AP Calculus AB: Rates of Change and Motion — Drill 1

About This Drill

AP Calculus AB: Rates of Change and Motion — Drill 1 is a Math practice drill covering Rates of Change and Motion. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice interpreting derivatives as rates of change in context and analyzing the motion of a particle along a line using position, velocity, and acceleration. These AP Calculus AB skills appear on both the multiple-choice and free-response sections.

Questions in This Drill

1. A company's revenue, in thousands of dollars, is modeled by \( R(t) \), where \( t \) is the number of years since 2010. If \( R'(5) = 12 \), which of the following best interprets this value?
2. The function \( g \) is continuous on \( (-\infty, \infty) \). The sign of \( g'(x) \) is positive for \( x 2 \). Which of the following must be true?
3. A particle moves along the \( x \)-axis with velocity \( v(t) = t^2 - 4t + 3 \) for \( t \geq 0 \). On which of the following intervals is the particle moving in the negative direction?
4. A particle moves along the \( x \)-axis with velocity \( v(t) = 3t^2 - 12t + 7 \) for \( t \geq 0 \). At \( t = 5 \), which of the following best describes the particle's motion?
5. A particle moves along the \( x \)-axis with velocity \( v(t) = t^2 - 6t + 8 \) on the interval \( 0 \leq t \leq 5 \). Which of the following statements is true?