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Calculus AB · AP · High school · Math
All Course and Exam Description units and topics for Calculus AB · AP. Topics marked with an asterisk (*) are assessed on the AP Exam; unmarked topics are course scope only. Click a topic for details and future study materials.
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Unit 1: Limits and Continuity
- 1.1 * — Introducing Calculus: Can Change Occur at an Instant? CHA-1
- 1.2 * — Represent limits analytically using correct notation.
- 1.3 * — Estimating Limit Values from Graphs LIM-1 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims
- 1.4 * — Estimating Limit Values from Tables LIM-1 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims
- 1.5 * — Determining Limits Using Algebraic Properties of Limits LIM-1 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims
- 1.6 * — Determining Limits Using Algebraic Manipulation LIM-1
- 1.7 * — Selecting Procedures for Determining Limits This topic is intended to focus on the skill of selecting an appropriate procedure for determining limits. Students should be given opportunities to practice when and how to apply all learning objectives relating to determining limits.
- 1.8 * — Determining Limits Using the Squeeze Theorem LIM-1
- 1.9 * — Connecting Multiple Representations of Limits This topic is intended to focus on connecting representations. Students should be given opportunities to practice when and how to apply all learning objectives relating to limits and translating mathematical information from a single representation or across multiple representations.
- 1.10 * — Exploring Types of Discontinuities LIM-2 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims about continuity.
- 1.11 * — Defining Continuity at a Point LIM-2 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims
- 1.12 * — Confirming Continuity over an Interval LIM-2 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims about continuity.
- 1.13 * — Removing Discontinuities LIM-2 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims about continuity.
- 1.14 * — Connecting Infinite Limits and Vertical Asymptotes LIM-2
- 1.15 * — Connecting Limits at Infinity and Horizontal Asymptotes LIM-2 Reasoningwithdefinitions,theorems,andpropertiescanbeusedtojustifyclaims
- 1.16 * — Working with the Intermediate Value Theorem (IVT) FUN-1
Unit 2: Differentiation — Definition and Fundamental Properties
- 2.1 * — Defining Average and Instantaneous Rates of Change at a Point CHA-2 Derivatives allow us to determine rates of change at an instant by applying limits to
- 2.2 * — Defining the Derivative of a Function and Using Derivative Notation CHA-2 Derivatives allow us to determine rates of change at an instant by applying limits to
- 2.3 * — Estimating Derivatives of a Function at a Point § Classroom Resource > Approximation
- 2.4 * — Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- 2.5 * — Applying the Power Rule FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 2.6 * — Derivative Rules: Constant, Sum, Difference, and Constant Multiple FUN-3
- 2.7 * — Derivatives of cos x, sin x, e x, and ln x FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 2.8 * — The Product Rule FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 2.9 * — The Quotient Rule FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 2.10 * — Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
Unit 3: Differentiation — Composite, Implicit, and Inverse Functions
- 3.1 * — The Chain Rule FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 3.2 * — Implicit Differentiation FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 3.3 * — Differentiating Inverse Functions FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
- 3.4 * — Differentiating Inverse Trigonometric Functions FUN-3
- 3.5 * — Selecting Procedures for Calculating Derivatives This topic is intended to focus on the skill of selecting an appropriate procedure for calculating derivatives. Students should be given opportunities to practice when and how to apply all learning objectives relating to calculating derivatives.
- 3.6 * — Calculating Higher -Order Derivatives FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation. Contextual Applications of Dif ferentiation
Unit 4: Contextual Applications of Differentiation
- 4.1 * — Interpreting the Meaning of the Derivative in Context CHA-3
- 4.2 * — Straight-Line Motion: Connecting Position, Velocity, and Acceleration CHA-3
- 4.3 * — Rates of Change in Applied Contexts Other Than Motion CHA-3
- 4.4 * — Introduction to Related Rates § Professional Development > Related
- 4.5 * — Solving Related Rates Problems CHA-3 Derivatives allow us to solve real-world problems involving rates of change.
- 4.6 * — Approximating Values of a Function Using Local Linearity and Linearization CHA-3 Derivatives allow us to solve real-world problems involving rates of change.
- 4.7 * — Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms LIM-4 L’Hospital’s Rule allows us to determine the limits of some indeterminate forms.
