Question 1

Find the fraction of a circle that encloses the given angle.
-$3 ^ { \circ }$

Accepted Answer

A)    1105\frac { 1 } { 105 }1051​ 
B)    190\frac { 1 } { 90 }901​ 
C)    130\frac { 1 } { 30 }301​ 
D)    1120\frac { 1 } { 120 }1201​ D

Question 2

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. 
-Find the straight-line distance between the bus stop and the theater.

Accepted Answer

A)  1.27 mi
B)  1.58 mi
C)  1.33 mi
D)  1.50 mi  A

Question 3

Solve the problem.
-Steve is 11% taller than Andy but proportioned in exactly the same way. If Andy is 75 inches tall, how tall is Steve?

Accepted Answer

A)  91 in.
B)  80 in.
C)  87 in.
D)  83 in. D

Question 4

Provide an appropriate response.
-Determine which surface is steeper between a road with a 26% grade or a road with a pitch of 1 in 2.

Accepted Answer

A)  a road with a pitch of 1 in 2
B)  a road with a 26% grade

Question 5

Provide an appropriate response.
-What mathematical tool is helpful in finding the fractal dimension?

Accepted Answer

A)  iteration
B)  integration
C)  tangent
D)  logarithm

Question 6

Use the formula relating angular size, physical size and distance.
-A planet has an angular diameter of about 1° and a distance of about 88 million kilometers. What is its true diameter?

Accepted Answer

A)  1.54 million kilometers
B)  10.34 million kilometers
C)  11.87 million kilometers
D)  3.07 million kilometers

Question 7

Find the dimension of the object and state whether or not it is a fractal.
-In measuring the volume of the object, when you reduce the length of your ruler by a factor of 3 the number of length elements increases by a factor of 27.

Accepted Answer

A)  The dimension is 1 and the object is ordinary (non-fractal) .
B)  The dimension is 2 and the object is ordinary (non-fractal) .
C)  The dimension is 3 and the object is a fractal.
D)  The dimension is 3 and the object is ordinary (non-fractal) .

Question 8

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. 
-Find the straight-line distance between the bus stop and the library.

Accepted Answer

A)  1.62 mi
B)  1.35 mi
C)  1.44 mi
D)  1.85 mi

Question 9

Solve the problem.
-City A is nearly at the same longitude as City B, but City A's latitude is 52°N while City B's latitude is 17°N. About how far away is City A from City B?

Accepted Answer

A)  3500 mi
B)  4830 mi
C)  2450 mi
D)  6900 mi

Question 10

Use the formula relating angular size, physical size and distance.
-What is the angular size of a quarter viewed from a distance of 20 yards?

Accepted Answer

A)  2.86°
B)  4.2°
C)  0.17°
D)  0.08°

Question 11

Find the area of the triangle.
-

Accepted Answer

A)    1104.5mi21104.5 \mathrm { mi } ^ { 2 }1104.5mi2 
B)    611mi2611 \mathrm { mi } ^ { 2 }611mi2 
C)    2444mi22444 \mathrm { mi } ^ { 2 }2444mi2 
D)    1222mi21222 \mathrm { mi } ^ { 2 }1222mi2

Question 12

Find the area of the triangle.
-

Accepted Answer

A)    1087.5ft21087.5 \mathrm { ft } ^ { 2 }1087.5ft2 
B)    1250ft21250 \mathrm { ft } ^ { 2 }1250ft2 
C)    2175ft22175 \mathrm { ft } ^ { 2 }2175ft2 
D)    1350ft21350 \mathrm { ft } ^ { 2 }1350ft2

Question 13

Solve.
-A 12-foot fence on the property line would cast a 20-foot shadow on the shortest day of the year, and the north side of the house is set back 60 feet from the property line. Find the maximum
Allowed height of the house.

Accepted Answer

A)  56 ft
B)  36 ft
C)  40 ft
D)  48 ft

Question 14

Find the dimension of the object and state whether or not it is a fractal.
-In measuring the area of the object, when you reduce the length of your ruler by a factor of 4 the number of length elements increases by a factor of 16.

Accepted Answer

A)  The dimension is 1 and the object is ordinary (non-fractal) .
B)  The dimension is 2 and the object is ordinary (non-fractal) .
C)  The dimension is 4 and the object is a fractal.
D)  The dimension is 3 and the object is ordinary (non-fractal) .

