AP Calculus Exam

Front

What is the definition of speed in calculus?

Back

Speed is the magnitude of velocity, defined as the rate of change of distance with respect to time. It is given by the derivative of the position function s(t) with respect to time t.

Front

How do you find acceleration from a position function?

Back

Acceleration is the second derivative of the position function s(t). If s(t) = t^3 - 6t^2 - 4, then acceleration a(t) = s''(t).

Front

What does it mean for acceleration to be zero?

Back

When acceleration is zero, the object is moving at a constant speed. This occurs at points where the velocity function is at a maximum or minimum.

Front

What is a slope field?

Back

A slope field is a graphical representation of the solutions to a first-order differential equation. Each point in the field has a small line segment that represents the slope of the solution curve at that point.

Front

How do you interpret dy/dx = 2x?

Back

This equation indicates that the slope of the tangent line to the curve at any point (x, y) is equal to 2 times the x-coordinate. It describes a linear relationship between x and y.

Front

What is the relationship between circumference and radius?

Back

The circumference C of a circle is related to its radius r by the formula C = 2πr. This means that as the radius increases, the circumference increases proportionally.

Front

How do you find the rate of change of area with respect to time for a circle?

Back

The area A of a circle is given by A = πr^2. To find the rate of change of area with respect to time, use the chain rule: dA/dt = (dA/dr)(dr/dt).

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by the formula A = πr^2, where r is the radius of the circle.

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist.' It indicates that the limit of a function does not approach a finite value as the input approaches a certain point.

Front

What is the limit of a function?

Back

The limit of a function describes the value that the function approaches as the input approaches a certain value. It is a fundamental concept in calculus.