AP CALCULUS BC Test Booklet
Introduction to Related Rates Quiz
1. A right triangle has base meters and height meters, where is constant and changes with respect to time ,
measured in seconds. The angle , measured in radians, is defined by . Which of the following best
describes the relationship between , the rate of change of with respect to time, and , the rate of change of
with respect to time?
(A) radians per second
(B) radians per second
(C) radians per second
(D) radians per second
2. In a certain factory, assume that the number of workers is constant. The number of minutes that it takes to make
a single unit of a product and the number of units of the product that are made per day satisfy the relationship
, where is a constant. Which of the following best describes the relationship between the rate of change,
with respect to time , of and the rate of change, with respect to time , of ?
(A)
(B)
(C)
(D)
3. Let and be functions of time such that the sum of and twice is constant. Which of the following equations
describes the relationship between the rate of change of with respect to time and the rate of change of with
respect to time?
(A)
(B)
(C)
(D) , where is a function of
4. A right triangle has base feet and height feet, where is constant and changes with respect to time ,
measured in seconds. The angle , measured in radians, is defined by . Which of the following best
describes the relationship between , the rate of change of with respect to time, and , the rate of change of
with respect to time?
(A) radians per second
(B) radians per second
(C) radians per second
(D) radians per second
AP Calculus BC Page 1 of 2
Test Booklet
Introduction to Related Rates Quiz
5. Boyle’s law states that if the temperature of an ideal gas is held constant, then the pressure of the gas and its
volume satisfy the relationship , where is a constant. Which of the following best describes the
relationship between the rate of change, with respect to time , of the pressure and the rate of change, with respect to
time , of the volume?
(A)
(B)
(C)
(D)
6. Let and be functions of time such that the sum of and is constant. Which of the following equations
describes the relationship between the rate of change of with respect to time and the rate of change of with
respect to time?
(A)
(B)
(C) , where is a function of
(D) , where is a function of
Page 2 of 2 AP Calculus BC
