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AP DAILY VIDEOS

AP Calculus BCAP Daily is a series of on-demand, short videos—created by expert AP teachers and faculty—that can be used for in-person, online, and blended/hybrid instruction. These videos cover every topic and skill outlined in the AP Course and Exam Description and are available in AP Classroom for students to watch anytime, anywhere.

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AP CALCULUS BC AP DAILY VIDEOS

Unit 1

Video Title Topic Video Focus Instructor

1.1: Daily Video 1 Introducing Calculus—Can Change Occur at an Instant?

Exploring the concept of instantaneous change, by using average rates of change to develop an intuitive understanding of instantaneous rates of change.

Bryan Passwater

1.1: Daily Video 2 Introducing Calculus—Can Change Occur at an Instant?

Methods to approximate instantaneous rates of change within multiple contexts and through multiple representations.

Bryan Passwater

1.2: Daily Video 1 Defining Limits and Using Limit Notation

An introduction to limits, using graphs, and the notation used to express limits; the differences between limit values and function values.

Bryan Passwater


Connecting limit notation across multiple representations; reinforcing the underlying concept of a limit.

Bryan Passwater


Practicing problems related to Topic 1.2, with an optional activity for additional practice with these concepts.

Bryan Passwater

1.3: Daily Video 1 Estimating Limit Values from Graphs

An introduction to one-sided limits, using graphs; verifying when a limit does or does not exist, using left- and right-sided limits.

Bryan Passwater


Three cases when limits may fail to exist; exploring the limitations of—and misconceptions about—using graphs to determine limits.

Bryan Passwater


Spotlight on the AP Exam: Multiple examples of how Topic 1.3 might appear.

Bryan Passwater

1.4: Daily Video 1 Estimating Limit Values from Tables

How tables can be used to estimate limits; the limitations of—and common errors made when—utilizing tables.

Bryan Passwater

1.4: Daily Video 2 Estimating Limit Values from Tables

Deeping the understanding of limits, using tables (with a full activity available for additional practice and reinforcement).

Bryan Passwater

1.5: Daily Video 1 Determining Limits Using Algebraic Properties of Limits

Transitioning from estimating limits to determining limits, using one-sided limits with piecewise-defined functions algebraically.

Bryan Passwater


How to determine limits algebraically, using properties of limits involving sums, differences, products, and quotients.

Bryan Passwater


Exploring problems where traditional limit laws cannot be applied; how to address limit problems involving compositions, sums, and products.

Bryan Passwater

© 2020 College Board.

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1.6: Daily Video 1 Determining Limits Using Algebraic Manipulation

An introduction to the idea that algebraic manipulation can sometimes be used to determine limit values, specifically by factoring rational functions.

Bryan Passwater


Additional examples of algebraic manipulation being used to determine limit values, including functions involving radical or trigonometric expressions.

Bryan Passwater


Spotlight on the AP Exam: Multiple examples of how Topic 1.6 might appear.

Bryan Passwater

1.7: Daily Video 1 Selecting Procedures for Determining Limits

Selecting algebraic procedures to determine limits of rational and piecewise functions, as well as functions involving trigonometry or radicals.

Bryan Passwater

1.7: Daily Video 2 Selecting Procedures for Determining Limits

Strategies for recognizing and applying procedures with all types of limits from previous topics and through multiple representations.

Bryan Passwater

1.8: Daily Video 1 Determining Limits Using the Squeeze Theorem

Introducing the squeeze theorem through an intuitive approach, utilizing graphs, and connecting it to an understandable context.

Bryan Passwater

1.8: Daily Video 2 Determining Limits Using the Squeeze Theorem

Implementing and reinforcing the conditions required to apply the squeeze theorem.

Bryan Passwater

1.9: Daily Video 1 Connecting Multiple Representations of Limits

Connecting all of the concepts of limits from previous topics, from one representation to another.

Bryan Passwater

1.9: Daily Video 2 Connecting Multiple Representations of Limits

Connecting all representations together, in the context of limits, through the exploration of an activity.

Bryan Passwater

1.10: Daily Video 1 Exploring Types of Discontinuities

Exploring functions graphically and algebraically to determine where, why, and how functions are discontinuous.

Theresa Horvath


How to analyze and compare tabular, graphical, analytical, and verbal function representations to determine points of discontinuity.

Theresa Horvath


Spotlight on the AP Exam: How Topic 1.10 might appear, with tips for showing proper justification.

Theresa Horvath

1.11: Daily Video 1 Defining Continuity at a Point

Defining continuity at a point, using graphical and piecewise function representations; a demonstration of proper notation and required justification.

Theresa Horvath


How to use graphical and analytical representations of functions to determine whether functions are continuous (or not) at specific points.

