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Math Problems
Algebra 2
Pythagorean Theorem and its converse
Giselle works as a carpenter and as a blacksmith.
\newline
She earns
$
20
\$ 20
$20
per hour as a carpenter and
$
25
\$ 25
$25
per hour as a blacksmith. Last week, Giselle worked both jobs for a total of
30
30
30
hours, and earned a total of
$
690
\$ 690
$690
.
\newline
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
\newline
Giselle worked as a carpenter for
□
\square
□
hours and as a blacksmith for hours last week.
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To visit his grandmother, Luis takes a train \\[\(6\).\(37\)\\] kilometers and a car \\[\(5\).\(45\)\\] kilometers. How many kilometers is Luis's journey in total? kilometers
\(\newline\)A) \(11\).\(82\)\(\newline\)B) \(10\).\(82\)\(\newline\)C) \(12\).\(82\)\(\newline\)D) \(11\).\(92\)
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The length of a rectangle is
3
3
3
inches longer than it is wide. If the area is
130
130
130
square inches, what are the dimensions of the rectangle?
\newline
The width, or shorter side is
□
\square
□
inches
\newline
The length, or longer side is
□
\square
□
inches
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A basketball game was scheduled to last
60
60
60
minutes, including the breaks between quarters. Several timeouts were used throughout the game, resulting in the game lasting a total of
72
72
72
minutes, including breaks. If each timeout was
90
90
90
seconds, how many total timeouts were used during the game?
\newline
_____
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5
5
5
years ago a man was
7
7
7
times as old as his son. After
5
5
5
years the father will be
3
3
3
time as old as his son. Find their present age.
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Every day, Gabrielle bicycles
3.6
3.6
3.6
miles due east from her house to school. After school, she bicycles due north from school to her friend Quinn's house, and then she bicycles home on a bike path that goes straight from Quinn's house to her own house. If the distance along the path from Quinn's house to Gabrielle's house is
8.9
8.9
8.9
miles, how far does Gabrielle bicycle each day? If necessary, round your answer to the nearest tenth.
\newline
____ miles
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Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be
$
6
\$6
$6
per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of
8
8
8
feet and a diagonal length of
17
17
17
feet. How much will the rug cost?
\newline
$
\$
$
____
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Hugo and Brenda are mountain climbing and want to climb up an
8
8
8
-meter vertical rock face. Hugo goes first while Brenda stands a few steps back from the rock face. When Hugo reaches the top, she is
10
10
10
meters away from Brenda. How far away from the rock face is Brenda standing?
\newline
_____ meters
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After school, Brandon skateboards directly from school to a movie theater and then from the movie theater to an ice cream parlor. The movie theater is \(5\) kilometers south of the school and the ice cream parlor is \(12\) kilometers east of the movie theater. What is the straight-line distance between the school and the ice cream parlor?______________kilometers
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Hazel has two cubes. The smaller cube has a volume of
27
27
27
cubic units. The larger cube's sides are twice as long as those of the small cube. What is the volume of the second cube?
\newline
____ cubic units
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Malik walked up and back down an empty
\newline
18
m
18\,\text{m}
18
m
long escalator at a constant rate. Since the escalator was going up at the time, it took him only
\newline
22.5
s
22.5\,\text{s}
22.5
s
. Going down took Malik
\newline
90
s
90\,\text{s}
90
s
. Assume the escalator speed is constant.
\newline
What was Malik's walking speed?
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Estelle is helping at a community food drive by boxing up cans of soup. There are two sizes of boxes, large and small. Estelle fills
3
3
3
large boxes and
5
5
5
small boxes with
170
170
170
soup cans total. The boy working next to her fills
4
4
4
large boxes and
4
4
4
small boxes with
184
184
184
soup cans total.
\newline
How many cans does each small box hold?
\newline
_
_
_
_
\_\_\_\_
____
cans
\newline
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Jane is going to walk once around the edge of a rectangular park. The park is
200
200
200
yards long and
300
300
300
feet wide. How far will Jane walk?
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Malik walked up and back down an empty
18
m
18\,\text{m}
18
m
long escalator at a constant rate. Since the escalator was going up at the time, it took him only
22.5
s
22.5\,\text{s}
22.5
s
. Going down took Malik
90
s
90\,\text{s}
90
s
. Assume the escalator speed is constant.
\newline
What was Malik's walking speed?
