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Math Problems
Grade 6
Understanding integers
Aaliyah is playing a quiz game on her tablet. When she answers a question about a popular music group incorrectly, a message says
−
5
-5
−
5
points. Then her score decreases by
5
5
5
points. When she answers a question about an award-winning movie correctly, a message says
7
7
7
points.
\newline
Which of these describes what happens to Aaliyah's score when she answers the movie question correctly?
\newline
Choices:
\newline
(A)It decreases by
7
7
7
points.
\newline
(B)It stays the same.
\newline
(C)It increases by
7
7
7
points.
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When the value of Coral Island Bookstore stock fell
5
5
5
points, the change was represented online as
−
5
-5
−
5
points.
\newline
The next day, the change in value of the stock was represented as
6
6
6
points. Which of these describes the change in the stock's value?
\newline
Choices:
\newline
(A)It fell
6
6
6
points.
\newline
(B)It neither rose nor fell.
\newline
(C)It rose
6
6
6
points.
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Spencer is playing his favorite board game, Road Race, with some friends. Players take turns picking cards that tell them how many spaces to move forward or backward. On his first turn, Spencer picked a
7
7
7
and moved forward
7
7
7
spaces.
\newline
If Spencer picks a
−
2
-2
−
2
on his next turn, what should he do?
\newline
Choices:
\newline
(A) move forward
2
2
2
spaces
\newline
(B) move backward
2
2
2
spaces
\newline
(C) do not move
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Chloe earned
8
8
8
$
\$
$
yesterday by walking her neighbor's dog. She immediately deposited the
8
8
8
$
\$
$
into her bank account. What integer represents the change in Chloe's account balance?
\newline
\newline
____ dollars
\newline
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Starfruit Furniture's stock fell
2
2
2
points yesterday.
\newline
What integer represents the change in the stock's value?
\newline
____ points
\newline
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Tony is using a math app to help him study for a quiz on integers. He knows that if the app shows the integer
8
8
8
, he needs to move
8
8
8
spots to the right on the number line.
\newline
If the app shows the integer
−
7
-7
−
7
, what does Tony need to do?
\newline
Choices:
\newline
(A)move
7
7
7
spots to the left
\newline
(B)move neither left nor right
\newline
(C)move
7
7
7
spots to the right
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When the value of TTT Sporting Goods stock lost
1
1
1
point, Lexi's stock market app represented the change as
−
1
-1
−
1
point.
\newline
The next day, the change in value of the stock was represented as
−
5
-5
−
5
points. Which of these describes the change in the stock's value?
\newline
Choices:
\newline
(A)It lost
5
5
5
points.
\newline
(B)It neither lost nor gained.
\newline
(C)It gained
5
5
5
points.
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When the value of UZX Technology stock fell
5
5
5
points, the change was represented online as
−
5
-5
−
5
points.
\newline
The next day, the change in value of the stock was represented as
7
7
7
points. Which of these describes the change in the stock's value?
\newline
Choices:
\newline
(A)It fell
7
7
7
points.
\newline
(B)It neither rose nor fell.
\newline
(C)It rose
7
7
7
points.
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Dakota had planned to go downhill skiing on Saturday, but she changed her mind when she learned the predicted high temperature for the day is
−
3
°
F
-3 \degree\text{F}
−
3°
F
. Which of these describes Saturday's predicted high temperature?
\newline
Choices:
\newline
(A) colder than
0
°
F
0 \degree\text{F}
0°
F
\newline
(B) warmer than
0
°
F
0 \degree\text{F}
0°
F
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Seventh grade
\newline
Y.
6
6
6
Write and solve equations using angle
\newline
r
r
r
\newline
You have prizes
\newline
Find the value of
\newline
x
x
x
.
\newline
x
=
x=
x
=
\newline
Submit
\newline
Work it out
\newline
Not feeling ready yet? These can help:
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Barbara decided to take a bicycle trip to the observatory. The road has a vertical rise of
306
306
306
feet for every
1800
1800
1800
feet of horizontal change. In percent, what is the grade of this road?
\newline
The grade of the road is
□
\square
□
%
\%
%
\newline
(Simplify your answer.)
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Points:
1
1
1
of
1
1
1
\newline
Save
\newline
Barbara decided to take a bicycle trip to the observatory. The road has a vertical rise of
306
306
306
feet ar ame horizental change. In percent, what is the grade of this road?
\newline
The grade of the road is
□
\square
□
\%. (Simplify your answer.)
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Show instructions
\newline
Question
1
1
1
(
1
1
1
point)
\newline
1
1
1
) Calculate the area of this figure.
\newline
squnits
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Enter the difference, in degrees, between the record low temperatures in Hawaii and South Dakota.
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1
1
1
point
\newline
Solve for
x
x
x
\newline
x
=
x=
x
=
type your answer...
\newline
What's the measure of the highlighted angle?
\newline
m of highlighted
∠
=
\angle=
∠
=
type your answer...
\newline
1
1
1
point
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20
20
20
. CRITICAL THINKING Is it more difficult to walk up the ramp or the hill? Explain.
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Lake Moeris in Egypt is located
43
m
43 \mathrm{~m}
43
m
below sea level.
