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Math Problems
Grade 7
Unit rates
the lire on a bicycle mode
380
380
380
ault totations in
m
m
m
minules. Whe on expression to tepresent The overage number of reveltions the fire made each minute.
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A compound when treated with concentrated hydrochloric acid gives off a green gas which bleaches moist red litmus paper. The gas given off is
1
1
1
hydrogen sulphide
\newline
2
2
2
chlorine
\newline
3
3
3
sulphur dioxide
\newline
4
4
4
nitrogen dioxide
\newline
1
1
1
\newline
2
2
2
\newline
3
3
3
\newline
4
4
4
\newline
Clear selection
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Paycheck Calculations - Use the information below to calculate each worker's net monthly income (NMI). Round to the nearest cent and show your work for partial credit.
\newline
Dorian works at a fast food restaurant during the school year and makes
$
9.35
\$ 9.35
$9.35
per hour. In a typical week he works
25
h
r
s
25 \mathrm{hrs}
25
hrs
. This month he worked
75
75
75
hrs.
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A bathtub is filling with water at a rate of
60
60
60
liters per minute.
\newline
How many liters of water are in the bathtub after
t
t
t
minutes?
\newline
Write your answer as an expression.
\newline
□
\square
□
liters
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Shelley's cup of tea cooled down
1
2
\frac{1}{2}
2
1
of a degree in
10
10
10
seconds. At what rate is her tea cooling down?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number. _______degrees per second
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A young sumo wrestler decided to go on a special diet to gain weight rapidly.
\newline
W
W
W
represents the wrestler's weight (in kilograms) as a function of time
t
t
t
(in months).
\newline
W
=
80
+
5.4
t
W=80+5.4t
W
=
80
+
5.4
t
\newline
How much weight does the wrestler gain every
2
2
2
months?
\newline
□
\square
□
kilograms
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Sol,
1
1
1
bags of Apples cost
=
$
42.50
=\$ 42.50
=
$42.50
\newline
70
70
70
bags of Apples cost
=
{
42.50
×
70
=\{42.50 \times 70
=
{
42.50
×
70
bags
\newline
42
,
50
×
70
\begin{array}{r} 42,50 \\ \times \quad 70 \\ \hline \end{array}
42
,
50
×
70
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A
5
5
5
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
6
6
6
meters per minute.
\newline
At a certain instant, the top of the ladder is
3
3
3
meters from the ground.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
-7
−
7
\newline
(B)
6
6
6
\newline
(C)
18
18
18
\newline
(D)
−
14
-14
−
14
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A
25
25
25
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
3
3
3
.
5
5
5
meters per minute.
\newline
At a certain instant, the top of the ladder is
7
7
7
meters from the ground.
\newline
What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
12
-12
−
12
\newline
(B)
−
7
-7
−
7
\newline
(C)
−
24
-24
−
24
\newline
(D)
−
3
-3
−
3
.
5
5
5
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A person stands
30
30
30
meters east of an intersection and watches a car driving away from the intersection to the north at
17
17
17
meters per second.
\newline
At a certain instant, the car is
16
16
16
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
34
34
34
\newline
(B)
8
8
8
\newline
(C)
36
36
36
.
125
125
125
\newline
(D)
1189
\sqrt{1189}
1189
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The side of a cube is increasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side is
1
1
1
.
5
5
5
kilometers.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
13.5
\mathbf{1 3 . 5}
13.5
\newline
(B)
16.5
\mathbf{1 6 . 5}
16.5
\newline
(C)
8
8
8
\newline
(D)
2
2
2
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The side of a cube is decreasing at a rate of
9
9
9
millimeters per minute.
\newline
At a certain instant, the side is
19
19
19
millimeters.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3249
-3249
−
3249
\newline
(B)
−
6859
-6859
−
6859
\newline
(C)
−
9747
-9747
−
9747
\newline
(D)
−
729
-729
−
729
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A
5
5
5
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
6
6
6
meters per minute.
\newline
At a certain instant, the top of the ladder is
3
3
3
meters from the ground.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
6
6
\newline
(B)
−
14
-14
−
14
\newline
(C)
18
\mathbf{1 8}
18
\newline
(D)
−
7
-7
−
7
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The base of a triangle is decreasing at a rate of
13
13
13
millimeters per minute and the height of the triangle is increasing at a rate of
6
6
6
millimeters per minute.
