AP Calculus
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Practice for the AP Calculus exam
AP Exam
Monday, May 10, 2027
8 a.m. local time (morning session)
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Unit 1: Limits and Continuity
- 1.1 - Introducing Calculus: Can Change Occur at an Instant?
- 1.2 - Defining Limits and Using Limit Notation
- 1.3 - Estimating Limit Values from Graphs
- 1.4 - Estimating Limit Values from Tables
- 1.5 - Determining Limits Using Algebraic Properties of Limits
- 1.6 - Determining Limits Using Algebraic Manipulation
- 1.7 - Selecting Procedures for Determining Limits
- 1.8 - Determining Limits Using the Squeeze Theorem
- 1.9 - Connecting Multiple Representations of Limits
- 1.10 - Exploring Types of Discontinuities
- 1.11 - Defining Continuity at a Point
- 1.12 - Confirming Continuity over an Interval
- 1.13 - Removing Discontinuities
- 1.14 - Connecting Infinite Limits and Vertical Asymptotes
- 1.15 - Connecting Limits at Infinity and Horizontal Asymptotes
- 1.16 - Working with the Intermediate Value Theorem (IVT)
Unit 2: Differentiation: Definition and Basic Derivative Rules
- 2.1 - Defining Average and Instantaneous Rates of Change at a Point
- 2.2 - Defining the Derivative of a Function and Using Derivative Notation
- 2.3 - Estimating Derivatives of a Function at a Point
- 2.4 - Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- 2.5 - Applying the Power Rule
- 2.6 - Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 - Derivatives of cos x, sin x, e^x, and ln x
- 2.8 - The Product Rule
- 2.9 - The Quotient Rule
- 2.10 - Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
- 4.1 - Interpreting the Meaning of the Derivative in Context
- 4.2 - Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- 4.3 - Rates of Change in Applied Contexts Other Than Motion
- 4.4 - Introduction to Related Rates
- 4.5 - Solving Related Rates Problems
- 4.6 - Approximating Values of a Function Using Local Linearity and Linearization
- 4.7 - Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Unit 5: Analytical Applications of Differentiation
- 5.1 - Using the Mean Value Theorem
- 5.2 - Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- 5.3 - Determining Intervals on Which a Function Is Increasing or Decreasing
- 5.4 - Using the First Derivative Test to Determine Relative (Local) Extrema
- 5.5 - Using the Candidates Test to Determine Absolute (Global) Extrema
- 5.6 - Determining Concavity of Functions over Their Domains
- 5.7 - Using the Second Derivative Test to Determine Extrema
- 5.8 - Sketching Graphs of Functions and Their Derivatives
- 5.9 - Connecting a Function, Its First Derivative, and Its Second Derivative
- 5.10 - Introduction to Optimization Problems
- 5.11 - Solving Optimization Problems
- 5.12 - Exploring Behaviors of Implicit Relations
Unit 6: Integration and Accumulation of Change
- 6.1 - Exploring Accumulations of Change
- 6.2 - Approximating Areas with Riemann Sums
- 6.3 - Riemann Sums, Summation Notation, and Definite Integral Notation
- 6.4 - The Fundamental Theorem of Calculus and Accumulation Functions
- 6.5 - Interpreting the Behavior of Accumulation Functions Involving Area
- 6.6 - Applying Properties of Definite Integrals
- 6.7 - The Fundamental Theorem of Calculus and Definite Integrals
- 6.8 - Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- 6.9 - Integrating Using Substitution
- 6.10 - Integrating Functions Using Long Division and Completing the Square
- 6.11 Integrating Using Integration by Parts (BC ONLY)
- 6.12 - Using Linear Partial Fractions (BC ONLY)
- 6.13 - Evaluating Improper Integrals (BC ONLY)
- 6.14 - Selecting Techniques for Antidifferentiation
Unit 7: Differential Equations
- 7.1 - Modeling Situations with Differential Equations
- 7.2 - Verifying Solutions for Differential Equations
- 7.3 - Sketching Slope Fields
- 7.4 - Reasoning Using Slope Fields
- 7.5 - Approximating Solutions Using Euler's Method (BC ONLY)
- 7.6 - Finding General Solutions Using Separation of Variables
- 7.7 - Finding Particular Solutions Using Initial Conditions and Separation of Variables
- 7.8 - Exponential Models with Differential Equations
- 7.9 - Logistic Models with Differential Equations (BC ONLY)
Unit 8: Applications of Integration
- 8.1 - Finding the Average Value of a Function on an Interval
- 8.2 - Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- 8.3 - Using Accumulation Functions and Definite Integrals in Applied Contexts
- 8.4 - Finding the Area Between Curves Expressed as Functions of x
- 8.5 - Finding the Area Between Curves Expressed as Functions of y
- 8.6 - Finding the Area Between Curves That Intersect at More Than Two Points
- 8.7 - Volumes with Cross Sections: Squares and Rectangles
- 8.8 - Volumes with Cross Sections: Triangles and Semicircles
- 8.9 - Volume with Disc Method: Revolving Around the x- or y-Axis
- 8.10 - Volume with Disc Method: Revolving Around Other Axes
- 8.11 - Volume with Washer Method: Revolving Around the x- or y-Axis
- 8.12 - Volume with Washer Method: Revolving Around Other Axes
- 8.13 - The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC ONLY)
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC ONLY)
- 9.1 - Defining and Differentiating Parametric Equations
- 9.2 - Second Derivatives of Parametric Equations
- 9.3 - Finding Arc Lengths of Curves Given by Parametric Equations
- 9.4 - Defining and Differentiating Vector-Valued Functions
- 9.5 - Integrating Vector-Valued Functions
- 9.6 - Solving Motion Problems Using Parametric and Vector-Valued Functions
- 9.7 - Defining Polar Coordinates and Differentiating in Polar Form
- 9.8 - Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
- 9.9 - Finding the Area of the Region Bounded by Two Polar Curves
Unit 10: Infinite Sequences and Series (BC ONLY)
- 10.1 - Defining Convergent and Divergent Infinite Series
- 10.2 - Working with Geometric Series
- 10.3 - The nth Term Test for Divergence
- 10.4 - Integral Test for Convergence
- 10.5 - Harmonic Series and p-Series
- 10.6 - Comparison Tests for Convergence
- 10.7 - Alternating Series Test for Convergence
- 10.8 - Ratio Test for Convergence
- 10.9 - Determining Absolute or Conditional Convergence
- 10.10 - Alternating Series Error Bound
- 10.11 - Finding Taylor Polynomial Approximations of Functions
- 10.12 - Lagrange Error Bound
- 10.13 - Radius and Interval of Convergence of Power Series
- 10.14 - Finding Taylor or Maclaurin Series for a Function
- 10.15 - Representing Functions as Power Series