AP DAILY VIDEOS AP calculus BC

AP DAILY VIDEOS AP Calculus BC AP DAILY VIDEOS AP Calculus BC AP 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 blen[.]

AP DAILY VIDEOS AP Calculus BC AP 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 AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 1.1: Daily Video 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 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 Defining Limits and Using Limit Notation An introduction to limits, using graphs, and the notation Bryan Passwater used to express limits; the differences between limit values and function values 1.2: Daily Video Defining Limits and Using Limit Notation Connecting limit notation across multiple representations; reinforcing the underlying concept of a limit Bryan Passwater 1.2: Daily Video Defining Limits and Using Limit Notation Practicing problems related to Topic 1.2, with an optional activity for additional practice with these concepts Bryan Passwater 1.3: Daily Video Estimating Limit Values from Graphs An introduction to one-sided limits, using graphs; verifying when a limit does or does not exist, using leftand right-sided limits Bryan Passwater 1.3: Daily Video Estimating Limit Values from Graphs Three cases when limits may fail to exist; exploring the limitations of—and misconceptions about—using graphs to determine limits Bryan Passwater 1.3: Daily Video Estimating Limit Values from Graphs Spotlight on the AP Exam: Multiple examples of how Topic Bryan Passwater 1.3 might appear 1.4: Daily Video 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 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 Determining Limits Using Algebraic Properties of Limits Transitioning from estimating limits to determining limits, Bryan Passwater using one-sided limits with piecewise-defined functions algebraically 1.5: Daily Video Determining Limits Using Algebraic Properties of Limits How to determine limits algebraically, using properties of Bryan Passwater limits involving sums, differences, products, and quotients 1.5: Daily Video Determining Limits Using Algebraic Properties of Limits Exploring problems where traditional limit laws cannot be applied; how to address limit problems involving compositions, sums, and products © 2020 College Board Bryan Passwater AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 1.6: Daily Video 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 1.6: Daily Video Determining Limits Using Algebraic Manipulation Additional examples of algebraic manipulation being used to determine limit values, including functions involving radical or trigonometric expressions Bryan Passwater 1.6: Daily Video Determining Limits Using Algebraic Manipulation Spotlight on the AP Exam: Multiple examples of how Topic Bryan Passwater 1.6 might appear 1.7: Daily Video Selecting Procedures for Determining Limits Selecting algebraic procedures to determine limits of rational and piecewise functions, as well as functions involving trigonometry or radicals 1.7: Daily Video Selecting Procedures for Determining Limits Strategies for recognizing and applying procedures with all Bryan Passwater types of limits from previous topics and through multiple representations 1.8: Daily Video Determining Introducing the squeeze theorem through an intuitive Limits Using the approach, utilizing graphs, and connecting it to an Squeeze Theorem understandable context Bryan Passwater 1.8: Daily Video Determining Implementing and reinforcing the conditions required to Limits Using the apply the squeeze theorem Squeeze Theorem Bryan Passwater 1.9: Daily Video 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 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 Exploring Types Exploring functions graphically and algebraically of Discontinuities to determine where, why, and how functions are discontinuous 1.10: Daily Video Exploring Types How to analyze and compare tabular, graphical, analytical, Theresa Horvath of Discontinuities and verbal function representations to determine points of discontinuity 1.10: Daily Video Exploring Types Spotlight on the AP Exam: How Topic 1.10 might appear, of Discontinuities with tips for showing proper justification Theresa Horvath 1.11: Daily Video 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 1.11: Daily Video Defining Continuity at a Point How to use graphical and analytical representations of functions to determine whether functions are continuous (or not) at specific points Theresa Horvath © 2020 College Board Bryan Passwater Theresa Horvath AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 1.11: Daily Video Defining Continuity at a Point Spotlight on the AP Exam: How Topic 1.11 might appear, with tips for showing proper justification Theresa Horvath 1.12: Daily Video 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 Confirming Continuity over an Interval Comparing and contrasting functions, both graphically Theresa Horvath and analytically, to determine whether they are continuous for all real numbers, on their domain, or neither 1.13: Daily Video 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 Removing Discontinuities Sample problems for practice with removing function discontinuities (or determining the discontinuity is non-removable) Theresa Horvath 1.14: Daily Video Connecting Infinite Limits and Vertical Asymptotes How one-sided limits of infinity can be used to prove the existence of vertical asymptotes Theresa Horvath 1.14: Daily Video Connecting Infinite Limits and Vertical Asymptotes Examining functions with vertical asymptotes; how to communicate about limits as the function approaches the vertical asymptote Theresa Horvath 1.14: Daily Video Connecting Infinite Limits and Vertical Asymptotes Examples of functions that possess vertical asymptotes and limits equal to infinity Theresa Horvath 1.15: Daily Video Connecting Limits at Infinity and Horizontal Asymptotes The connection between limits at infinity and the existence