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

Question 1

A chocolate cake recipe calls for a flour-to-sugar ratio of 2:3. If you're making a cake that needs 9 cups of sugar, how many cups of flour do you need?

Accepted Answer

6

Answer

2

Answer

9

Question 2

In a bag, there are 3 red marbles, 4 blue marbles, and 5 green marbles. What is the ratio of red marbles to the total number of marbles?

Accepted Answer

3:12

Answer

1:3

Answer

4:12

Answer

5:12

Question 3

A map has a scale of 1:250,000. Two towns are 5 centimeters apart on the map. What is the actual distance between the towns in kilometers?

Accepted Answer

12.5 km

Answer

25 km

Answer

50 km

Answer

100 km

Question 4

When two quantities, x and y, are directly proportional, which of the following remains constant?

Accepted Answer

The ratio of x to y

Answer

The difference between x and y

Answer

The sum of x and y

Question 5

The ratio of the weight of apples to the weight of oranges in a bag is 2:3. If the bag of apples weighs 2 kg, what is the weight of the bag of oranges?

Accepted Answer

1.5 kg

Answer

1 kg

Answer

2 kg

Answer

3 kg

Question 6

Which of the following represents an inverse proportion?

Accepted Answer

y varies inversely with x

Answer

y varies directly with x

Answer

y = x + 2

Answer

y = 2x - 3

Question 7

A recipe asks for 2 cups of flour for every 3 cups of milk. What is the proportion of flour to milk in the recipe?

Accepted Answer

2 : 3

Answer

3 : 2

Answer

2 : 5

Answer

5 : 2

Question 8

A car travels 120 miles in 2 hours. Calculate its average speed in miles per hour.

Accepted Answer

60 mph

Answer

30 mph

Answer

90 mph

Answer

120 mph

Question 9

An enlargement of a shape has a scale factor of 3. What is meant by a scale factor of 3?

Accepted Answer

Each side length of the enlargement is 3 times larger than the original shape.

Answer

Each side length of the original shape is 3 times larger than the enlargement.

Answer

The area of the enlargement is 3 times larger than the original shape.

Answer

The area of the original shape is 3 times larger than the enlargement.

Question 10

Two triangles have the same base and height. The ratio of their areas is 9:4. What is the ratio of their heights?

Accepted Answer

4:3

Answer

3:2

Answer

6:4

Answer

8:5

Question 11

Which of the following represents an inverse proportion?

Accepted Answer

y = x / 2

Answer

y = 2x

Answer

y = x + 1

Answer

y = x^2

Question 12

A cake recipe requires 2 cups of flour to 3 cups of sugar. If you want to make a larger cake and use 4 cups of flour, how much sugar will you need?

Accepted Answer

6 cups

Answer

2 cups

Answer

3 cups

Answer

4 cups

Question 13

A cake recipe uses flour and sugar in a ratio of 2:3. If you use 6 cups of flour, how many cups of sugar do you need?

Accepted Answer

9 cups

Answer

2 cups

Answer

3 cups

Answer

12 cups

Question 14

A recipe for 6 people requires 250g of flour. If you want to make the same recipe for 12 people, how much flour will you need?

Accepted Answer

500g

Answer

125g

Answer

250g

Answer

750g

Question 15

A car travels 120 miles in 2 hours. Calculate its average speed in miles per hour.

Accepted Answer

60

Answer

50

Answer

40

Answer

70

Question 16

Which of the following relationships represents a direct proportion?

Accepted Answer

The time taken to travel a distance compared to the speed of travel

Answer

The number of apples in a basket compared to the weight of the basket

Answer

The area of a square compared to its perimeter

Answer

The volume of a cube compared to its surface area

Question 17

Which of the following is an example of direct proportion in real-life?

Accepted Answer

The amount of fuel consumed by a car compared to the distance travelled

Answer

The weight of a bag of sugar compared to the number of cubes in the bag

Answer

The height of a tree compared to the length of its shadow

Answer

The volume of a balloon compared to the pressure inside it

Question 18

The ratio of the length of a side of a square to the length of its diagonal is:

Accepted Answer

1:√2

Answer

√2:1

Answer

1:2

Answer

2:1

Question 19

Which graph represents a direct proportion?

Accepted Answer

A straight line passing through the origin with a positive slope

Answer

A straight line passing through the origin with a negative slope

Answer

A curved line passing through the origin

Answer

A curved line not passing through the origin

Question 20

Determine if the proportion 12/15 = 4/5 is true:

Accepted Answer

Yes

Answer

No

Question 21

In a class with a 3:4 ratio of boys to girls, and 24 boys, how many girls are there?

Accepted Answer

16

Answer

24

Answer

32

Answer

36

Question 22

Which characteristic is NOT associated with direct proportion?

Accepted Answer

Decrease in one quantity leads to an increase in the other

Answer

Constant ratio between quantities

Answer

Linear graph

Answer

Non-zero constant of proportionality

Question 23

Express the total cost of a taxi ride, where the first 2 miles cost £12 and each additional mile costs £1.50, using the variable 'x' for additional miles:

Accepted Answer

12 + 1.5x

Answer

12 - 1.5x

Answer

12x + 1.5

Answer

1.5x + 12

Question 24

What does the gradient of a straight-line distance-time graph represent?

