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Math Problems
Grade 7
Scale drawings: word problems
3
7
\frac{3}{7}
7
3
of his pokemon cards give to his little brother and had
24
24
24
cards left. How many cards did his little brother receive?
\newline
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Two candles start burning at the same time. One candle is
15
cm
15\,\text{cm}
15
cm
tall and burns at a rate of
5
cm
5\,\text{cm}
5
cm
every
6
6
6
hours. The other candle is
25
cm
25\,\text{cm}
25
cm
tall and burns at a rate of
2
1
2
cm
2\frac{1}{2}\,\text{cm}
2
2
1
cm
every hour. How tall will the candles be when they first burn down to the same height?
\newline
□
cm
\square\,\text{cm}
□
cm
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Johnny measured a city park and made a scale drawing. The soccer field is
6
6
6
millimeters wide in the drawing. The actual field is
60
60
60
meters wide. What scale did Johnny use for the drawing?
\newline
1
1
1
millimeter :
_
_
_
\_\_\_
___
meters
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A boy weighs
77
77
77
pounds. How much does he weigh in kilograms? Use the following conversion:
1
1
1
kilogram is
2.2
2.2
2.2
pounds.
\newline
kg
\text{kg}
kg
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An accountant for a certain state models the sales tax revenue that the state has earned over several years. The model shows that sales tax revenue grew by
15
%
15\%
15%
per year until
2
2
2
years ago, when it started to grow by
$
179.5
\$179.5
$179.5
million per year. If the sales tax revenue
2
2
2
years ago was
$
2.1
\$2.1
$2.1
billion, approximately how much lower is the sales tax revenue this year than it would be if it had continued growing by
15
%
15\%
15%
per year? (Note:
1
1
1
billion
=
1
,
000
= 1,000
=
1
,
000
million)
\newline
Choose
1
1
1
answer:
\newline
(A)
$
136
\$136
$136
million
\newline
(B)
$
318
\$318
$318
million
\newline
(C)
$
2.05
\$2.05
$2.05
billion
\newline
(D)
$
5.24
\$5.24
$5.24
billion
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Agent Hunt is transferring classified files from the CIA mainframe into his flash drive.
\newline
S
S
S
represents the size of the files on the drive (in megabytes) after
t
t
t
seconds.
\newline
S
=
5
t
+
45
S=5t+45
S
=
5
t
+
45
\newline
What was the file size on the drive before the transfer?
\newline
□
\square
□
megabytes
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A baker uses a coffee mug with a diameter of
8
c
m
8 \mathrm{~cm}
8
cm
to cut out circular cookies from a big sheet of cookie dough.
\newline
What is the area
A
A
A
of each cookie? Give your answer in terms of pi.
\newline
A
=
□
A=\square
A
=
□
c
m
2
\mathrm{~cm}^{2}
cm
2
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A park has a large circle painted in the middle of the playground area. The circle is divided into
4
4
4
equal sections, and each section is painted a different color. The radius of the circle is
10
10
10
meters.
\newline
What is the area
A
A
A
of each section of the circle?
\newline
Give your answer in terms of pi.
\newline
A
=
□
A=\square
A
=
□
m
2
\mathrm{m}^{2}
m
2
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An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is
24
π
24 \pi
24
π
inches. The artist plans to fill the inside of each dot with blue colored glass.
\newline
What is the area of the blue glass will be needed to fill each butterfly dot?
\newline
Give your answer in terms of pi.
\newline
A
=
□
A=\square
A
=
□
inches
2
\text {inches }^{2}
inches
2
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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was
533
533
533
with a margin of error of
27
27
27
. Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors?
\newline
565
565
565
.
7
7
7
\newline
516
516
516
\newline
493
493
493
.
9
9
9
\newline
564
564
564
.
6
6
6
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A scale on a map shows that
2
2
2
.
5
5
5
centimeters represents
15
15
15
kilometers.
\newline
What number of actual kilometers are represented by
17
17
17
.
5
5
5
centimeters on the map?
\newline
□
\square
□
kilometers
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A cone has a volume of
365
m
m
3
365 \mathrm{~mm}^{3}
365
mm
3
. If a scale factor of
0
0
0
.
5
5
5
were applied to the cone, what would its new volume be?
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Quincy measured a house and made a scale drawing. The living room, which is
4
4
4
meters long in real life, is
2
2
2
millimeters long in the drawing. What is the scale of the drawing?
\newline
1
1
1
millimeter :
_
_
_
\_\_\_
___
meters
\newline
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Eric drew a scale drawing of the high school. The parking lot, which is
54
54
54
meters wide in real life, is
6
6
6
centimeters wide in the drawing. What is the scale of the drawing?
\newline
1
1
1
centimeter :
_
_
_
_
\_\_\_\_
____
meters
\newline
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Scarlett drew a scale drawing of a campsite. The tent, which is
8
8
8
feet wide in real life, is
2
2
2
inches wide in the drawing. What is the scale of the drawing?
