Direct and Inverse Variation Concepts

The video tutorial covers direct and inverse variation, key concepts in SAT math. Direct variation is when two quantities increase or decrease together, represented by a proportion. An example is given where 'a' is directly proportional to 'b'. Inverse variation is when one quantity increases as the other decreases, represented by a product. An example is provided where 'x' varies inversely with 'y'. The tutorial emphasizes understanding these concepts for tackling harder SAT questions.

What is the significance of understanding direct and inverse variation for SAT questions?

• They are not included in the SAT.

• They are crucial for tackling harder questions.

• They are only relevant for easy questions.

• They are only relevant for verbal sections.

In direct variation, what happens to one quantity when the other increases?

• It becomes zero.

• It decreases.

• It remains constant.

• It also increases.

How is direct variation mathematically represented?

• x1 / y1 = x2 / y2

• x1 - y1 = x2 - y2

• x1 + y1 = x2 + y2

• x1 * y1 = x2 * y2

What is the constant of proportionality in direct variation?

• The product of the variables.

• The ratio of the variables.

• The sum of the variables.

• The difference of the variables.

In the context of physics, how is direct variation often expressed?

• y = kx

• y = x - k

• y = x/k

• y = x + k

If a is directly proportional to b, and a = 10 when b = 2, what is a when b = 6?

• 20

• 15

• 25

• 30

What is the result of cross-multiplying in a direct variation problem?

• A sum of terms.

• A product of terms.

• An equation of equality.

• A difference of terms.

What distinguishes inverse variation from direct variation?

• Inverse variation involves subtraction.

• Inverse variation involves multiplication.

• Inverse variation involves division.

• Inverse variation involves addition.

In inverse variation, what happens to one quantity when the other increases?

• It increases.

• It remains constant.

• It decreases.

• It becomes zero.

How is inverse variation mathematically represented?

• x1 - y1 = x2 - y2

• x1 + y1 = x2 + y2

• x1 * y1 = x2 * y2

• x1 / y1 = x2 / y2