Guide to AP® Calculus AB-BC

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Limits

Begin studying for the AP® Calculus AB or BC test by examining limits. Part of the conceptual backbone of calculus, limits help us understand the behavior of functions as they approach specific points or even infinity, identify continuity, and determine points or intervals of discontinuity.

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Limits Reveal the Behavior of Functions

Learn about the power of limits to describe functions and their features.
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Writing and interpreting limitsFree

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Estimating limits of functionsFree

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Determining limits of functions

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Deduce and interpret behavior of functions with limits

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Exploring Continuity

Apply limits to functions to define intervals of continuity or points of discontinuity and to test major calculus theorems.
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Derivatives

Understand the connection between limits, secant slopes, and derivatives to calculate the instantaneous rate of change of one variable with respect to another. Make sure to include this essential section in your AP® Calculus AB review!

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

The Derivative Expressed as a Limit Function

Apply limits to secant lines to define a derivative as an instantaneous rate of change.
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Derivative representations

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Mixed derivative practice

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Higher order derivatives

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Difference quotients

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Derivatives from tables

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Derivatives from graphs

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Product rule

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Quotient rule

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Power rule

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Exponential derivatives

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Logarithm derivatives

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Polynomial derivatives

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Chain rule

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Vector-valued functions, parametric functions, and functions in polar coordinates (BC)

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Trigonometric derivatives

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Understanding a Function Through Its Derivative

Use the derivative of a function to identify key features including increasing and decreasing intervals, concavity, inflection points, relative extrema, and local linearity.
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Features of derivatives

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Differentiability and continuity

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Multiple Interpretations of the Derivative

Apply derivatives in a diverse range of problems involving motion, optimization, and related rates.
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Second derivative

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Derivative applications

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Tangent lines

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Parametric, polar, vector-valued functions (BC)

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Euler's method (BC)

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Graphical representations

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Slope fields

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The Mean Value Theorem

Explore how the Mean Value Theorem can determine the average rate of change of a function over a given interval.
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Integrals and the Fundamental Theorem of Calculus

Explore the relationship between integration and differentiation as summarized by the Fundamental Theorem of Calculus. Use integration techniques to solve problems involving rate accumulation, particle motion, area, and volume.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

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Antidifferentiation is the Opposite of Differentiation

The reverse process of differentiating consists of finding a function, given its derivative.
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The Definite Integral

The definite integral represents a value defined by the accumulation of a given function over a specific interval.
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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus provides a mechanism for evaluating definite integrals.
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Applications of the Definite Integral

Explore the utility of the definite integral in problems ranging from kinematics to accumulation to volume calculations.
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Interpretation of definite integrals

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Area and volume

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Area with polar curves (BC)

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Motion

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Motion using parametric or vector-valued functions (BC)

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Integrals in various context

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Solving Separable Differential Equations

Apply the power of differential equations to determine general and particular solutions in various contexts.
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Series

Specifically for the AP® Calculus BC exam, practice working with Taylor and Maclaurin series and utilize power series to reach an approximation of given functions. In addition, learn how to determine when series converge and diverge.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Sum of Series and Convergence

Examine different series by calculating or approximating their sums and use tests to determine if a given series converges or diverges.
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Power Series

Examine, derive, differentiate and integrate power series including Taylor and Maclaurin Series and also calculate the radius and interval of convergence for a given series.
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Taylor polynomials

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Writing power series for a function

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