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

Question 1

A map has a scale of 1 cm to 50000 cm. A building on the map is 4 cm long. What is the actual length of the building in centimeters?

Accepted Answer

200000

Answer

20000

Answer

250000

Answer

50000

Question 2

An investment of £5,000 is invested for 10 years at an annual interest rate of 5%, compounded annually. Calculate the total amount of money in the investment after the 10-year period.

Accepted Answer

£5,512.50

Answer

£5,250

Answer

£6,000

Answer

£5,000

Question 3

A recipe requires 3 cups of flour to 2 cups of sugar. Express the proportion of sugar to flour in the recipe.

Accepted Answer

3:2

Answer

2:3

Answer

2:5

Answer

3:5

Question 4

If the scale of a map is 1:50000, what is the actual distance between two points on the map that are 5 cm apart?

Accepted Answer

250 m

Answer

100 m

Answer

500 m

Answer

1000 m

Question 5

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

Accepted Answer

6

Answer

3

Answer

4

Answer

8

Question 6

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

Accepted Answer

60

Answer

40

Answer

80

Answer

100

Question 7

Which of the following accurately defines a ratio?

Accepted Answer

A comparison of two or more quantities expressed as their relative sizes

Answer

A fraction representing a portion of a whole

Answer

The difference between two quantities

Answer

The product of two quantities

Question 8

The ratio 3:4 can be written as which of the following fractions?

Accepted Answer

3/4

Answer

1/4

Answer

1/8

Answer

4/3

Question 9

What does a constant slope on a graph of a rate of change indicate?

Accepted Answer

Constant rate of change

Answer

Increasing rate of change

Answer

Decreasing rate of change

Answer

Zero rate of change

Question 10

Which graph represents a direct proportion between two quantities?

Accepted Answer

A straight line passing through the origin

Answer

A curve with increasing steepness as the x-value increases

Answer

A curve with decreasing steepness as the x-value increases

Answer

A parabola that opens upwards

Question 11

A car travels 150 miles in 2.5 hours. Determine the car's average speed in miles per hour.

Accepted Answer

62.5

Answer

60

Answer

50

Answer

55

Question 12

A town with 10,000 residents has a yearly population growth rate of 1.5%. What will be the town's population after 3 years?

Accepted Answer

10,459

Answer

10,150

Answer

10,618

Answer

10,780

Question 13

A car travels 240 miles in 4 hours. Calculate its average speed in miles per hour.

Accepted Answer

50

Answer

40

Answer

60

Answer

70

Question 14

A car travels 240 miles in 4 hours. What is its average speed in miles per hour?

Accepted Answer

60 mph

Answer

40 mph

Answer

80 mph

Answer

120 mph

Question 15

A recipe requires 3 cups of flour to make 12 cookies. How many cups of flour are needed to make 18 cookies?

Accepted Answer

6

Answer

4.5

Answer

9

Answer

12

Question 16

The ratio of the number of boys to the number of girls in a class is 2:3. If there are 18 boys, how many girls are there?

Accepted Answer

27

Answer

12

Answer

36

Answer

54

Question 17

Which of the following is equivalent to the ratio 3:5?

Accepted Answer

3/5

Answer

5/3

Answer

15:8

Answer

8:15

Question 18

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

Accepted Answer

60 km/h

Answer

40 km/h

Answer

80 km/h

Answer

100 km/h

Question 19

A company increases its production output by 20%. If the original production was 500 units, what is the new production output?

Accepted Answer

600 units

Answer

550 units

Answer

650 units

Answer

700 units

Question 20

An investment of $1000 is deposited into an account that earns 5% interest per year, compounded annually. What will be the total amount of money in the account after 10 years?

Accepted Answer

$1628.89

Answer

$1500

Answer

$1750

Answer

$1800

Question 21

A car depreciates in value by 20% each year. If the car was initially worth £20000, what will be its value after 3 years?

Accepted Answer

£10648

Answer

£15000

Answer

£9600

Answer

£12000

Question 22

Which equation represents a linear relationship?

