Question 1

A model of a truck is built to a scale of 1 to 54. If the model will hold 7 cubic inches, how much will the actual truck hold?

Accepted Answer

A)  378 cubic feet 
B)  638 cubic feet 
C)  1544 cubic feet 
D)  4536 cubic feet 
A)  378 cubic feet 
B)  638 cubic feet 
C)  1544 cubic feet 
D)  4536 cubic feet B

Question 2

Create an example of an advertisement which misuses proportional change through its use of percent growth.

Accepted Answer

For example, "Half-price rings another 25% off" implies a 75% discount.

Question 3

A spherical balloon has a circumference of 10 inches. If it expands to twice the volume, what happens to its surface area?

Accepted Answer

A)  Its surface area more than doubles. 
B)  Its surface area doubles. 
C)  Its surface area increases but does not double. 
A)  Its surface area more than doubles. 
B)  Its surface area doubles. 
C)  Its surface area increases but does not double. C

Question 4

The cost of photographic paper is nearly proportional to the area of the paper. You own a painting whose dimensions are 24 inches by 30 inches. You create a photographic reproduction whose smaller side is 8 inches. How does its area compare with that of the original painting?

Accepted Answer

A)  0.3333 
B)  0.2667 
C)  0.1111 
D)  0.0711 
A)  0.3333 
B)  0.2667 
C)  0.1111 
D)  0.0711

Question 5

An artist wishes to melt 2000 copper pennies to create a large penny proportional to an ordinary penny. The diameter of a penny is approximately 3/4 in. What will be the diameter of the large penny?

Accepted Answer

A)  approximately 0.78 ft 
B)  approximately 2.2 ft 
C)  approximately 5 ft 
D)  approximately 9.4 ft 
A)  approximately 0.78 ft 
B)  approximately 2.2 ft 
C)  approximately 5 ft 
D)  approximately 9.4 ft

Question 6

You own a painting whose dimensions are 24 inches by 30 inches. If you create a full-size copy of this painting as a poster, what is the scaling factor for the poster?

Accepted Answer

A)  1 
B)  4/5 
C)  1/24 
D)  1/30 
A)  1 
B)  4/5 
C)  1/24 
D)  1/30

Question 7

Ground steak costs about $2.50 per pound in the United States. If an Australian dollar exchanges for 80 U.S. cents and a kilogram is about 2.2 pounds, what is the equivalent cost in Australian dollars?

Accepted Answer

A)  $0.91 per kilogram 
B)  $1.42 per kilogram 
C)  $4.40 per kilogram 
D)  $6.88 per kilogram 
A)  $0.91 per kilogram 
B)  $1.42 per kilogram 
C)  $4.40 per kilogram 
D)  $6.88 per kilogram

Question 8

A scale model of a truck is 5 inches long. If the model is built to a scale of 1 to 54, what is the length of the actual truck?

Accepted Answer

A)  270 feet 
B)  101 feet 
C)  36.7 feet 
D)  22.5 feet 
A)  270 feet 
B)  101 feet 
C)  36.7 feet 
D)  22.5 feet

Question 9

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 11 inches by 17 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?

Accepted Answer

11/24, app

Question 10

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 8.5 inches by 11 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?

Accepted Answer

8.5/24, ap

Question 11

If points (1,23) and (3,38) lie on the graph of y = bxa, solve for a.

Accepted Answer

A)  $a$ = 0.200 
B)  $a$ = 0.457 
C)  $a$ = 0.810 
D)  $a$ = 1.235 
A)  $a$ = 0.200 
B)  $a$ = 0.457 
C)  $a$ = 0.810 
D)  $a$ = 1.235

Question 12

If a car drives 230 km in 3 hours, in how many hours can the car drive 150 miles?

Accepted Answer

A)  2.6 
B)  2.9 
C)  3.2 
D)  3.7 
A)  2.6 
B)  2.9 
C)  3.2 
D)  3.7

Question 13

Why is allometric growth an appropriate model when the National Center for Missing and Exploited Children create sketches of missing people?

Accepted Answer

Children's features

Question 14

Why do spike heels cause more damage to hardwood floors than loafers?

Accepted Answer

The weight is suppor

Question 15

Melissa's tractor-trailer gets 5 miles per gallon. What is this in kilometers per liter?

Accepted Answer

A)  about 2 km per liter 
B)  about 10 km per liter 
C)  about 20 km per liter 
D)  None of the above. 
A)  about 2 km per liter 
B)  about 10 km per liter 
C)  about 20 km per liter 
D)  None of the above.

