College Board · AP Calculus AB+BC
AP Calculus (AB+BC) Resources
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Units and topics
Choose a topic to see its available materials.
Unit 1 - Limits and Continuity16 topics
Open this unit →- Topic 1.1 Introducing Calculus: Can Change Occur at an Instant?Materials
- Topic 1.2 Defining Limits and Using Limit NotationMaterials
- Topic 1.3 Estimating Limit Values from GraphsMaterials
- Topic 1.4 Estimating Limit Values from TablesMaterials
- Topic 1.5 Determining Limits Using Algebraic Properties of LimitsMaterials
- Topic 1.6 Determining Limits Using Algebraic ManipulationMaterials
- Topic 1.7 Selecting Procedures for Determining LimitsMaterials
- Topic 1.8 Determining Limits Using the Squeeze TheoremMaterials
- Topic 1.9 Connecting Multiple Representations of LimitsMaterials
- Topic 1.10 Exploring Types of DiscontinuitiesMaterials
- Topic 1.11 Defining Continuity at a PointMaterials
- Topic 1.12 Confirming Continuity over an IntervalMaterials
- Topic 1.13 Removing DiscontinuitiesMaterials
- Topic 1.14 Connecting Infinite Limits and Vertical AsymptotesMaterials
- Topic 1.15 Connecting Limits at Infinity and Horizontal AsymptotesMaterials
- Topic 1.16 Working with the Intermediate Value Theorem (IVT)Materials
Unit 2 - Differentiation: Definition and Fundamental Properties10 topics
Open this unit →- Topic 2.1 Defining Average and Instantaneous Rates of Change at a PointMaterials
- Topic 2.2 Defining the Derivative of a Function and Using Derivative NotationMaterials
- Topic 2.3 Estimating Derivatives of a Function at a PointMaterials
- Topic 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not ExistMaterials
- Topic 2.5 Applying the Power RuleMaterials
- Topic 2.6 Derivative Rules: Constant, Sum, Difference, and Constant MultipleMaterials
- Topic 2.7 Derivatives of cos x, sin x, e^x, and ln xMaterials
- Topic 2.8 The Product RuleMaterials
- Topic 2.9 The Quotient RuleMaterials
- Topic 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant FunctionsMaterials
Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions6 topics
Open this unit →- Topic 3.1 The Chain RuleMaterials
- Topic 3.2 Implicit DifferentiationMaterials
- Topic 3.3 Differentiating Inverse FunctionsMaterials
- Topic 3.4 Differentiating Inverse Trigonometric FunctionsMaterials
- Topic 3.5 Selecting Procedures for Calculating DerivativesMaterials
- Topic 3.6 Calculating Higher-Order DerivativesMaterials
Unit 4 - Contextual Applications of Differentiation7 topics
Open this unit →- Topic 4.1 Interpreting the Meaning of the Derivative in ContextMaterials
- Topic 4.2 Straight-Line Motion: Connecting Position, Velocity, and AccelerationMaterials
- Topic 4.3 Rates of Change in Applied Contexts Other Than MotionMaterials
- Topic 4.4 Introduction to Related RatesMaterials
- Topic 4.5 Solving Related Rates ProblemsMaterials
- Topic 4.6 Approximating Values of a Function Using Local Linearity and LinearizationMaterials
- Topic 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate FormsMaterials
Unit 5 - Analytical Applications of Differentiation12 topics
Open this unit →- Topic 5.1 Using the Mean Value TheoremMaterials
- Topic 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical PointsMaterials
- Topic 5.3 Determining Intervals on Which a Function Is Increasing or DecreasingMaterials
- Topic 5.4 Using the First Derivative Test to Determine Relative (Local) ExtremaMaterials
- Topic 5.5 Using the Candidates Test to Determine Absolute (Global) ExtremaMaterials
- Topic 5.6 Determining Concavity of Functions over Their DomainsMaterials
- Topic 5.7 Using the Second Derivative Test to Determine ExtremaMaterials
- Topic 5.8 Sketching Graphs of Functions and Their DerivativesMaterials
- Topic 5.9 Connecting a Function, Its First Derivative, and Its Second DerivativeMaterials
- Topic 5.10 Introduction to Optimization ProblemsMaterials
- Topic 5.11 Solving Optimization ProblemsMaterials
- Topic 5.12 Exploring Behaviors of Implicit RelationsMaterials
Unit 6 - Integration and Accumulation of Change14 topics
Open this unit →- Topic 6.1 Exploring Accumulations of ChangeMaterials
- Topic 6.2 Approximating Areas with Riemann SumsMaterials
- Topic 6.3 Riemann Sums, Summation Notation, and Definite Integral NotationMaterials
- Topic 6.4 The Fundamental Theorem of Calculus and Accumulation FunctionsMaterials
