HUNTERTUTORING

Calculus BC · AP

High school · Math

Curriculum programs

AP Course and Exam Description (College Board)

Standards

Full Course and Exam Description framework, including course-scope topics not assessed on the AP Exam. Topics marked with an asterisk (*) are assessed on the exam.

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 Fundamental Properties

  • 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, eˣ, 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

  • 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

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
  • 6.12 * — Using Linear Partial Fractions
  • 6.13 * — Evaluating Improper Integrals
  • 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
  • 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

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

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

  • 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

  • 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

* Assessed on the AP Exam (per the Course and Exam Description). All topics listed; unmarked topics are course scope only.

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