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AP®︎/College Calculus BC

Learn AP®︎ Calculus BC—everything from AP®︎ Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP®︎ test.

11 units489 videos50 hours

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Unit 1: Limits and continuity

About the course

Define limits and using limit notation

Estimate limit values from graphs

Estimate limit values from tables

Determine limits using algebraic properties of limits: limit properties

Determine limits using algebraic properties of limits: direct substitution

Determine limits using algebraic manipulation

Select procedures for determining limits

Determine limits using the squeeze theorem

Explore types of discontinuities

Define continuity at a point

Confirm continuity over an interval

Remove discontinuities

Connect infinite limits and vertical asymptotes

Connect limits at infinity and horizontal asymptotes

Work with the intermediate value theorem

Optional videos

Free response questions: limits and continuity

Unit 2: Differentiation: definition and basic derivative rules

Define average and instantaneous rates of change at a point

Define the derivative of a function and using derivative notation

Estimate derivatives of a function at a point

Connect differentiability and continuity: determining when derivatives do and do not exist

Apply the power rule

Derivative rules: constant, sum, difference, and constant multiple: introduction

Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule

Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

Practice to connect derivatives and limits

The product rule

The quotient rule

Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

Optional videos

Free response questions: differentiation definition and basic derivative rules

Unit 3: Differentiation: composite, implicit, and inverse functions

The chain rule: introduction

The chain rule: further practice

Implicit differentiation

Differentiate inverse functions

Differentiate inverse trigonometric functions

Select procedures for calculating derivatives: strategy

Select procedures for calculating derivatives: multiple rules

Calculate higher-order derivatives

Optional videos

Free response questions: differentiation of composite, implicit, and inverse functions

Unit 4: Contextual applications of differentiation

Interpret the meaning of the derivative in context

Straight-line motion: connecting position, velocity, and acceleration

Rates of change in other applied contexts (non-motion problems)

Introduction to related rates

Solve related rates problems

Approximate values of a function using local linearity and linearization

Using L’Hôpital’s rule for finding limits of indeterminate forms

Optional videos

Free response questions: contextual applications of differentiation

Unit 5: Analytical applications of differentiation

Use the mean value theorem

Extreme value theorem, global versus local extrema, and critical points

Determine intervals on which a function is increasing or decreasing

Use the first derivative test to find relative (local) extrema

Use the candidates test to find absolute (global) extrema

Determine concavity of intervals and finding points of inflection: graphical

Determine concavity of intervals and finding points of inflection: algebraic

Use the second derivative test to find extrema

Sketch curves of functions and their derivatives

Connect a function, its first derivative, and its second derivative

Solve optimization problems

Explore behaviors of implicit relations

Free response questions: analytical applications of differentiation

Unit 6: Integration and accumulation of change

Exploring accumulations of change

Approximating areas with Riemann sums

Riemann sums, summation notation, and definite integral notation

The fundamental theorem of calculus and accumulation functions

Interpreting the behavior of accumulation functions involving area

Applying properties of definite integrals

The fundamental theorem of calculus and definite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule

Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals

Integrating using substitution

Integrating functions using long division and completing the square

Using integration by parts

Integrating using linear partial fractions

Evaluating improper integrals

Optional videos

Unit 7: Differential equations

Modeling situations with differential equations

Verifying solutions for differential equations

Sketching slope fields

Reasoning using slope fields

Approximating solutions using Euler’s method

Finding general solutions using separation of variables

Finding particular solutions using initial conditions and separation of variables

Exponential models with differential equations

Logistic models with differential equations

Unit 8: Applications of integration

Finding the average value of a function on an interval

Connecting position, velocity, and acceleration functions using integrals

Using accumulation functions and definite integrals in applied contexts

Finding the area between curves expressed as functions of x

Finding the area between curves expressed as functions of y

Volumes with cross sections: squares and rectangles

Volumes with cross sections: triangles and semicircles

Volume with disc method: revolving around x- or y-axis

Volume with disc method: revolving around other axes

Volume with washer method: revolving around x- or y-axis

Volume with washer method: revolving around other axes

The arc length of a smooth, planar curve and distance traveled

Unit 9: Parametric equations, polar coordinates, and vector-valued functions

Defining and differentiating parametric equations

Second derivatives of parametric equations

Finding arc lengths of curves given by parametric equations

Defining and differentiating vector-valued functions

Solving motion problems using parametric and vector-valued functions

Defining polar coordinates and differentiating in polar form

Finding the area of a polar region or the area bounded by a single polar curve

Finding the area of the region bounded by two polar curves

Calculator-active practice

Unit 10: Infinite sequences and series

Defining convergent and divergent infinite series

Working with geometric series

The nth-term test for divergence

Integral test for convergence

Harmonic series and p-series

Comparison tests for convergence

Alternating series test for convergence

Ratio test for convergence

Determining absolute or conditional convergence

Alternating series error bound

Finding Taylor polynomial approximations of functions

Lagrange error bound

Radius and interval of convergence of power series

Finding Taylor or Maclaurin series for a function

Representing functions as power series

Optional videos

Unit 11: AP Calculus BC solved exams

AP Calculus BC 2017

AP Calculus BC 2015

AP Calculus BC 2011

AP Calculus BC 2008

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