- Topic 6.5 Interpreting the Behavior of Accumulation Functions Involving AreaMaterials
- Topic 6.6 Applying Properties of Definite IntegralsMaterials
- Topic 6.7 The Fundamental Theorem of Calculus and Definite IntegralsMaterials
- Topic 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and NotationMaterials
- Topic 6.9 Integrating Using SubstitutionMaterials
- Topic 6.10 Integrating Functions Using Long Division and Completing the SquareMaterials
- Topic 6.11 Integrating Using Integration by Parts (BC only)Materials
- Topic 6.12 Using Linear Partial Fractions (BC only)Materials
- Topic 6.13 Evaluating Improper Integrals (BC only)Materials
- Topic 6.14 Selecting Techniques for AntidifferentiationMaterials
Unit 7 - Differential Equations9 topics
Open this unit →- Topic 7.1 Modeling Situations with Differential EquationsMaterials
- Topic 7.2 Verifying Solutions for Differential EquationsMaterials
- Topic 7.3 Sketching Slope FieldsMaterials
- Topic 7.4 Reasoning Using Slope FieldsMaterials
- Topic 7.5 Approximating Solutions Using Euler's Method (BC only)Materials
- Topic 7.6 Finding General Solutions Using Separation of VariablesMaterials
- Topic 7.7 Finding Particular Solutions Using Initial Conditions and Separation of VariablesMaterials
- Topic 7.8 Exponential Models with Differential EquationsMaterials
- Topic 7.9 Logistic Models with Differential Equations (BC only)Materials
Unit 8 - Applications of Integration13 topics
Open this unit →- Topic 8.1 Finding the Average Value of a Function on an IntervalMaterials
- Topic 8.2 Connecting Position, Velocity, and Acceleration of Functions Using IntegralsMaterials
- Topic 8.3 Using Accumulation Functions and Definite Integrals in Applied ContextsMaterials
- Topic 8.4 Finding the Area Between Curves Expressed as Functions of xMaterials
- Topic 8.5 Finding the Area Between Curves Expressed as Functions of yMaterials
- Topic 8.6 Finding the Area Between Curves That Intersect at More Than Two PointsMaterials
- Topic 8.7 Volumes with Cross Sections: Squares and RectanglesMaterials
- Topic 8.8 Volumes with Cross Sections: Triangles and SemicirclesMaterials
- Topic 8.9 Volume with Disc Method: Revolving Around the x- or y-AxisMaterials
- Topic 8.10 Volume with Disc Method: Revolving Around Other AxesMaterials
- Topic 8.11 Volume with Washer Method: Revolving Around the x- or y-AxisMaterials
- Topic 8.12 Volume with Washer Method: Revolving Around Other AxesMaterials
- Topic 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)Materials
Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only)9 topics
Open this unit →- Topic 9.1 Defining and Differentiating Parametric EquationsMaterials
- Topic 9.2 Second Derivatives of Parametric EquationsMaterials
- Topic 9.3 Finding Arc Lengths of Curves Given by Parametric EquationsMaterials
- Topic 9.4 Defining and Differentiating Vector-Valued FunctionsMaterials
- Topic 9.5 Integrating Vector-Valued FunctionsMaterials
- Topic 9.6 Solving Motion Problems Using Parametric and Vector-Valued FunctionsMaterials
- Topic 9.7 Defining Polar Coordinates and Differentiating in Polar FormMaterials
- Topic 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar CurveMaterials
- Topic 9.9 Finding the Area of the Region Bounded by Two Polar CurvesMaterials
Unit 10 - Infinite Sequences and Series (BC only)15 topics
Open this unit →- Topic 10.1 Defining Convergent and Divergent Infinite SeriesMaterials
- Topic 10.2 Working with Geometric SeriesMaterials
- Topic 10.3 The nth Term Test for DivergenceMaterials
- Topic 10.4 Integral Test for ConvergenceMaterials
- Topic 10.5 Harmonic Series and p-SeriesMaterials
- Topic 10.6 Comparison Tests for ConvergenceMaterials
- Topic 10.7 Alternating Series Test for ConvergenceMaterials
- Topic 10.8 Ratio Test for ConvergenceMaterials
- Topic 10.9 Determining Absolute or Conditional ConvergenceMaterials
- Topic 10.10 Alternating Series Error BoundMaterials
- Topic 10.11 Finding Taylor Polynomial Approximations of FunctionsMaterials
- Topic 10.12 Lagrange Error BoundMaterials
- Topic 10.13 Radius and Interval of Convergence of Power SeriesMaterials
- Topic 10.14 Finding Taylor or Maclaurin Series for a FunctionMaterials
- Topic 10.15 Representing Functions as Power SeriesMaterials
Teaching slides
This course has 111 published PPTX files. A few shortcuts are shown below; open the course topics for the full set and previews.