Theresa Horvath of horizontal asymptotes on the graph of functions 1.15: Daily Video Connecting Limits at Infinity and Horizontal Asymptotes How to analyze functions of various representations to determine their limits at infinity and the location of horizontal asymptotes Theresa Horvath 1.15: Daily Video Connecting Limits at Infinity and Horizontal Asymptotes Examining the end behavior of functions using limits at infinity; comparing magnitudes of functions to evaluate limits Theresa Horvath 1.16: Daily Video 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 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 © 2020 College Board AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus 2.1: Daily Video Defining Average and Instantaneous Rates of Change at a Point This video will present a discovery of the difference Theresa Horvath quotients for average rates of change and usage of limits to express instantaneous rates of change 2.1: Daily Video Defining Average and Instantaneous Rates of Change at a Point This video will demonstrate processes to compute average and instantaneous rates of change using multiple representations 2.1: Daily Video Defining Average and Instantaneous Rates of Change at a Point This video will look at ways Topic 2.1 might appear on the Theresa Horvath AP Exam Tips will be shared for showing proper notation 2.2: Daily Video 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 2.2: Daily Video Defining the Derivative of a Function and Using Derivative Notation This video will demonstrate correct procedures to compute Theresa Horvath the derivative of a function and tangent line equations using multiple representations 2.2: Daily Video Defining the Derivative of a Function and Using Derivative Notation This video will look at ways Topic 2.2 might appear on the Theresa Horvath AP Exam Tips will be shared for showing proper notation 2.3: Daily Video 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 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 Connecting This video will define differentiability and look at examples when the derivative exists, or fails to exist, and Differentiability and Continuity— how this connects with the continuity of a function Determining When Derivatives Do and Do Not Exist © 2020 College Board Instructor Theresa Horvath Theresa Horvath Theresa Horvath AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 2.4: Daily Video 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 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 Derivative This video will introduce the basic differentiation rules Rules—Constant, involving a constant, a sum, a difference, and a constant Sum, Difference, multiple and Multiple Tony Record 2.6: Daily Video Derivative This video will expand upon all previously taught Rules—Constant, differentiation rules by introducing problems involving Sum, Difference, graphical and numerical representations of functions and Constant Multiple Tony Record 2.6: Daily Video Derivative This video will focus on problems involving equations of Rules—Constant, tangent lines while utilizing all the differentiation rules Sum, Difference, that have been taught thus far and Constant Multiple Tony Record 2.7: Daily Video Derivatives of cos This video will introduce the basic rules for differentiating Tony Record four of the most common transcendental functions—cos x, x, sin x, ex, and ln x sin x, ex, and ln x 2.8: Daily Video 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 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 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 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 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 © 2020 College Board AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 3.1: Daily Video The Chain Rule This video will introduce how the chain rule can be used to differentiate composite functions Tony Record 3.1: Daily Video The Chain Rule This video will feature a variety of scenarios in which the Tony Record chain rule must be utilized, including problems that feature multiple representations of functions 3.1: Daily Video 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 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 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 Differentiating This video will introduce three ways in which the Inverse Functions derivative of an inverse function may be computed Tony Record 3.3: Daily Video Differentiating This video will focus on a method that works best in Inverse Functions all situations when taking the derivative of an inverse function Tony Record 3.4: Daily Video Differentiating Inverse Trigonometric Functions This video will introduce, develop, and implement differentiation rules for inverse trigonometric functions Bryan Passwater 3.4: Daily Video 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 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 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 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 Calculating Higher-Order Derivatives This video will work through several examples involving higher order derivatives as part of a “Twinning” activity Bryan Passwater © 2020 College Board AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 4.1: Daily Video 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 4.1: Daily Video Interpreting the Meaning of the Derivative in Context This video will focus on how to interpret a derivative in context, including strategies to ensure proper responses on the AP Exam Bryan Passwater 4.1: Daily Video Interpreting the Meaning of the Derivative in Context 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 Straight-Line This video will introduce straight-line motion and the Motion— connections between position, velocity, and acceleration Connecting while incorporating multiple representations Position, Velocity, and Acceleration Bryan Passwater 4.2: Daily Video Straight-Line Motion— Connecting