Ratio, Proportion and Rates of Change Quizzes | Year 11 Mathematics

Question 1

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

Accepted Answer

60 mph

Answer

55 mph

Answer

65 mph

Answer

70 mph

Question 2

A light travels a distance of 300,000 km in 1 second. What is its speed in million of metres per second?

Accepted Answer

3 x 10^8 m/s

Answer

3 x 10^5 m/s

Answer

3 x 10^2 m/s

Answer

3 x 10^-2 m/s

Question 3

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

Accepted Answer

30 kilometers

Answer

3 kilometers

Answer

300 kilometers

Answer

3000 kilometers

Question 4

Find the gradient of the line passing through the points (2, 3) and (5, 7).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 5

Two quantities are inversely proportional. If one quantity doubles, what happens to the other quantity?

Accepted Answer

Halves

Answer

Doubles

Answer

Increases by 50%

Answer

Decreases by 50%

Question 6

Which of the following is NOT an example of a direct proportion?

Accepted Answer

Area and perimeter

Answer

Distance and time

Answer

Pressure and volume

Answer

Mass and weight

Question 7

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

Accepted Answer

Temperature and volume of gas

Answer

Speed and distance

Answer

Mass and volume

Answer

Force and acceleration

Question 8

Two cars travel the same distance. Car A takes 4 hours, while Car B takes 6 hours. Express the ratio of Car A's speed to Car B's speed as a simplified fraction.

Accepted Answer

2:3

Answer

3:2

Answer

4:6

Answer

6:4

Question 9

A line has a gradient of -2. Determine which point lies on the line.

Accepted Answer

(1, -2)

Answer

(2, 4)

Answer

(3, 6)

Answer

(4, 8)

Question 10

A map has a scale of 1:50,000. Determine the actual distance represented by 5 cm on the map.

Accepted Answer

25,000 cm

Answer

250,000 cm

Answer

2,500 cm

Answer

250 cm

Question 11

A train 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 12

The population of a town decreases by 5% each year. If the current population is 10,000, what will be the population in 3 years?

Accepted Answer

8574

Answer

9045

Answer

9524

Answer

10,000

Question 13

Which of the following is the standard form for expressing the ratio of 3 to 5?

Accepted Answer

3:5

Answer

5:3

Answer

3/5

Answer

5/3

Question 14

If the rate of change of a function is -2, what does this indicate?

Accepted Answer

The function is decreasing at a rate of -2 units per unit change in x

Answer

The function is increasing at a rate of 2 units per unit change in x

Answer

The function is decreasing at a rate of 2 units per unit change in x

Answer

The function is increasing at a rate of -2 units per unit change in x

Question 15

Two quantities, A and B, are in direct proportion. If quantity A is doubled, what happens to quantity B?

Accepted Answer

Doubled

Answer

Halved

Answer

Trebled

Answer

Reduced by a quarter

Question 16

A car travels 150 miles in a time of 2 hours and 30 minutes. Calculate the average speed of the car in kilometers per hour (km/h).

Accepted Answer

80 km/h

Answer

60 km/h

Answer

100 km/h

Answer

120 km/h

Question 17

Calculate the gradient of the line represented by the equation y = 2x + 3.

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 18

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

Accepted Answer

60 mph

Answer

30 mph

Answer

90 mph

Answer

120 mph

Question 19

Which of the following is the correct formula for calculating the gradient of a line?

Accepted Answer

Gradient = (y2 - y1) / (x2 - x1)

Answer

Gradient = (x2 - x1) / (y2 - y1)

Answer

Gradient = (y1 - y2) / (x1 - x2)

Answer

Gradient = (x1 - x2) / (y1 - y2)

Question 20

Which of the following is NOT a real-world application of ratio and proportion?

Accepted Answer

Calculating the surface area of a sphere

Answer

Mixing paints to achieve a desired color

Answer

Calculating the scale of a map

Answer

Determining the ingredients needed for a recipe

Question 21

The graph of a line is a straight line. Which of the following is NOT a possible value for its gradient?

Accepted Answer

Infinite

Answer

0

Answer

1

Answer

2

Question 22

What is the definition of ratio?

Accepted Answer

The comparison of two or more quantities of the same kind using division

Answer

The rate at which one quantity changes in relation to another

Answer

The difference between two quantities

Answer

The product of two quantities

Question 23

A model car is made to a scale of 1:24. If the actual car is 4.5 meters long, how long is the model car?

Accepted Answer

18.75 cm

Answer

15 cm

Answer

12.5 cm

Answer

10 cm

Question 24

An inverse proportion is represented by the equation y = k/x. What happens to y if x increases?

Accepted Answer

y decreases

Answer

y increases

Answer

y remains the same

Answer

y is squared

Question 25

A car travels 240 kilometers in 3 hours. What is its average speed in kilometers per hour?

Accepted Answer

80 km/h

Answer

60 km/h

Answer

40 km/h

Answer

20 km/h

Question 26

A cyclist leaves London at 9:00 am and arrives in Brighton at 12:00 pm, having traveled 100 kilometers. What is the cyclist's average speed in kilometers per hour?

Accepted Answer

33.33 km/h

Answer

50 km/h

Answer

25 km/h

Answer

20 km/h

Question 27

A graph shows a straight line with a gradient of 3. What does this mean?

Accepted Answer

For every 1 unit increase in the x-axis, the y-axis increases by 3 units

Answer

For every 1 unit increase in the y-axis, the x-axis increases by 3 units

Answer

The line is parallel to the y-axis

Answer

The line is perpendicular to the y-axis

Question 28

Which of the following is the equation of a line with a gradient of -2 and a y-intercept of 1?