\newline
Which number represents the elevation of Lake Moeris in meters?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
43
-43
−
43
\newline
(B)
43
43
43
\newline
Related content
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The elevation of Death Valley, CA is
−
86
m
-86 \mathrm{~m}
−
86
m
.
\newline
What does the number
−
86
-86
−
86
mean?
\newline
Choose
1
1
1
answer:
\newline
(A) Death Valley is located
86
m
86 \mathrm{~m}
86
m
above sea level.
\newline
(B) Death Valley is located
86
m
86 \mathrm{~m}
86
m
below sea level.
\newline
Related content
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A bank uses positive numbers to represent deposits and negative numbers to represent withdrawals.
\newline
Which number represents a deposit of
126
126
126
dollars?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
126
-126
−
126
dollars
\newline
(B)
126
126
126
dollars
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The shaded region is revolved around the
y
y
y
-axis. Find the volume accurate to the nearest thousandth.
\newline
Volume
=
[
?
]
\text { Volume }=[?]
Volume
=
[
?]
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The balance of a certain loan increases at a rate that is proportional at any time to the balance at that time.
\newline
The loan balance is
$
1600
\$1600
$1600
initially, and it is
$
1920
\$1920
$1920
after one year (
365
365
365
days).
\newline
What is the balance of the loan after
90
90
90
days?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
1529.66
\$1529.66
$1529.66
\newline
(B)
$
1673.57
\$1673.57
$1673.57
\newline
(C)
$
1678.90
\$1678.90
$1678.90
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5
5
5
:
52
52
52
PM Sun Apr
14
14
14
\newline
Brooke Seward's practice
\newline
Z.
1
1
1
Find the slope from a
\newline
What is the slope of this line?
\newline
Submit
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find the probability of getting a royal flush
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7
7
7
. On vacation, Jose went deep sea diving. Hectarted ar
3
3
3
fee And he dovg fown (
5
5
5
foet What integer represents how far was when he dove down?
\newline
a.
−
18
-18
−
18
\newline
c.
12
12
12
\newline
b.
−
12
-12
−
12
\newline
d.
18
18
18
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7
7
7
. On vacation, Jose went deep sea diving. Hestarted a
3
3
3
feet above sea level. And he dove down
15
15
15
feet. What integer represents how far below sea level Jose was when he dove down?
\newline
a.
−
18
-18
−
18
\newline
c.
12
12
12
\newline
b.
−
12
-12
−
12
\newline
d.
18
18
18
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If the temperature at
6
6
6
AM was
18
°
F
18\degree F
18°
F
, and
6
6
6
hours later it dropped to
18
°
18\degree
18°
below zero, what was the temperature’s rate of change?
\newline
E.
4
°
4\degree
4°
per hour
\newline
F.
5
°
5\degree
5°
per hour
\newline
G.
6
°
6\degree
6°
per hour
\newline
H.
8
°
8\degree
8°
per hour
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My IXL
\newline
Learning
\newline
Assessment
\newline
5
5
5
Sale prices
\newline
5
G
H
5 \mathrm{GH}
5
GH
\newline
The briginal price of a model solar system is
$
96
\$ 96
$96
. What is the sale price?
\newline
$
\$
$
□
\square
□
\newline
Submit
\newline
Work it out
\newline
Not feeling ready yet? These can help:
\newline
48
48
48
\newline
Pricents of numbers and money amounts.
\newline
2008
2008
2008
\newline
X
\newline
800
800
800
\newline
Which is the better count
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Question
1
1
1
(
4
4
4
points)
\newline
Solve (Answers in Proper Scientific Notation):
\newline
A computer can perform
4.7
×
1
0
8
4.7 \times 10^{8}
4.7
×
1
0
8
calculations per second.
\newline
A) How many calculations can this computer perform in
1
1
1
minute?
\newline
B) How many calculations can this computer perform ini
1
1
1
hour?
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Kai goes out to lunch with their friends. At the end of the meal, they receive a bill for
euros
\text{euros}
euros
. Which number represents the change in the amount of money Kai and their friends have? Choose
1
1
1
answer:
\newline
(Choice A)
euros
\text{euros}
euros
A
A
A
euros
\text{euros}
euros
\newline
(Choice B)
euros
\text{euros}
euros
B
B
B
euros
\text{euros}
euros
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A ladder
12
ft
12\text{ft}
12
ft
long leans against a building and makes a
32
32
32
degree angle with level ground. How far up the building does the ladder reach? What type of angle is this? Draw a picture and find the angle
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You can buy a property today for
$
3
\$ 3
$3
million and sell it in
5
5
5
years for
$
4
\$ 4
$4
million. (You earn no rental income on the property.)
\newline
a. If the interest rate is
8
%
8 \%
8%
, what is the present value of the sales price?
\newline
Note: Do not round intermediate calculations. Enter your answer in millions rounded to
3
3
3
decimal places.)
\newline
b. Is the property investment attractive to you?
\newline
c
−
1
-1
−
1
. What is the present value of the future cash flows if you also could earn
$
200
,
000
\$ 200,000
$200
,
000
per-year rent on the property? The rent is paid at the end of each year.
