AP Calculus BC
111 lessons across 10 topics
1. Limits and Continuity
1Confirming Continuity Over An Interval2Connecting Infinite Limits And Vertical Asymptotes3Connecting Limits At Infinity And Horizontal Asymptotes4Connecting Multiple Representations Of Limits5Defining Continuity At A Point6Defining Limits And Using Limit Notation7Determining Limits Using Algebraic Manipulation8Determining Limits Using Algebraic Properties Of Limits9Determining Limits Using The Squeeze Theorem10Estimating Limit Values From Graphs11Estimating Limit Values From Tables12Exploring Types Of Discontinuities13Introducing Calculus: Can Change Occur At An Instant?14Removing Discontinuities15Selecting Procedures For Determining Limits16Working With The Intermediate Value Theorem (ivt)
2. Differentiation(COLON) Definition and Fundamental Properties
17Applying The Power Rule18Connecting Differentiability And Continuity: Determining When Derivatives Do And Do Not Exist19Defining Average And Instantaneous Rates Of Change At A Point20Defining The Derivative Of A Function And Using Derivative Notation21Derivative Rules: Constant, Sum, Difference, And Constant Multiple22Derivatives Of Cos X, Sin X, E^x, And Ln X23Estimating Derivatives Of A Function At A Point24Finding The Derivatives Of Tangent, Cotangent, Secant, And/or Cosecant Functions25The Product Rule26The Quotient Rule
3. Differentiation(COLON) Composite, Implicit, and Inverse Functions
4. Contextual Applications of Differentiation
33Approximating Values Of A Function Using Local Linearity And Linearization34Interpreting The Meaning Of The Derivative In Context35Introduction To Related Rates36Rates Of Change In Applied Contexts Other Than Motion37Solving Related Rates Problems38Straight-line Motion: Connecting Position, Velocity, And Acceleration39Using L’hospital’s Rule For Determining Limits Of Indeterminate Forms
5. Analytical Applications of Differentiation
40Connecting A Function, Its First Derivative, And Its Second Derivative41Determining Concavity Of Functions Over Their Domains42Determining Intervals On Which A Function Is Increasing Or Decreasing43Exploring Behaviors Of Implicit Relations44Extreme Value Theorem, Global Versus Local Extrema, And Critical Points45Introduction To Optimization Problems46Sketching Graphs Of Functions And Their Derivatives47Solving Optimization Problems48Using The Candidates Test To Determine Absolute (global) Extrema49Using The First Derivative Test To Determine Relative (local) Extrema50Using The Mean Value Theorem51Using The Second Derivative Test To Determine Extrema
6. Integration and Accumulation of Change
52Applying Properties Of Definite Integrals53Approximating Areas With Riemann Sums54Evaluating Improper Integrals55Exploring Accumulations Of Change56Finding Antiderivatives And Indefinite Integrals: Basic Rules And Notation57Integrating Functions Using Long Division And Completing The Square58Integrating Using Integration By Parts59Integrating Using Linear Partial Fractions60Integrating Using Substitution61Interpreting The Behavior Of Accumulation Functions Involving Area62Riemann Sums, Summation Notation, And Definite Integral Notation63Selecting Techniques For Antidifferentiation64The Fundamental Theorem Of Calculus And Accumulation Functions65The Fundamental Theorem Of Calculus And Definite Integrals
7. Differential Equations
66Approximating Solutions Using Euler’s Method67Exponential Models With Differential Equations68Finding General Solutions Using Separation Of Variables69Finding Particular Solutions Using Initial Conditions And Separation Of Variables70Logistic Models With Differential Equations71Modeling Situations With Differential Equations72Reasoning Using Slope Fields73Sketching Slope Fields74Verifying Solutions For Differential Equations
8. Applications of Integration
75Connecting Position, Velocity, And Acceleration Of Functions Using Integrals76Finding The Area Between Curves Expressed As Functions Of X77Finding The Area Between Curves Expressed As Functions Of Y78Finding The Area Between Curves That Intersect At More Than Two Points79Finding The Average Value Of A Function On An Interval80The Arc Length Of A Smooth, Planar Curve And Distance Traveled81Using Accumulation Functions And Definite Integrals In Applied Contexts82Volume With Disc Method: Revolving Around Other Axes83Volume With Disc Method: Revolving Around The X- Or Y-axis84Volume With Washer Method: Revolving Around Other Axes85Volume With Washer Method: Revolving Around The X- Or Y-axis86Volumes With Cross Sections: Squares And Rectangles87Volumes With Cross Sections: Triangles And Semicircles
9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
88Defining And Differentiating Parametric Equations89Defining And Differentiating Vector-valued Functions90Defining Polar Coordinates And Differentiating In Polar Form91Finding Arc Lengths Of Curves Given By Parametric Equations92Finding The Area Of A Polar Region Or The Area Bounded By A Single Polar Curve93Finding The Area Of The Region Bounded By Two Polar Curves94Integrating Vector-valued Functions95Second Derivatives Of Parametric Equations96Solving Motion Problems Using Parametric And Vector-valued Functions
10. Infinite Sequences and Series
97Alternating Series Error Bound98Alternating Series Test For Convergence99Comparison Tests For Convergence100Defining Convergent And Divergent Infinite Series101Determining Absolute Or Conditional Convergence102Finding Taylor Or Maclaurin Series For A Function103Finding Taylor Polynomial Approximations Of Functions104Harmonic Series And P-series105Integral Test For Convergence106Lagrange Error Bound107Radius And Interval Of Convergence Of Power Series108Ratio Test For Convergence109Representing Functions As Power Series110The Nth Term Test For Divergence111Working With Geometric Series