Accepted Answer

y = -2x + 1

Answer

y = 2x + 1

Answer

y = -2x - 1

Answer

y = 2x - 1

Question 29

A rectangular garden is 10 m long and 5 m wide. If the width of the garden is increased by 20%, what will be the new area of the garden?

Accepted Answer

60 m²

Answer

55 m²

Answer

65 m²

Answer

70 m²

Question 30

The gradient of a line is -1/2. What does this indicate about the line?

Accepted Answer

It has a negative slope.

Answer

It has a positive slope.

Answer

It is a horizontal line.

Answer

It is a vertical line.

Question 31

The cost of renting a car is directly proportional to the number of days it is rented for. If it costs £50 to rent a car for 2 days, what would be the cost of renting the car for 5 days?

Accepted Answer

£100

Answer

£75

Answer

£125

Answer

£150

Question 32

A map has a scale of 1:25,000. If the distance between two cities on the map is 4 cm, what is the actual distance between the cities?

Accepted Answer

10 km

Answer

1 km

Answer

100 km

Answer

1,000 km

Question 33

Two quantities are inversely proportional. If one quantity increases by 50%, describe what happens to the other quantity.

Accepted Answer

It decreases by 50%

Answer

It doubles

Answer

It increases by 50%

Answer

It remains the same

Question 34

A company's profit increased from £50,000 in 2021 to £60,000 in 2022. Determine the percentage increase in profit.

Accepted Answer

20%

Answer

40%

Answer

10%

Answer

30%

Question 35

A scale drawing of a building uses a scale of 1 cm to represent 5 meters. If the building measures 12 cm in the drawing, what is its actual height?

Accepted Answer

60 m

Answer

15 m

Answer

24 m

Answer

12 m

Question 36

A line has a gradient of 2. Which of the following is the equation of this line?

Accepted Answer

y = 2x

Answer

y = x + 2

Answer

y = -2x

Answer

y = 1/2x

Question 37

A triangle is enlarged using a scale factor of 3. What is the ratio of the area of the original triangle to the area of the enlarged triangle?

Accepted Answer

1:9

Answer

3:1

Answer

1:3

Answer

9:1

Question 38

The volume of a sphere is 36π cm³. What is the radius of the sphere?

Accepted Answer

3 cm

Answer

12 cm

Answer

6 cm

Answer

9 cm

Question 39

Which ratio is equivalent to 3:4?

Accepted Answer

6:8

Answer

7:9

Answer

4:6

Answer

5:7

Question 40

The price of a product increases from £10 to £12. What is the percentage increase in price?

Accepted Answer

20%

Answer

10%

Answer

40%

Answer

30%

Question 41

Which equation represents a direct proportion?

Accepted Answer

y = kx

Answer

y = x^2

Answer

y = 1/x

Answer

y = x + 1

Question 42

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

Accepted Answer

60

Answer

30

Answer

90

Answer

120

Question 43

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

Accepted Answer

18

Answer

24

Answer

12

Question 44

A train travels 250 kilometers in 4 hours. What is the train's average speed in kilometers per hour?

Accepted Answer

62.5

Answer

1000

Answer

100

Answer

250

Question 45

A line has a gradient of -3. Which of the following equations represents this line?

Accepted Answer

y = -3x

Answer

y = -3 + x

Answer

y = x / 3

Answer

y = x - 3

Question 46

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

Accepted Answer

10

Answer

12

Answer

20

Answer

5

Question 47

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

Accepted Answer

2.5 km

Answer

1.25 km

Answer

25 km

Answer

5 km

Question 48

A recipe for 6 people requires 180g of flour. How much flour would you need to make the same recipe for 9 people?

Accepted Answer

270g

Answer

120g

Answer

360g

Answer

240g

Question 49

If 5 workers can complete a task in 12 days, how long would it take 3 workers to complete the same task? (Assume everyone works at the same rate.)

Accepted Answer

20 days

Answer

10 days

Answer

8 days

Question 50

A car travels at a constant speed of 60 miles per hour. How far will it travel in 2 hours and 30 minutes?

Accepted Answer

150 miles

Answer

135 miles

Answer

180 miles

Answer

120 miles

Question 51

A straight line passes through the points (2, 5) and (6, 13). What is the gradient of this line?

Accepted Answer

2

Answer

1/2

Answer

-2

Answer

4

Question 52

A map has a scale of 1:50,000. If the distance between two points on the map is 4 centimeters, what is the actual distance in kilometers?

Accepted Answer

2 km

Answer

0.5 km

Answer

20 km

Answer

4 km

Question 53

The price of a phone increased by 25%. If the original price was £200, what is the new price?

Accepted Answer

£250

Answer

£225

Answer

£240

Question 54

A shop offers a 15% discount on all items. What is the sale price of a jacket originally priced at £80?

Accepted Answer

£68

Answer

£72

Answer

£75

Answer

£60

Question 55

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

Accepted Answer

20

Answer

15

Answer

9

Answer

24

Question 56

A cyclist travels 30 kilometers in 2 hours. What is their average speed in kilometers per hour?

Accepted Answer

15 km/h

Answer

60 km/h

Answer

10 km/h

Answer

20 km/h

Question 57

The exchange rate between pounds (£) and euros (€) is £1 = €1.15. How many euros can you get for £50?

Accepted Answer

€57.50

Answer

€55

Answer

€43.48

Answer

€65