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Math Problems
Algebra 2
Pythagorean Theorem and its converse
Lauren went shopping for a new phone. Sales tax where she lives is
6.5
%
6.5 \%
6.5%
. If the price of the phone is
p
p
p
dollars and cents, which expression does NOT represent the total price plus tax?
\newline
1
+
0.065
p
1+0.065 p
1
+
0.065
p
\newline
(
1
+
0.065
)
p
(1+0.065) p
(
1
+
0.065
)
p
\newline
1.065
p
1.065 p
1.065
p
\newline
p
+
0.065
p
p+0.065 p
p
+
0.065
p
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Jackson was out at a restaurant for dinner when the bill came. He wanted to leave a
24
%
24 \%
24%
tip. If dinner cost
d
d
d
dollars and cents, which expression represents the cost of dinner plus tip?
\newline
(
1
+
0.24
)
d
(1+0.24) d
(
1
+
0.24
)
d
\newline
d
+
0.24
d+0.24
d
+
0.24
\newline
1
1
1
.
24
24
24
\newline
0.24
d
0.24 d
0.24
d
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Arianna used a discount coupon for
15
%
15 \%
15%
off at her favorite clothing store. She bought
10
10
10
pairs of pants for
x
x
x
dollars each and
7
7
7
coats for
y
y
y
dollars each. Which expression represents the total amount Arianna paid after the coupon was applied?
\newline
0.85
(
10
x
+
7
y
)
0.85(10 x+7 y)
0.85
(
10
x
+
7
y
)
\newline
(
10
x
+
7
y
)
−
0.85
(
10
x
+
7
y
)
(10 x+7 y)-0.85(10 x+7 y)
(
10
x
+
7
y
)
−
0.85
(
10
x
+
7
y
)
\newline
(
10
x
+
7
y
)
+
0.15
(
10
x
+
7
y
)
(10 x+7 y)+0.15(10 x+7 y)
(
10
x
+
7
y
)
+
0.15
(
10
x
+
7
y
)
\newline
15
(
10
x
+
7
y
)
15(10 x+7 y)
15
(
10
x
+
7
y
)
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The volume of a rectangular prism is
140
i
n
3
140 \mathrm{in}^{3}
140
in
3
. Carter measures the sides to be
2
2
2
.
22
22
22
in by
10
10
10
in by
6.59
i
n
6.59 \mathrm{in}
6.59
in
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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Nathaniel was out at a restaurant for dinner when the bill came. He wanted to leave a
14
%
14 \%
14%
tip. If dinner cost
d
d
d
dollars and cents, which expression does NOT represent the cost of dinner plus tip?
\newline
1.014
d
1.014 d
1.014
d
\newline
d
+
0.14
d
d+0.14 d
d
+
0.14
d
\newline
1.14
d
1.14 d
1.14
d
\newline
1
d
+
0.14
d
1 d+0.14 d
1
d
+
0.14
d
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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is
22
1
4
22\frac{1}{4}
22
4
1
tall. It has a rectangular shape and an area of
890
cm
890\,\text{cm}
890
cm
. How wide across is Keala's book cover?
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Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled
60
60
60
miles, and the eastbound airplane has traveled
80
80
80
miles. How far apart are the two airplanes?
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2
2
2
. A garden's dimensions are
32
32
32
feet by
18
18
18
feet. How much fencing is needed if a fence will be constructed
7
7
7
feet from the garden on all sides?
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A bouncy ball is dropped such that the height of its first bounce is
3
3
3
feet and each successive bounce is
75
%
75 \%
75%
of the previous bounce's height. What would be the height of the
8
8
8
th bounce of the ball? Round to the nearest tenth (if necessary).
\newline
Answer:
□
\square
□
feet
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A bouncy ball is dropped such that the height of its first bounce is
3
3
3
.
75
75
75
feet and each successive bounce is
79
%
79 \%
79%
of the previous bounce's height. What would be the height of the
12
12
12
th bounce of the ball? Round to the nearest tenth (if necessary).
\newline
Answer:
□
\square
□
feet
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An observer in a hot-air balloon sees a building that is
50
m
50 \mathrm{~m}
50
m
away. The balloon has a height of
165
m
165 \mathrm{~m}
165
m
.
\newline
What is the angle of depression from the balloon to the building?
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A person stands on a building that is
12
12
12
.
6
6
6
tall. A phone is on the ground
58
58
58
.
5
5
5
meters away from the building.
\newline
Find the angle of depression from your eyes to the object.
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Sanjay makes souvenir pyramids by pouring liquid into a pyramid-shaped mold. The mold he uses has a square base with a side length of
10
c
m
10 \mathrm{~cm}
10
cm
, and the height of the mold is
10
c
m
10 \mathrm{~cm}
10
cm
.
\newline
Sanjay wants to make a smaller pyramid using the same mold, so he plans to fill the mold
2
c
m
2 \mathrm{~cm}
2
cm
from the top.
\newline
What is the approximate volume of this smaller pyramid?
\newline
Round to the nearest cubic centimeter.