Theresa Horvath


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Spotlight on the AP Exam: How Topic 1.11 might appear, with tips for showing proper justification.

Theresa Horvath

1.12: Daily Video 1 Confirming Continuity over an Interval

Examining functions graphically and analytically, to determine the intervals on which the function is continuous.

Theresa Horvath

1.12: Daily Video 2 Confirming Continuity over an Interval

Comparing and contrasting functions, both graphically and analytically, to determine whether they are continuous for all real numbers, on their domain, or neither.

Theresa Horvath

1.13: Daily Video 1 Removing Discontinuities

A discussion of which types of discontinuities can be removed; if removable, methods are shown for modifying function definitions in order to remove the discontinuity.

Theresa Horvath

1.13: Daily Video 2 Removing Discontinuities

Sample problems for practice with removing function discontinuities (or determining the discontinuity is non-removable).

Theresa Horvath

1.14: Daily Video 1 Connecting Infinite Limits and Vertical Asymptotes

How one-sided limits of infinity can be used to prove the existence of vertical asymptotes.

Theresa Horvath


Examining functions with vertical asymptotes; how to communicate about limits as the function approaches the vertical asymptote.

Theresa Horvath


Examples of functions that possess vertical asymptotes and limits equal to infinity.

Theresa Horvath

1.15: Daily Video 1 Connecting Limits at Infinity and Horizontal Asymptotes

The connection between limits at infinity and the existence of horizontal asymptotes on the graph of functions.

Theresa Horvath


How to analyze functions of various representations to determine their limits at infinity and the location of horizontal asymptotes.

Theresa Horvath


Examining the end behavior of functions using limits at infinity; comparing magnitudes of functions to evaluate limits.

Theresa Horvath

1.16: Daily Video 1 Working with the Intermediate Value Theorem (IVT)

The intermediate value theorem (IVT), its conditions, and examples of its application.

Theresa Horvath

1.16: Daily Video 2 Working with the Intermediate Value Theorem (IVT)

Spotlight on the AP Exam: How Topic 1.16 might appear, with tips for showing proper justification and confirming that theorem conditions have been met, using multiple representations.

Theresa Horvath


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Unit 2


2.1: Daily Video 1 Defining Average and Instantaneous Rates of Change at a Point

This video will present a discovery of the difference quotients for average rates of change and usage of limits to express instantaneous rates of change.

Theresa Horvath


This video will demonstrate processes to compute average and instantaneous rates of change using multiple representations.

Theresa Horvath


This video will look at ways Topic 2.1 might appear on the AP Exam. Tips will be shared for showing proper notation.

Theresa Horvath

2.2: Daily Video 1 Defining the Derivative of a Function and Using Derivative Notation

This video will define the derivative of a function and apply the definition in various situations, including tangent line equations, using appropriate mathematical notation.

Theresa Horvath


This video will demonstrate correct procedures to compute the derivative of a function and tangent line equations using multiple representations.

Theresa Horvath


This video will look at ways Topic 2.2 might appear on the AP Exam. Tips will be shared for showing proper notation.

Theresa Horvath

2.3: Daily Video 1 Estimating Derivatives of a Function at a Point

This video will explore methods used to approximate the derivative of a function at a point using data from a variety of representations, with and without technology.

Theresa Horvath

2.3: Daily Video 2 Estimating Derivatives of a Function at a Point

This video will look at ways Topic 2.3 might appear on the AP Exam. Tips will be shared for showing proper notation and justification.

Theresa Horvath

2.4: Daily Video 1 Connecting Differentiability and Continuity—Determining When Derivatives Do and Do Not Exist

This video will define differentiability and look at examples when the derivative exists, or fails to exist, and how this connects with the continuity of a function.

Theresa Horvath


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2.4: Daily Video 2 Connecting Differentiability and Continuity—Determining When Derivatives Do and Do Not Exist

This video will expand upon the topic of differentiability and explore questions involving multiple representations. Proper rationales for justifying conclusions will be demonstrated.

Theresa Horvath

2.5: Daily Video 1 Applying the Power Rule

This video will show a proof of the Power Rule. Examples will be shown applying this rule to find the derivative of power functions with a coefficient of one.

Theresa Horvath

2.6: Daily Video 1 Derivative Rules—Constant, Sum, Difference, and Multiple

This video will introduce the basic differentiation rules involving a constant, a sum, a difference, and a constant multiple.

Tony Record

2.6: Daily Video 2 Derivative Rules—Constant, Sum, Difference, and Constant Multiple

This video will expand upon all previously taught differentiation rules by introducing problems involving graphical and numerical representations of functions.

Tony Record

2.6: Daily Video 3 Derivative Rules—Constant, Sum, Difference, and Constant Multiple

This video will focus on problems involving equations of tangent lines while utilizing all the differentiation rules that have been taught thus far.

