Proportional Relationships: Master Proportions and Scale Factors

Question 1

In a classroom, the number of desks is directly proportional to the number of students. If there are 24 students in a class with 12 desks, how many students would there be in a class with 18 desks?

Accepted Answer

36

Answer

18

Answer

27

Answer

48

Question 2

A store offers a 15% discount on all items for customers with a loyalty card. If an item originally costs $40, what will be the discounted price?

Accepted Answer

$34

Answer

$25

Answer

$45

Answer

$50

Question 3

Which graph below represents a proportional relationship?

Accepted Answer

A line passing through the origin

Answer

A curve

Answer

A circle

Answer

A square

Question 4

If two shapes are similar, what is the ratio of the area of the larger shape to the area of the smaller shape?

Accepted Answer

The ratio of the squares of the corresponding sides

Answer

The ratio of the corresponding sides

Answer

The ratio of the perimeters

Answer

The ratio of the heights

Question 5

Which of the following statements about proportional relationships is true?

Accepted Answer

The slope of a proportional relationship is equal to the constant of proportionality.

Answer

The constant of proportionality is always less than 1.

Answer

The graph of a proportional relationship is an ellipse.

Answer

Proportional relationships are only useful in math class.

Question 6

Which equation represents a proportional relationship, where the ratio of y to x is constant?

Accepted Answer

y = 4x

Answer

y = 2x + 1

Answer

y = 3 - x

Answer

y = x^2

Question 7

Which of the following equations represents an inverse proportional relationship, where the product of y and x is constant?

Accepted Answer

y = 1/x

Answer

y = 2x

Answer

y = x^2

Answer

y = x + 1

Question 8

Which equation represents a proportional relationship?

Accepted Answer

y = 4x

Answer

y = 2x + 1

Answer

y = 3

Answer

y = x^2

Question 9

A recipe calls for 2 cups of flour to make 12 cookies. If you want to make 36 cookies, how much flour will you need?

Accepted Answer

6 cups

Answer

2 cups

Answer

12 cups

Answer

36 cups

Question 10

What is the scale factor if a model car is 1/40 the size of the actual car?

Accepted Answer

1/40

Answer

1/160

Answer

40

Answer

160

Question 11

If two triangles are similar, what do you know about the ratio of their side lengths?

Accepted Answer

They are all proportional.

Answer

They are all equal.

Answer

They are different for each triangle.

Answer

They cannot be determined.

Question 12

A company charges $10 for every 5 pounds of apples they sell. Which equation represents this relationship?

Accepted Answer

y = 10x

Answer

y = 2x

Answer

y = 5x

Answer

y = x/2

Question 13

Which of the following equations represents a relationship where the value of y is always twice the value of x?

Accepted Answer

y = 2x

Answer

y = x^2

Answer

y = 1/x

Answer

y = x + 2

Question 14

A company charges $5 for each hour of work. If a worker works 8 hours, how much will they earn?

Accepted Answer

$40

Answer

$5

Answer

$10

Answer

$20

Question 15

Which of the following graphs represents a proportional relationship?

Accepted Answer

(Image of a straight line passing through the origin with a positive slope)

Answer

(Image of a straight line not passing through the origin)

Answer

(Image of a parabola)

Answer

(Image of a circle)

Question 16

If a school has 200 students and the number of students increases by 10%, what is the new number of students?

Accepted Answer

210 students

Answer

180 students

Answer

200 students

Answer

220 students

Question 17

Which equation shows a proportional relationship between x and y?

Accepted Answer

y = 3x

Answer

y = x^2

Answer

y = 2 + x

Answer

y = 1 / x

Question 18

Which graph represents a proportional relationship?

Accepted Answer

A straight line passing through the origin

Answer

A straight line with a positive y-intercept

Answer

A curved line

Answer

A circle

Question 19

What is the main characteristic of a proportional relationship?

Accepted Answer

The ratio of the variables stays the same.

Answer

The graph of the relationship is always a curve.

Answer

The difference between the variables is constant.

Answer

The product of the variables is always positive.

Question 20

Which characteristic is NOT associated with proportional relationships?

Accepted Answer

Increase in one variable leads to decrease in the other

Answer

Constant ratio of corresponding parts

Answer

Linear graph passing through the origin

Answer

Expressible as y = kx

Question 21

If two similar figures have a scale factor of 2, and the length of a side in the smaller figure is 5 inches, what is the length of the corresponding side in the larger figure?

