AP Calculus AB Help - Learn by Concept

Learn by Concept

Concepts

• AP Calculus AB

  • Derivatives

    • Applications of Derivatives

      • Analysis of curves, including the notions of monotonicity and concavity

      • Implicit differentiation

      • Interpretation of the derivative as a rate of change

      • Modeling rates of change, including related rates problems­

      • Optimization, both global and local extrema

    • Computation of the Derivative

      • Chain rule and implicit differentiation

      • Derivative rules for sums, products, and quotients of functions

      • Derivatives of functions

    • Concept of the Derivative

      • Derivative defined as the limit of the difference quotient

      • Derivative interpreted as an instantaneous rate of change

      • Relationship between differentiability and continuity

    • Derivative as a function

      • Corresponding characteristics of graphs of ƒ and ƒ'

      • Equations involving derivatives

      • Mean Value Theorem

      • Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ'

    • Derivative at a point

      • Approximate rate of change from graphs and tables of values

      • Slope of a curve at a point

      • Tangent line to a curve at a point and local linear approximation

    • Second Derivatives

      • Corresponding characteristics of the graphs of ƒ, ƒ', and ƒ''

      • Points of inflection

      • Relationship between the concavity of ƒ and the sign of ƒ''

  • Functions, Graphs, and Limits

    • Asymptotic and Unbounded Behavior

      • Asymptotic behavior in terms of limits involving infinity

      • Comparing relative magnitudes of functions and their rates of change

      • Graphical behavior of asymptotes

    • Continunity as a property of functions

      • An intuitive understanding of continuity

      • Geometric understanding of graphs of continuous functions

      • Understanding continuity in terms of limits

    • Limits of Functions (including one-sided limits)

      • Calculating limits using algebra

      • Estimating limits from graphs or tables

      • Understanding the limiting process.

  • Integrals

    • Applications of antidifferentiation

      • Finding specific antiderivatives using initial conditions, including applications to motion along a line

      • Solving separable differential equations and using them in modeling

    • Fundamental Theorem of Calculus

      • Use of the Fundamental Theorem to evaluate definite integrals

      • Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined

    • Interpretations and properties of definite integrals

      • Basic properties of definite integrals (additivity and linearity)

      • Definite integral as a limit of Riemann sums

      • Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval

    • Numerical approximations to definite integrals

      • Riemann sums (left, right, and midpoint evaluation points)

      • Trapezoidal sums

    • Techniques of antidifferentiation

      • Antiderivatives by substitution of variables

      • Antiderivatives following directly from derivatives of basic functions