Unit 5: Analytical Applications of Differentiation
- 5.1 * — Using the Mean Value Theorem FUN-1 Existence theorems allow us to draw conclusions about a function’s behavior on an
- 5.2 * — Extreme Value Theorem, Global Versus Local Extrema, and Critical Points FUN-1
- 5.3 * — Determining Intervals on Which a Function Is Increasing or Decreasing FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.4 * — Using the First Derivative Test to Determine Relative (Local) Extrema FUN-4
- 5.5 * — Using the Candidates Test to Determine Absolute (Global) Extrema FUN-4
- 5.6 * — Determining Concavity of Functions over Their Domains § AP Online Teacher Community
- 5.7 * — Using the Second Derivative Test to Determine Extrema FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.8 * — Sketching Graphs of Functions and Their Derivatives FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.9 * — Connecting a Function, Its First Derivative, and Its Second Derivative FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.10 * — Introduction to Optimization Problems FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.11 * — Solving Optimization Problems FUN-4 A function’s derivative can be used to understand some behaviors of the function.
- 5.12 * — Exploring Behaviors of Implicit Relations FUN-4 A function’s derivative can be used to understand some behaviors of the function.
Unit 6: Integration and Accumulation of Change
- 6.1 * — Exploring Accumulations of Change Use appropriate units of measure.
- 6.2 * — Approximating Areas with Riemann Sums LIM-5 Definiteintegralscanbeapproximatedusinggeometricandnumericalmethods.
- 6.3 * — Riemann Sums, Summation Notation, and Definite Integral Notation LIM-5
- 6.4 * — The Fundamental Theorem of Calculus and Accumulation Functions FUN-5
- 6.5 * — Interpreting the Behavior of Accumulation Functions Involving Area FUN-5 TheFundamentalTheoremofCalculusconnectsdifferentiationandintegration.
- 6.6 * — Applying Properties of Definite Integrals FUN-6 Recognizing opportunities to apply knowledge of geometry and mathematical rules
- 6.7 * — The Fundamental Theorem of Calculus and Definite Integrals § Professional Development > The Fundamental Theorem
- 6.8 * — Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation FUN-6 Recognizing opportunities to apply knowledge of geometry and mathematical rules
- 6.9 * — Integrating Using Substitution § Professional Development > Applying Procedures
- 6.10 * — Integrating Functions Using Long Division and Completing the Square FUN-6 Recognizing opportunities to apply knowledge of geometry and mathematical rules
- 6.11 * — Integrating Using Integration by Parts bc only FUN-6 Recognizing opportunities to apply knowledge of geometry and mathematical rules
- 6.12 * — Integrating Using Linear Partial Fractions bc only FUN-6 Recognizing opportunities to apply knowledge of geometry and mathematical rules
- 6.13 * — Evaluating Improper Integrals bc only § AP Online Teacher Community Discussion > U-Substitution with
- 6.14 * — Selecting Techniques for Antidifferentiation This topic is intended to focus on the skill of selecting an appropriate procedure for antidifferentiation.Studentsshouldbegivenopportunitiestopracticewhenandhow toapplyalllearningobjectivesrelatingtoantidifferentiation.
Unit 7: Differential Equations
- 7.1 * — Modeling Situations with Differential Equations FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.2 * — Verifying Solutions for Differential Equations FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.3 * — Sketching Slope Fields FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.4 * — Reasoning Using Slope Fields FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.5 * — Approximating Solutions Using Euler’s Method bc only FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.6 * — Finding General Solutions Using Separation of Variables FUN-7
- 7.7 * — Finding Particular Solutions Using Initial Conditions and Separation of Variables FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.8 * — Exponential Models with Differential Equations FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
- 7.9 * — Logistic Models with Differential Equations bc only FUN-7 Solvingdifferentialequationsallowsustodeterminefunctionsanddevelopmodels.
Unit 8: Applications of Integration
- 8.1 * — Finding the Average Value of a Function on an Interval CHA-4 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchange
- 8.2 * — Connecting Position, Velocity, and Acceleration of Functions Using Integrals CHA-4 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchange
- 8.3 * — Using Accumulation Functions and Definite Integrals in Applied Contexts § Professional
- 8.4 * — Finding the Area Between Curves Expressed as Functions of x Required Course Content CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.5 * — Finding the Area Between Curves Expressed as Functions of y CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.6 * — Finding the Area Between Curves That Intersect at More Than Two Points CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.7 * — Volumes with Cross Sections: Squares and Rectangles CHA-5
- 8.8 * — Volumes with Cross Sections: Triangles and Semicircles CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.9 * — Volume with Disc Method: Revolving Around the x- or y-Axis CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.10 * — Volume with Disc Method: Revolving Around Other Axes CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.11 * — Volume with Washer Method: Revolving Around the x- or y-Axis CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.12 * — Volume with Washer Method: Revolving Around Other Axes CHA-5 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
- 8.13 * — The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only CHA-6 Definiteintegralsallowustosolveproblemsinvolvingtheaccumulationofchangein
* Assessed on the AP Exam (per the Course and Exam Description). All topics listed; unmarked topics are course scope only.
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