Common Core · AP Calculus AB
CHA-3.B
AP Calculus AB, Unit 4 — Calculate rates of change in applied contexts, including position, velocity and acceleration.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 4 — Calculate rates of change in applied contexts, including straight-line motion.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 2 skills that cover it
- Applications of DerivativesUse derivatives to find tangent lines, velocities, and maximum and minimum values.Read the lesson →
- Motion Along a LineRead a moving particle from its position, velocity or acceleration: when it stops and turns, when it speeds up or slows down, how far it travels against how far it ends up, and where it is from where it started.Read the lesson →
What a student should be able to do
- Write the equation of a tangent line at a point.
- Relate position, velocity and acceleration.
- Find critical points and classify maxima and minima.
- Solve a simple optimisation problem.
- Find when a particle is at rest and when it changes direction, from a formula or a velocity graph.
- Decide whether a particle is speeding up or slowing down from the signs of velocity and acceleration.
- Find total distance and displacement over an interval, splitting the journey at every turn.
- Recover position from velocity, and velocity from acceleration, with an initial condition, including an object thrown straight up.