Position, Velocity, and Acceleration 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 4.2: Daily Video Straight-Line Motion— Connecting Position, Velocity, and Acceleration 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 Rates of Change in Applied Contexts Other Than Motion This video will explore how units help us understand rates Jamil Siddiqui of change 4.3: Daily Video 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 Introduction to Related Rates This video will focus on differentiating equations with respect to different variables Jamil Siddiqui 4.4: Daily Video Introduction to Related Rates This video will look at how to create an equation that will connect rates Jamil Siddiqui 4.4: Daily Video Introduction to Related Rates This video will demonstrate the process of solving a related rates problem Jamil Siddiqui 4.5: Daily Video Solving Related Rates Problems This video will focus on interpreting the answer to a related rates problem Jamil Siddiqui 4.5: Daily Video Solving Related Rates Problems This video will focus on solving related rates problems Jamil Siddiqui 4.5: Daily Video Solving Related Rates Problems This video will expand on solving related rates problems by looking at more examples Jamil Siddiqui © 2020 College Board AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 4.6: Daily Video Approximating This video will explore how functions will behave linearly Values of a if looked at on a small enough interval Function Using Local Linearity and Linearization Jamil Siddiqui 4.6: Daily Video Approximating This video will focus on using tangent lines to Values of a approximate values Function Using Local Linearity and Linearization Jamil Siddiqui 4.7: Daily Video Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms This video will introduce L’Hospital’s rule and show the Bryan Passwater proper notation and implementation required to apply it on the AP Exam 4.7: Daily Video 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 © 2020 College Board Video Focus Instructor Bryan Passwater AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 5.1: Daily Video 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 5.1: Daily Video Using the Mean Value Theorem This video will focus on the conditions needed to apply the mean value theorem using both examples and nonexamples over multiple representations Karen Hyers 5.1: Daily Video Using the Mean Value Theorem This video will look at ways the mean value theorem might Karen Hyers appear on the AP Exam Tips will be shared for showing proper justification and notation 5.2: Daily Video Extreme Value Theorem, Global Versus Local Extrema, and Critical Points This video will introduce the extreme value theorem (EVT) Jamil Siddiqui and show examples Conditions of this theorem will also be discussed 5.2: Daily Video Extreme Value Theorem, Global Versus Local Extrema, and Critical Points This video will compare and contrast local extrema, global extrema, and critical points 5.3: Daily Video Determining This video will define increasing and decreasing and look Intervals on at introductory examples Which a Function Is Increasing or Decreasing Jamil Siddiqui 5.3: Daily Video This video will look at different representations of Determining functions and their derivatives and how to interpret them Intervals on Which a Function on the AP Exam Is Increasing or Decreasing Jamil Siddiqui 5.4: Daily Video Using the First Derivative Test to Determine Relative (Local) Extrema This video will look at the first derivative test for relative extrema and how to apply it 5.4: Daily Video Using the First Derivative Test to Determine Relative (Local) Extrema Jamil Siddiqui This video will look at the first derivative test and how it can be used with different representations of functions and their derivatives 5.5: Daily Video This video will look at how to find the location of the Using the Candidates Test absolute extrema on an interval once the critical values are known to Determine Absolute (Global) Extrema © 2020 College Board 10 Jamil Siddiqui Jamil Siddiqui Jamil Siddiqui AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 5.5: Daily Video Using the This video will look at using the candidates test to locate Candidates Test absolute extrema Common errors will also be discussed to Determine Absolute (Global) Extrema 5.6: Daily Video Determining Concavity of Functions over Their Domains In this video we will define concave up, concave down, and Jamil Siddiqui inflection points and learn how to determine each 5.6: Daily Video 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 5.7: Daily Video Using the Second In this video, we will learn how knowing the concavity of Jamil Siddiqui Derivative Test a function can help us understand the type of critical point to Determine we have Extrema 5.7: Daily Video Using the Second In this video, we will look at the second derivative test and Derivative Test how it can be used when an explicit function is not given to Determine Extrema Jamil Siddiqui 5.8: Daily Video Sketching Graphs This video will relate concavity and increasing and of Functions and decreasing behaviors with the graphs of f, f’, and f” Their Derivatives Karen Hyers 5.8: Daily Video Sketching Graphs In this video, we will look at the derivatives of a function of Functions and presented in multiple representations and use them to Their Derivatives make conclusions about the graph of the function Karen Hyers 5.9: Daily Video 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” 5.9: Daily Video Connecting a Function, Its First Derivative, and Its Second Derivative This video will focus on the graph of the second derivative, Karen Hyers f”, and determine how we can obtain key information about the graphs of both f and f’ 5.10: Daily Video Introduction to Optimization Problems This video will apply techniques for finding maxima and minima in applications Karen Hyers 5.10: Daily Video Introduction to Optimization Problems In this video, we will