\newline
1
1
1
inch :
_
_
\_\_
__
feet
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Alana drew a scale drawing of an apartment. The broom closet, which is
6
6
6
feet wide in real life, is
3
3
3
inches wide in the drawing. What is the scale of the drawing?
\newline
1
1
1
inch :
_
_
_
\_\_\_
___
feet
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Jenna measured a swimming pool and made a scale drawing. The pool is
20
centimeters
20\,\text{centimeters}
20
centimeters
long in the drawing. The actual pool is
40
meters
40\,\text{meters}
40
meters
long. What scale did Jenna use for the drawing?
\newline
1
centimeter
:
_
_
_
_
meters
1\,\text{centimeter} : \_\_\_\_\,\text{meters}
1
centimeter
:
____
meters
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Rabia walks dogs after school to make extra money. Once a week, she walks
5
5
5
dogs for
$
3
\$ 3
$3
each. She also receives
$
10
\$ 10
$10
in tips each week.
\newline
How much money does Rabia make walking dogs in one week?
\newline
(
_
_
_
×
$
_
_
_
)
+
$
_
_
_
=
$
_
_
_
\left(\_\_\_ \times \$ \_\_\_ \right)+\$ \_\_\_ =\$\_\_\_
(
___
×
$___
)
+
$___
=
$___
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The value of
x
x
x
is decreased by
14
%
14 \%
14%
. Which expression represents this situation?
\newline
0.986
x
0.986 x
0.986
x
\newline
0.86
x
0.86 x
0.86
x
\newline
0.14
x
0.14 x
0.14
x
\newline
14
x
14 x
14
x
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A certain town has an area of
4
4
4
.
36
36
36
square miles. What is the area, in square yards, of this town? (
1
1
1
mile
=
1
,
760
=1,760
=
1
,
760
yards)
\newline
A)
404
404
404
1
,
760
×
4.36
=
7
,
673
1,760 \times 4.36=7,673
1
,
760
×
4.36
=
7
,
673
\newline
B)
7
7
7
,
674
674
674
\newline
C)
710
710
710
,
459
459
459
\newline
\newline
D)
13
,
505
,
536
13,505,536
13
,
505
,
536
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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a triangle. Which of the following solids could have resulted in that cross section?
\newline
right hexagonal prism
\newline
sphere
\newline
right triangular prism
\newline
right cone
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Polygon
Y
Y
Y
has an area of
11
11
11
square units. Celia drew a scaled version of Polygon
Y
Y
Y
using a scale factor of
3
3
3
and labeled it Polygon
Z
Z
Z
.
\newline
What is the area of Polygon
Z
Z
Z
?
\newline
square units
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Polygon
C
C
C
has an area of
7
7
7
square units. Jennie drew a scaled version of Polygon
C
C
C
and labeled it Polygon
D
D
D
. Polygon
D
D
D
has an area of
28
28
28
square units.
\newline
What scale factor did Jennie use to go from Polygon
C
C
C
to Polygon
D
D
D
?
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A scale on a blue print drawing of a house shows that
10
10
10
centimeters represents
2
2
2
meters.
\newline
What number of actual meters are represented by
18
18
18
centimeters on the blue print?
\newline
meters
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Polygon
C
C
C
has an area of
40
40
40
square units. Kennan drew a scaled version of Polygon
C
C
C
using a scale factor of
1
2
\frac{1}{2}
2
1
and labeled it Polygon
D
D
D
.
\newline
What is the area of Polygon
D
D
D
?
\newline
square units
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We want to solve the following equation.
\newline
x
+
1
3
=
2
x
+
2
\sqrt[3]{x+1}=2 x+2
3
x
+
1
=
2
x
+
2
\newline
Two of the solutions are
x
≈
−
0.6
x \approx-0.6
x
≈
−
0.6
and
x
=
−
1
x=-1
x
=
−
1
.
\newline
Find the other solution.
\newline
Hint: Use a graphing calculator.
\newline
Round your answer to the nearest tenth.
\newline
x
≈
x \approx
x
≈
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We want to solve the following equation.
\newline
2
x
+
8
=
5
log
3
(
x
)
\sqrt{2 x+8}=5 \log _{3}(x)
2
x
+
8
=
5
lo
g
3
(
x
)
\newline
One of the solutions is
x
≈
352
x \approx 352
x
≈
352
.
\newline
Find the other solution.
\newline
Hint: Use a graphing calculator.
\newline
Round your answer to the nearest tenth.
\newline
x
≈
x \approx
x
≈
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We want to solve the following equation.
\newline
x
2
−
4
=
2
x
3
x^{2}-4=\sqrt[3]{2 x}
x
2
−
4
=
3
2
x
\newline
One of the solutions is
x
≈
2.4
x \approx 2.4
x
≈
2.4
.
\newline
Find the other solution.
\newline
Hint: Use a graphing calculator.
\newline
Round your answer to the nearest tenth.
\newline
x
≈
x \approx
x
≈
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We want to solve the following equation.
