AP Calculus Unit 4 Review (4.1-4.5)

Front

What is the formula for the volume of a rectangular prism?

Back

Volume = length × width × height.

Front

How do you find the rate of change of the water level in a pool being filled?

Back

Use the formula: dV/dt = A * (dh/dt), where A is the area of the base and dh/dt is the rate of change of height.

Front

What is the relationship between the rates of change of the sides of a right triangle?

Back

Using the Pythagorean theorem, if x is the distance from the wall and y is the height, then x² + y² = L² (length of the ladder).

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3)πr³, where r is the radius.

Front

How do you determine when a particle is at rest?

Back

A particle is at rest when its velocity v(t) = 0.

Front

What does it mean for an object to be speeding up?

Back

An object is speeding up if its velocity is increasing, which occurs when acceleration and velocity have the same sign.

Front

What is the derivative of the volume of a sphere with respect to time?

Back

dV/dt = 4πr²(dr/dt), where dr/dt is the rate of change of the radius.

Front

How do you apply related rates in calculus?

Back

Identify the variables involved, write an equation relating them, differentiate with respect to time, and solve for the desired rate.

Front

What is the significance of the second derivative in motion?

Back

The second derivative indicates acceleration; if it's positive, the object is speeding up, and if negative, it's slowing down.

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.