solve optimization problems in a variety of contexts Karen Hyers 5.11: Daily Video Solving Optimization Problems This video will focus on interpreting maxima and minima within the context of a variety of applications Karen Hyers © 2020 College Board Video Focus Instructor 11 Jamil Siddiqui Jamil Siddiqui Karen Hyers AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 5.12: Daily Video Exploring This video will focus on solving for critical points with Behaviors of implicitly defined relations Implicit Relations Karen Hyers 5.12: Daily Video Exploring This video will focus on finding the second derivative of Behaviors of implicit relations including examples that involve x, y, and Implicit Relations dy/dx Karen Hyers 5.12: Daily Video Exploring This video will focus on practice problems which use the Behaviors of first and second derivatives of implicit relations to draw Implicit Relations conclusions about their graphs Karen Hyers © 2020 College Board Video Focus Instructor 12 AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic 6.1: Daily Video Exploring We will explore the connection between area and the Accumulations of accumulation of a rate of change in context Change Kimberley Thomas 6.1: Daily Video Exploring We will explore positive and negative accumulation and Accumulations of practice solving problems involving accumulation of Change change over an interval Kimberley Thomas 6.2: Daily Video Approximating Areas with Riemann Sums We will use left and right Riemann sums to approximate the area under a curve Kimberley Thomas 6.2: Daily Video Approximating Areas with Riemann Sums We will use midpoint Riemann sums and trapezoidal sums Kimberley Thomas to approximate the area under the curve 6.2: Daily Video Approximating Areas with Riemann Sums We will make the connection between the behavior of Kimberley Thomas the function and whether an approximation for a definite integral is an underestimate or overestimate when possible 6.3: Daily Video 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 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 The Fundamental We will discuss how the Fundamental Theorem of Calculus connects differentiation and integration Theorem of Calculus and Accumulation Functions Kimberley Thomas 6.4: Daily Video The Fundamental We will practice solving problems by applying the Fundamental theorem of Calculus Theorem of Calculus and Accumulation Functions Kimberley Thomas 6.5: Daily Video 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 Interpreting the Behavior of Accumulation Functions Involving Area We will practice finding information about accumulation functions defined by a definite integral Kimberley Thomas © 2020 College Board Video Focus Instructor 13 AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 6.6: Daily Video Applying Properties of Definite Integrals We will understand and apply the properties of definite integrals Kimberley Thomas 6.6: Daily Video Applying Properties of Definite Integrals We will work with functions that have removable or jump discontinuities Kimberley Thomas 6.6: Daily Video Applying Properties of Definite Integrals We will practice calculating definite integrals using geometric areas and properties of definite integrals Kimberley Thomas 6.7: Daily Video The Fundamental We will understand what is meant by antiderivative and Theorem of apply the Fundamental Theorem of Calculus to evaluate Calculus and definite integrals Definite Integrals Kimberley Thomas 6.7: Daily Video The Fundamental We will apply the Fundamental Theorem of Calculus to Theorem of solve problems Calculus and Definite Integrals Kimberley Thomas 6.7: Daily Video The Fundamental We will practice evaluating definite integrals using the Theorem of Fundamental Theorem of Calculus Calculus and Definite Integrals Kimberley Thomas 6.8: Daily Video 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 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 Integrating Using This video will introduce the technique of u-substitution Substitution and connect it with the chain rule for derivatives Karen Hyers 6.9: Daily Video Integrating Using This video will demonstrate how to apply the technique of Substitution u-substitution to definite integrals Karen Hyers 6.10: Daily Video 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 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 © 2020 College Board 14 AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 6.11: Daily Video Integrating Using This video will introduce the technique of integration by Integration by parts and connect it with the product rule for derivatives Parts Karen Hyers 6.11: Daily Video Integrating Using This video will focus on additional practice with the Integration by technique of integration by parts Parts Karen Hyers 6.11: Daily Video Integrating Using This video will extend our work with integration by Integration by parts to definite integrals, including problems with Parts tabular functions Karen Hyers 6.12: Daily Video Integrating Using This video will apply the algebraic technique of Linear Partial partial fraction decomposition to integrals involving Fractions rational functions Karen Hyers 6.13: Daily Video 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 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 Selecting This video will focus on strategies for deciding Techniques for which integration technique to use based on the form of Antidifferentiation the integrand Karen Hyers 6.14: Daily Video This video will focus on distinguishing among similar Karen Hyers Selecting integrands to determine which integration technique to apply Techniques for Antidifferentiation © 2020 College Board Video Focus Instructor 15 AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 7.1: Daily Video Modeling Situations with Differential Equations We will translate verbal descriptions of differential equations into algebraic representations Kimberley Thomas 7.1: Daily Video Modeling Situations