Tony Record

2.7: Daily Video 1 Derivatives of cos x, sin x, ex, and ln x

This video will introduce the basic rules for differentiating four of the most common transcendental functions—cos x, sin x, ex, and ln x.

Tony Record

2.8: Daily Video 1 The Product Rule This video will introduce the method by which the derivative of a product of two functions can be calculated.

Tony Record

2.8: Daily Video 2 The Product Rule In this video, students will compute derivatives using the product rule given graphical and numerical representations of functions.

Tony Record

2.9: Daily Video 1 The Quotient Rule

This video will introduce the method by which the derivative of a quotient of two functions can be calculated.

Tony Record

2.9: Daily Video 2 The Quotient Rule

In this video, students will compute derivatives using the quotient rule given graphical and numerical representations of functions.

Tony Record

2.10: Daily Video 1 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

This video will introduce the basic formulas for differentiating the remaining four trigonometric functions—tan x, cot x, sec x, and csc x.

Tony Record


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Unit 3


3.1: Daily Video 1 The Chain Rule This video will introduce how the chain rule can be used to differentiate composite functions.

Tony Record

3.1: Daily Video 2 The Chain Rule This video will feature a variety of scenarios in which the chain rule must be utilized, including problems that feature multiple representations of functions.

Tony Record

3.1: Daily Video 3 The Chain Rule This video will feature problems whose functions require two applications of the chain rule in order to differentiate.

Tony Record

3.2: Daily Video 1 Implicit Differentiation

This video will introduce the concept of implicit differentiation by outlining the process by which the derivative of several expressions and relations can be calculated.

Tony Record

3.2: Daily Video 2 Implicit Differentiation

This video will expand upon the concept of implicit differentiation by focusing on a few more problem types that require this technique.

Tony Record

3.3: Daily Video 1 Differentiating Inverse Functions

This video will introduce three ways in which the derivative of an inverse function may be computed.

Tony Record

3.3: Daily Video 2 Differentiating Inverse Functions

This video will focus on a method that works best in all situations when taking the derivative of an inverse function.

Tony Record

3.4: Daily Video 1 Differentiating Inverse Trigonometric Functions

This video will introduce, develop, and implement differentiation rules for inverse trigonometric functions.

Bryan Passwater

3.4: Daily Video 2 Differentiating Inverse Trigonometric Functions

This video will connect inverse trigonometric derivatives to previous topics and explore how these problems may appear on the AP Exam through a “5 for 5” activity.

Bryan Passwater

3.5: Daily Video 1 Selecting Procedures for Calculating Derivatives

This video will focus on strategies for identifying proper differentiation techniques needed with a variety of problems involving multiple representations.

Bryan Passwater

3.5: Daily Video 2 Selecting Procedures for Calculating Derivatives

This video will continue to implement strategies for identifying and selecting procedures for differentiation. Several AP style examples will be included.

Bryan Passwater

3.6: Daily Video 1 Calculating Higher-Order Derivatives

This video will introduce higher-order derivatives and the notation used to represent them. The video will include a “Find the Error” activity to reinforce these ideas.

Bryan Passwater

3.6: Daily Video 2 Calculating Higher-Order Derivatives

This video will work through several examples involving higher order derivatives as part of a “Twinning” activity.

Bryan Passwater


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Unit 4


4.1: Daily Video 1 Interpreting the Meaning of the Derivative in Context

This video will introduce the concept of a derivative in context. Understanding and connecting units with functions and their derivatives will also be emphasized.

Bryan Passwater


This video will focus on how to interpret a derivative in context, including strategies to ensure proper responses on the AP Exam.

Bryan Passwater


This video will discuss interpreting the rate of a rate in context while also introducing a “Find the Error” activity that targets common errors on the AP Exam.

Bryan Passwater

4.2: Daily Video 1 Straight-Line Motion—Connecting Position, Velocity, and Acceleration

This video will introduce straight-line motion and the connections between position, velocity, and acceleration while incorporating multiple representations.

Bryan Passwater


This video will cover the concepts of “speeding up” and “slowing down” as well as using graphing calculator technology appropriately with particle motion on the AP Exam.

Bryan Passwater


This video will look at how particle motion problems may appear on the AP Exam in a variety of ways including equations, graphs, and tables, as well as with and without technology.

Bryan Passwater

4.3: Daily Video 1 Rates of Change in Applied Contexts Other Than Motion

This video will explore how units help us understand rates of change.

Jamil Siddiqui

4.3: Daily Video 2 Rates of Change in Applied Contexts Other Than Motion

This video will focus on interpreting rates of change in applied contexts.

Jamil Siddiqui

4.4: Daily Video 1 Introduction to Related Rates

This video will focus on differentiating equations with respect to different variables.

