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Math Problems
Grade 6
Which word problem matches the one-step equation?
Niu has decorated
x
x
x
cards. He started with
24
24
24
stickers, and he used
4
4
4
stickers per card.
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Fen completed a triathlon race whose total distance is
D
D
D
kilometers. First, she swam a distance of
0.5
0.5
0.5
kilometer. Then, she rode a bicycle for
x
x
x
hours at an average speed of
20
20
20
kilometers per hour. Finally, she ran for
0.5
0.5
0.5
hour at an average speed of
v
v
v
kilometers per hour. Write an equation that relates
D
D
D
,
x
x
x
, and
v
v
v
.
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A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is
20
%
20\%
20%
more than the number of shoppers the day before. The total number of shoppers over the first
4
4
4
days is
671
671
671
. How many shoppers were at the mall on the first day?
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Samir spent
1
2
\frac{1}{2}
2
1
as long working on his physics homework as Cory did. If Samir spent
40
40
40
minutes on his physics homework, how long did Cory spend on his physics homework?
\newline
A)
20
20
20
minutes
\newline
B)
40
40
40
minutes
\newline
C)
60
60
60
minutes
\newline
D)
80
80
80
minutes
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Pick the story that can be modeled by the equation
x
−
24
=
8
x - 24 = 8
x
−
24
=
8
.
\newline
Choices:
\newline
(A)Maura opened a bag containing
x
x
x
ounces of birdseed. She used
24
24
24
ounces of birdseed to fill her bird feeder. There are
8
8
8
ounces left in the bag.
\newline
(B)Maura opened a bag containing
24
24
24
ounces of birdseed. She used
x
x
x
ounces of birdseed to fill her bird feeder. There are
8
8
8
ounces left in the bag.
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Pick the story that can be modeled by the equation
12
−
x
=
9
12 - x = 9
12
−
x
=
9
.
\newline
Choices:
\newline
(A) Sidney is making her family scrambled eggs for breakfast, so she takes out a carton containing
x
x
x
eggs. She adds
9
9
9
eggs to the pan and places the remaining
12
12
12
eggs back in the fridge.
\newline
(B) Sidney is making her dad a birthday cake, so she takes out a carton containing
12
12
12
eggs. She adds
x
x
x
eggs to the cake batter and places the remaining
9
9
9
eggs back in the fridge.
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Pick the story that can be modeled by the equation
x
−
15
=
45
x - 15 = 45
x
−
15
=
45
.
\newline
Choices:
\newline
(A) Malia opened a bag containing
x
x
x
lollipops and used
15
15
15
of them for favors at her Halloween party. Then, she poured the remaining
45
45
45
lollipops in a bowl to hand out to trick-or-treaters.
\newline
(B) To make the favors for her Halloween party, Malia opened a bag containing
45
45
45
lollipops. She divided them evenly among
15
15
15
favor bags, putting
x
x
x
lollipops in each bag.
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A student solved the equation
x
2
=
123
x^{2}=123
x
2
=
123
to find the length of the diagonal of a square in inches. What is the measurement of
x
x
x
, the length of the diagonal of the square, rounded to the nearest tenth?
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7
7
7
. A certain amount of money is shared between Rui Feng and Vishal in the ratio
5
:
9
5: 9
5
:
9
. If Rui Feng gets
$
44
\$ 44
$44
less than Vishal, find the total amount of money that is shared between the two boys.
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Solve the following:
\newline
a. Mr. Doers is going to remove all of the ceramic tiles in his kitchen in order to replace them with new ones. There are
18
18
18
tiles along the width of the kitchen and
21
21
21
tiles along the length. How many tiles will he have to remove?
\newline
b. The kitchen floor is
168
168
168
square feet. New ceramic tiles will cost
$
7.50
\$ 7.50
$7.50
per square foot. How much will it cost to replace the kitchen floor?
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Without dividing, determine if
10
10
10
,
769
769
769
is divisible by
9
9
9
and explain how you know.
\newline
10
,
769
□
10,769 \square
10
,
769
□
divisible by
9
9
9
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m
+
p
=
23
m
−
7
=
p
\begin{array}{l} m+p=23 \\ m-7=p \end{array}
m
+
p
=
23
m
−
7
=
p
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns. Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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The sum of two consecutive odd numbers is
2012
2012
2012
. What is the larger number?
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\begin{cases} m+p=23 \\\newline m-7=p \end{cases}
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns.
\newline
Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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Mara is
m
m
m
years old, and her younger brother Kyle is
k
k
k
years old. If Mara is
3
3
3
years older than Kyle, which of the following correctly expresses
k
k
k
in terms of
m
m
m
? Choose
1
1
1
answer:
\newline
(A)
k
=
m
+
3
k=m+3
k
=
m
+
3
\newline
(B)
k
=
m
−
3
k=m-3
k
=
m
−
3
\newline
(C)
k
=
3
m
k=3m
k
=
3
m
\newline
(D)
k
=
3
−
m
k=3-m
k
=
3
−
m
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Find all vertical asymptotes of the following function.
\newline
f
(
x
)
=
2
x
+
10
x
2
−
16
f(x)=\frac{2 x+10}{x^{2}-16}
f
(
x
)
=
x
2
−
16
2
x
+
10
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m
+
p
=
23
m+p=23
m
+
p
=
23
\newline
m
−
7
=
p
m-7=p
m
−
7
=
p
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns. Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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