AP Calculus Learner Outcomes
LIMITS
I
can…
o
Express limits symbolically using correct notation.
o
Interpret limits expressed symbolically.
o
Estimate limits of functions.
o
Determine limits of functions.
o
Deduce and interpret behavior of functions using limits.
o
Analyze functions for intervals of continuity and points of discontinuity
o
Determine the applicability of important calculus theorems using continuity
DERIVATIVES
I
can…
o
Identify the derivative of a function as the limit of a difference quotient
o
Estimate derivatives from tables and graphs
o
Calculate derivatives
o
Determine higher order derivatives
o
Use derivatives to analyze properties of functions
o
Recognize the connection between differentiability and continuity
o
Interpret the meaning of a derivative within a problem
o
Solve problems involving slope of a tangent line
o
Solve problems involving related rates, optimization, and rectilinear motion
o
Solve problems involving rates of change in applied contexts
o
Verify solutions to differential equations
o
Estimate solutions to differential equations
o
Apply the MVT to describe the behavior of a function over an interval
Integrals and the Fundamental Theorem of Calculus
I
can…
o
Recognize antiderivatives of basic functions
o
Interpret the definite integral as the limit of a Riemann sum
o
Express the limit of a Riemann sum in integral notation (and vice versa)
o
Approximate a definite integral
o
Calculate a definite integral using areas and properties of definite integrals
o
Analyze functions defined by an integral
o
Calculate antiderivatives
o
Interpret the meaning of a definite integral within a problem
o
Apply definite integrals to problems involving the average value of a function
o
Apply definite integrals to problems involving motion
o
Apply definite integrals to problems involving area and volume
o
Use the definite integral to solve problems in various contexts
o
Analyze differential equations to obtain general and specific (particular)
solutions
o
Interpret, create, and solve differential equations from problems in context