Accepted Answer

10 inches

Answer

2.5 inches

Answer

5 inches

Answer

20 inches

Question 22

Which graph represents a proportional relationship?

Accepted Answer

Straight line through the origin

Answer

Circle

Answer

Parabola

Answer

Hyperbola

Question 23

Identify the constant of proportionality in the equation: y = 4x

Accepted Answer

4

Answer

1

Answer

2

Answer

8

Question 24

Which graph best represents a proportional relationship?

Accepted Answer

A straight line passing through the origin

Answer

A parabola

Answer

A circle

Question 25

What is the equation of a proportional relationship if the constant of proportionality is 2?

Accepted Answer

y = 2x

Answer

y = x / 2

Question 26

Which of the following graphs best represents an inverse proportional relationship?

Accepted Answer

A hyperbola

Answer

A parabola

Question 27

What is a key characteristic of a proportional relationship?

Accepted Answer

The ratio of the quantities is constant.

Answer

The quantities are always equal.

Question 28

If y is directly proportional to x, and y = 10 when x = 5, what is the value of y when x = 15?

Accepted Answer

30

Answer

5

Answer

10

Answer

15

Question 29

Which of the following equations represents an inverse proportional relationship?

Accepted Answer

y = 1/x

Answer

y = 2x

Answer

y = x/2

Answer

y = x^2

Question 30

If two quantities A and B are proportional, and A = 12 when B = 6, what is the value of A when B = 10?

Accepted Answer

15

Answer

5

Answer

10

Answer

30

Question 31

What is the constant of proportionality in the equation y = 1/2x?

Accepted Answer

1/2

Answer

2

Answer

-1/2

Answer

-2

Question 32

Two triangles are similar. The first triangle has a base of 10 cm and a height of 8 cm. The second triangle has a base of 15 cm. What is the height of the second triangle?

Accepted Answer

12 cm

Answer

10 cm

Answer

8 cm

Answer

5 cm

Question 33

Which of the following equations represents a proportional relationship?

Accepted Answer

y = 2x

Answer

y = x + 3

Answer

y = 1/x

Answer

y = x^2

Question 34

A house blueprint is drawn to a scale of 1 inch to 5 feet. If the blueprint measures 12 inches long, what is the actual length of the house it shows?

Accepted Answer

60 feet

Answer

5 feet

Answer

15 feet

Answer

120 feet

Question 35

Which of the following graphs represents a proportional relationship?

Accepted Answer

A straight line passing through the origin

Answer

A curved line passing through the origin

Answer

A straight line not passing through the origin

Answer

A curved line not passing through the origin

Question 36

A grocery store sells bananas for $0.50 per pound. How much will it cost to buy 3 pounds of bananas?

Accepted Answer

$1.50

Answer

$0.50

Answer

$1.00

Answer

$2.00

Question 37

Which of the following is NOT a characteristic of a proportional relationship?

Accepted Answer

The relationship can be expressed as an equation of the form y = mx + b.

Answer

The ratio of the two quantities is constant.

Answer

The graph of the relationship is a straight line.

Answer

The relationship can be represented by a table of values.

Question 38

A recipe requires 2 cups of flour to make 12 cookies. Determine the number of cups of flour needed to make 30 cookies.

Accepted Answer

7.5

Answer

2.5

Answer

5

Answer

10

Question 39

A car travels 120 miles over a 2-hour period. Determine the car's average speed in miles per hour.

Accepted Answer

60 mph

Answer

40 mph

Answer

80 mph

Answer

100 mph

Question 40

What is the formula to calculate the scale factor of two similar figures?

Accepted Answer

Scale factor = Length of new figure / Length of original figure

Answer

Scale factor = Length of original figure / Length of new figure

Answer

Scale factor = Width of new figure / Width of original figure

Answer

Scale factor = Area of new figure / Area of original figure

Question 41

Two similar triangles have side lengths of 3 cm and 4 cm for one triangle, and 6 cm and 8 cm for the other. What is the scale factor of the larger triangle to the smaller triangle?

Accepted Answer

2:1

Answer

1:2

Answer

1:4

Answer

4:1

Question 42

A key characteristic of proportional relationships is that:

Accepted Answer

The ratio of the two variables is constant.

Answer

The sum of the two variables is constant.

Answer

The difference between the two variables is constant.

Answer

The product of the two variables is constant.

Question 43

Which of the following graphs represents a proportional relationship?