Jamil Siddiqui


This video will look at how to create an equation that will connect rates.

Jamil Siddiqui


This video will demonstrate the process of solving a related rates problem.

Jamil Siddiqui

4.5: Daily Video 1 Solving Related Rates Problems

This video will focus on interpreting the answer to a related rates problem.

Jamil Siddiqui


This video will focus on solving related rates problems. Jamil Siddiqui


This video will expand on solving related rates problems by looking at more examples.

Jamil Siddiqui


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4.6: Daily Video 1 Approximating Values of a Function Using Local Linearity and Linearization

This video will explore how functions will behave linearly if looked at on a small enough interval.

Jamil Siddiqui

4.6: Daily Video 2 Approximating Values of a Function Using Local Linearity and Linearization

This video will focus on using tangent lines to approximate values.

Jamil Siddiqui

4.7: Daily Video 1 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

This video will introduce L’Hospital’s rule and show the proper notation and implementation required to apply it on the AP Exam.

Bryan Passwater

4.7: Daily Video 2 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

This video will look at a variety of examples that utilize L’Hospital’s rule including problems involving equations, graphs, tables, and functions defined by other functions.

Bryan Passwater


© 2020 College Board. 10


Unit 5


5.1: Daily Video 1 Using the Mean Value Theorem

This video will introduce the mean value theorem. We will explore this connection between average and instantaneous rates of change.

Karen Hyers


This video will focus on the conditions needed to apply the mean value theorem using both examples and non-examples over multiple representations.

Karen Hyers


This video will look at ways the mean value theorem might appear on the AP Exam. Tips will be shared for showing proper justification and notation.

Karen Hyers

5.2: Daily Video 1 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

This video will introduce the extreme value theorem (EVT) and show examples. Conditions of this theorem will also be discussed.

Jamil Siddiqui

5.2: Daily Video 2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

This video will compare and contrast local extrema, global extrema, and critical points.

Jamil Siddiqui

5.3: Daily Video 1 Determining Intervals on Which a Function Is Increasing or Decreasing

This video will define increasing and decreasing and look at introductory examples.

Jamil Siddiqui

5.3: Daily Video 2 Determining Intervals on Which a Function Is Increasing or Decreasing

This video will look at different representations of functions and their derivatives and how to interpret them on the AP Exam.

Jamil Siddiqui

5.4: Daily Video 1 Using the First Derivative Test to Determine Relative (Local) Extrema

This video will look at the first derivative test for relativeextrema and how to apply it.

Jamil Siddiqui

5.4: Daily Video 2 Using the First Derivative Test to Determine Relative (Local) Extrema

This video will look at the first derivative test and how it can be used with different representations of functions and their derivatives.

Jamil Siddiqui

5.5: Daily Video 1 Using the Candidates Test to Determine Absolute (Global) Extrema

This video will look at how to find the location of the absolute extrema on an interval once the critical values are known.

Jamil Siddiqui




5.5: Daily Video 2 Using the Candidates Test to Determine Absolute (Global) Extrema

This video will look at using the candidates test to locate absolute extrema. Common errors will also be discussed.

Jamil Siddiqui

5.6: Daily Video 1 Determining Concavity of Functions over Their Domains

In this video we will define concave up, concave down, and inflection points and learn how to determine each.

Jamil Siddiqui

5.6: Daily Video 2 Determining Concavity of Functions over Their Domains

In this video we will explore the relationship between the concavity of a function and its first derivative.

Jamil Siddiqui

5.7: Daily Video 1 Using the Second Derivative Test to Determine Extrema

In this video, we will learn how knowing the concavity of a function can help us understand the type of critical point we have.

Jamil Siddiqui

5.7: Daily Video 2 Using the Second Derivative Test to Determine Extrema

In this video, we will look at the second derivative test and how it can be used when an explicit function is not given.

Jamil Siddiqui

5.8: Daily Video 1 Sketching Graphs of Functions and Their Derivatives

This video will relate concavity and increasing and decreasing behaviors with the graphs of f, f’, and f”.

Karen Hyers

5.8: Daily Video 2 Sketching Graphs of Functions and Their Derivatives

In this video, we will look at the derivatives of a function presented in multiple representations and use them to make conclusions about the graph of the function.

Karen Hyers

5.9: Daily Video 1 Connecting a Function, Its First Derivative, and Its Second Derivative

This video will focus on the graph of the first derivative, f’, and determine how we can obtain key information about the graphs of both f and f”.

Karen Hyers

5.9: Daily Video 2 Connecting a Function, Its First Derivative, and Its Second Derivative

This video will focus on the graph of the second derivative, f”, and determine how we can obtain key information about the graphs of both f and f’.

Karen Hyers

5.10: Daily Video 1 Introduction to Optimization Problems

This video will apply techniques for finding maxima and minima in applications.

