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Algebra 2
Solve a system of equations using any method
Eva and Jamir like to bake cookies. Eva baked
24
24
24
chocolate chip cookies, and Jamir baked
p
p
p
peanut butter cookies. Together they baked a total of
56
56
56
cookies.
\newline
Write an equation to describe this situation.
\newline
How many cookies did Jamir bake?
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What is the period of
\newline
y
=
−
5
cos
(
π
8
x
)
+
3
?
y=-5 \cos \left(\frac{\pi}{8} x\right)+3 ?
y
=
−
5
cos
(
8
π
x
)
+
3
?
\newline
Give an exact value.
\newline
units
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In an
8
8
8
-minute long game, a professional video game player performed a total of
2
2
2
,
400
400
400
actions. What is the player's average number of actions per minute?
\newline
Choose
1
1
1
answer:
\newline
(A)
30
30
30
\newline
(B)
160
160
160
\newline
(C)
300
300
300
\newline
(D)
400
400
400
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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
percent 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
percent 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
\mathbf{1 8 9}
189
\newline
(C)
405
405
405
\newline
(D)
11
11
11
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For the perfect cup of hot cocoa, Eva uses
3
3
3
scoops of hot cocoa mix,
10
10
10
miniature marshmallows, and
8
8
8
ounces of water.
\newline
What is the ratio of miniature marshmallows to scoops of hot cocoa?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
8
8
to
10
10
10
\newline
(B)
3
3
3
to
10
10
10
\newline
(C)
10
10
10
to
3
3
3
\newline
(D)
10
10
10
to
8
8
8
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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 small airplane can carry passengers, luggage, and mail as long as their total weight is less than
1
1
1
,
700
700
700
pounds. Tuesday's load of mail weighs
490
490
490
pounds. If the average combined weight of each passenger and their luggage is
170
170
170
pounds, what is the greatest possible number of passengers that can travel on the airplane on Tuesday?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
7
7
\newline
(B)
8
8
8
\newline
(C)
10
10
10
\newline
(D)
12
12
12
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Ni Hua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits.
\newline
In the last decade, Ni Hua went skydiving a total of
45
45
45
times in the
19
19
19
islands and peninsulas that he visited.
\newline
How many islands and peninsulas did Ni Hua visit?
\newline
Choose
1
1
1
answer:
\newline
(A) Ni Hua visited
12
12
12
islands and
7
7
7
peninsulas.
\newline
(B) Ni Hua visited
7
7
7
islands and
12
12
12
peninsulas.
\newline
(C) There is not enough information to determine the exact number of islands and peninsula Ni Hua visited.
\newline
(D) The given information describes an impossible situation.
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In \(45\) years, Gabriela will be \(4\) times as old as she is right now.
\newline
How old is she right now?
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Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.
\newline
How old is Michael?
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A fruit stand has to decide what to charge for their produce. They need
$
10
\$ 10
$10
for
4
4
4
apples and
4
4
4
oranges. They also need
$
12
\$ 12
$12
for
6
6
6
apples and
6
6
6
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
A Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.50
\$ 1.50
$1.50
for an orange.
\newline
B Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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Ben is \(4\) times as old as Ishaan. \(6\) years ago, Ben was \(6\) times as old as Ishaan.
\newline
How old is Ben now?
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Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher.
\newline
How old is Christopher?
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Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.
\newline
How old is Ben?
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Ben is \(3\) times as old as Daniel and is also \(4\) years older than Daniel.
\newline
How old is Daniel?
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Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.
\newline
How old is Ben now?
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In \(36\) years, Ishaan will be \(3\) times as old as he is right now.
\newline
How old is he right now?
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Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.
\newline
How old is Brandon?
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Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.
\newline
How old is Kevin now?
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Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher.
\newline
How old is Ishaan?
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In \(56\) years, Daniel will be \(5\) times as old as he is right now.
\newline
How old is he right now?
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Ben is \(30\) years old and Daniel is \(2\) years old.
\newline
How many years will it take until Ben is only \(3\) times as old as Daniel?
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Ben is \(39\) years old and Ishaan is \(3\) years old.
\newline
How many years will it take until Ben is only \(4\) times as old as Ishaan?
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Kevin is \(39\) years old and Daniel is \(3\) years old.