Accepted Answer

y = 2x + 1

Answer

y = sin(x)

Answer

y = 1/x

Answer

y = x^2

Question 23

Which of the following equations represents an inverse proportion?

Accepted Answer

y = k/x

Answer

y = kx^2

Answer

y = k*sin(x)

Answer

y = kx + 1

Question 24

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

Accepted Answer

1.5

Answer

2

Answer

1

Answer

3

Question 25

The population of a town is increasing at a rate of 2% per year. If the current population is 10,000, what will be the population in 5 years?

Accepted Answer

11,025

Answer

10,200

Answer

13,000

Answer

12,000

Question 26

The ratio of the number of boys to the number of girls in a class is 3:4. If there are 24 boys in the class, how many girls are there?

Accepted Answer

32

Answer

36

Answer

20

Answer

28

Question 27

A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

Accepted Answer

5 cups

Answer

2 cups

Answer

3 cups

Answer

4 cups

Question 28

A train travels 120 miles in 2 hours and then 180 miles in 3 hours. What is the average speed of the train, in miles per hour?

Accepted Answer

60

Answer

80

Answer

40

Answer

100

Question 29

The ratio of the lengths of two sides of a triangle is 3:4. If the shorter side is 12 cm, what is the length of the longer side?

Accepted Answer

16 cm

Answer

8 cm

Answer

6 cm

Answer

24 cm

Question 30

A car travels 180 miles in 3 hours. What is the average speed of the car in miles per hour?

Accepted Answer

60 mph

Answer

120 mph

Answer

90 mph

Answer

30 mph

Question 31

If 4 apples cost £1.20, how much would 8 apples cost?

Accepted Answer

£2.40

Answer

£3.00

Answer

£1.80

Answer

£6.00

Question 32

A map has a scale of 1 cm representing 10 km on the ground. If two towns are 5 cm apart on the map, what is the actual distance between them?

Accepted Answer

50 km

Answer

500 km

Answer

100 km

Answer

10 km

Question 33

The length of a rectangle is 5 times its width. If the width is 6 cm, what is the length?

Accepted Answer

30 cm

Answer

20 cm

Answer

15 cm

Answer

5 cm

Question 34

A recipe needs 2 cups of flour to make 12 cookies. How many cups of flour are needed for 24 cookies?

Accepted Answer

4 cups

Answer

1 cup

Answer

8 cups

Answer

6 cups

Question 35

A cake recipe calls for 2 cups of flour for every 1 cup of sugar. If you want to use 6 cups of flour, how much sugar do you need?

Accepted Answer

3 cups

Answer

2 cups

Answer

4 cups

Answer

6 cups

Question 36

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

Accepted Answer

60

Answer

120

Answer

30

Answer

90

Question 37

A scale drawing of a building has a length of 10 cm and a width of 5 cm. If the actual length of the building is 20 meters, what is the actual width of the building?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 38

A company's profit increased from £10,000 to £15,000 over a period of 5 years. What is the average annual increase in profit?

Accepted Answer

£1,000

Answer

£2,000

Answer

£5,000

Answer

£10,000

Question 39

A company's revenue increased from £200,000 to £250,000 over a period of 3 years. What is the average annual percentage increase in revenue?

Accepted Answer

8.33%

Answer

4.17%

Answer

12.50%

Answer

16.67%

Question 40

The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

Accepted Answer

10

Answer

12

Answer

18

Answer

5

Question 41

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

Accepted Answer

60 miles per hour

Answer

30 miles per hour

Answer

80 miles per hour

Answer

40 miles per hour

Question 42

A plant grows 2 cm every day. How much will it grow in 5 days?

Accepted Answer

10 cm

Answer

12 cm

Answer

5 cm

Answer

7 cm

Question 43

A train travels at a constant speed of 80 km/h. How far will it travel in 3 hours?

Accepted Answer

240 km

Answer

200 km

Answer

160 km

Answer

320 km

Question 44

A car uses 5 liters of petrol to travel 100 km. How much petrol will it need to travel 250 km?