with Differential Equations We will practice translating verbal descriptions of differential equations into algebraic representations Kimberley Thomas 7.2: Daily Video 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 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 Sketching Slope Fields We will graph slope fields by hand as well as sketching in a Kimberley Thomas particular solution through an initial condition 7.3: Daily Video Sketching Slope Fields We will practice matching slope fields to differential equations Kimberley Thomas 7.4: Daily Video 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 Reasoning Using Slope Fields We will continue to practice our reasoning skills with Kimberley Thomas differential equations and the slope fields that model them 7.5: Daily Video 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 7.5: Daily Video Approximating Solutions Using Euler’s Method We will practice using Euler’s method to approximate a solution to a differential equation or a point on a solution curve Kimberley Thomas 7.5: Daily Video Approximating Solutions Using Euler’s Method 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 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 Finding General Solutions Using Separation of Variables We will continue to practice using separation of variables Hooman Behzadpour to find the general solution to a given differential equation 7.7: Daily Video We will use separation of variables to find the particular Finding solution to a given differential equation and initial condition Particular Solutions Using Initial Conditions and Separation of Variables © 2020 College Board 16 Hooman Behzadpour AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 7.7: Daily Video Finding We will continue using separation of variables to find the Particular particular solution to a given differential equation and Solutions Using initial condition Initial Conditions and Separation of Variables 7.7: Daily Video Finding We will demonstrate our mastery of separation of variables Hooman Behzadpour Particular by successfully completing free-response questions from Solutions Using prior AP Exams Initial Conditions and Separation of Variables 7.8: Daily Video 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 (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 (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 © 2020 College Board Video Focus Instructor 17 Hooman Behzadpour AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic Video Focus Instructor 8.1: Daily Video 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 Finding the Average Value of a Function on an Interval We will continue finding the average value of a function on Hooman Behzadpour a given interval in a variety of contexts 8.2: Daily Video Connecting We will use indefinite integrals to connect position, Position, Velocity, velocity, and acceleration functions and Acceleration of Functions Using Integrals 8.2: Daily Video Connecting We will use definite integrals of velocity functions to define Hooman Behzadpour Position, Velocity, and find displacement, distance, and position and Acceleration of Functions Using Integrals 8.2: Daily Video Connecting We will continue using integration to solve motion problems Position, Velocity, and Acceleration of Functions Using Integrals 8.3: Daily Video 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 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 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 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 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 © 2020 College Board 18 Hooman Behzadpour AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 8.5: Daily Video 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 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 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 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 Volumes with Cross Sections— Triangles and Semicircles We will find the volume of a solid with triangular cross sections Vicki Carter 8.8: Daily Video Volumes with Cross Sections— Triangles and Semicircles We will find the volume of a solid with semicircular cross sections Vicki Carter 8.8: Daily Video Volumes with Cross Sections— Triangles and Semicircles We will find the volume of a solid with other geometrically defined cross sections Vicki Carter 8.9: Daily Video 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 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 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 We will find the volume of a solid of revolution around the Volume with Washer Method— x-axis whose cross sections are ring shaped Revolving Around the x- or y-Axis Vicki Carter © 2020 College Board 19 AP CALCULUS BC AP DAILY VIDEOS Video Title Topic 8.11: Daily Video Volume with We will find the volume of a solid of revolution around the Washer Method— y-axis whose cross sections are ring shaped Revolving Around the x- or y-Axis Vicki Carter 8.12: Daily Video Volume with We will find the volume of a solid of revolution around Washer Method— any horizontal or vertical line whose cross sections are Revolving ring shaped Around Other Axes Vicki Carter 8.13: Daily Video (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 (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 © 2020 College Board Video Focus Instructor 20 ... Theresa Horvath AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 1.11: Daily Video Defining Continuity at a Point Spotlight on the AP Exam: How Topic 1.11 might appear, with... Focus Instructor 13 AP CALCULUS BC AP DAILY VIDEOS Video Title Topic Video Focus Instructor 6.6: Daily Video Applying Properties of Definite Integrals We will understand and apply the properties... Relations conclusions about their graphs Karen Hyers © 2020 College Board Video Focus Instructor 12 AP CALCULUS BC AP DAILY VIDEOS Unit Video Title Topic 6.1: Daily Video Exploring We will explore