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Math Problems
Grade 8
Experimental probability
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?
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Answer:
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Four students are running a race. How many different ways can they come in first, second, third, and fourth?
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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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Given that
f
(
x
)
=
−
3
x
,
g
(
x
)
=
x
+
1
f(x)=-3 x, \quad g(x)=x+1
f
(
x
)
=
−
3
x
,
g
(
x
)
=
x
+
1
and
h
(
x
)
=
2
f
(
x
−
3
)
−
2
g
(
x
)
h(x)=2 f(x-3)-2 g(x)
h
(
x
)
=
2
f
(
x
−
3
)
−
2
g
(
x
)
, then what is the value of
h
(
3
)
h(3)
h
(
3
)
?
\newline
Answer:
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In a class of
29
29
29
students,
10
10
10
have a cat and
12
12
12
have a dog. There are
9
9
9
students who do not have a cat or a dog. What is the probability that a student who has a dog also has a cat?
\newline
Answer:
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Miguel has some dimes and some quarters. He has a minimum of
18
18
18
coins worth a maximum of
$
2
\$2
$2
.
70
70
70
combined. If Miguel has
3
3
3
quarters, determine all possible values for the number of dimes that he could have.
\newline
Answer:
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Bilquis is younger than Mav. Their ages are consecutive even integers. Find Bilquis's age if the sum of Bilquis's age and
2
2
2
times Mav's age is
82
{8 2}
82
.
\newline
Answer:
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Kadeesha is older than Cameron. Their ages are consecutive integers. Find Kadeesha's age if the sum of Kadeesha's age and
3
3
3
times Cameron's age is
17
17
17
.
\newline
Answer:
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Bao is older than Jeriel. Their ages are consecutive integers. Find Bao's age if the sum of Bao's age and
2
2
2
times Jeriel's age is
40
40
40
.
\newline
Answer:
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When an integer is subtracted from
8
8
8
times the next consecutive integer, the difference is
−
13
-13
−
13
. Find the value of the greater integer.
\newline
Answer:
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When an integer is subtracted from
5
5
5
times the next consecutive even integer, the difference is
−
22
-22
−
22
. Find the value of the lesser integer.
\newline
Answer:
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If
(
20
y
+
5
)
(
4
y
−
30
)
=
80
y
2
+
b
y
−
150
(20 y+5)(4y-30)=80y^{2}+by-150
(
20
y
+
5
)
(
4
y
−
30
)
=
80
y
2
+
b
y
−
150
for all values of
y
y
y
where
b
b
b
is a constant, then which of the following is the value of
b
b
b
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
580
-580
−
580
\newline
(B)
−
40
-40
−
40
\newline
(C)
0
0
0
\newline
(D)
620
620
620
\newline
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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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A baseball team has three different pitchers. Randy allowed
2
2
2
runs and pitched
3
3
3
innings. Felix allowed
4
4
4
runs and pitched
5
5
5
innings. Johan allowed
5
5
5
runs and pitched
7
7
7
innings.
\newline
Which pitcher has the lowest number of runs allowed per inning?
\newline
Choose
1
1
1
answer:
\newline
(A) Randy
\newline
(B) Felix
\newline
(C) Johan
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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? Choose the best answer. 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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