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The lengths of the three sides of a triangle (in inches) are consecutive integers. If the perimeter is
69
69
69
inches, find the value of the shortest of the three side lengths.
\newline
Answer: inches
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A boat is heading towards a lighthouse, whose beacon-light is
113
113
113
feet above the water. The boat’s crew measures the angle of elevation to the beacon,
1
1
∘
11^\circ
1
1
∘
. What is the ship’s horizontal distance from the lighthouse (and the shore)?
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A right triangular prism is pictured below. Select the type of cross section formed when the figure is cut perpendicular to its base.
\newline
rectangle
\newline
triangle
\newline
circle
\newline
square
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One of the legs of a right triangle measures
3
c
m
3 \mathrm{~cm}
3
cm
and the other leg measures
4
c
m
4 \mathrm{~cm}
4
cm
. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
3
c
m
3 \mathrm{~cm}
3
cm
and its hypotenuse measures
5
c
m
5 \mathrm{~cm}
5
cm
.
\newline
Find the measure of the other leg. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
8
c
m
8 \mathrm{~cm}
8
cm
and the other leg measures
16
c
m
16 \mathrm{~cm}
16
cm
.
\newline
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
1
c
m
1 \mathrm{~cm}
1
cm
and the other leg measures
8
c
m
8 \mathrm{~cm}
8
cm
. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
5
c
m
5 \mathrm{~cm}
5
cm
and the other leg measures
12
c
m
12 \mathrm{~cm}
12
cm
.
\newline
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
12
c
m
12 \mathrm{~cm}
12
cm
and the other leg measures
16
c
m
16 \mathrm{~cm}
16
cm
. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
8
c
m
8 \mathrm{~cm}
8
cm
and its hypotenuse measures
17
c
m
17 \mathrm{~cm}
17
cm
. Find the measure of the other leg. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
6
c
m
6 \mathrm{~cm}
6
cm
and the other leg measures
8
c
m
8 \mathrm{~cm}
8
cm
. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
7
c
m
7 \mathrm{~cm}
7
cm
and the other leg measures
3
c
m
3 \mathrm{~cm}
3
cm
. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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One of the legs of a right triangle measures
15
c
m
15 \mathrm{~cm}
15
cm
and the other leg measures
9
c
m
9 \mathrm{~cm}
9
cm
.
\newline
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
\newline
Answer:
□
\square
□
c
m
\mathrm{cm}
cm
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Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are
36
36
36
inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?
\newline
Choose
1
1
1
answer:
\newline
(A)
32
32
32
inches
\newline
(B)
42
42
42
inches
\newline
(C)
55
55
55
inches
\newline
(D)
60
60
60
inches
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A circle has a circumference of
1
,
133.54
1,133.54
1
,
133.54
units.
\newline
What is the diameter of the circle?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is
10
,
000
c
m
3
10,000 \mathrm{~cm}^{3}
10
,
000
cm
3
. The base of the box is
25
c
m
25 \mathrm{~cm}
25
cm
by
10
c
m
10 \mathrm{~cm}
10
cm
.
\newline
How tall is the box of cereal?
\newline
□
\square
□
c
m
\mathrm{cm}
cm
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Ben and Cam are scuba diving. Ben is
15
15
15
meters below the surface of the water. Cam is
4
4
4
meters above Ben.
\newline
What is Cam's position relative to the surface of the water?
\newline
meters
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Joelle is working on a school report in a word processor. She wants to place an oversized image which is
30.51
c
m
30.51 \mathrm{~cm}
30.51
cm
wide so that it appears centered on the page. The width of the page is
21.59
c
m
21.59 \mathrm{~cm}
21.59
cm
. In the program, horizontal positions to the right of the leftmost edge of the page are positive.
\newline
What horizontal position for the left edge of the image should Joelle use to center the image?
\newline
c
m
\mathrm{cm}
cm
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The Olympic-size pool at the recreational center is a right rectangular prism
50
m
50 \mathrm{~m}
50
m
long and
25
m
25 \mathrm{~m}
25
m
wide. The pool contains
3000
m
3
3000 \mathrm{~m}^{3}
3000
m
3
of water.
\newline
How deep is the water in the pool?
\newline
m
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According to Jax's pedometer, he walked
2.783
k
m
2.783 \mathrm{~km}
2.783
km
while taking care of the livestock in the morning and
3.124
k
m
3.124 \mathrm{~km}
3.124
km
taking care of the livestock in the evening.
\newline
How far did Jax walk while taking care of the livestock today?
\newline
k
m
\mathrm{km}
km
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At full price, Melvin would pay
1
1
1
.
679
679
679
dollars per liter of gasoline. Using his loyalty card, Melvin only pays
1
1
1
.
439
439
439
dollars per liter.
\newline
How much less does Melvin pay per liter using his loyalty card?
\newline
dollars
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Cristian put a large rock on the bottom of the terrarium he made for his pet turtle. The rock is a right rectangular prism
10
c
m
10 \mathrm{~cm}
10
cm
wide by
12
c
m
12 \mathrm{~cm}
12
cm
long. The rock displaces
1800
c
m
3
1800 \mathrm{~cm}^{3}
1800
cm
3
of water.