\newline
Note: Do not round intermediate calculations. Enter your answer in millions rounded to
3
3
3
decimal places. c
−
2
-2
−
2
. Is the property investment attractive to you now?
\newline
\begin{tabular}{|l|}
\newline
\hline a. Present value \\
\newline
\hline b. Is the property investment attractive to you? \\
\newline
\hline c
−
1
-1
−
1
. Present value \\
\newline
\hline c
−
2
-2
−
2
. Is the property investment attractive to you now? \\
\newline
\hline
\newline
\end{tabular}
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s) The table shows the elevations of
6
6
6
cities in California.
\newline
\begin{tabular}{|l|c|}
\newline
\hline \multicolumn{
1
1
1
}{|c|}{ City } & \begin{tabular}{c}
\newline
Elevation \\
\newline
(meters)
\newline
\end{tabular} \\
\newline
\hline Westmorland &
−
48
-48
−
48
\\
\newline
\hline Brentwood &
24
24
24
\\
\newline
\hline Holtville &
−
3
-3
−
3
\\
\newline
\hline Imperial &
−
18
-18
−
18
\\
\newline
\hline Bombay Beach &
−
69
-69
−
69
\\
\newline
\hline Los Altos &
48
48
48
\\
\newline
\hline
\newline
\end{tabular}
\newline
How many meters greater is the elevation of Brentwood than the elevation of Bombay Beach?
\newline
Show your work.
\newline
Answer meters
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An open-topped glass aquarium with a square base is designed to hold
32
32
32
cubic feet of water. What is the minimum possible exterior surface area of the aquarium?
\newline
square feet
\newline
Stuck? Review related articles/videos or use a hint.
\newline
Report a problem
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E
E
E
represents the anchor's elevation relative to the water's surface (in meters) as a function of time
t
t
t
(in seconds).
\newline
E
=
−
2.4
t
+
75
E=-2.4t+75
E
=
−
2.4
t
+
75
\newline
How far does the anchor drop every
5
5
5
seconds?
\newline
meters
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\newline
You are skiing on a mountain with an altitude of
1200
1200
1200
meters. The angle of depression is
2
1
∘
21^{\circ}
2
1
∘
. How far do you ski down the mountain? (Round to the nearest meter)
\newline
Select the correct response:
\newline
1873
1873
1873
meters
\newline
3349
3349
3349
meters
\newline
1285
1285
1285
meters
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A pitcher that holds
0.5
L
0.5\,\text{L}
0.5
L
will hold how many
militers
\text{militers}
militers
?
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A pitcher that holds
0.52
L
0.52\,\text{L}
0.52
L
will hold how many milliliters?
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An airplane takes off
200
200
200
yards in front of a
180
180
180
yard building.
\newline
Find the angle of elevation for the plane so it does not hit the building.
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2
2
2
. An airplane takes off
200
200
200
yards in front of a
180
180
180
yard building.
\newline
Find the angle of elevation for the planes it does not hit the building.
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A conical paper cup is
10
cm
10\text{cm}
10
cm
tall with a radius of
20
cm
20\text{cm}
20
cm
. The bottom of the cup is punctured so that the water level goes down at a rate of
3
cm/sec
3\text{cm/sec}
3
cm/sec
. At what rate is the volume of water in the cup changing when the water level is
4
cm
4\text{cm}
4
cm
?
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A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was
64
64
64
. The number increased by
50
%
50\%
50%
each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by
50
%
50\%
50%
per year. What is the difference in the number of chickens between these two situations two years from now?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
189
189
189
\newline
(C)
405
405
405
\newline
(D)
11
11
11
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The balance of a certain loan increases at a rate that is proportional at any time to the balance at that time.
\newline
The loan balance is
$
1600
\$ 1600
$1600
initially, and it is
$
1920
\$ 1920
$1920
after one year (
365
365
365
days).
\newline
What is the balance of the loan after
90
90
90
days?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
1529.66
\$ 1529.66
$1529.66
\newline
(B)
$
1673.57
\$ 1673.57
$1673.57
\newline
(C)
$
1678.90
\$ 1678.90
$1678.90
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The processing speeds of Peach brand computers is increasing at a rate of
r
(
t
)
r(t)
r
(
t
)
megahertz per year (where
t
t
t
is the time in years). When
t
=
4
t=4
t
=
4
, the computers had a processing speed of
2500
2500
2500
megahertz.
\newline
What does
2500
+
∫
4
7
r
(
t
)
d
t
2500+\int_{4}^{7} r(t) d t
2500
+
∫
4
7
r
(
t
)
d
t
represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The average rate of change in the processing speed of the computers between
t
=
4
t=4
t
=
4
and
t
=
7
t=7
t
=
7
\newline
(B) The processing speed of the computers when
t
=
7
t=7
t
=
7
\newline
(C) The net change in processing speeds of the computers between
t
=
4
t=4
t
=
4
and
t
=
7
t=7
t
=
7
\newline
(D) The average processing speed of the computers between
t
=
4
t=4
t
=
4
and
t
=
7
t=7
t
=
7
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