Question 16

Multiply the following measurements and give an answer with the correct number of significant digits: 3.1 cm, 2.15 cm, and 0.5 cm.

Accepted Answer

A)  3.3325 $\mathrm { cm } ^ { 3 }$ 
B)  3.3 $\mathrm { cm } ^ { 3 }$ 
C)  3 $\mathrm { cm } ^ { 3 }$ 
D)  3.0 $\mathrm { cm } ^ { 3 }$ 
A)  3.3325 $\mathrm { cm } ^ { 3 }$ 
B)  3.3 $\mathrm { cm } ^ { 3 }$ 
C)  3 $\mathrm { cm } ^ { 3 }$ 
D)  3.0 $\mathrm { cm } ^ { 3 }$

Question 17

How does a whale's size affect the depth to which it can descend into the water?

Accepted Answer

For exampl

Question 18

When comparing prices for pizzas, you discover that the large pizza has twice as much surface area of a medium pizza and costs less than two medium pizzas. However, your group decides to order two medium pizzas anyway. What additional factors could be omitted in the mathematical model?

Accepted Answer

for exampl

Question 19

Apples cost about $1.75 Canadian dollars per kilogram in Canada. If a Canadian dollar exchanges for 75 U.S. cents and a kilogram is about 2.2 pounds, what is the equivalent cost in U.S. dollars?

Accepted Answer

A)  $0.60 U.S. per pound 
B)  $1.06 U.S. per pound 
C)  $2.89 U.S. per pound 
D)  $5.13 U.S. per pound 
A)  $0.60 U.S. per pound 
B)  $1.06 U.S. per pound 
C)  $2.89 U.S. per pound 
D)  $5.13 U.S. per pound

Question 20

A section of US farm land is a square mile. This is about:

Accepted Answer

A)  200 hectares. 
B)  250 hectares. 
C)  260 hectares. 
D)  300 hectares. 
A)  200 hectares. 
B)  250 hectares. 
C)  260 hectares. 
D)  300 hectares.

Exam 18: Growth and Form

A model of a truck is built to a scale of 1 to 54. If the model will hold 7 cubic inches, how much will the actual truck hold?

Create an example of an advertisement which misuses proportional change through its use of percent growth.

A spherical balloon has a circumference of 10 inches. If it expands to twice the volume, what happens to its surface area?

The cost of photographic paper is nearly proportional to the area of the paper. You own a painting whose dimensions are 24 inches by 30 inches. You create a photographic reproduction whose smaller side is 8 inches. How does its area compare with that of the original painting?

An artist wishes to melt 2000 copper pennies to create a large penny proportional to an ordinary penny. The diameter of a penny is approximately 3/4 in. What will be the diameter of the large penny?

You own a painting whose dimensions are 24 inches by 30 inches. If you create a full-size copy of this painting as a poster, what is the scaling factor for the poster?

Ground steak costs about $2.50 per pound in the United States. If an Australian dollar exchanges for 80 U.S. cents and a kilogram is about 2.2 pounds, what is the equivalent cost in Australian dollars?

A scale model of a truck is 5 inches long. If the model is built to a scale of 1 to 54, what is the length of the actual truck?

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 11 inches by 17 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 8.5 inches by 11 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?

If points (1,23) and (3,38) lie on the graph of y = bxa, solve for a.

If a car drives 230 km in 3 hours, in how many hours can the car drive 150 miles?

Why is allometric growth an appropriate model when the National Center for Missing and Exploited Children create sketches of missing people?

Why do spike heels cause more damage to hardwood floors than loafers?

Melissa's tractor-trailer gets 5 miles per gallon. What is this in kilometers per liter?

Multiply the following measurements and give an answer with the correct number of significant digits: 3.1 cm, 2.15 cm, and 0.5 cm.

How does a whale's size affect the depth to which it can descend into the water?

When comparing prices for pizzas, you discover that the large pizza has twice as much surface area of a medium pizza and costs less than two medium pizzas. However, your group decides to order two medium pizzas anyway. What additional factors could be omitted in the mathematical model?

Apples cost about $1.75 Canadian dollars per kilogram in Canada. If a Canadian dollar exchanges for 75 U.S. cents and a kilogram is about 2.2 pounds, what is the equivalent cost in U.S. dollars?

A section of US farm land is a square mile. This is about:

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

Filters

If points (1,23) and (3,38) lie on the graph of y = bx^a, solve for a.