AP Calculus BC Cram Sheet

Every BC unit and its current exam weighting, including parametric work and series, with the guide that teaches the method.

Weightings are from the current Course at a Glance. Open a unit if a line is still fuzzy.

How the exam breaks down

Unit 1: Limits and Continuity

5-10% of the BC exam

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)

Method pages: How to Find Limits: Every Method, in Order, Continuity and the Three Types of Discontinuity, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 2: Differentiation: Definition and Fundamental Properties

5-10% of the BC exam

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

Method pages: Product Rule vs Quotient Rule: How and When to Use Each, Derivatives of Trig Functions: Table and Memory Tricks, Derivative of ln x, e^x, and a^x: Answers and Proofs, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

5-10% of the BC exam

3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives

Method pages: Chain Rule: Spot the Composition, Then Differentiate, Implicit Differentiation: Finding dy/dx Step by Step, Derivatives of Trig Functions: Table and Memory Tricks, Derivative of ln x, e^x, and a^x: Answers and Proofs.

Unit 4: Contextual Applications of Differentiation

5-10% of the BC exam

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

Method pages: Related Rates: The 5-Step Method for Any Word Problem, L'Hopital's Rule: When You Can and Cannot Use It, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 5: Analytical Applications of Differentiation

10-15% of the BC exam

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

Method pages: Optimization Word Problems: Setup, Constraint, Solve, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 6: Integration and Accumulation of Change

15-20% of the BC exam

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
6.12 Integrating Using Linear Partial Fractions
6.13 Evaluating Improper Integrals
6.14 Selecting Techniques for Antidifferentiation

Method pages: U-Substitution: How to Choose u and Integrate It, Integration by Parts: LIATE, When to Use It, Examples, U-Sub vs Integration by Parts vs Partial Fractions, The Fundamental Theorem of Calculus: Part 1 vs Part 2.

Unit 7: Differential Equations

5-10% of the BC exam

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
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

Method pages: Separable Differential Equations: Step-by-Step Method, Slope Fields and Euler's Method Explained, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 8: Applications of Integration

5-10% of the BC exam

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

Method pages: Disk vs Washer vs Shell: Choosing the Volume Method, Area Between Two Curves: Setup, dx vs dy, Examples, How to Study for AP Calculus AB: Unit-by-Unit Plan.

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

10-15% of the BC exam

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

Method pages: Parametric and Polar Calculus: Derivatives and Area.

Unit 10: Infinite Sequences and Series

15-20% of the BC exam

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

Method pages: Which Series Convergence Test Should I Use?, The Ratio Test: How It Works and When to Use It, Taylor and Maclaurin Series: How to Build Them.

Related rates, step by step: walk through a related-rates shock. Course hub: AP Calculus BC.