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Math Problems
Grade 8
Experimental probability
Of the last
20
20
20
trains to arrive at Danville Station,
15
15
15
were on time. What is the experimental probability that the next train to arrive will be on time?
\newline
Write your answer as a fraction or whole number.
\newline
P
(
\mathrm{P}(
P
(
on time
)
=
)=
)
=
□
\square
□
\newline
Submit
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Cordelia surveyed a random sample of
57
57
57
students at Sunnydale High about their favorite season. Of the students surveyed,
31
31
31
chose summer as their favorite season. If there are
721
721
721
students at Sunnydale High, what is the most reasonable estimate of the number of students whose favorite season is summer?
\newline
Choose
1
1
1
answer:
\newline
(A)
224
224
224
\newline
(B)
329
329
329
\newline
(C)
392
392
392
\newline
(D)
411
411
411
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The mass of Stewart's favorite frying pan is
0.52
0.52
0.52
kilograms. What is the mass of the frying pan in grams?
\newline
(
1
1
1
kilogram
=
=
=
1
,
000
1,000
1
,
000
grams)
\newline
Choose
1
1
1
answer:
\newline
(A)
5.2
5.2
5.2
\newline
(B)
52
52
52
\newline
(C)
520
520
520
\newline
(D)
5
,
200
5,200
5
,
200
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Conclusion and Scientific Claim
\newline
Using the data that you collected, write a scientific claim, with evidence and reasoning, to answer the following prompt.
\newline
Of the three mammals - an Australopithecus africanus, a female gorilla, and a Homo sapien-which are more closely related?
\newline
Claim:
\newline
Evidence:
\newline
Reasoning:
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If the sum of three consecutive even integers is
60
60
60
, what is the first of the three even integers? (Hint: If
x
x
x
and
x
+
2
x+2
x
+
2
represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
\newline
The first of the three even integers is
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Three divers kept track of the number of crabs they've seen this year.
\newline
\begin{tabular}{lcc}
\newline
Diver & Crabs observed & Dives \\
\newline
\hline Scuba Sam &
33
33
33
&
11
11
11
\\
\newline
Wet Suit Willy &
81
81
81
&
18
18
18
\\
\newline
Deep Diving Dan &
104
104
104
&
26
26
26
\newline
\end{tabular}
\newline
Which diver saw the most crabs per dive?
\newline
Choose
1
1
1
answer:
\newline
(A) Scuba Sam
\newline
(B) Wet Suit Willy
\newline
(C) Deep Diving Dan
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←
\leftarrow
←
\newline
Module
4
4
4
, Quiz
1
1
1
: Lessons
1
1
1
−
3
-3
−
3
\newline
2
2
2
MA
06
06
06
B Math
06
06
06
B - Sem
2
2
2
MSP -
2023
2023
2023
/
2024
2024
2024
/Percentages
\newline
1
1
1
.
\newline
Lucas has some leftover pizza.
\newline
What fraction represents how much pizza Lucas has left (the shaded part).
\newline
3
4
\frac{3}{4}
4
3
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Pat's Pizza made
21
21
21
cheese pizzas,
14
14
14
veggie pizzas,
23
23
23
pepperoni pizzas, and
14
14
14
sausage pizzas yesterday.
\newline
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
\newline
Choose the best answer.
\newline
Choose
1
1
1
answer:
\newline
(A)
51
%
51\%
51%
\newline
(B)
66
%
66\%
66%
\newline
(C)
71
%
71\%
71%
\newline
(D)
81
%
81\%
81%
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(D) The median is
1
1
1
.
\newline
3
3
3
. The box plot shows the protein, in grams, in each serving of
7
7
7
different brands of nutritional shakes.
\newline
In
75
%
75 \%
75%
of the shakes, Paula found at least how many grams of protein?
\newline
(A)
15
15
15
\newline
(C)
25
25
25
\newline
(B)
16
16
16
.
5
5
5
\newline
(D)
27
27
27
\newline
Assessment, Form B
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Solve (Answers in Proper Scientific Notation):
\newline
About
8.4
×
1
0
11
8.4 \times 10^{11}
8.4
×
1
0
11
drops of water flow over Niagra Falls each minute. Each drop of water contains about
2
x
1
0
21
2 x 10^{21}
2
x
1
0
21
molecules of water. About how many molecules of water flow over the Niagra Falls each minute?
\newline
Each minute, approximately _ molecules of water flow over the Niagra Falls.
\newline
Solve (Answers in Proper Scientific Notation):
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
9
9
9
boys and
14
14
14
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
14
14
14
boys and
5
5
5
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
12
12
12
boys and
14
14
14
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
5
5
5
boys and
14
14
14
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
7
7
7
boys and
14
14
14
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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A committee must be formed with
4
4
4
teachers and
4
4
4
students. If there are
7
7
7
teachers to choose from, and
14
14
14
students, how many different ways could the committee be made?
\newline
Answer:
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There were
20
20
20
students running in a race. How many different arrangements of first, second, and third place are possible?
\newline
Answer:
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There were
21
21
21
students running in a race. How many different arrangements of first, second, and third place are possible?
\newline
Answer:
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There were
13
13
13
students running in a race. How many different arrangements of first, second, and third place are possible?
