Question 1

Find the area of the triangle.
-

Accepted Answer

A)  $610.5 \mathrm { ft } ^ { 2 }$ 
B)  $544.5 \mathrm { ft } ^ { 2 }$ 
C)  $1320 \mathrm { ft } ^ { 2 }$ 
D)  $660 \mathrm { ft } ^ { 2 }$ 
A)  $610.5 \mathrm { ft } ^ { 2 }$ 
B)  $544.5 \mathrm { ft } ^ { 2 }$ 
C)  $1320 \mathrm { ft } ^ { 2 }$ 
D)  $660 \mathrm { ft } ^ { 2 }$

Question 2

Solve the problem.
-(i)In general terms, how does the surface-area-to-volume ratio of a squirrel compare to that of a moose?
(ii)Which animal must maintain a higher rate of metabolism to replace the heat lost through the
Skin?

Accepted Answer

A) (i)Cannot compare the two because one type of creature is a mammal and the other is not. (ii)Cannot compare the two because one type of creature is a mammal and the other is not. 
B) (i)The surface-area-to-volume ratio of a squirrel is equal to the surface-area-to-volume ratio of a moose.
(ii)Both animals must maintain the same rate of metabolism. 
C) (i)The surface-area-to-volume ratio of a squirrel is lower than the surface-area-to-volume ratio of a moose.
(ii)The moose must maintain a higher rate of metabolism. 
D) (i)The surface-area-to-volume ratio of a squirrel is higher than the surface-area-to-volume ratio of a moose.
(ii)The squirrel must maintain a higher rate of metabolism. 
A) (i)Cannot compare the two because one type of creature is a mammal and the other is not. (ii)Cannot compare the two because one type of creature is a mammal and the other is not. 
B) (i)The surface-area-to-volume ratio of a squirrel is equal to the surface-area-to-volume ratio of a moose.
(ii)Both animals must maintain the same rate of metabolism. 
C) (i)The surface-area-to-volume ratio of a squirrel is lower than the surface-area-to-volume ratio of a moose.
(ii)The moose must maintain a higher rate of metabolism. 
D) (i)The surface-area-to-volume ratio of a squirrel is higher than the surface-area-to-volume ratio of a moose.
(ii)The squirrel must maintain a higher rate of metabolism.

Question 3

Convert the given degree measure into degrees, minutes, and seconds of arc.
-$290.49 ^ { \circ }$

Accepted Answer

A)  $290 ^ { \circ } 29 ^ { \prime } 49 ^ { \prime \prime }$ 
B)  $290 ^ { \circ } 30 ^ { \prime } 23 ^ { \prime \prime }$ 
C)  $290 ^ { \circ } 23 ^ { \prime } 49 ^ { \prime \prime }$ 
D)  $290 ^ { \circ } 29 ^ { \prime } 24 ^ { \prime \prime }$ 
A)  $290 ^ { \circ } 29 ^ { \prime } 49 ^ { \prime \prime }$ 
B)  $290 ^ { \circ } 30 ^ { \prime } 23 ^ { \prime \prime }$ 
C)  $290 ^ { \circ } 23 ^ { \prime } 49 ^ { \prime \prime }$ 
D)  $290 ^ { \circ } 29 ^ { \prime } 24 ^ { \prime \prime }$

Question 4

Find the perimeter.
-

Accepted Answer

A)  $29 \mathrm {~cm}$ 
B)  $30 \mathrm {~cm}$ 
C)  $28 \mathrm {~cm}$ 
D)  $49 \mathrm {~cm}$ 
A)  $29 \mathrm {~cm}$ 
B)  $30 \mathrm {~cm}$ 
C)  $28 \mathrm {~cm}$ 
D)  $49 \mathrm {~cm}$

Question 5

Provide an appropriate response.
-In fractal geometry, the shorter the ruler .

Accepted Answer

A) the less accurate the measurement 
B) the longer the perimeter 
C) the more accurate the measurement 
D) the shorter the perimeter 
A) the less accurate the measurement 
B) the longer the perimeter 
C) the more accurate the measurement 
D) the shorter the perimeter

Question 6

Find the degree measure of the angle created by the given part of a circle.
-$\frac { 1 } { 4 }$ circle

Accepted Answer

A)  $120 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $72 ^ { \circ }$ 
A)  $120 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $72 ^ { \circ }$

Question 7

Convert the given angle measure into degrees and decimal fractions of a degree.
-$78 ^ { \circ } 57 ^ { \prime }$

Accepted Answer

A)  $78.91 ^ { \circ }$ 
B)  $79.01 ^ { \circ }$ 
C)  $78.96 ^ { \circ }$ 
D)  $78.95 ^ { \circ }$ 
A)  $78.91 ^ { \circ }$ 
B)  $79.01 ^ { \circ }$ 
C)  $78.96 ^ { \circ }$ 
D)  $78.95 ^ { \circ }$