\newline
At a certain instant, the base is
5
5
5
millimeters and the height is
1
1
1
millimeter.
\newline
What is the rate of change of the area of the triangle at that instant (in square millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
21
21
21
.
5
5
5
\newline
(B)
−
8
-8
−
8
.
5
5
5
\newline
(C)
−
21
-21
−
21
.
5
5
5
\newline
(D)
8
8
8
.
5
5
5
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A
39
39
39
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
10
10
10
meters per minute.
\newline
At a certain instant, the bottom of the ladder is
36
\mathbf{3 6}
36
meters from the wall.
\newline
What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
12
-12
−
12
\newline
(B)
−
25
6
-\frac{25}{6}
−
6
25
\newline
(C)
−
24
-24
−
24
\newline
(D)
−
10
-10
−
10
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The side of a cube is increasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side is
1
1
1
.
5
5
5
kilometers.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
16.5
\mathbf{1 6 . 5}
16.5
\newline
(C)
8
8
8
\newline
(D)
13.5
\mathbf{1 3 . 5}
13.5
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The side length of a square is decreasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side length is
9
9
9
kilometers.
\newline
What is the rate of change of the area of the square at that instant (in square kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
324
-324
−
324
\newline
(B)
−
4
-4
−
4
\newline
(C)
−
36
-36
−
36
\newline
(D)
−
81
-81
−
81
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The side length of a square is increasing at a rate of
15
15
15
millimeters per second.
\newline
At a certain instant, the side length is
22
22
22
millimeters.
\newline
What is the rate of change of the area of the square at that instant (in square millimeters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
225
225
225
\newline
(B)
660
660
660
\newline
(C)
484
484
484
\newline
(D)
30
30
30
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A
10
10
10
-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at
3
3
3
meters per minute.
\newline
At a certain instant, the bottom of the ladder is
6
6
6
meters from the wall.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
12
12
12
\newline
(B)
−
7
2
-\frac{7}{2}
−
2
7
\newline
(C)
7
7
7
\newline
(D)
−
6
-6
−
6
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The side of a cube is decreasing at a rate of
9
9
9
millimeters per minute.
\newline
At a certain instant, the side is
19
19
19
millimeters.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
729
-729
−
729
\newline
(B)
−
9747
-9747
−
9747
\newline
(C)
−
6859
-6859
−
6859
\newline
(D)
−
3249
-3249
−
3249
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The expenses and income of an individual are given in table form. Find the net monthly cash flow (it could be positive or negative). Assume salaries and wages are after taxes, that
1
1
1
month
=
4
=4
=
4
weeks, and that
1
1
1
year
=
12
=12
=
12
months. Round your answer to the nearest dollar.
\newline
\begin{tabular}{|c|c|}
\newline
\hline \multirow{
6
6
6
}{*}{\begin{tabular}{l}
\newline
Income \\
\newline
Salary
$
64500
/
\$ 64500 /
$64500/
year \\
\newline
Jewelyy sales:
$
400
/
\$ 400 /
$400/
month
\newline
\end{tabular}} & Expenses \\
\newline
\hline & Mortagage:
$
3450
/
\$ 3450 /
$3450/
month \\
\newline
\hline & Groceries
$
150
/
\$ 150 /
$150/
week \\
\newline
\hline & Household expenses
$
240
/
\$ 240 /
$240/
mon \\
\newline
\hline & \begin{tabular}{l}
\newline
Car traurance
$
2150
\$ 2150
$2150
semiaurut \\
\newline
Donatione:
$
500
\$ 500
$500
year
\newline
\end{tabular} \\
\newline
\hline & \begin{tabular}{l}
\newline
Donations:
$
500
\$ 500
$500
year \\
\newline
Miscellaneous:
=
12
=12
=
12
0
0
0
month
\newline
\end{tabular} \\
\newline
\hline
\newline
\end{tabular}
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Bark A citers a one-year
C
D
C D
C
D
at a rate of
7.4
%
7.4 \%
7.4%
compounded semiannually. Bank B offers a one-year CD at a rate of
7.3
%
7.3 \%
7.3%
compounded daily. Compute the annual percentage yield for each CD and determine which offer the bether deal.
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Rate of cha
\newline
ixl.com/math/grade
−
8
-8
−
8
/rate-of-change-of-a-linear-function-graphs
\newline
bookmarks
\newline
This graph shows how a sapling's height depends on its age.
