Exploring Direct Variation Concepts

The video tutorial covers the concept of direct variation, which is related to proportions learned in junior high. It explains how to solve proportions using cross multiplication, providing several example problems. The tutorial also includes real-world applications, such as using map scales and calculating water height over time, to demonstrate the practical use of these mathematical concepts.

What is the concept of direct variation closely related to?

• Proportions

• Fractions

• Equations

• Inequalities

In a direct variation problem, if y is 42 when x is 21, what is the value of x when y is 16?

• 8

• 4

• 10

• 2

What is the first step in solving a direct variation problem?

• Subtracting the values

• Adding the values

• Setting up the proportion

• Dividing the values

If y is directly proportional to x, and y is 11 when x is 6, what is the value of y when x is 9?

• 20.5

• 18.5

• 16.5

• 14.5

When setting up a proportion for direct variation, what must be equal?

• x/y ratios

• y/x ratios

• y values

• x values

In a map scale problem, if 2 cm equals 15 miles, how many miles are represented by 11.2 cm?

• 56

• 84

• 168

• 112

What is the distance in miles between two cities that are 11.2 cm apart on a map with a scale of 2 cm to 15 miles?

• 168 miles

• 84 miles

• 56 miles

• 112 miles

If the height of water in a bucket varies directly with time, and the water is 4 inches high after 9 seconds, how high will it be after 15 seconds?

• 20 inches

• 15 inches

• 10 inches

• 6 inches

In a direct variation problem involving water height, if the water is 4 inches high after 9 seconds, how many seconds will it take for the water to be 15 inches high?

• 39.75 seconds

• 36.75 seconds

• 33.75 seconds

• 30.75 seconds

If 20,000 people produce 12 tonnes of waste, how many people would produce 90 tonnes?

• 150,000

• 120,000

• 180,000

• 100,000