AP Calculus AB
81 lessons across 8 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 Sums54Exploring Accumulations Of Change55Finding Antiderivatives And Indefinite Integrals: Basic Rules And Notation56Integrating Functions Using Long Division And Completing The Square57Integrating Using Substitution58Interpreting The Behavior Of Accumulation Functions Involving Area59Riemann Sums, Summation Notation, And Definite Integral Notation60Selecting Techniques For Antidifferentiation61The Fundamental Theorem Of Calculus And Accumulation Functions62The Fundamental Theorem Of Calculus And Definite Integrals
7. Differential Equations
63Exponential Models With Differential Equations64Finding General Solutions Using Separation Of Variables65Finding Particular Solutions Using Initial Conditions And Separation Of Variables66Modeling Situations With Differential Equations67Reasoning Using Slope Fields68Sketching Slope Fields69Verifying Solutions For Differential Equations
8. Applications of Integration
70Connecting Position, Velocity, And Acceleration Of Functions Using Integrals71Finding The Area Between Curves Expressed As Functions Of X72Finding The Area Between Curves Expressed As Functions Of Y73Finding The Area Between Curves That Intersect At More Than Two Points74Finding The Average Value Of A Function On An Interval75Using Accumulation Functions And Definite Integrals In Applied Contexts76Volume With Disc Method: Revolving Around Other Axes77Volume With Disc Method: Revolving Around The X- Or Y-axis78Volume With Washer Method: Revolving Around Other Axes79Volume With Washer Method: Revolving Around The X- Or Y-axis80Volumes With Cross Sections: Squares And Rectangles81Volumes With Cross Sections: Triangles And Semicircles