Oregon flagOregon: AP Calculus Learning Objectives Math Standards

81 standards · 3 domains

LIMITS

  • CB.Calc.LIM-1.A Represent limits analytically using correct notation.
  • CB.Calc.LIM-1.B Interpret limits expressed in analytic notation.
  • CB.Calc.LIM-1.C Estimate limits of functions.
  • CB.Calc.LIM-1.D Determine the limits of functions using limit theorems.
  • CB.Calc.LIM-1.E Determine the limits of functions using equivalent expressions for the function or the squeeze theorem.
  • CB.Calc.LIM-2.A Justify conclusions about continuity at a point using the definition.
  • CB.Calc.LIM-2.B Determine intervals over which a function is continuous.
  • CB.Calc.LIM-2.C Determine values of x or solve for parameters that make discontinuous functions continuous, if possible.
  • CB.Calc.LIM-2.D Interpret the behavior of functions using limits involving infinity.
  • CB.Calc.LIM-3.A Interpret a limit as a definition of a derivative.
  • CB.Calc.LIM-4.A Determine limits of functions that result in indeterminate forms.
  • CB.Calc.LIM-5.A Approximate a definite integral using geometric and numerical methods.
  • CB.Calc.LIM-5.B Interpret the limiting case of the Riemann sum as a definite integral.
  • CB.Calc.LIM-5.C Represent the limiting case of the Riemann sum as a definite integral.
  • CB.Calc.LIM-6.A Evaluate an improper integral or determine that the integral diverges.
  • CB.Calc.LIM-7.A Determine whether a series converges or diverges.
  • CB.Calc.LIM-7.B Approximate the sum of a series.
  • CB.Calc.LIM-8.A Represent a function at a point as a Taylor polynomial.
  • CB.Calc.LIM-8.B Approximate function values using a Taylor polynomial.
  • CB.Calc.LIM-8.C Determine the error bound associated with a Taylor polynomial approximation.
  • CB.Calc.LIM-8.D Determine the radius of convergence and interval of convergence for a power series.
  • CB.Calc.LIM-8.E Represent a function as a Taylor series or a Maclaurin series.
  • CB.Calc.LIM-8.F Interpret Taylor series and Maclaurin series.
  • CB.Calc.LIM-8.G Represent a given function as a power series.

CHANGE

  • CB.Calc.CHA-1.A Interpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.
  • CB.Calc.CHA-2.A Determine average rates of change using difference quotients.
  • CB.Calc.CHA-2.B Represent the derivative of a function as the limit of a difference quotient.
  • CB.Calc.CHA-2.C Determine the equation of a line tangent to a curve at a given point.
  • CB.Calc.CHA-2.D Estimate derivatives.
  • CB.Calc.CHA-3.A Interpret the meaning of a derivative in context.
  • CB.Calc.CHA-3.B Calculate rates of change in applied contexts.
  • CB.Calc.CHA-3.C Interpret rates of change in applied contexts.
  • CB.Calc.CHA-3.D Calculate related rates in applied contexts.
  • CB.Calc.CHA-3.E Interpret related rates in applied contexts.
  • CB.Calc.CHA-3.F Approximate a value on a curve using the equation of a tangent line.
  • CB.Calc.CHA-3.G Calculate derivatives of parametric functions.
  • CB.Calc.CHA-3.H Calculate derivatives of vector-valued functions.
  • CB.Calc.CHA-4.A Interpret the meaning of areas associated with the graph of a rate of change in context.
  • CB.Calc.CHA-4.B Determine the average value of a function using definite integrals.
  • CB.Calc.CHA-4.C Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
  • CB.Calc.CHA-4.D Interpret the meaning of a definite integral in accumulation problems.
  • CB.Calc.CHA-4.E Determine net change using definite integrals in applied contexts.
  • CB.Calc.CHA-5.A Calculate areas in the plane using the definite integral.
  • CB.Calc.CHA-5.B Calculate volumes of solids with known cross sections using definite integrals.
  • CB.Calc.CHA-5.C Calculate volumes of solids of revolution using definite integrals.
  • CB.Calc.CHA-5.D Calculate areas of regions defined by polar curves using definite integrals.
  • CB.Calc.CHA-6.A Determine the length of a curve in the plane defined by a function, using a definite integral.
  • CB.Calc.CHA-6.B Determine the length of a curve in the plane defined by parametric functions, using a definite integral.

ANALYSIS OF FUNCTIONS

  • CB.Calc.FUN-1.A Explain the behavior of a function on an interval using the Intermediate Value Theorem.
  • CB.Calc.FUN-1.B Justify conclusions about functions by applying the Mean Value Theorem over an interval.
  • CB.Calc.FUN-1.C Justify conclusions about functions by applying the Extreme Value Theorem.
  • CB.Calc.FUN-2.A Explain the relationship between differentiability and continuity.
  • CB.Calc.FUN-3.A Calculate derivatives of familiar functions.
  • CB.Calc.FUN-3.B Calculate derivatives of products and quotients of differentiable functions.
  • CB.Calc.FUN-3.C Calculate derivatives of compositions of differentiable functions.
  • CB.Calc.FUN-3.D Calculate derivatives of implicitly defined functions.
  • CB.Calc.FUN-3.E Calculate derivatives of inverse and inverse trigonometric functions.
  • CB.Calc.FUN-3.F Determine higher order derivatives of a function.
  • CB.Calc.FUN-3.G Calculate derivatives of functions written in polar coordinates.
  • CB.Calc.FUN-4.A Justify conclusions about the behavior of a function based on the behavior of its derivatives.
  • CB.Calc.FUN-4.B Calculate minimum and maximum values in applied contexts or analysis of functions.
  • CB.Calc.FUN-4.C Interpret minimum and maximum values calculated in applied contexts.
  • CB.Calc.FUN-4.D Determine critical points of implicit relations.
  • CB.Calc.FUN-4.E Justify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives.
  • CB.Calc.FUN-5.A Represent accumulation functions using definite integrals.
  • CB.Calc.FUN-6.A Calculate a definite integral using areas and properties of definite integrals.
  • CB.Calc.FUN-6.B Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.
  • CB.Calc.FUN-6.C Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
  • CB.Calc.FUN-6.D Use substitution and rearrangements into equivalent forms, such as long division and completing the square, for integrands requiring these techniques.
  • CB.Calc.FUN-6.E Use integration by parts for integrands requiring this technique.
  • CB.Calc.FUN-6.F Use integration by linear partial fractions for integrands requiring this technique.
  • CB.Calc.FUN-7.A Interpret verbal statements of problems as differential equations involving a derivative expression.
  • CB.Calc.FUN-7.B Verify solutions to differential equations.
  • CB.Calc.FUN-7.C Estimate solutions to differential equations.
  • CB.Calc.FUN-7.D Determine general solutions to differential equations.
  • CB.Calc.FUN-7.E Determine particular solutions to differential equations.
  • CB.Calc.FUN-7.F Interpret the meaning of a differential equation and its variables in context.
  • CB.Calc.FUN-7.G Determine general and particular solutions for problems involving differential equations in context.
  • CB.Calc.FUN-7.H Interpret the meaning of the logistic growth model in context.
  • CB.Calc.FUN-8.A Determine a particular solution given a rate vector and initial conditions.
  • CB.Calc.FUN-8.B Determine values for positions and rates of change in problems involving planar motion.