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Math Problems
Grade 6
Understanding integers
Jeanne's bank account earns interest annually. The equation shows her starting balance of
$
500
\$500
$500
and her balance at the end of three years,
$
546.36
\$546.36
$546.36
. At what rate
r
r
r
did Jeanne earn interest?
\newline
546.36
=
500
(
1
+
r
)
546.36 = 500(1 + r)
546.36
=
500
(
1
+
r
)
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There are \\[\(128\)\\] ounces in a gallon. There are \\[\(4\)\\] quarts in a gallon. How many ounces are in a quart?
\(\newline\)A) \(32\)\(\newline\)B) \(64\)\(\newline\)C) \(16\)\(\newline\)D) \(8\)
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In the board game Super Trivia Buffs, players take turns picking question cards that tell them how many spaces to move forward or backward. If a card says
−
4
-4
−
4
spaces, the player moves backward
4
4
4
spaces.
\newline
What should the player do if a card says
3
3
3
spaces?
\newline
Choices:
\newline
(A)move backward
3
3
3
spaces
\newline
(B)do not move
\newline
(C)move forward
3
3
3
spaces
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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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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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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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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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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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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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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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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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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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