Question 8

Convert the given angle measure into degrees and decimal fractions of a degree.
-$114 ^ { \circ } 20 ^ { \prime } 19 ^ { \prime \prime }$

Accepted Answer

A)  $114.339 ^ { \circ }$ 
B)  $114.299 ^ { \circ }$ 
C)  $114.349 ^ { \circ }$ 
D)  $114.399 ^ { \circ }$ 
A)  $114.339 ^ { \circ }$ 
B)  $114.299 ^ { \circ }$ 
C)  $114.349 ^ { \circ }$ 
D)  $114.399 ^ { \circ }$

Question 9

Find the dimension of the object and state whether or not it is a fractal.
-You generate the object from a line segment by deleting the middle third of each line segment of the current figure.

Accepted Answer

A) The dimension is between 1 and 2 and the object is fractal (Cantor set). 
B) The dimension is less than 1 and the object is fractal (Cantor set). 
C) The dimension is equal to 1 and the object is ordinary (non-fractal). 
D) The dimension is greater than 2 and the object is ordinary (non-fractal). 
A) The dimension is between 1 and 2 and the object is fractal (Cantor set). 
B) The dimension is less than 1 and the object is fractal (Cantor set). 
C) The dimension is equal to 1 and the object is ordinary (non-fractal). 
D) The dimension is greater than 2 and the object is ordinary (non-fractal).

Question 10

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

Accepted Answer

A)  $x = 10$ 
B)  $x = 7$ 
C)  $x = 14$ 
D)  $x = 21$ 
A)  $x = 10$ 
B)  $x = 7$ 
C)  $x = 14$ 
D)  $x = 21$

Question 11

Solve. Round your answer to the nearest tenth.
-Find the circumference of a circle with a diameter of 32 feet.

Accepted Answer

A) 50.2 ft 
B) 803.8 ft 
C) 100.5 ft 
D) 201.0 ft 
A) 50.2 ft 
B) 803.8 ft 
C) 100.5 ft 
D) 201.0 ft

Question 12

Provide an appropriate response.
-The fractal dimension of a coastline .

Accepted Answer

A) is less than 1 
B) is between 1 and 2 
C) is between 0 and 1 
D) is greater than 2 
A) is less than 1 
B) is between 1 and 2 
C) is between 0 and 1 
D) is greater than 2

Question 13

Solve the problem.
-You build an architectural model of a new office complex using a scale factor of 55. Suppose you wanted to fill both the scale model office complex and the actual office complex with marbles.
How many times the number of marbles required for the model would be required for the actual
Building?

Accepted Answer

A) 55 times as many 
B) 165 times as many 
C) 3025 times as many 
D) 166,375 times as many 
A) 55 times as many 
B) 165 times as many 
C) 3025 times as many 
D) 166,375 times as many

Question 14

Solve the problem.
-Find the area of the window. Round to the nearest tenth.

Accepted Answer

A)  $53.9 \mathrm { ft } ^ { 2 }$ 
B)  $59.8 \mathrm { ft } ^ { 2 }$ 
C)  $128.5 \mathrm { ft } ^ { 2 }$ 
D)  $89.3 \mathrm { ft } ^ { 2 }$ 
A)  $53.9 \mathrm { ft } ^ { 2 }$ 
B)  $59.8 \mathrm { ft } ^ { 2 }$ 
C)  $128.5 \mathrm { ft } ^ { 2 }$ 
D)  $89.3 \mathrm { ft } ^ { 2 }$

Question 15

Provide an appropriate response.
-The closer away an object is located from you, the smaller it will appear in angular size.

Accepted Answer

A) True 
 B)False

Question 16

Solve the problem.
-Suppose you build an architectural model of a new concert hall using a scale factor of 34. How will the volume of the actual concert hall compare to the volume of the square model?

Accepted Answer

A) 34 times as great 
B) 39,304 times as great 
C) 1156 times as great 
D) 102 times as great 
A) 34 times as great 
B) 39,304 times as great 
C) 1156 times as great 
D) 102 times as great

Question 17

Solve.
-Determine the area of a circular enclosure and a square enclosure made with 1495 yards of fence. Use $\pi = 3.1416 .$

Accepted Answer

A)  Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $558,756 \mathrm { yd } ^ { 2 }$ 
B)  Circular: $177,857 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$ 
C)  Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$ 
D)  $\text { Circular: } 177,857 \mathrm{yd}^{2} \text {; square: } 558,756 \mathrm{yd}^{2}$ 
A)  Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $558,756 \mathrm { yd } ^ { 2 }$ 
B)  Circular: $177,857 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$ 
C)  Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$ 
D)  $\text { Circular: } 177,857 \mathrm{yd}^{2} \text {; square: } 558,756 \mathrm{yd}^{2}$