\newline
How many years will it take until Kevin is only \(4\) times as old as Daniel?
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In \(56\) years, Kevin will be \(9\) times as old as he is right now.
\newline
How old is he right now?
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Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.
\newline
How old is Michael now?
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Christopher is \(20\) years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was \(3\) times as old as Christopher.
\newline
How old is Ishaan now?
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A fruit stand has to decide what to charge for their produce. They need
$
5.30
\$ 5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also need
$
7.30
\$ 7.30
$7.30
for
1
1
1
apple and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.30
\$ 3.30
$3.30
for an apple and
$
2.00
\$ 2.00
$2.00
for an orange.
\newline
B Yes; they should charge
$
2.00
\$ 2.00
$2.00
for an apple and
$
3.30
\$ 3.30
$3.30
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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A fruit stand has to decide what to charge for their produce. They decide to charge
$
5.30
\$ 5.30
$5.30
for
1
1
1
apple and
1
1
1
orange. They also plan to charge
$
14
\$ 14
$14
for
2
2
2
apples and
2
2
2
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
3.00
\$ 3.00
$3.00
for an apple and
$
2.30
\$ 2.30
$2.30
for an orange.
\newline
B Yes; they should charge
$
3.00
\$ 3.00
$3.00
for an apple and
$
4.00
\$ 4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel.
\newline
How old is Daniel?
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Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.
\newline
How old is Michael now?
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Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.
\newline
How old is Ishaan?
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Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.
\newline
How old is Brandon now?
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Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.
\newline
How old is Daniel now?
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Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.
\newline
How old is Ishaan now?
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Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.
\newline
How old is Gabriela now?
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A fruit stand has to decide what to charge for their produce. They need
$
5
\$ 5
$5
for
1
1
1
apple and
1
1
1
orange. They also need
$
15
\$ 15
$15
for
3
3
3
apples and
3
3
3
oranges. Put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
A Yes; they should charge
$
2.00
\$ 2.00
$2.00
for an apple and
$
3.00
\$ 3.00
$3.00
for an orange.
\newline
B Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
4.00
\$ 4.00
$4.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
D
N
o
\mathrm{No}
No
; the system has no solution.
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Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.
\newline
How old is Kevin now?
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A fruit stand has to decide what to charge for their produce. They need
$
10
\$ 10
$10
for
4
4
4
apples and
4
4
4
oranges. They also need
$
15
\$ 15
$15
for
6
6
6
apples and
6
6
6
oranges. We put this information into a system of linear equations.
\newline
Can we find a unique price for an apple and an orange?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.50
\$ 1.50
$1.50
for an orange.
\newline
B Yes; they should charge
$
1.50
\$ 1.50
$1.50
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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Ben is \(12\) years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was \(4\) times as old as Ishaan.
\newline
How old is Ben now?
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Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.
\newline
How old is Christopher now?
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At Imelda's fruit stand, you bought
5
5
5
apples and
4
4
4
oranges for
$
10
\$ 10
$10
, and your friend bought
5
5
5
apples and
5
5
5
oranges for
$
11
\$ 11
$11
.
\newline
Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; they should charge
$
1.00
\$ 1.00
$1.00
for an apple and
$
1.25
\$ 1.25
$1.25
for an orange.
\newline
B Yes; they should charge
$
1.20
\$ 1.20
$1.20
for an apple and
$
1.00
\$ 1.00
$1.00
for an orange.
\newline
(C) No; the system has many solutions.
\newline
(D)
N
o
\mathrm{No}
No
; the system has no solution.
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Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.
\newline
How old is Kevin now?
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Ben is \(4\) times as old as Ishaan. \(6\) years ago, Ben was \(6\) times as old as Ishaan.
\newline
How old is Ishaan now?
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In \(16\) years, Ben will be \(3\) times as old as he is right now.
\newline
How old is he right now?
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Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.
\newline
How old is Brandon now?
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Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel.
\newline
How old is Kevin?
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Ben is \(20\) years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was \(3\) times as old as Daniel.
\newline
How old is Daniel now?
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Tiffany is \(34\) years old and Vanessa is \(6\) years old.
\newline
How many years will it take until Tiffany is only \(3\) times as old as Vanessa?
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Ben is \(12\) years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was \(4\) times as old as Ishaan.
\newline
How old is Ishaan now?
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