Karen Hyers

5.10: Daily Video 2 Introduction to Optimization Problems

In this video, we will solve optimization problems in a variety of contexts.

Karen Hyers

5.11: Daily Video 1 Solving Optimization Problems

This video will focus on interpreting maxima and minima within the context of a variety of applications.

Karen Hyers

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5.12: Daily Video 1 Exploring Behaviors of Implicit Relations

This video will focus on solving for critical points with implicitly defined relations.

Karen Hyers


This video will focus on finding the second derivative of implicit relations including examples that involve x, y, and dy/dx.

Karen Hyers


This video will focus on practice problems which use the first and second derivatives of implicit relations to draw conclusions about their graphs.

Karen Hyers


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Unit 6


6.1: Daily Video 1 Exploring Accumulations of Change

We will explore the connection between area and the accumulation of a rate of change in context.

Kimberley Thomas

6.1: Daily Video 2 Exploring Accumulations of Change

We will explore positive and negative accumulation and practice solving problems involving accumulation of change over an interval.

Kimberley Thomas

6.2: Daily Video 1 Approximating Areas with Riemann Sums

We will use left and right Riemann sums to approximate the area under a curve.

Kimberley Thomas


We will use midpoint Riemann sums and trapezoidal sums to approximate the area under the curve.

Kimberley Thomas


We will make the connection between the behavior of the function and whether an approximation for a definite integral is an underestimate or overestimate when possible.

Kimberley Thomas

6.3: Daily Video 1 Riemann Sums, Summation Notation, and Definite Integral Notation

We will connect the limit of a Riemann sum to a definite integral.

Kimberley Thomas

6.3: Daily Video 2 Riemann Sums, Summation Notation, and Definite Integral Notation

We will connect a definite integral to the limit of a Riemann sum.

Kimberley Thomas

6.4: Daily Video 1 The Fundamental Theorem of Calculus and Accumulation Functions

We will discuss how the Fundamental Theorem of Calculus connects differentiation and integration.

Kimberley Thomas

6.4: Daily Video 2 The Fundamental Theorem of Calculus and Accumulation Functions

We will practice solving problems by applying the Fundamental theorem of Calculus.

Kimberley Thomas

6.5: Daily Video 1 Interpreting the Behavior of Accumulation Functions Involving Area

We will apply the Fundamental Theorem of Calculus to analyze functions defined by an integral.

Kimberley Thomas

6.5: Daily Video 2 Interpreting the Behavior of Accumulation Functions Involving Area

We will practice finding information about accumulation functions defined by a definite integral.

Kimberley Thomas


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6.6: Daily Video 1 Applying Properties of Definite Integrals

We will understand and apply the properties of definite integrals.

Kimberley Thomas


We will work with functions that have removable or jump discontinuities.

Kimberley Thomas


We will practice calculating definite integrals using geometric areas and properties of definite integrals.

Kimberley Thomas

6.7: Daily Video 1 The Fundamental Theorem of Calculus and Definite Integrals

We will understand what is meant by antiderivative and apply the Fundamental Theorem of Calculus to evaluate definite integrals.

Kimberley Thomas


We will apply the Fundamental Theorem of Calculus to solve problems.

Kimberley Thomas


We will practice evaluating definite integrals using the Fundamental Theorem of Calculus.

Kimberley Thomas

6.8: Daily Video 1 Finding Antiderivatives and Indefinite Integrals—Basic Rules and Notation

This video will introduce indefinite integrals. We will connect them with our rules for derivatives.

Karen Hyers

6.8: Daily Video 2 Finding Antiderivatives and Indefinite Integrals—Basic Rules and Notation

This video will focus on examples of indefinite integrals using a variety of function types.

Karen Hyers

6.9: Daily Video 1 Integrating Using Substitution

This video will introduce the technique of u-substitution and connect it with the chain rule for derivatives.

Karen Hyers

6.9: Daily Video 2 Integrating Using Substitution

This video will demonstrate how to apply the technique of u-substitution to definite integrals.

Karen Hyers

6.10: Daily Video 1 Integrating Functions Using Long Division and Completing the Square

This video will apply the algebraic technique of long division to integrals involving rational functions.

Karen Hyers

6.10: Daily Video 2 Integrating Functions Using Long Division and Completing the Square

This video will apply the algebraic technique of completing the square to integrals of functions involving quadratic polynomials in the denominator.

Karen Hyers


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6.11: Daily Video 1 Integrating Using Integration by Parts

This video will introduce the technique of integration by parts and connect it with the product rule for derivatives.

Karen Hyers


This video will focus on additional practice with the technique of integration by parts.

Karen Hyers


This video will extend our work with integration by parts to definite integrals, including problems with tabular functions.

