Ratio, Proportion and Rates of Change Quizzes - Test Your Understanding

Question 1

A swimming pool is filled at a rate of 10 gallons per minute. How many gallons of water will be in the pool after 30 minutes?

Accepted Answer

300

Answer

15

Answer

30

Answer

600

Question 2

Which statement represents a proportion?

Accepted Answer

12 is to 4 as 3 is to 1

Answer

12 + 4 = 3 + 1

Answer

12 - 4 = 3 - 1

Answer

12 ÷ 4 = 3 ÷ 1

Question 3

A rectangular garden measures 10 meters in length and 5 meters in width. If the length is increased by 20%, what is the percentage increase in the area?

Accepted Answer

25%

Answer

10%

Answer

15%

Answer

20%

Question 4

A car travels 240 kilometers in 4 hours. What is its average speed in miles per hour (mph)? (1 mile = 1.609 kilometers)

Accepted Answer

97 mph

Answer

60 mph

Answer

120 mph

Answer

153 mph

Question 5

A car travels 120 miles in 2 hours. What is the car's average speed in miles per hour?

Accepted Answer

60

Answer

50

Answer

70

Answer

80

Question 6

A recipe calls for 3 cups of flour to 2 cups of sugar. If I want to double the recipe, how many cups of sugar will I need?

Accepted Answer

6

Answer

3

Answer

4

Answer

5

Question 7

A car travels 120 miles in 2 hours. What is its average speed in miles per hour?

Accepted Answer

60

Answer

30

Answer

80

Answer

100

Question 8

The scale of a map is 1 cm to 5 km. What is the actual distance between two cities that are 12 cm apart on the map?

Accepted Answer

60 km

Answer

24 km

Answer

80 km

Answer

100 km

Question 9

A company's profit increases from £10,000 to £12,000 in one year. What percentage increase in profit is this?

Accepted Answer

15%

Answer

10%

Answer

20%

Answer

25%

Question 10

A population of bacteria doubles every 2 hours. If the population starts with 100 bacteria, how many bacteria will there be after 6 hours?

Accepted Answer

1600

Answer

200

Answer

400

Answer

800

Question 11

A car travels 240 miles in 4 hours. What is the average speed of the car?

Accepted Answer

60 miles per hour

Answer

40 miles per hour

Answer

80 miles per hour

Answer

100 miles per hour

Question 12

What is the ratio of 3 meters to 5 meters?

Accepted Answer

3:5

Answer

5:3

Answer

0.75

Answer

1

Question 13

Which of the following is an example of a proportion?

Accepted Answer

10 is to 5 as 20 is to 10

Answer

The area of a square is equal to the square of its side length

Answer

The volume of a cube is three times its side length

Answer

The sum of two numbers is 10

Question 14

The distance between two towns is 150 miles. A car travels the first half of the distance at 60 mph and the second half at 80 mph. What is the average speed of the car?

Accepted Answer

63.5 mph

Answer

62.5 mph

Answer

64.5 mph

Answer

65.5 mph

Question 15

Which of the following is a graph of a linear relationship?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

An ellipse

Question 16

Identify the equation that represents a proportion:

Accepted Answer

2:3 = 4:6

Answer

2 + 3 = 4 + 6

Answer

2 - 3 = 4 - 6

Answer

2 x 3 = 4 x 6

Question 17

A company employs 120 people, consisting of 60 males and 60 females. Express the ratio of male to female employees in its simplest form.

Accepted Answer

1:1

Answer

1:2

Answer

2:1

Answer

2:3

Question 18

A rectangular garden has a length of 6 meters and a width of 4 meters. If the garden is enlarged to have a length of 12 meters, what is the scale factor of the enlargement?

Accepted Answer

2:1

Answer

1:2

Answer

1:3

Answer

3:1

Question 19

What is the formula for finding the mean proportional between two numbers, a and b?

Accepted Answer

√ab

Answer

a + b

Answer

a - b

Answer

ab

Question 20

Which expression is NOT a valid ratio?

Accepted Answer

100%

Answer

1:2

Answer

3/4

Answer

2 out of 3

Question 21

Simplify the ratio 12:18 to its lowest form.

Accepted Answer

2:3

Answer

3:2

Answer

4:6

Answer

6:4

Question 22

Which of the following equations represents a direct proportion?

Accepted Answer

y = 2x

Answer

y = x^2

Answer

y = 1/x

Answer

y = log(x)

Question 23

Which of the following scenarios represents an inverse proportion?

Accepted Answer

The volume of a gas and its pressure

Answer

The number of workers needed and the time taken to complete a task

Answer

The distance traveled and the speed of a car

Answer

The temperature of a liquid and its boiling point

Question 24

Which of the following is NOT a type of ratio?

Accepted Answer

Part-to-whole-to-part

Answer

Part-to-part

Answer

Part-to-whole

Answer

Whole-to-whole

Question 25

Which of the following is a proportion?

