Master Ratios, Proportions, and Rates of Change: Practice Quiz

Question 1

A car travels 240 miles in 4 hours. Calculate the car's average speed in kilometres per hour, given that 1 mile is approximately 1.6 km.

Accepted Answer

96 km/h

Answer

60 km/h

Answer

120 km/h

Answer

144 km/h

Question 2

Which of the following relationships is NOT proportional?

Accepted Answer

Height of a child and their age

Answer

Distance traveled and time taken (constant speed)

Answer

Number of people and amount of food needed

Answer

Temperature of water and amount of heat added

Question 3

A company's profit increases by £5000 each year. Calculate the rate of change of profit with respect to time.

Accepted Answer

£5000 per year

Answer

£2500 per year

Answer

£10000 per year

Answer

£20000 per year

Question 4

Which of the following is NOT a type of ratio expression?

Accepted Answer

Equation

Answer

Percentage

Answer

Fraction

Answer

Rate

Question 5

A company pays its employees in the ratio of 2:3:5. If the lowest paid employee earns £1200 per month, find the monthly salary of the highest paid employee.

Accepted Answer

£3600

Answer

£1800

Answer

£2400

Answer

£3000

Question 6

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

Accepted Answer

18

Answer

12

Answer

24

Answer

36

Question 7

The scale of a map is given as 1 cm to 5 km. If the distance between two cities on the map is 15 cm, what is the actual distance between the cities in kilometers?

Accepted Answer

100 km

Answer

75 km

Answer

125 km

Answer

150 km

Question 8

The ratio of the length of a rectangle to its width is 5:3. If the perimeter of the rectangle is 40 cm, what is its width?

Accepted Answer

8 cm

Answer

5 cm

Answer

10 cm

Answer

12 cm

Question 9

In a class, the ratio of boys to girls is 3:5. If there are 12 boys in the class, how many girls are there?

Accepted Answer

15

Answer

10

Answer

20

Answer

25

Question 10

A rectangular garden has a length of 12 meters and a width of 8 meters. If the length of the garden is increased by 25%, what would be the percentage increase in the area of the garden?

Accepted Answer

37.5%

Answer

12.5%

Answer

25%

Answer

50%

Question 11

Which of the following techniques is NOT used to solve proportions?

Accepted Answer

Subtracting the means

Answer

Cross-multiplication

Answer

Adding the extremes

Answer

Divide and multiply

Question 12

The population of a town decreases at a rate of 2% annually. If the current population is 5,000, estimate the population in 5 years.

Accepted Answer

4,950

Answer

4,500

Answer

4,750

Answer

4,850

Question 13

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

Accepted Answer

1:2

Answer

1:4

Question 14

The rate of change of a linear function is:

Accepted Answer

The slope of the line

Answer

The y-intercept of the line

Answer

The x-intercept of the line

Question 15

If the rate of change of a function is negative, the function is:

Accepted Answer

Decreasing

Answer

Increasing

Question 16

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

Accepted Answer

A straight line sloping upwards

Answer

A straight line sloping downwards

Question 17

The rate of change of the function f(x) = x^2 + 2x - 3 at x = 1 is:

Accepted Answer

2

Answer

1

Question 18

The ratio of boys to girls in a class is 3:4. If there are 21 girls in the class, how many boys are there?

Accepted Answer

15

Answer

12

Answer

18

Answer

24

Question 19

A train departs London at 9:00 AM and arrives in Manchester at 11:30 AM, covering a distance of 210 miles. What is the average speed of the train?

Accepted Answer

70 miles per hour

Answer

60 miles per hour

Answer

80 miles per hour

Answer

90 miles per hour

Question 20

A train travels 360 km in 6 hours. What is the speed of the train in km/h?

Accepted Answer

60

Answer

70

Answer

50

Answer

80

Question 21

A car travels 120 miles in 2 hours. Calculate the unit rate of speed in miles per hour.

Accepted Answer

60 miles per hour

Answer

120 miles per hour

Answer

2 miles per hour

Answer

2 hours per mile

Question 22

Which of the following is NOT a proportion?

Accepted Answer

2/3 = 4/7

Answer

3:6 = 1:2

Answer

10/15 = 2/3

Answer

5:10 = 1:4

Question 23

What is the ratio of the length 6 cm to the width 4 cm?

Accepted Answer

3:2

Answer

2:3

Answer

1:2

Answer

2:1

Question 24

A car travels 180 km in 3 hours. What is its average speed in km/h?