Karen Hyers

6.12: Daily Video 1 Integrating Using Linear Partial Fractions

This video will apply the algebraic technique of partial fraction decomposition to integrals involving rational functions.

Karen Hyers

6.13: Daily Video 1 Evaluating Improper Integrals

This video will introduce improper integrals. We will use limits to determine if an improper integral converges or diverges.

Karen Hyers

6.13: Daily Video 2 Evaluating Improper Integrals

In this video, we will practice more examples of improper integrals, including ones that require multiple calculus techniques.

Karen Hyers

6.14: Daily Video 1 Selecting Techniques for Antidifferentiation

This video will focus on strategies for deciding which integration technique to use based on the form of the integrand.

Karen Hyers

6.14: Daily Video 2 Selecting Techniques for Antidifferentiation

This video will focus on distinguishing among similar integrands to determine which integration technique to apply.

Karen Hyers


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Unit 7


7.1: Daily Video 1 Modeling Situations with Differential Equations

We will translate verbal descriptions of differential equations into algebraic representations.

Kimberley Thomas

7.1: Daily Video 2 Modeling Situations with Differential Equations

We will practice translating verbal descriptions of differential equations into algebraic representations.

Kimberley Thomas

7.2: Daily Video 1 Verifying Solutions for Differential Equations

We will verify that a proposed function is a solution to a differential equation.

Kimberley Thomas

7.2: Daily Video 2 Verifying Solutions for Differential Equations

We will apply the skill of verifying solutions to differential equations to solve problems presented in different ways.

Kimberley Thomas

7.3: Daily Video 1 Sketching Slope Fields

We will graph slope fields by hand as well as sketching in a particular solution through an initial condition.

Kimberley Thomas

7.3: Daily Video 2 Sketching Slope Fields

We will practice matching slope fields to differential equations.

Kimberley Thomas

7.4: Daily Video 1 Reasoning Using Slope Fields

We will work with differential equations and the slope fields that model them to answer questions.

Kimberley Thomas

7.4: Daily Video 2 Reasoning Using Slope Fields

We will continue to practice our reasoning skills with differential equations and the slope fields that model them.

Kimberley Thomas

7.5: Daily Video 1 Approximating Solutions Using Euler’s Method

We will learn what Euler’s method is and how it is used to approximate a solution to a differential equation or a point on a solution curve.

Kimberley Thomas


We will practice using Euler’s method to approximate a solution to a differential equation or a point on a solution curve.

Kimberley Thomas


We will continue to practice using Euler’s method to approximate a solution to a differential equation or a point on a solution curve.

Kimberley Thomas

7.6: Daily Video 1 Finding General Solutions Using Separation of Variables

We will use antidifferentiation and the method of separation of variables to find the general solution to a given differential equation.

Hooman Behzadpour

7.6: Daily Video 2 Finding General Solutions Using Separation of Variables

We will continue to practice using separation of variables to find the general solution to a given differential equation.

Hooman Behzadpour

7.7: Daily Video 1 Finding Particular Solutions Using Initial Conditions and Separation of Variables

We will use separation of variables to find the particular solution to a given differential equation and initial condition.

Hooman Behzadpour


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We will continue using separation of variables to find the particular solution to a given differential equation and initial condition.

Hooman Behzadpour


We will demonstrate our mastery of separation of variables by successfully completing free-response questions from prior AP Exams.

Hooman Behzadpour

7.8: Daily Video 1 Exponential Models with Differential Equations

We will show how models of exponential growth and decay derive from the simple differential equation dy/dt = ky.

Hooman Behzadpour

7.9: Daily Video 1 (BC ONLY) Logistic Models with Differential Equations

We will understand the forms of the logistic differential equation dy/dt = ky(a-y) and its key characteristics.

Hooman Behzadpour

7.9: Daily Video 2 (BC ONLY) Logistic Models with Differential Equations

We will analyze and interpret the logistic differential equation dy/dt = ky(a-y) in various contexts.

Hooman Behzadpour


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Unit 8


8.1: Daily Video 1 Finding the Average Value of a Function on an Interval

We will find the average value of a function on an interval. Hooman Behzadpour

8.1: Daily Video 2 Finding the Average Value of a Function on an Interval

We will continue finding the average value of a function on a given interval in a variety of contexts.

Hooman Behzadpour

8.2: Daily Video 1 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

We will use indefinite integrals to connect position, velocity, and acceleration functions.

Hooman Behzadpour


We will use definite integrals of velocity functions to define and find displacement, distance, and position.

Hooman Behzadpour


We will continue using integration to solve motion problems.

8.3: Daily Video 1 Using Accumulation Functions and Definite Integrals in Applied Contexts

We will evaluate and interpret the meaning of definite integrals in a variety of contexts.