\newline
Height of a sapling
\newline
What is the rate of change?
\newline
Write your answer as a decimal or integer.
\newline
□
\square
□
inches per year
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11
11
11
. A man travels from Town
A
A
A
to Town
B
B
B
at an average speed of
4
k
m
/
h
4 \mathrm{~km} / \mathrm{h}
4
km
/
h
and from Town B to Town A at an average speed of
6
k
m
/
h
6 \mathrm{~km} / \mathrm{h}
6
km
/
h
. If he takes
45
45
45
minutes to complete the entire journey, find
h
is
h_{\text {is }}
h
is
total distance travelled.
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In
2009
2009
2009
, Usain Bolt set the world record for sprinting
100
m
100\,\text{m}
100
m
in approximately
9.58
9.58
9.58
seconds. Find his average speed in meters per second.
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If your faucet drips at
1
1
1
drop per second, it will dispense
6000
6000
6000
gallons of waters per year you have three faucets in your house which leak at
3
3
3
drops of water per second how many gallons of water will leak from these faucets in six months
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Shandra read
1
1
1
book in
5
5
5
months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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Kaylee read
12
12
12
books in
4
4
4
months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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Fwam read
10
10
10
books in
5
5
5
months. What was his rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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Luke can paint
91
91
91
portraits in
7
7
7
weeks. How many portraits can Luke paint in
4
4
4
weeks?
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The side of the base of a square prism is decreasing at a rate of
−
7
-7
−
7
kilometers per minute and the height of the prism is increasing at a rate of
10
10
10
kilometers per minute.
\newline
At a certain instant, the base's side is
4
4
4
kilometers and the height is
9
9
9
kilometers.
\newline
What is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)?
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7
k
g
=
7 \mathrm{~kg}=
7
kg
=
\newline
g
\newline
>
>
>
Next Question
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A pigeon weighs
150
grams
150\,\text{grams}
150
grams
plus half a pigeon
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Maddy is carrying a
5
liter
5\,\text{liter}
5
liter
jug of sports drink that weighs
7.5
kg
7.5\,\text{kg}
7.5
kg
. She wants to know how many kilograms a
2
liter
2\,\text{liter}
2
liter
jug of sports drink would weigh
(
w
)
(w)
(
w
)
. She assumes the relationship between volume and weight is proportional. What is the weight of the
2
liter
2\,\text{liter}
2
liter
jug?
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Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks
303
303
303
times in
3
3
3
minutes. What is her blinking rate, in blinks per minute?
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Jack earns
$
275
\$275
$275
each week, but
$
25
\$25
$25
is withheld for medical insurance. Find the ratio of medical insurance to total pay. Reduce the ratio to lowest terms.
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Claire is a teacher and takes home
90
90
90
papers to grade over the weekend. She can grade at a rate of
11
11
11
papers per hour. How many papers would Claire have remaining to grade after working for
5
5
5
hours?
\newline
Answer:
□
\square
□
papers
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P
=
47.4
(
G
−
174.5
)
P = 47.4(G - 174.5)
P
=
47.4
(
G
−
174.5
)
The profit,
P
P
P
, in dollars, to an amusement park serving
G
G
G
guests over one day is given by the equation. What is the minimum number of guests that need to be served in order to make a positive profit?
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Harvey the wonder hamster can run
3
1
6
k
m
3 \frac{1}{6} \mathrm{~km}
3
6
1
km
in
1
4
\frac{1}{4}
4
1
hour. Harvey runs at a constant rate.
\newline
Find his average speed in kilometers per hour.
\newline
kilometers per hour
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In
2009
2009
2009
, Usain Bolt set the world record for sprinting
100
m
100 \mathrm{~m}
100
m
in approximately
9
3
5
9 \frac{3}{5}
9
5
3
seconds.
\newline
Find his average speed in meters per second.
\newline
meters per second
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The energy usages per day (in kilowatt-hours) of houses on Hamlet Avenue are listed below.
\newline
30
,
23
,
38
,
36
,
33
30,23,38,36,33
30
,
23
,
38
,
36
,
33
\newline
Find the mean energy usage per day.
\newline
k
W
h
\mathrm{kWh}
kWh
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To determine her resting heart rate, an athlete counts her pulse for
10
10
10
seconds. She counts
9
9
9
beats in
10
10
10
seconds. What is her resting heart rate in beats per minute (bpm)?
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