AP Calculus AB Flashcards

Master AP Calculus AB concepts with interactive flashcards

Need a quick way to review key AP Calculus AB concepts? Our extensive collection of flashcards allows you to study efficiently, reinforcing important terms and formulas at your own pace, ensuring you're ready for exam day.

Derivatives

27 decks

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''

Integrals

16 decks

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

Functions, Graphs, and Limits

12 decks

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.

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