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Math Problems
Algebra 2
Pythagorean Theorem and its converse
The diameter of a circle is
10
10
10
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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11
11
11
) Alan drives from his house to his mother's house in
20
20
20
hours. He drives at an average speed of
66
66
66
miles per hour. What is the distance from Alan's house to his mother's house?
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1
1
1
:
13
13
13
PM Sun Apr
14
14
14
\newline
⋯
\cdots
⋯
\newline
HAlg
11
11
11
.
5
5
5
B Mid-Point Formula
\newline
SHORT RESPONSE The point of no return in aviation is the farthest point to which a plane can fly and still have enough fuel to return to its starting place or to fly to an alternative landing destination. After a plane passes the point of no return, it must fly to its planned destination. The distance between consecutive grid lines represents
50
50
50
nautical miles.
\newline
The flight path of a plane is from airport A to airport B. The plane is currently at the midpoint of the flight path. How far away is the plane from airport A? Round your answer to the nearest nautical mile.
\newline
□
\square
□
\newline
The plane's point of no return is calculated to be
200
200
200
nautical miles.
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A pedestrian underpass is constructed beneath a roadway using a cylindrical pipe with radius
1.8
m
1.8 \mathrm{~m}
1.8
m
. The bottom of the pipe will be filled and paved. The headroom at the centre of the path is
2.8
m
2.8 \mathrm{~m}
2.8
m
. How wide is the path?
\newline
ake It Further
\newline
A spherical fish bowl has diameter
26
c
m
26 \mathrm{~cm}
26
cm
. The surface of the water in the bowl is a
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Question
8
8
8
\newline
Joe was trying to determine the distance across a point, so he made the measurements shown below.
\newline
All images created for VVA,
2022
2022
2022
'
\newline
Which is closest to the distance from
M
\mathrm{M}
M
to
N
\mathrm{N}
N
?
\newline
48.2
m
48.2 \mathrm{~m}
48.2
m
\newline
33.2
m
33.2 \mathrm{~m}
33.2
m
\newline
59.3
m
59.3 \mathrm{~m}
59.3
m
\newline
22.4
m
22.4 \mathrm{~m}
22.4
m
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mae mowed two lawns. One of them measured
10
m
10 \, \text{m}
10
m
by
13
m
13 \, \text{m}
13
m
and the other
15
m
15 \, \text{m}
15
m
by
10
m
10 \, \text{m}
10
m
. Keili's rate is
$
3
\$3
$3
per
10
m
2
10\,\text{m}^2
10
m
2
. How much money did she get for the two lawns?
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Question
4
4
4
\newline
Jenna is creating a mural for her bedroom wall. She would like to copy a picture that is
2
2
2
inches by
2
2
2
.
5
5
5
inches. She uses a copy machine to enlarge it by a scale factor of
4
4
4
. Then she projects it on her wall by a scale factor of
12
12
12
.
\newline
Part A
\newline
What are the dimensions of the mural? Write the smaller dimension first and the larger dimension second.
\newline
□
\square
□
inches by
□
\square
□
inches
\newline
Part B
\newline
Are both of the enlarged pictures similar to the original? Write yes or no.
\newline
□
\square
□
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Tina wants to find the height of a flagpole at Wagstaff. She walks along the shadow of the flagpole for
20
20
20
feet until her shadow ends at the same place as the flagpole shadow. She is
4
4
4
ft
6
6
6
inches and her shadow is
5
5
5
feet. How tall is the flagpole?
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13
13
13
. A scuba diver swam north at
1.5
m
/
s
1.5 \mathrm{~m} / \mathrm{s}
1.5
m
/
s
, across a current running from east to west at
2.0
m
/
s
2.0 \mathrm{~m} / \mathrm{s}
2.0
m
/
s
. She swam for
3
m
i
n
3 \mathrm{~min}
3
min
and then surfaced.
\newline
a) Draw a diagram showing where the dive boat will pick her up relative to where she dove.
\newline
b) How far did she travel?