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Whitney is making a strawberry cake for her brother's birthday. The cake pan is a right rectangular prism
20
cm
20\,\text{cm}
20
cm
wide by
28
cm
28\,\text{cm}
28
cm
long. Whitney puts
1848
cm
3
1848\,\text{cm}^{3}
1848
cm
3
of batter into the pan.
\newline
How deep is the cake batter?
\newline
□
cm
\square\,\text{cm}
□
cm
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Jaquan passed a checkpoint jogging at a constant speed of
9
9
9
km
h
\frac{\text{km}}{\text{h}}
h
km
. Then,
2
2
2
minutes later, Odalis passed the same checkpoint.
\newline
If Odalis runs at a constant speed of
12
12
12
km
h
\frac{\text{km}}{\text{h}}
h
km
then how far past the checkpoint will Odalis be when they catch up to Jaquan?
\newline
□
km
\square \,\text{km}
□
km
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Aspen has
306
306
306
green beads and
210
210
210
silver beads. For every
5
cm
5\,\text{cm}
5
cm
of a belt that Aspen sews, they use
40
40
40
green beads and
24
24
24
silver beads.
\newline
After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?
\newline
□
\square
□
cm
\text{cm}
cm
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The tires of a go-kart are
1
m
1 \mathrm{~m}
1
m
in circumference. The tires revolve
15
15
15
times per second.
\newline
What is the distance the go-kart travels in
40
40
40
seconds?
\newline
□
\square
□
m
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Camilla is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp starts
44
44
44
inches from the cinder block and the piece of wood is
55
55
55
inches long, how tall is the cinder block?
\newline
_
_
_
_
\_\_\_\_
____
inches
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Jasper takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is
85
85
85
inches long and the width of the paper is
51
51
51
inches. What is the paper's length?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
inches
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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
28
kilometers
28\,\text{kilometers}
28
kilometers
, and the eastbound airplane has traveled
96
kilometers
96\,\text{kilometers}
96
kilometers
. How far apart are the two airplanes?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
kilometers
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A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is
24
24
24
meters and the distance between the gopher's holes is
26
26
26
meters. How wide is the yard?
\newline
_
_
_
\_\_\_
___
meters
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Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins
45
45
45
inches from the block and the block is
28
28
28
inches tall, how long is the piece of wood?
\newline
_____ inches
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Lila takes a
52
52
52
-centimeter by
39
39
39
-centimeter rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Lila has two equally sized triangles of plywood. What is the perimeter of each triangle?
\newline
_____ centimeters
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After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is
12
12
12
kilometers south of the school and the movie theater is
5
5
5
kilometers east of the game store. What is the straight-line distance between the school and the movie theater?
\newline
_
_
_
_
\_\_\_\_
____
kilometers
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A rake is leaning against a wall. The top of the rake hits the wall
63
63
63
inches above the ground and the bottom of the rake is
16
16
16
inches away from the base of the wall. A beetle crawls from the bottom of the rake to the top of the rake. Then the beetle climbs down to the base of the wall and back to the bottom of the rake. How far does the beetle travel in all?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
inches
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Brookfield Street, which is
16
16
16
meters wide, intersects with Greenville Avenue, which is
12
12
12
meters wide. Eduardo walks his dog across Brookfield Street and then turns and walks across Greenville Avenue. Suddenly, Eduardo's dog runs diagonally across the intersection back to the corner they started on. How far does Eduardo's dog travel in all?
\newline
\newline
cent;____ meters
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The area of an extra large circular pizza from Gambino's Pizzeria is
484
π
c
m
2
484 \pi \mathrm{cm}^{2}
484
π
cm
2
.
\newline
What is the diameter of an extra large pizza from Gambino's Pizzeria?
\newline
□
\square
□
c
m
\mathrm{cm}
cm
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A flying squirrel's nest is
10
10
10
feet high in a tree. From its nest, the flying squirrel glides
26
26
26
feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?
\newline
_____ feet
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The diameter of a circle is
16
16
16
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The radius of a circle is
1
1
1
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The radius of a circle is
5
5
5
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The radius of a circle is
3
3
3
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The diameter of a circle is
4
4
4
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The diameter of a circle is
2
2
2
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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A circle has a circumference of
11
11
11
,
304
304
304
units.
\newline
What is the diameter of the circle? 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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A circle has a circumference of
7
7
7
,
850
850
850
units.
\newline
What is the radius of the circle? 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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The diameter of a circle is
6
6
6
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The radius of a circle is
8
8
8
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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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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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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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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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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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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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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2
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