Question 15

Solve the problem.
-Suppose you build an architectural model of a new office complex using a scale factor of 67. How will the amount of paint needed for the exterior of the actual office complex compare to the amount
Of paint needed for the scale model?

Accepted Answer

A)  67 times as much
B)  134 times as much
C)  4489 times as much
D)  300,763 times as much

Question 16

Refer to the given map. Assume that the length of each east-west block is $\frac { 1 } { 8 }$ mile and the length of each north-southblock is $\frac { 1 } { 4 }$ mile. 
-Find the straight-line distance between the grocery store and the library.

Accepted Answer

A)  0.75 mi
B)  0.63 mi
C)  0.48 mi
D)  0.56 mi

Question 17

Provide an appropriate response.
-Who was the first mathematician to summarize many of the ideas of geometry?

Accepted Answer

A)  Euclid
B)  Pascal
C)  Pythagoras
D)  Newton

Question 18

Provide an appropriate response.
-Longitude measures positions east or west position.

Accepted Answer

A) True 
 B)False

Question 19

The two triangles below are similar. Find the missing lengths.
-

Accepted Answer

A)    x=22.5;y=31.5x = 22.5 ; y = 31.5x=22.5;y=31.5 
B)    x=7;y=13x = 7 ; y = 13x=7;y=13 
C)    x=12;y=16x = 12 ; y = 16x=12;y=16 
D)    x=10;y=14x = 10 ; y = 14x=10;y=14

Question 20

Solve. Round your answer to the nearest tenth.
-Find the area of a circle with a diameter of 7 centimeters.

Accepted Answer

A)    44 cm244 \mathrm {~cm} ^ { 2 }44 cm2 
B)    22 cm222 \mathrm {~cm} ^ { 2 }22 cm2 
C)    153.9 cm2153.9 \mathrm {~cm} ^ { 2 }153.9 cm2 
D)    38.5 cm238.5 \mathrm {~cm} ^ { 2 }38.5 cm2

Exam 10: Modeling With Geometry

Find the fraction of a circle that encloses the given angle. - $3 ^ { \circ }$

Solve the problem. -Steve is 11% taller than Andy but proportioned in exactly the same way. If Andy is 75 inches tall, how tall is Steve?

Provide an appropriate response. -Determine which surface is steeper between a road with a 26% grade or a road with a pitch of 1 in 2.

Provide an appropriate response. -What mathematical tool is helpful in finding the fractal dimension?

Use the formula relating angular size, physical size and distance. -A planet has an angular diameter of about 1° and a distance of about 88 million kilometers. What is its true diameter?

Find the dimension of the object and state whether or not it is a fractal. -In measuring the volume of the object, when you reduce the length of your ruler by a factor of 3 the number of length elements increases by a factor of 27.

Solve the problem. -City A is nearly at the same longitude as City B, but City A's latitude is 52°N while City B's latitude is 17°N. About how far away is City A from City B?

Use the formula relating angular size, physical size and distance. -What is the angular size of a quarter viewed from a distance of 20 yards?

Find the area of the triangle. - $Find the area of the triangle. - A) 1104.5 \mathrm { mi } ^ { 2 } B) 611 \mathrm { mi } ^ { 2 } C) 2444 \mathrm { mi } ^ { 2 } D) 1222 \mathrm { mi } ^ { 2 }$

Find the area of the triangle. - $Find the area of the triangle. - A) 1087.5 \mathrm { ft } ^ { 2 } B) 1250 \mathrm { ft } ^ { 2 } C) 2175 \mathrm { ft } ^ { 2 } D) 1350 \mathrm { ft } ^ { 2 }$

Solve. -A 12-foot fence on the property line would cast a 20-foot shadow on the shortest day of the year, and the north side of the house is set back 60 feet from the property line. Find the maximum Allowed height of the house.

Find the dimension of the object and state whether or not it is a fractal. -In measuring the area of the object, when you reduce the length of your ruler by a factor of 4 the number of length elements increases by a factor of 16.

Solve the problem. -Suppose you build an architectural model of a new office complex using a scale factor of 67. How will the amount of paint needed for the exterior of the actual office complex compare to the amount Of paint needed for the scale model?

Provide an appropriate response. -Who was the first mathematician to summarize many of the ideas of geometry?

Provide an appropriate response. -Longitude measures positions east or west position.

The two triangles below are similar. Find the missing lengths. -

Solve. Round your answer to the nearest tenth. -Find the area of a circle with a diameter of 7 centimeters.