\newline
4
x
2
−
16
x
+
13
=
3
log
2
(
x
)
4 x^{2}-16 x+13=3 \log _{2}(x)
4
x
2
−
16
x
+
13
=
3
lo
g
2
(
x
)
\newline
One of the solutions is
x
≈
1.1
x \approx 1.1
x
≈
1.1
.
\newline
Find the other solution.
\newline
Hint: Use a graphing calculator.
\newline
Round your answer to the nearest tenth.
\newline
x
≈
x \approx
x
≈
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Morgan is designing a rectangular quilt. The quilt will be
1
3
5
m
1 \frac{3}{5} \mathrm{~m}
1
5
3
m
wide and will have an area of
6
m
2
6 \mathrm{~m}^{2}
6
m
2
.
\newline
How long is the quilt?
\newline
m
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Drake and
C
l
e
o
\mathrm{Cleo}
Cleo
are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit
28
28
28
students in a
756
756
756
square foot area. Assuming that each student has a spot
x
x
x
feet wide and
3
3
3
times as long, what is the length, in feet, of the space they are allotting to each student?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
feet
\newline
(B)
3
3
3
feet
\newline
(C)
9
9
9
feet
\newline
(D)
27
27
27
feet
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A cylindrical soda can has a volume of
108
π
108 \pi
108
π
cubic centimeters
(
c
m
3
)
\left(\mathrm{cm}^{3}\right)
(
cm
3
)
and a height of
12
c
m
12 \mathrm{~cm}
12
cm
. What is the surface area of the soda can in square centimeters?
\newline
Choose
1
1
1
answer:
\newline
(A)
18
π
c
m
2
18 \pi \mathrm{cm}^{2}
18
π
cm
2
\newline
(B)
36
π
c
m
2
36 \pi \mathrm{cm}^{2}
36
π
cm
2
\newline
(C)
72
π
c
m
2
72 \pi \mathrm{cm}^{2}
72
π
cm
2
\newline
(D)
90
π
c
m
2
90 \pi \mathrm{cm}^{2}
90
π
cm
2
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Mindy is a sculptor. She has a cylinder of stone with a radius of
3
3
3
meters
(
m
)
(\mathrm{m})
(
m
)
and a height of
2
m
2 \mathrm{~m}
2
m
. She needs to carve out a sphere of radius
1
m
1 \mathrm{~m}
1
m
from the cylinder. Mindy must cut away
v
3
π
\frac{v}{3} \pi
3
v
π
cubic meters
(
m
3
)
\left(\mathrm{m}^{3}\right)
(
m
3
)
of stone from the cylinder in order to be left with the sphere. What is the value of
v
v
v
?
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A soap company changes the design of its soap from a cone to a sphere. The cone had a height of
3
3
3
centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
and a radius of
2
c
m
2 \mathrm{~cm}
2
cm
. The sphere has a diameter of
3
c
m
3 \mathrm{~cm}
3
cm
. The new design contains
π
f
\frac{\pi}{f}
f
π
cubic centimeters more soap than the old design. What is the value of
f
f
f
?
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s
=
−
11.8
(
t
−
1.2
)
2
+
17
s=-11.8(t-1.2)^{2}+17
s
=
−
11.8
(
t
−
1.2
)
2
+
17
\newline
The equation models the horizontal distance,
s
s
s
, in centimeters, of a particular image on a computer screen from the left-hand edge of the screen,
t
t
t
seconds after appearing. If the image moves in from the left-hand edge of the screen during an on-screen animation, how far to the right does the image travel?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
.
2
2
2
centimeters
\newline
(B)
5
5
5
.
2
2
2
centimeters
\newline
(C)
17
17
17
centimeters
\newline
(D)
34
34
34
centimeters
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A
(
x
)
=
(
8
+
2
x
)
2
A(x)=(8+2 x)^{2}
A
(
x
)
=
(
8
+
2
x
)
2
\newline
Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border
x
x
x
inches wide. What are the dimensions of the picture without the border?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
by
2
2
2
inches
\newline
(B)
6
6
6
by
6
6
6
inches
\newline
(C)
8
8
8
by
8
8
8
inches
\newline
(D)
10
10
10
by
10
10
10
inches
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A factory designs cylindrical cans
10
c
m
10 \mathrm{~cm}
10
cm
in height to hold exactly
500
c
m
3
500 \mathrm{~cm}^{3}
500
cm
3
of liquid. Which of the following best approximates the radius of these cans?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
c
m
4 \mathrm{~cm}
4
cm
\newline
(B)
8
c
m
8 \mathrm{~cm}
8
cm
\newline
(C)
12.5
c
m
12.5 \mathrm{~cm}
12.5
cm
\newline
(D)
15.9
c
m
15.9 \mathrm{~cm}
15.9
cm
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A die is created by smoothing the corners of a plastic cube and carving indented pips. The original cube had an edge length of
2
2
2
centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
. The volume of the final die is
7.5
c
m
3
7.5 \mathrm{~cm}^{3}
7.5
cm
3
. What is the volume of the waste generated by creating the die from the cube in
c
m
3
\mathrm{cm}^{3}
cm
3
?
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