The correct choice is A.
Standardized Test Practice - Cumulative, Chapters 1-8
1. What is the value of x in the figure below?
ANSWER: A
2. A baseball diamond is a square with 90-ft sides.
What is the length from 3rd base to 1st base? Round
to the nearest tenth.
A 22.5
B 23
C 23.5
D 24
SOLUTION: Use the Pythagorean theorem to find the value of x.
F 155.9 ft
G 141.6 ft
H 127.3 ft
J 118.2 ft
SOLUTION: Use the Pythagorean theorem to find the length from
rd
The correct choice is A.
st
3 base to 1 base.
rd
st
Let d be the length from 3 base to 1 base.
ANSWER: A
2. A baseball diamond is a square with 90-ft sides.
What is the length from 3rd base to 1st base? Round
to the nearest tenth.
Therefore, the correct choice is H.
ANSWER: H
3. The scale of a map is 1 inch = 4.5 kilometers. What
is the distance between two cities that are 2.4 inches
apart on the map?
A 10.8 kilometers
B 11.1 kilometers
C 11.4 kilometers
D 11.5 kilometers
F 155.9 ft
G 141.6 ft
H 127.3 ft
J 118.2 ft
SOLUTION: Use the Pythagorean theorem to find the length from
rd
st
3 base to 1 base.
rd
st
Let d be the length from 3 base to 1 base.
SOLUTION: 1 inch = 4.5 kilometers
So, 2.4 inches will be equal to (2.4)(4.5) or 10.8
kilometers.
Therefore, the correct choice is A.
ANSWER: A
4. What is the value of x in the figure below? Round to
the nearest tenth.
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Therefore, the correct choice is H.
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kilometers.
Therefore, the correct choice is A.
ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-8
A
4. What is the value of x in the figure below? Round to
the nearest tenth.
F 10.5
G 11.1
H 13.6
J 14.2
Therefore, the correct choice is G.
ANSWER: G
6. Grant is flying a kite on the end of a string that is 350
feet long. The angle elevation from Grant to the kite
is 74º. How high above the ground is the kite? Round
your answer to the nearest tenth if necessary.
F 336.4ft
G 295.6 ft
H 141.2 ft
J 96.5 ft
SOLUTION: SOLUTION: Use the cosine ratio to find the value of x.
Therefore, the correct choice is G.
ANSWER: G
6. Grant is flying a kite on the end of a string that is 350
feet long. The angle elevation from Grant to the kite
is 74º. How high above the ground is the kite? Round
your answer to the nearest tenth if necessary.
F 336.4ft
G 295.6 ft
H 141.2 ft
J 96.5 ft
SOLUTION: Use the sine ratio to find the value of y .
The kite is 336.4 ft above the ground.
Therefore, the correct choice is F.
ANSWER: F
7. GRIDDED RESPONSE Find x in the figure below.
Round your answer to the nearest tenth if
necessary.
Use the sine ratio to find the value of y .
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SOLUTION: Use the Law of Cosines to find the value of x.
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The kite is 336.4 ft above the ground.
Therefore, the correct choice is F.
ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-8
F
Write the direction vector for wind in component
form.
40 east of north is equivalent to 50° from the horizontal.
7. GRIDDED RESPONSE Find x in the figure below.
Round your answer to the nearest tenth if
necessary.
The component form for the wind’s vector is
.
Add the vectors for Amy and the wind.
SOLUTION: Use the Law of Cosines to find the value of x.
Now determine the vector's magnitude by using
Pythagorean theorem.
Let v be the velocity of Amy.
The velocity is about 12.3 feet per second.
Now find the vector's direction.
Let a be the angle made by Amy with the horizontal.
ANSWER: 93.9
8. Amy is paddling her canoe across a lake at a speed
of 10 feet per second headed due north. The wind is
blowing 40º east of north with a velocity of 2.8 feet.
What is Amy’s resultant velocity? Express your
answer as a vector. Show your work.
SOLUTION: Write the direction vector for Amy in component
form.
Due north is equivalent to 90° from the horizontal.
The component form for Amy’s vector is
Write the direction vector for wind in component
form.
40 east of north is equivalent to 50° from the horizontal.
81.6° with the horizontal is equivalent to 8.4° east of north.
The resultant velocity is about 12.3 feet per second
at a heading of 8.4°east of north, .
ANSWER: about 12.3 feet per second at a heading of 8.4°east of north,
9. Janice used a 16-inch dowel and a 21-inch dowel to
build a kite as shown below. What is the perimeter
her kite?
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The component form for the wind’s vector is
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SOLUTION: ANSWER: about 12.3 feet per second at a heading of 8.4°east Standardized
Test Practice - Cumulative, Chapters 1-8
of north,
9. Janice used a 16-inch dowel and a 21-inch dowel to
build a kite as shown below. What is the perimeter
her kite?
Therefore, the perimeter of the kite is 2(10 + 17)in or
54 in.
ANSWER: 54 in.
10. GRIDDED RESPONSE A model airplane takes
off at an angle of elevation of 30º. How high will the
plane be after traveling 100 feet horizontally? Round
to the nearest tenth. Show your work.
SOLUTION: Let x be the height of the plane from the ground after
traveling 100 ft horizontally.
Use tangent ratio to find the value of x.
SOLUTION: Use the Pythagorean theorem to find the side length
of the kite.
Find the length of the smaller side.
The diagonal divides the kite into two congruent
Isosceles triangles.
So, the other smaller side is also 10 in.
The plane is 57.7 ft high after traveling 100 feet
horizontally.
ANSWER: 57.7 ft
15. Refer to the triangle shown below.
The length of the longer side is 17 in.
Therefore, the perimeter of the kite is 2(10 + 17)in or
54 in.
ANSWER: 54 in.
10. GRIDDED RESPONSE A model airplane takes
off at an angle of elevation of 30º. How high will the
plane be after traveling 100 feet horizontally? Round
to the nearest tenth. Show your work.
SOLUTION: Let x be the height of the plane from the ground after
traveling 100 ft horizontally.
Use tangent ratio to find the value of x.
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a. Find x to the nearest tenth.
b. Find y to the nearest tenth.
c. Find z to the nearest tenth.
SOLUTION: Use the properties of similar triangles.
Separate all three triangles and show them according
to their similar sides.
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Standardized Test Practice - Cumulative, Chapters 1-8
Triangles with sides z, 12.5, x and y, x, 8 are similar.
Triangles with sides y, x, 8 and 20.5, z, y are similar.
Triangles with sides z, 12.5, x and 20.5, z, y are
similar.
ANSWER: a. 10
b. 12.8
c. 16.0
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