Hooman Behzadpour

8.3: Daily Video 2 Using Accumulation Functions and Definite Integrals in Applied Contexts

We will continue to evaluate accumulation functions and definite integrals in a variety of contexts.

Hooman Behzadpour

8.4: Daily Video 1 Finding the Area Between Curves Expressed as Functions of x

We will find the area of the bounded region between two curves expressed as functions of x.

Hooman Behzadpour

8.4: Daily Video 2 Finding the Area Between Curves Expressed as Functions of x

We will continue to find the area of the bounded region between two curves expressed as functions of x.

Hooman Behzadpour

8.5: Daily Video 1 Finding the Area Between Curves Expressed as Functions of y

We will find the area of the bounded region between two curves expressed as functions of y.

Hooman Behzadpour


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8.5: Daily Video 2 Finding the Area Between Curves Expressed as Functions of y

We will continue to find the area of the bounded region between two curves expressed as functions of y.

Hooman Behzadpour

8.6: Daily Video 1 Finding the Area Between Curves That Intersect at More Than Two Points

We will find the total area of the bounded regions between two curves that intersect at more than two points.

Hooman Behzadpour

8.7: Daily Video 1 Volumes with Cross Sections—Squares and Rectangles

We will find the volume of a solid with square and rectangular cross sections.

Vicki Carter

8.7: Daily Video 2 Volumes with Cross Sections— Squares and Rectangles

We will continue to find the volume of a solid with square and rectangular cross sections.

Vicki Carter

8.8: Daily Video 1 Volumes with Cross Sections—Triangles and Semicircles

We will find the volume of a solid with triangular cross sections.

Vicki Carter


We will find the volume of a solid with semicircular cross sections.

Vicki Carter


We will find the volume of a solid with other geometrically defined cross sections

Vicki Carter

8.9: Daily Video 1 Volume with Disc Method—Revolving Around the x- or y-Axis

We will find the volume of a solid of revolution around the x-axis.

Vicki Carter

8.9: Daily Video 2 Volume with Disc Method—Revolving Around the x- or y-Axis

We will find the volume of a solid of revolution around the y-axis.

Vicki Carter

8.10: Daily Video 1 Volume with Disc Method—Revolving Around Other Axes

We will find the volume of a solid of revolution around any horizontal or vertical line in the plane.

Vicki Carter

8.11: Daily Video 1 Volume with Washer Method—Revolving Around the x- or y-Axis

We will find the volume of a solid of revolution around the x-axis whose cross sections are ring shaped.

Vicki Carter


20



8.11: Daily Video 2 Volume with Washer Method—Revolving Around the x- or y-Axis

We will find the volume of a solid of revolution around the y-axis whose cross sections are ring shaped.

Vicki Carter

8.12: Daily Video 1 Volume with Washer Method—Revolving Around Other Axes

We will find the volume of a solid of revolution around any horizontal or vertical line whose cross sections are ring shaped.

Vicki Carter

8.13: Daily Video 1 (BC ONLY) The Arc Length of a Smooth, Planar Curve and Distance Traveled

We will find the length of a smooth, planar curve. Vicki Carter

8.13: Daily Video 2 (BC ONLY) The Arc Length of a Smooth, Planar Curve and Distance Traveled

We will find the distance traveled along a smooth, planar curve.

Vicki Carter


21


Unit 9


9.1: Daily Video 1 Defining and Differentiating Parametric Equations

This video will review parametric equations by investigating their graphs as well as introducing how to take their derivatives.

Tony Record

9.1: Daily Video 2 Defining and Differentiating Parametric Equations

This video will demonstrate how to use the derivatives of parametric equations to find vertical and horizontal tangent lines.

Tony Record

9.2: Daily Video 1 Second Derivatives of Parametric Equations

This video will demonstrate how to find the second derivative of parametric equations and use it to determine the concavity of their graphs.

Tony Record

9.3: Daily Video 1 Finding Arc Lengths of Curves Given by Parametric Equations

This video will demonstrate how to find the length of a curve given by parametric equations.

Tony Record

9.4: Daily Video 1 Defining and Differentiating Vector-Valued Functions

This video will introduce vector-valued functions and demonstrate how to find their domains, sketch their graphs, and calculate their limits.

Tony Record

9.4: Daily Video 2 Defining and Differentiating Vector-Valued Functions

This video will demonstrate how to take the derivative of a vector-valued function.

Tony Record

9.5: Daily Video 1 Integrating Vector-Valued Functions

This video will demonstrate how to calculate both indefinite and definite integrals of vector-valued functions.

Tony Record

9.5: Daily Video 2 Integrating Vector-Valued Functions

This video will demonstrate how to solve differential equations involving vector-valued functions that provide initial conditions.