Accepted Answer

Speed of the object

Answer

Distance covered by the object

Answer

Time taken by the object

Answer

Acceleration of the object

Question 25

A rectangular garden has a length of 6 meters and a width of 4 meters. Find the ratio of the perimeter to the area of the garden:

Accepted Answer

1:8

Answer

1:6

Answer

1:10

Answer

1:12

Question 26

A bag contains 5 red marbles and 7 blue marbles. What is the ratio of red marbles to the total number of marbles?

Accepted Answer

5 : 12

Answer

7 : 12

Answer

5 : 7

Answer

7 : 5

Question 27

The scale of a map is 1 : 25000. What is the actual distance between two points on the map that are 5 cm apart?

Accepted Answer

1250 m

Answer

125 m

Answer

2500 m

Answer

25000 m

Question 28

Which of the following is an example of an inverse proportion?

Accepted Answer

Temperature and volume

Answer

Height and weight

Answer

Speed and distance

Answer

Time and distance

Question 29

A recipe requires 2 cups of flour for every 3 cups of sugar. If you want to make 6 cups of sugar, how much flour do you need?

Accepted Answer

4 cups

Answer

2 cups

Answer

6 cups

Answer

8 cups

Question 30

Two quantities are in proportion if they have:

Accepted Answer

Equal ratios

Answer

Equal products

Answer

Equal differences

Answer

Equal sums

Question 31

If a car travels at a speed of 60 miles per hour, how many miles will it travel in 2 hours?

Accepted Answer

120 miles

Answer

30 miles

Answer

60 miles

Answer

180 miles

Question 32

Which of the following graphs represents an inverse proportion?

Accepted Answer

A straight line with a negative slope

Answer

A straight line with a positive slope

Answer

A curve that increases at a decreasing rate

Answer

A curve that decreases at an increasing rate

Question 33

If the scale of a map is 1:250,000, what distance on the map represents 10 kilometers in real life?

Accepted Answer

4 cm

Answer

2 cm

Answer

20 cm

Answer

40 cm

Question 34

Two quantities are directly proportional. If one quantity increases by 10%, by what percentage does the other quantity increase?

Accepted Answer

10%

Answer

5%

Answer

15%

Answer

20%

Question 35

The speed of a car is inversely proportional to the time taken to cover a certain distance. If the speed of the car decreases by 30%, by what percentage does the time taken increase?

Accepted Answer

30%

Answer

15%

Answer

45%

Answer

60%

Question 36

A recipe for a cake calls for 2 cups of flour for every 3 cups of sugar. How many cups of sugar are needed if 6 cups of flour are used?

Accepted Answer

9 cups

Answer

4 cups

Answer

6 cups

Answer

12 cups

Question 37

A rectangular garden has a length of 6 meters and a width of 4 meters. If the length is increased by 25%, what is the new length of the garden?

Accepted Answer

7.5 meters

Answer

8 meters

Answer

6.5 meters

Answer

5 meters

Question 38

A company's profit increased from £10,000 to £12,000. What is the percentage increase in profit?

Accepted Answer

20%

Answer

10%

Answer

30%

Answer

40%

Question 39

A company's profit increased from £12,000 to £15,000. What is the percentage increase in profit?

Accepted Answer

25%

Answer

20%

Answer

15%

Answer

30%

Question 40

A recipe for 12 cupcakes needs 200g of flour.  How much flour would you need for 36 cupcakes?

Accepted Answer

600g

Answer

300g

Answer

800g

Answer

400g

Question 41

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

Accepted Answer

12

Answer

27

Answer

9

Answer

6

Question 42

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

Accepted Answer

60 km/h

Answer

120 km/h

Answer

30 km/h

Answer

240 km/h

Question 43

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

Accepted Answer

£6.00

Answer

£3.00

Answer

£7.50

Answer

£4.50

Question 44

A cyclist covers 24km in 3 hours.  If they keep the same speed, how long would it take to travel 40km?

Accepted Answer

5 hours

Answer

2 hours

Answer

6 hours

Answer

3 hours

Question 45

There are 20 blue marbles in a bag. The ratio of red marbles to blue marbles is 4:5. How many red marbles are there?

Accepted Answer

16

Answer

8

Answer

4

Answer

25

Question 46

A printer can print 60 pages in 5 minutes. What is its printing rate in pages per minute?

Accepted Answer

12 pages/minute

Answer

65 pages/minute

Answer

5 pages/minute

Answer

300 pages/minute

Question 47

Two quantities are in inverse proportion. If one quantity is doubled, what happens to the other quantity?

Accepted Answer

It is halved

Answer

It is doubled

Answer

It is tripled

Answer

It remains the same

Question 48

A map has a scale of 1:50,000. The distance between two towns on the map is 6cm. What is the actual distance between the towns?

Accepted Answer

3km

Answer

6km

Answer

300km

Answer

30km

Question 49

A train travels at a constant speed of 80km/h. How far will it travel in 3.5 hours?

Accepted Answer

280km

Answer

320km

Answer

112km

Answer

83.5km