Accepted Answer

A line passing through the origin

Answer

A line not passing through the origin

Answer

A circle

Answer

A parabola

Question 44

If two quantities are inversely proportional, and one quantity decreases by 25%, what happens to the other quantity?

Accepted Answer

Decreases by 25%

Answer

Increases by 25%

Answer

Increases by 50%

Answer

Decreases by 50%

Question 45

A garden has a length of 10 feet and a width of 5 feet. If the length is increased by 50%, what will be the new area of the garden?

Accepted Answer

125 sq ft

Answer

75 sq ft

Answer

100 sq ft

Answer

150 sq ft

Question 46

Given the points (3, 6) and (6, 12), determine if the relationship is proportional. If it is, what is the constant of proportionality?

Accepted Answer

Yes, the constant of proportionality is 2.

Answer

No, the ratio of the changes is not constant.

Answer

Insufficient information is given.

Answer

Yes, the constant of proportionality is 3.

Question 47

Which equation represents a proportional relationship?

Accepted Answer

y = 3x

Answer

y = x^2

Answer

y = 1/x

Answer

y = 2 + x

Question 48

Which of the following graphs represents a proportional relationship?

Accepted Answer

Graph with a straight line passing through the origin

Answer

Graph with a circle

Answer

Graph with a parabola

Question 49

A store sells apples for $0.50 per pound. How much will it cost to buy 3.5 pounds of apples?

Accepted Answer

$1.75

Answer

$1.00

Answer

$2.50

Answer

$3.50

Question 50

Which of the following equations represents a proportional relationship?

Accepted Answer

y = 2x

Answer

y = x^2

Answer

y = x + 1

Answer

y = 1/x

Question 51

Which of the following statements is true about proportional relationships?

Accepted Answer

The ratio of the corresponding values is constant.

Answer

The sum of the corresponding values is constant.

Answer

The difference between the corresponding values is constant.

Answer

The product of the corresponding values is constant.

Question 52

A company charges a flat fee of $50 plus $10 per hour for its services. If a customer pays $120, how many hours of service did they receive?

Accepted Answer

7 hours

Answer

10 hours

Answer

5 hours

Question 53

Which of the following is not a way to represent a proportional relationship?

Accepted Answer

Table with non-constant ratios

Answer

Graph with a straight line passing through the origin

Answer

Equation with a constant of proportionality

Question 54

Which of the following equations represents a proportional relationship between x and y, where the constant of proportionality is 2?

Accepted Answer

y = 2x

Answer

y = x + 2

Answer

y = x^2

Answer

y = 1/x

Question 55

A grocery store sells apples for $0.50 each. If you buy 6 apples, how much will you pay?

Accepted Answer

$3.00

Answer

$3.50

Answer

$2.50

Question 56

Which of the following graphs represents a proportional relationship?

Accepted Answer

A straight line passing through the origin

Answer

A circle

Answer

A parabola

Answer

A hyperbola

Question 57

Which of the following is a characteristic of proportional relationships?

Accepted Answer

The ratio of the variables remains constant as the values increase.

Answer

The variables vary inversely with each other.

Answer

The graph is a curved line.

Question 58

Which of the following equations represents an inverse proportional relationship, where the constant of proportionality is k?

Accepted Answer

y = k/x

Answer

y = x - k

Answer

y = kx

Answer

y = x + k

Question 59

A recipe requires 2 cups of flour to make 12 cookies. If you want to make 36 cookies, how many cups of flour will you need?

Accepted Answer

6

Answer

1

Answer

12

Answer

3

Question 60

A map has a scale of 1:100,000. If the distance between two cities on the map is 10 cm, what is the actual distance between the cities?

Accepted Answer

100 km

Answer

50 km

Answer

25 km

Answer

200 km

Question 61

Which of the following equations represents a proportional relationship, where the variable y varies directly with the variable x?

Accepted Answer

y = 2x

Answer

y = x + 1

Answer

y = 1/x

Answer

y = x^2

Question 62

A rectangular garden has a length of 12 feet and a width of 8 feet. If the length of the garden is increased to 18 feet, what is the new scale factor?

Accepted Answer

3/2

Answer

2/3

Answer

1/2

Answer

4/3

Question 63

Which of the following graphs represents a proportional relationship?

Accepted Answer

A straight line passing through the origin

Answer

A hyperbola

Answer

A circle

Answer

A parabola

Question 64

A store sells apples at a rate of 3 apples for $1. What is the constant of proportionality that represents the unit rate?

Accepted Answer

1/3

Answer

3 apples

Answer

3

Answer

$1