\newline
How high is the rock?
\newline
cm
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Martene got a small aquarium for her birthday. The aquarium is a right rectangular prism
18.5
c
m
18.5 \mathrm{~cm}
18.5
cm
long by
15
c
m
15 \mathrm{~cm}
15
cm
wide. Martene put
3885
c
m
3
3885 \mathrm{~cm}^{3}
3885
cm
3
of water in the aquarium.
\newline
How deep is the water in the aquarium?
\newline
cm
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The YMCA lap pool is a right rectangular prism
36.8
m
36.8 \mathrm{~m}
36.8
m
long by
20
m
20 \mathrm{~m}
20
m
wide. The pool contains
1472
m
3
1472 \mathrm{~m}^{3}
1472
m
3
of water.
\newline
How deep is the water in the pool?
\newline
m
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Takumi plants a tree in his backyard and studies how the number of branches grows over time.
\newline
He predicts that the relationship between
N
N
N
, the number of branches on the tree, and
t
t
t
, the elapsed time, in years, since the tree was planted can be modeled by the following equation.
\newline
N
=
5
⋅
1
0
0.3
t
N=5 \cdot 10^{0.3 t}
N
=
5
⋅
1
0
0.3
t
\newline
According to Takumi's model, in how many years will the tree have
100
100
100
branches?
\newline
Give an exact answer expressed as a base
−
10
-10
−
10
logarithm.
\newline
years
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Marco's class is painting a mural on the side of their school. The mural covers a
3
1
2
m
3 \frac{1}{2} \mathrm{~m}
3
2
1
m
high, rectangular wall. It has an area of
28
m
2
28 \mathrm{~m}^{2}
28
m
2
.
\newline
What is the length of the mural?
\newline
m
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Yuki works at an aquarium. To clean a tank, she calculates
7
900
\frac{7}{900}
900
7
of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be
2
1
3
L
2 \frac{1}{3} \mathrm{~L}
2
3
1
L
of cleaning solution.
\newline
What is the total volume of the tank?
\newline
liters
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Japhet is making small rectangular tiles for a mosaic. Each tile has an area of
7
c
m
2
7 \mathrm{~cm}^{2}
7
cm
2
and is
1
1
4
c
m
1 \frac{1}{4} \mathrm{~cm}
1
4
1
cm
wide.
\newline
How long is each tile?
\newline
c
m
\mathrm{cm}
cm
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Claire is making a frame to display a drawing she made. The frame is
11
1
5
c
m
11 \frac{1}{5} \mathrm{~cm}
11
5
1
cm
wide. The frame has a rectangular shape and an area of
560
c
m
2
560 \mathrm{~cm}^{2}
560
cm
2
.
\newline
How tall is the frame?
\newline
c
m
\mathrm{cm}
cm
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Nisha likes to make small rectangular paintings of cats. One of her paintings has an area of
33
c
m
2
33 \mathrm{~cm}^{2}
33
cm
2
and a width of
7
1
2
c
m
7 \frac{1}{2} \mathrm{~cm}
7
2
1
cm
.
\newline
What is the height of this painting?
\newline
c
m
\mathrm{cm}
cm
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Lian's dog eats
1
20
\frac{1}{20}
20
1
of a bag of dog food each week. Lian currently has
5
8
\frac{5}{8}
8
5
of a bag remaining.
\newline
How many weeks will it take Lian's dog to finish this remaining food?
\newline
weeks
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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is
22
1
4
c
m
22 \frac{1}{4} \mathrm{~cm}
22
4
1
cm
tall. It has a rectangular shape and an area of
890
c
m
2
890 \mathrm{~cm}^{2}
890
cm
2
.
\newline
How wide across is Keala's book cover?
\newline
cm
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An electrician plans to install solar panels on a rectangular section of roof with an area of
180
m
2
180 \mathrm{~m}^{2}
180
m
2
. This width of this section of roof is
7
1
5
m
7 \frac{1}{5} \mathrm{~m}
7
5
1
m
across.
\newline
What is the length of this section of roof?
\newline
m
\mathrm{m}
m
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Sako's garden is
6
6
6
yards long. What is the length of his garden in feet?
\newline
(
1
1
1
yard
=
3
=3
=
3
feet)
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The length of an
8000
8000
8000
square foot rectangular gymnasium is
20
20
20
feet greater than its width. What is its width, in feet?
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A cylinder and sphere have equal volumes and radii of equal length. If the height of the cylinder is
8
8
8
centimeters, then what is the length of the radius of each shape in centimeters?
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A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of
196
196
196
centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
, and the tent is
250
c
m
250 \mathrm{~cm}
250
cm
long. What is the height, in centimeters, of the tent?
\newline
Choose
1
1
1
answer:
\newline
(A)
98
98
98
\newline
(B)
98
3
98 \sqrt{3}
98
3
\newline
(C)
125
3
125 \sqrt{3}
125
3
\newline
(D)
196
3
196 \sqrt{3}
196
3
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