AP Calculus Unit 4 Review

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³, where r is the radius of the sphere.

Front

How do you find the rate of change of volume with respect to time for a sphere?

Back

Use the chain rule: dV/dt = dV/dr * dr/dt.

Front

If the radius of a sphere is decreasing, how does it affect the volume?

Back

The volume decreases as the radius decreases.

Front

What is the relationship between the radius and volume of a sphere?

Back

The volume of a sphere is proportional to the cube of its radius.

Front

What does v(t) > 0 indicate about a particle's motion?

Back

The particle is moving to the right.

Front

How do you calculate acceleration from a position function?

Back

Acceleration is the second derivative of the position function with respect to time.

Front

What is the derivative of x = 3t² + 5t³ - 2t?

Back

v(t) = 6t + 15t² - 2.

Front

What is the significance of a constant speed in motion problems?

Back

Constant speed means the velocity does not change over time.

Front

How do you determine the rate of change of distance between two moving objects?

Back

Use the Pythagorean theorem and differentiate with respect to time.

Front

What is the formula for the volume of a balloon as a function of its radius?

Back

V = (4/3)πr³.