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You and your friend are using ribbon to make cards. Your ribbon is
78
inch
78\,\text{inch}
78
inch
wide. Your friend's ribbon is
58
inch
58\,\text{inch}
58
inch
wide. How much wider is the ribbon you are using?
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There are two slides in a park. The first slide is
9.5
m
9.5 \mathrm{~m}
9.5
m
tall. The second slide is
300
c
m
300 \mathrm{~cm}
300
cm
shorter than the first slide. How tall is the second slide in centimetres? Show your work.
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A soccer field is a rectangle
90
90
90
meters wide and
120
120
120
meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance? Use a calculator!
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An aquarium can be modeled as a right rectangular prism. Its dimensions are
17
17
17
in by
13
13
13
in by
12
12
12
in. How many cubic inches of water are in it when it is full? Round your answer to the nearest tenth if necessary.
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A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of
60
m
p
h
60 \mathrm{mph}
60
mph
. Two hours later, a special agent in a helicopter starts chasing the spy. The special agent travels the same route at a speed of
90
m
p
h
90 \mathrm{mph}
90
mph
.
\newline
*At what speed
\newline
Chapter Reference should the special agent chase the spy if the evacuation spot is
240
240
240
miles from the starting point?
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A hot-air balloon is rising vertically
5
m/s
5\,\text{m/s}
5
m/s
while the wind is blowing horizontally at
3
m/s
3\,\text{m/s}
3
m/s
. Find the speed
v
v
v
of the balloon and the angle
θ
\theta
θ
it makes with the horizontal.
5
m/s
5\,\text{m/s}
5
m/s
Balloon
3
m/s
3\,\text{m/s}
3
m/s
Wind
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From clue
6
6
6
, Roger is not the singer. I can complete the rest of the chart. Peter
\newline
\begin{tabular}{|l|c|c|c|}
\newline
\hline & Pavan & Attwell &
D
D
D
: \\
\newline
\hline Anna &
X
X
X
&
y
e
s
y e s
yes
& \\
\newline
\hline Peter &
y
e
s
y e s
yes
&
X
X
X
& \\
\newline
\hline Roger &
X
X
X
&
X
X
X
&
Y
Y
Y
\\
\newline
\hline
\newline
\end{tabular}
\newline
4
4
4
Look Back
\newline
I checked to make sure that my answer wo
\newline
A Checking
\newline
4
4
4
. The hypotenuse in a right scalene triangle is
7.0
c
m
7.0 \mathrm{~cm}
7.0
cm
. What must be the length of one of the legs?
\newline
A.
8.0
c
m
8.0 \mathrm{~cm}
8.0
cm
\newline
C.
X
X
X
0
0
0
\newline
B.
X
X
X
1
1
1
\newline
D.
7.0
c
m
7.0 \mathrm{~cm}
7.0
cm
\newline
Chapter
10
10
10
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6
0
∘
60^{\circ}
6
0
∘
\newline
1
2
\frac{\sqrt{1}}{2}
2
1
\newline
1
2
\frac{1}{2}
2
1
\newline
3
\sqrt{3}
3
\newline
A windshield wiper has length of
50
cm
50\,\text{cm}
50
cm
. The wiper rotates from its resting position at
3
0
∘
30^\circ
3
0
∘
, in standard positon, to
15
0
∘
150^\circ
15
0
∘
. Determine the exact horizontal distance that the tip of the viper travels in one suipe,
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\begin{tabular}{|l|l|l|l|}
\newline
\hline
6
0
∘
60^{\circ}
6
0
∘
&
1
2
\frac{1}{2}
2
1
&
1
2
\frac{1}{2}
2
1
&
3
\sqrt{3}
3
\\
\newline
\hline
\newline
\end{tabular}
\newline
8
8
8
. A windshield wiper has length of
50
c
m
50 \mathrm{~cm}
50
cm
. The wiper rotates from its resting position at
30
%
30 \%
30%
, in standard positon, to
150
150
150
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1
1
1
. A zip wire runs between two posts,
25
m
25 \mathrm{~m}
25
m
apart. The zip wire is at an angle of
1
0
∘
10^{\circ}
1
0
∘
to the horizontal. Calculate the length of the zip wire.