Tony Record

9.6: Daily Video 1 Solving Motion Problems Using Parametric and Vector-Valued Functions

We will use derivatives to determine velocity, speed, and acceleration of a particle moving along a curve.

Vicki Carter


We will use the definite integral to determine a particle’s displacement or total distance traveled.

Vicki Carter


We will look at some free-response questions from prior AP Exams that focus on motion along a curve.

Vicki Carter


22



9.7: Daily Video 1 Defining Polar Coordinates and Differentiating in Polar Form

We will calculate derivatives of functions written in polar form.

Vicki Carter

9.7: Daily Video 2 Defining Polar Coordinates and Differentiating in Polar Form

We will use derivatives of functions written in polar form to provide information about the curve.

Vicki Carter

9.8: Daily Video 1 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

We will calculate the area of a region defined by a polar curve.

Vicki Carter

9.8: Daily Video 2 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

We will focus on some questions from prior AP Exams that focus on the area of a polar region.

Vicki Carter

9.9: Daily Video 1 Finding the Area of the Region Bounded by Two Polar Curves

We will calculate the area of a region bounded by two polar curves.

Vicki Carter




Unit 10


10.1: Daily Video 1 Defining Convergent and Divergent Infinite Series

In this video, we will review sequences and introduce the concept of partial sums while focusing on the convergence or divergence of both.

Tony Record

10.2: Daily Video 1 Working with Geometric Series

In this video, we will investigate the infinite geometric series and determine the criteria for which such a series converges.

Tony Record

10.3: Daily Video 1 The nth Term Test for Divergence

In this video, we will introduce the nth term test for divergence and show how it can be used to determine if an infinite series diverges.

Tony Record

10.4: Daily Video 1 Integral Test for Convergence

In this video, we will introduce the integral test for convergence and focus on the three conditions that must be satisfied in order to apply the test.

Tony Record

10.4: Daily Video 2 Integral Test for Convergence

In this video, we will use the integral test for convergence to determine whether an infinite series converges or diverges.

Tony Record

10.5: Daily Video 1 Harmonic Series and p-Series

In this video, we will introduce the p-series and determine the conditions for which these series converge or diverge.

Tony Record

10.6: Daily Video 1 Comparison Tests for Convergence

In this video, we will discuss how to use the direct comparison test to determine the convergence or divergence of an infinite series.

Tony Record

10.6: Daily Video 2 Comparison Tests for Convergence

In this video, we will discuss how to use the limit comparison test to determine the convergence or divergence of an infinite series.

Tony Record

10.7: Daily Video 1 Alternating Series Test for Convergence

In this video, we will introduce the alternating series test and demonstrate how it can be used to determine the convergence or divergence of an alternating series.

Tony Record

10.8: Daily Video 1 Ratio Test for Convergence

In this video, we will use the ratio test to determine the convergence or divergence of an infinite series.

Tony Record

10.9: Daily Video 1 Determining Absolute or Conditional Convergence

This video will introduce and determine absolute versus conditional convergence of an infinite series.

Bryan Passwater

10.10: Daily Video 1 Alternating Series Error Bound

This video will introduce the alternating series error bound and explore examples of how this concept may be tested on the AP Exam.

Bryan Passwater

10.11: Daily Video 1 Finding Taylor Polynomial Approximations of Functions

This video will introduce the concept of a Taylor polynomial along with an example of writing a Taylor polynomial.

Bryan Passwater


This video will develop the general concept of a Taylor polynomial, leading to the general form that is used in AP Calculus BC.

Bryan Passwater


This video will focus on several examples of Taylor polynomials, including AP Exam–style problems.

Bryan Passwater

24



10.12: Daily Video 1 Lagrange Error Bound

This video will introduce Taylor’s theorem and give an overview of the Lagrange error bound.

Bryan Passwater

10.13: Daily Video 1 Radius and Interval of Convergence of Power Series

This video will introduce the power series along with the concept of the radius and interval of convergence for a given power series.

Bryan Passwater

10.13: Daily Video 2 Radius and Interval of Convergence of Power Series

This video will focus on using the ratio test to find the radius and interval of convergence for a power series.

Bryan Passwater

10.14: Daily Video 1 Finding Taylor or Maclaurin Series for a Function

This video will introduce the Maclaurin series for three important functions and use these series to construct the Maclaurin series for other functions.

Bryan Passwater

10.14: Daily Video 2 Finding Taylor or Maclaurin Series for a Function

This video will focus on functions that can be defined as a geometric series.

Bryan Passwater

10.15: Daily Video 1 Representing Functions as Power Series

This video will focus on using a known series to find a power series for a given function by differentiating or integrating the terms of the series.

Bryan Passwater

10.15: Daily Video 2 Representing Functions as Power Series

This video will focus on using algebraic processes and substitutions on a known series to find a power series for a given function.

Bryan Passwater


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