Question 18

Convert the given degree measure into degrees, minutes, and seconds of arc.
-$59.14 ^ { \circ }$

Accepted Answer

A)  $59 ^ { \circ } 18 ^ { \prime } 24 ^ { \prime \prime }$ 
B)  $59 ^ { \circ } 8 ^ { \prime } 24 ^ { \prime \prime }$ 
C)  $59 ^ { \circ } 8 ^ { \prime } 14 ^ { \prime \prime }$ 
D)  $59 ^ { \circ } 18 ^ { \prime } 14 ^ { \prime \prime }$ 
A)  $59 ^ { \circ } 18 ^ { \prime } 24 ^ { \prime \prime }$ 
B)  $59 ^ { \circ } 8 ^ { \prime } 24 ^ { \prime \prime }$ 
C)  $59 ^ { \circ } 8 ^ { \prime } 14 ^ { \prime \prime }$ 
D)  $59 ^ { \circ } 18 ^ { \prime } 14 ^ { \prime \prime }$

Question 19

Find the perimeter and area of the figure.
-A square with sides of length 3.9 feet

Accepted Answer

A)  $P = 15.6 \mathrm { ft } , \mathrm { A } = 15.21 \mathrm { ft } ^ { 2 }$ 
B)  $P = 25.6 \mathrm { ft } , \mathrm { A } = 30.42 \mathrm { ft } ^ { 2 }$ 
C)  $P = 7.8 \mathrm { ft } , \mathrm { A } = 30.42 \mathrm { ft } ^ { 2 }$ 
D)  $P = 30.42 \mathrm { ft } , \mathrm { A } = 15.21 \mathrm { ft } ^ { 2 }$ 
A)  $P = 15.6 \mathrm { ft } , \mathrm { A } = 15.21 \mathrm { ft } ^ { 2 }$ 
B)  $P = 25.6 \mathrm { ft } , \mathrm { A } = 30.42 \mathrm { ft } ^ { 2 }$ 
C)  $P = 7.8 \mathrm { ft } , \mathrm { A } = 30.42 \mathrm { ft } ^ { 2 }$ 
D)  $P = 30.42 \mathrm { ft } , \mathrm { A } = 15.21 \mathrm { ft } ^ { 2 }$

Question 20

Use the formula relating angular size, physical size and distance.
-A planet has an angular diameter of about 0.9° and a distance of about 135 million kilometers. What is its true diameter?

Accepted Answer

A) 14.27 million kilometers 
B) 16.39 million kilometers 
C) 2.12 million kilometers 
D) 4.24 million kilometers 
A) 14.27 million kilometers 
B) 16.39 million kilometers 
C) 2.12 million kilometers 
D) 4.24 million kilometers

Find the area of the triangle. -

Solve the problem. -(i)In general terms, how does the surface-area-to-volume ratio of a squirrel compare to that of a moose? (ii)Which animal must maintain a higher rate of metabolism to replace the heat lost through the Skin?

Convert the given degree measure into degrees, minutes, and seconds of arc. - $290.49 ^ { \circ }$

Find the perimeter. -

Provide an appropriate response. -In fractal geometry, the shorter the ruler .

Find the degree measure of the angle created by the given part of a circle. - $\frac { 1 } { 4 }$ circle

Convert the given angle measure into degrees and decimal fractions of a degree. - $78 ^ { \circ } 57 ^ { \prime }$

Convert the given angle measure into degrees and decimal fractions of a degree. - $114 ^ { \circ } 20 ^ { \prime } 19 ^ { \prime \prime }$

Find the dimension of the object and state whether or not it is a fractal. -You generate the object from a line segment by deleting the middle third of each line segment of the current figure.

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

Solve. Round your answer to the nearest tenth. -Find the circumference of a circle with a diameter of 32 feet.

Provide an appropriate response. -The fractal dimension of a coastline .

Solve the problem. -Find the area of the window. Round to the nearest tenth.

Provide an appropriate response. -The closer away an object is located from you, the smaller it will appear in angular size.

Solve the problem. -Suppose you build an architectural model of a new concert hall using a scale factor of 34. How will the volume of the actual concert hall compare to the volume of the square model?

Solve. -Determine the area of a circular enclosure and a square enclosure made with 1495 yards of fence. Use $\pi = 3.1416 .$

Convert the given degree measure into degrees, minutes, and seconds of arc. - $59.14 ^ { \circ }$

Find the perimeter and area of the figure. -A square with sides of length 3.9 feet

Use the formula relating angular size, physical size and distance. -A planet has an angular diameter of about 0.9° and a distance of about 135 million kilometers. What is its true diameter?

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Probability: Living With the Odds

Exponential Astonishment

Modeling Our World

Mathematics and the Arts

Filters

Exam 10: Modeling With Geometry