\newline
25.4
m
25.4 m
25.4
m
\newline
144.0
m
144.0 \mathrm{~m}
144.0
m
\newline
141.8
m
141.8 m
141.8
m
\newline
24.6
m
24.6 m
24.6
m
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The referee at a college football game is standing
12
12
12
yards behind the ball. The back judge is standing
22
22
22
yards in front of the ball. The field judge is standing exactly halfway between them. Using coordinates to model the situation, find how far in front of the ball the field judge is. Explain.
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The actual dimensions of a rectangle are
3
c
m
3 \mathrm{~cm}
3
cm
by
8
c
m
8 \mathrm{~cm}
8
cm
. Eric measures the sides to be
2.57
c
m
2.57 \mathrm{~cm}
2.57
cm
by
8.02
c
m
8.02 \mathrm{~cm}
8.02
cm
. In calculating the area, what is the relative error, to the nearest thousandth.
\newline
Answer:
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Jacob went shopping for a new pair of sneakers. Sales tax where he lives is
7.5
%
7.5 \%
7.5%
. If the price of the pair of sneakers is
p
p
p
dollars and cents, which expression represents the total price plus tax?
\newline
0.075
p
0.075 p
0.075
p
\newline
1
+
0.075
1+0.075
1
+
0.075
\newline
1
+
0.075
p
1+0.075 p
1
+
0.075
p
\newline
p
+
0.075
p
p+0.075 p
p
+
0.075
p
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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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Question
9
9
9
of?
\newline
PREV
\newline
NEXT
\newline
A piano mover uses a ramp to move a piano into a house. The doorway to the house is
2
2
2
feet above the ground and the ramp starts
7
7
7
feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.
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Two boats are anchored in still water, along a straight line from a lighthouse of height
41
41
41
meters. From the beacon on top of the lighthouse, the angle to the nearer boat is
43
43
43
degrees and the angle to the farther boat is
67
67
67
.
6
6
6
degrees. Determine the distance that the light travels from the lighthouse to each boat, and the distance between the two boats.
\newline
Use the diagram to determine the measure of the sought sides.
\newline
What is the distance between the two boats?
\newline
meters
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Akoni, a painter, painted a circular helicopter landing pad one color. Next she painted over a
3
3
3
meter radius circle in the center, in a different color. If the second coat of paint covered an area half the size of the first coat, which of the following is most nearly the radius of the landing pad?
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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
2
890\,\text{cm}^2
890
cm
2
. How wide across is Keala's book cover?
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A boat heading out to sea starts out at Point
A
A
A
, at a horizontal distance of
734
734
734
feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be
1
4
∘
14^\circ
1
4
∘
. At some later time, the crew measures the angle of elevation from point
B
B
B
to be
6
∘
6^\circ
6
∘
. Find the distance from point
A
A
A
to point
B
B
B
. Round your answer to the nearest foot if necessary.
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Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of
5.00
m
5.00 \mathrm{~m}
5.00
m
. A person is standing
12.0
m
12.0 \mathrm{~m}
12.0
m
away from the wall, equidistant from the loudspeakers. When the person moves
1.00
m
1.00 \mathrm{~m}
1.00
m
parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is
343
343
343
m
/
s
\mathrm{m} / \mathrm{s}
m
/
s
.
\newline
A)
211
H
z
211 \mathrm{~Hz}
211
Hz
\newline
B)
674
H
z
674 \mathrm{~Hz}
674
Hz
\newline
C)
256
H
z
256 \mathrm{~Hz}
256
Hz
\newline
D)
512
H
z
512 \mathrm{~Hz}
512
Hz
\newline
(E)
422
H
z
422 \mathrm{~Hz}
422
Hz
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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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8
8
8
. 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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3
3
3
. 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
Get tutor help
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