
150
150
centimeters.
\newline
(C) Kana had the same height at
150
150
150
months old and at
160
160
160
months old.
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Alek went for a walk.
\newline
D
(
t
)
D(t)
D
(
t
)
models the distance Alek walked (in kilometers) after
t
t
t
hours.
\newline
What does the statement
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
D(0.5) < D(1)-D(0.5)
D
(
0.5
)
<
D
(
1
)
−
D
(
0.5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.
\newline
(B) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.
\newline
(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.
Get tutor help
Baby Amelia's parents measure her height every month.
\newline
H
(
t
)
H(t)
H
(
t
)
models Amelia's height (in centimeters) when she was
t
t
t
months old.
\newline
What does the statement
H
(
30
)
=
H
(
25
)
+
5
H(30) = H(25) + 5
H
(
30
)
=
H
(
25
)
+
5
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) It took Amelia
5
5
5
months to grow from a height of
25
25
25
centimeters to a height of
30
30
30
centimeters.
\newline
(B) The sum of Amelia's heights at
5
5
5
months and
25
25
25
months old is equal to her height at
30
30
30
months old.
\newline
(C) When Amelia was
30
30
30
months old, she was
5
5
5
centimeters taller than when she was
25
25
25
months old.
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Kaori is taking a free-throw.
\newline
H
(
d
)
H(d)
H
(
d
)
models the basketball's height (in meters) at a horizontal distance of
d
d
d
meters from Kaori.
\newline
What does the statement
H
(
R
)
=
4
H(R) = 4
H
(
R
)
=
4
mean?
\newline
Choose
1
1
1
answer:
\newline
A
A
A
The ball was at the same height at the horizontal distances of
4
4
4
meters and
R
R
R
meters.
\newline
B
B
B
At a horizontal distance of
R
R
R
meters from Kaori, the ball's height was equal to
4
4
4
meters.
\newline
C
C
C
At a horizontal distance of
4
4
4
meters from Kaori, the ball's height was equal to
R
R
R
meters.
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Jayce is a taxi driver.
\newline
M
(
n
)
M(n)
M
(
n
)
models Jayce's fee (in dollars) for his
n
th
n^{\text{th}}
n
th
drive on a certain day.
\newline
What does the statement
M
(
10
)
=
K
M(10)=K
M
(
10
)
=
K
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Jayce's fee for his
K
th
K^{\text{th}}
K
th
drive is equal to
$
10
\$10
$10
.
\newline
(B) Jayce's fees for his
K
th
K^{\text{th}}
K
th
drive and his
1
0
th
10^{\text{th}}
1
0
th
drive are equal.
\newline
(C) Jayce's fee for his
1
0
th
10^{\text{th}}
1
0
th
drive is equal to
K
K
K
dollars.
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Tessa's class had a math exam where the grades were between
0
0
0
and
10
10
10
.
\newline
N
(
g
)
N(g)
N
(
g
)
models the number of students whose grade on the exam was
g
g
g
.
\newline
What does the statement
\newline
N
(
8
)
>
2
⋅
N
(
5
)
N(8) > 2 \cdot N(5)
N
(
8
)
>
2
⋅
N
(
5
)
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) The number of students whose grade was higher than
5
5
5
is greater than the number of students whose grade was
5
5
5
or lower.
\newline
(B) The number of students whose grade was
8
8
8
is more than twice the number of students whose grade was
5
5
5
.
\newline
(C) There are
8
8
8
students whose grade was higher than twice the grade of another group of
5
5
5
students.
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