AP Calculus Unit 4 Review

Front

What does it mean for a particle to be at rest?

Back

A particle is at rest when its velocity, v(t), is equal to 0.

Front

How do you find the rate at which the top of a ladder is sliding down a wall when the bottom is sliding away?

Back

Use related rates and the Pythagorean theorem to relate the height of the ladder on the wall and the distance from the wall.

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 calculate the rate of change of volume of a balloon as its radius increases?

Back

Use the formula dV/dt = dV/dr * dr/dt, where dV/dr is the derivative of the volume with respect to the radius.

Front

What is the relationship between the volume of a cone and its dimensions?

Back

V = (1/3)πr²h, where r is the radius and h is the height of the cone.

Front

How do you determine the acceleration of an object from its position function?

Back

Take the second derivative of the position function x(t) with respect to time.

Front

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

Back

The derivative is v(t) = 6t + 15t² - 2.

Front

What is the significance of the second derivative in motion?

Back

The second derivative represents acceleration, indicating how velocity changes over time.

Front

How do you find the rate at which the water level is rising in a cone-shaped cup?

Back

Use related rates to relate the volume of water to the height and radius of the cone.

Front

What is the formula for the volume of a cone?

Back

V = (1/3)πr²h.