Accepted Answer

12.5 liters

Answer

10 liters

Answer

25 liters

Answer

6.25 liters

Question 45

A recipe for 12 cookies requires 2 cups of flour. How many cups of flour are needed for 36 cookies?

Accepted Answer

6 cups

Answer

4 cups

Answer

3 cups

Answer

8 cups

Question 46

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

Accepted Answer

60 miles per hour

Answer

80 miles per hour

Answer

100 miles per hour

Answer

40 miles per hour

Question 47

A shirt is reduced in price by 20%. If the original price was £30, what is the new price?

Accepted Answer

£24

Answer

£28

Answer

£25

Answer

£20

Question 48

A train travels at a constant speed of 80 km/h. How far will it travel in 3 hours?

Accepted Answer

240 km

Answer

320 km

Answer

200 km

Answer

160 km

Question 49

A recipe for 6 servings requires 300g of pasta. How much pasta is needed for 9 servings?

Accepted Answer

450g

Answer

500g

Answer

350g

Answer

400g

Question 50

A car travels 200 km in 4 hours. What is its average speed in km/h?

Accepted Answer

50 km/h

Answer

60 km/h

Answer

80 km/h

Answer

40 km/h

Question 51

A bag contains red, blue, and green marbles in the ratio 2:3:5. If there are 60 red marbles, how many blue marbles are there?

Accepted Answer

45

Answer

30

Answer

20

Answer

90

Question 52

A rectangular garden has a length to width ratio of 3:2. If the length is 15 meters, what is the width?

Accepted Answer

10 meters

Answer

30 meters

Answer

5 meters

Answer

15 meters

Question 53

A recipe for 12 cupcakes requires 2 cups of flour. How many cups of flour are needed for 36 cupcakes?

Accepted Answer

6 cups

Answer

3 cups

Answer

8 cups

Answer

4 cups

Question 54

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

Accepted Answer

60 mph

Answer

40 mph

Answer

80 mph

Answer

100 mph

Question 55

The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

Accepted Answer

10 girls

Answer

5 girls

Answer

12 girls

Answer

18 girls

Question 56

A map has a scale of 1:50,000. This means that 1 cm on the map represents 50,000 cm in real life. If a distance on the map is 5 cm, what is the actual distance in kilometers?

Accepted Answer

2.5 km

Answer

5 km

Answer

10 km

Answer

1 km

Question 57

A train travels at a constant speed of 80 km per hour. How far will it travel in 3 hours?

Accepted Answer

240 km

Answer

200 km

Answer

320 km

Answer

160 km

Question 58

If 5 apples cost £2.50, how much would 12 apples cost?

Accepted Answer

£6

Answer

£4.50

Answer

£3

Answer

£7.50

Question 59

A painter can paint 2 rooms in 3 hours.  Assuming he paints at a constant rate, how many rooms can he paint in 9 hours?

Accepted Answer

6 rooms

Answer

4 rooms

Answer

3 rooms

Answer

9 rooms

Question 60

The ratio of red to blue marbles in a bag is 4:3. If there are 12 red marbles, how many blue marbles are there?

Accepted Answer

9 blue marbles

Answer

12 blue marbles

Answer

16 blue marbles

Answer

6 blue marbles

Question 61

A cake recipe uses 1 cup of sugar for every 2 cups of flour. If you use 5 cups of flour, how much sugar do you need?

Accepted Answer

2.5 cups

Answer

5 cups

Answer

3 cups

Answer

1 cup

Question 62

A cyclist travels 20 km in 1 hour. What is their average speed in meters per second (m/s)?

Accepted Answer

5.56 m/s

Answer

10 m/s

Answer

20 m/s

Answer

1 km/s

Question 63

A bag has 12 red marbles and 8 blue marbles. What is the simplified ratio of red marbles to blue marbles?

Accepted Answer

3 : 2

Answer

4 : 3

Answer

3 : 4

Answer

2 : 3

Question 64

A car travels 150 miles in 3 hours. What is the average speed of the car in miles per hour?

Accepted Answer

50

Answer

100

Answer

75

Answer

25