\newline
Answer:
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There were
18
18
18
students running in a race. How many different arrangements of first, second, and third place are possible?
\newline
Answer:
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A pizza shop has available toppings of pepperoni, bacon, anchovies, onions, sausage, and peppers. How many different ways can a pizza be made with
3
3
3
toppings?
\newline
Answer:
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There were
12
12
12
students running in a race. How many different arrangements of first, second, and third place are possible?
\newline
Answer:
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A pizza shop has available toppings of sausage, mushrooms, onions, olives, anchovies, pepperoni, and peppers. How many different ways can a pizza be made with
2
2
2
toppings?
\newline
Answer:
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A pizza shop has available toppings of mushrooms, peppers, onions, olives, anchovies, and sausage. How many different ways can a pizza be made with
2
2
2
toppings?
\newline
Answer:
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A pizza shop has available toppings of peppers, sausage, pepperoni, bacon, and mushrooms. How many different ways can a pizza be made with
2
2
2
toppings?
\newline
Answer:
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A pizza shop has available toppings of bacon, anchovies, pepperoni, onions, olives, and mushrooms. How many different ways can a pizza be made with
2
2
2
toppings?
\newline
Answer:
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A blood bank needs
4
4
4
people to help with a blood drive.
11
11
11
people have volunteered.
\newline
Find how many different groups of
4
4
4
can be formed from the
11
11
11
volunteers.
\newline
Answer:
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A blood bank needs
12
12
12
people to help with a blood drive.
18
18
18
people have volunteered. Find how many different groups of
12
12
12
can be formed from the
18
18
18
volunteers.
\newline
Answer:
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Three different golfers played a different number of holes today. Shanika played
9
9
9
holes and had a total of
43
43
43
strokes. Alicia played
18
18
18
holes and had a total of
79
79
79
strokes. Rickie played
27
27
27
holes and had a total of
123
123
123
strokes.
\newline
Which golfer had the lowest number of strokes per hole?
\newline
Choose
1
1
1
answer:
\newline
(A) Shanika
\newline
(B) Alicia
\newline
(C) Rickie
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At a football stadium,
20
%
20 \%
20%
of the fans in attendance were teenagers. If there were
390
390
390
teenagers at the football stadium, what was the total number of people at the stadium?
\newline
Answer:
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold
33
33
33
cards, which was
5
%
5 \%
5%
of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
\newline
Answer:
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800
800
800
people attended a football game. If
4
%
4 \%
4%
of the people who attended were teenagers, how many teenagers attended the game?
\newline
Answer:
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1200
1200
1200
people attended a football game. If
4
%
4 \%
4%
of the people who attended were teenagers, how many teenagers attended the game?
\newline
Answer:
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1700
1700
1700
people attended a football game. If
4
%
4 \%
4%
of the people who attended were teenagers, how many teenagers attended the game?
\newline
Answer:
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If
12
%
12 \%
12%
of a number equals
2
2
2
, find
60
%
60 \%
60%
of that number.
\newline
Answer:
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If
30
%
30 \%
30%
of a number is
84
84
84
and
70
%
70 \%
70%
of the same number is
196
196
196
, find
40
%
40 \%
40%
of that number.
\newline
Answer:
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A lock has a
3
3
3
-number code made up of
21
21
21
numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
\newline
Answer:
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Five students, Leah, Fawzia, Yusuf, Hailey, and Autumn, line up one behind the other. How many different ways can they stand in line?
\newline
Answer:
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A lock has a
3
3
3
-number code made up of
28
28
28
numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
\newline
Answer:
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There are
23
23
23
students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?
\newline
Answer:
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Three students are running a race. How many different ways can they come in first, second, and third?
\newline
Answer:
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A lock has a
3
3
3
-number code made up of
23
23
23
numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
\newline
Answer:
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There are
16
16
16
students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, and Treasurer?
\newline
Answer:
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There are
26
26
26
students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?
\newline
Answer:
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There are
5
5
5
athletes at a track meet. How many different ways can they finish first or second?
\newline
Answer:
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There are
26
26
26
students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, and Treasurer?
\newline
Answer:
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Four students are running a race. How many different ways can they come in first, second, third, and fourth?
\newline
Answer:
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Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs
$
2.00
\$ 2.00
$2.00
per pound while drought-resistant seed costs
$
3.00
\$ 3.00
$3.00
per pound. If for a particular day the two types of grass seed totaled
$
68.00
\$ 68.00
$68.00
and together weighed
25
25
25
pounds, how many pounds of bluegrass seed did Devin prepare?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
\newline
(B)
7
7
7
\newline
(C)
18
18
18
\newline
(D)
21
21
21
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Find an explicit formula for the geometric sequence
\newline
3
3
3
,
15
15
15
,
75
75
75
,
375
375
375
, .......
\newline
Note: the first term should be
a
(
1
)
a(1)
a
(
1
)
.
\newline
a
(
n
)
=
a(n)=
a
(
n
)
=
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Francisco bought
12
12
12
plants to arrange along the border of his garden. How many distinct arrangements can he make if the plants are comprised of
6
6
6
tulips,
3
3
3
roses, and
3
3
3
daisies?
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