Accepted Answer

3:6 = 1:2

Answer

3:6 < 1:2

Answer

3:6 > 1:2

Answer

3 + 6 = 1 + 2

Question 26

Solve for x in the proportion: 5:x = 3:6

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 27

Which of the following graphs represents a positive rate of change?

Accepted Answer

A straight line with a positive slope

Answer

A parabola that opens downwards

Answer

A hyperbola that has a negative slope

Answer

A circle

Question 28

A train travels 120 miles in 2 hours. What is the average speed of the train in miles per hour?

Accepted Answer

60 mph

Answer

30 mph

Answer

90 mph

Answer

120 mph

Question 29

The scale factor of a model of a car is 1:10. If the length of the actual car is 5 meters, what is the length of the model?

Accepted Answer

0.5 m

Answer

0.75 m

Answer

1 m

Answer

1.5 m

Question 30

A train travels at a speed of 80 km/h. How many meters does it travel in 1 minute?

Accepted Answer

1333 m

Answer

800 m

Answer

2667 m

Answer

4000 m

Question 31

A cyclist travels 15 km in 30 minutes. What is their average speed in meters per second (m/s)?

Accepted Answer

6.25 m/s

Answer

7.5 m/s

Answer

8.75 m/s

Answer

10 m/s

Question 32

The scale of a map is 1:25,000. What is the actual distance between two towns if the distance on the map is 5 centimeters?

Accepted Answer

1.25 kilometers

Answer

1 kilometer

Answer

1.5 kilometers

Answer

1.75 kilometers

Question 33

In the equation y = 4x, what is the constant of variation?

Accepted Answer

4

Answer

1

Answer

2

Answer

8

Question 34

A car travels an average of 50 mph. If it travels 200 miles, how many hours did the journey take?

Accepted Answer

4 hours

Answer

2 hours

Answer

3 hours

Answer

5 hours

Question 35

Which of the following is NOT a proportion?

Accepted Answer

12:6 = 18:9

Answer

1/2 = 2/4

Answer

3:6 = 1:2

Answer

5/8 = 10/16

Question 36

The scale factor of a map is 1:50000. What is the actual distance represented by 10 cm on the map?

Accepted Answer

5 km

Answer

25000 cm

Answer

50000 cm

Answer

10 km

Question 37

A car travels 120 miles in 2 hours. Calculate the average speed of the car in miles per hour (mph).

Accepted Answer

60 mph

Answer

40 mph

Answer

80 mph

Answer

100 mph

Question 38

In a class, the ratio of boys to girls is 2:3. If there are 24 boys in the class, how many girls are there?

Accepted Answer

18

Answer

12

Answer

24

Answer

30

Question 39

The ratio of the length of a side of a square to its perimeter is 1:4. Calculate the length of a side of the square in centimeters (cm).

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 40

The value of a car depreciates by 10% each year. If a car is currently worth £12,000, what will be its value in 5 years?

Accepted Answer

£8,219

Answer

£12,000

Answer

£10,800

Answer

£9,600

Question 41

A bag has 2 red marbles, 3 blue marbles, and 5 green marbles. What is the ratio of red marbles to the total number of marbles in the bag?

Accepted Answer

2:10

Answer

1:5

Answer

1:3

Answer

2:3

Question 42

A map has a scale of 1:50,000. If the distance between two towns on the map is 6 cm, what is the actual distance between the towns in kilometers?

Accepted Answer

3

Answer

60

Answer

30

Answer

0.3

Question 43

The price of a movie ticket is in the ratio of 3:4 to the price of a popcorn. If a movie ticket costs £6, what is the cost of a popcorn?

Accepted Answer

£8

Answer

£4

Answer

£12

Answer

£3

Question 44

A recipe needs 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 36 cookies?

Accepted Answer

6

Answer

2

Answer

3

Answer

9

Question 45

A company produces 200 units per hour. If the production rate stays the same, how many units will be produced in 3 hours?

Accepted Answer

600

Answer

1200

Answer

100

Answer

300

Question 46

The scale factor between a model and the real object is 1:25. If the model is 10 cm tall, how tall is the real object?

Accepted Answer

250 cm

Answer

125 cm

Answer

10 cm

Answer

50 cm

Question 47

A ball is dropped from a height of 50m. Its height after t seconds is given by the formula h(t) = 50 - 5t. What is the ball's initial velocity (rate of change of height at t=0)?

Accepted Answer

-5 m/s

Answer

5 m/s

Answer

0 m/s

Answer

-10 m/s

Question 48

A company's revenue is decreasing at a rate of 5% per quarter. If the current revenue is £100,000, what will be the revenue in 4 quarters?

Accepted Answer

£85,738

Answer

£80,000

Answer

£70,000

Answer

£90,000