Accepted Answer

60 km/h

Answer

120 km/h

Answer

90 km/h

Answer

30 km/h

Question 25

Which of the following equations represents a constant rate of change?

Accepted Answer

y = mx + c

Answer

y = 1/x

Answer

y = x³

Answer

y = √x

Question 26

A company's revenue is directly proportional to the number of products sold. If the revenue is £900 when 150 products are sold, what is the revenue when 225 products are sold?

Accepted Answer

£1,350

Answer

£2,250

Answer

£675

Answer

£1,125

Question 27

In a fruit basket, the ratio of apples to oranges is 3:5. If this represents the number of each type of fruit, what fraction of the fruits are oranges?

Accepted Answer

5/8

Answer

5/3

Answer

3/8

Question 28

A class has 30 students. If 25% are boys, how many girls are there in the class?

Accepted Answer

22

Answer

25

Answer

24

Question 29

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

Accepted Answer

60

Answer

30

Answer

90

Question 30

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 the distance between two points on the map is 5 cm, what is the actual distance between them in kilometers?

Accepted Answer

2.5

Answer

5

Answer

0.5

Question 31

A car uses 12 gallons of petrol to travel 240 miles. What is its fuel efficiency (miles per gallon)?

Accepted Answer

20

Answer

10

Answer

30

Answer

40

Question 32

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

Accepted Answer

5

Answer

6

Answer

4

Answer

3

Question 33

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

24

Answer

9

Answer

15

Question 34

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

Accepted Answer

60 mph

Answer

80 mph

Answer

100 mph

Answer

40 mph

Question 35

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

Accepted Answer

£24

Answer

£28

Answer

£27

Answer

£25

Question 36

A map has a scale of 1:50,000. If the distance between two towns on the map is 5 cm, what is the actual distance between the towns in kilometers?

Accepted Answer

2.5

Answer

5

Answer

1

Question 37

A cyclist covers 10 kilometers in 30 minutes. What is their average speed in kilometers per hour?

Accepted Answer

20 km/h

Answer

30 km/h

Answer

10 km/h

Question 38

A recipe for 6 servings needs 200g of cheese. How much cheese is needed for 9 servings?

Accepted Answer

300g

Answer

150g

Answer

250g

Answer

400g

Question 39

A painter can paint 15 square meters of wall in 2 hours. At this rate, how many square meters can they paint in 5 hours?

Accepted Answer

37.5 square meters

Answer

30 square meters

Answer

40 square meters

Answer

25 square meters

Question 40

The ratio of red marbles to blue marbles in a bag is 5:3. If there are 24 blue marbles, how many red marbles are there?

Accepted Answer

40

Answer

15

Answer

60

Answer

30

Question 41

A car depreciates in value by 10% each year. If its current value is £10,000, what will its value be after one year?

Accepted Answer

£9,000

Answer

£9,500

Answer

£10,500

Answer

£8,000

Question 42

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

Accepted Answer

5 cups

Answer

3 cups

Answer

4 cups

Answer

6 cups

Question 43

In a class, the ratio of boys to girls is 3:5. If there are 24 boys in the class, how many girls are there?

Accepted Answer

40

Answer

30

Answer

60

Answer

15

Question 44

A car travels 150 miles in 3 hours. What is the car's average speed?

Accepted Answer

50 miles per hour

Answer

75 miles per hour

Answer

60 miles per hour

Answer

45 miles per hour

Question 45

A plant grows 2 inches every 3 days. At this rate, how many inches will it grow in 15 days?

Accepted Answer

10 inches

Answer

12 inches

Answer

5 inches

Answer

8 inches

Question 46

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

Accepted Answer

£24

Answer

£20

Answer

£28

Answer

£25

Question 47

A map has a scale of 1:50,000. Two towns are 10 cm apart on the map. What is the actual distance between the towns in kilometers?

Accepted Answer

5 km

Answer

1 km

Answer

50 km

Answer

10 km

Question 48

A cyclist travels 20 miles in 1.5 hours. What is their average speed in miles per hour?

Accepted Answer

13.33 mph (approximately)

Answer

15 mph

Answer

10 mph

Answer

20 mph

Question 49

A recipe for 6 servings of soup requires 400g of vegetables. How many grams of vegetables are needed for 15 servings of soup?

Accepted Answer

1000g

Answer

1200g

Answer

600g

Answer

800g

Question 50

A train travels 240 km in 3 hours. If it maintains a constant speed, how far will it travel in 5 hours?

Accepted Answer

400 km

Answer

360 km

Answer

300 km

Answer

480 km