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AP Calculus BC

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Open to: Grades 8 - 12

Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Precalculus or the equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: This is an AP Calculus course, equivalent to a year-long Calculus BC sequence.

Course Code: CBC

Course Description


This online and individually-paced course in Advanced Placement (AP) Calculus is approved by the College Board and covers topics in single variable differential and integral calculus typically found in a first year, two-semester, college Calculus I and II course sequence. CTY does not register students for, or administer the College Board AP Calculus AB/BC Exams. However, if students chose to take the AP Calculus BC exam after this course, they will be well prepared. Students who have successfully completed AP Calculus AB may wish to enroll in Calculus C instead.

In this course, students will learn calculus by actively engaging with their instructor, the textbook, a graphing calculator, and online videos and animations. Students may progress at their own rate with full comprehension of the course materials. The student’s knowledge will be assessed by homework assignments, free-response questions, and chapter tests. There are three cumulative unit exams and a final exam based on the actual AP Calculus AB/BC exams. For assignments and exams, students will solve problems by hand, as well as use technology, and be expected to compose clearly written solutions. Students will be required to solve both applied and abstract problems involving limits, derivatives, and integrals. This course prepares students to succeed on the AP Calculus BC exam and in subsequent courses that draw on that material.

Terms and Conditions

This course does not have any synchronous class meetings, but students may schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns.

Virtual classrooms, and student activities in the classroom, may be recorded and added to the course as an ongoing asset for all class students to review. Students may be invited to interact in CTY community spaces that include students and instructors and potentially specially invited guests that are not enrolled in their course. Student contributions (e.g., projects, forum posts, etc.) may remain in the course after the student completes the course. These artifacts may be preserved to showcase student work or to continue important conversations.

Topics Include:

  • Functions and Models
  • Limits
  • The Derivative
  • Applications of Differentiation
  • Integration
  • Applications of Integration
  • Techniques of Integration
  • Differential Equations
  • Infinite Sequences and Series
  • Parametric Equations and Polar Coordinates

Materials Needed

A graphing calculator is required, such as:

  • TI-83 PLUS
  • TI-84 PLUS
  • TI-85
  • TI-86
  • TI-89

To see a full list of allowable calculators, visit the College Board website to view the AP Calculus calculator policy. Most of the calculator screen illustrations in the eBook and lessons are from the Texas Instruments TI-84 Plus CE.

Hard Copy Textbook (Optional)

Calculus for AP, 1st Edition, by James Stewart and Stephen Kokoska. Published by Cengage. ISBN-13: 978-1337282765. Note that the course comes with access to the electronic textbook (eBook) and online homework system, WebAssign.

Headphone with microphone: You'll need this to participate in virtual classroom sessions and reviews with your instructor.

Full List of Topics

List of Topics

Chapter 1: Functions and Models

  • The Rule of Four
  • Mathematical Models: A Catalog of Essential Functions
  • Trigonometric Functions
  • New Functions from Old Functions
  • Exponential Functions
  • Inverse Functions and Logarithms
  • Technology in AP® Calculus

Chapter 2: Limits

  • The Tangent and Velocity Problems
  • An Introduction to the Limit of a Function
  • Calculating Limits Using the Limit Laws
  • Limits at Infinity and Horizontal Asymptotes
  • Continuity
  • The Precise Definition of a Limit

Chapter 3: The Derivative

  • Derivatives and Rates of Change
  • The Derivative as a Function
  • Derivatives of Polynomials and Exponential Functions
  • The Product and Quotient Rules
  • Derivatives of Trigonometric Functions
  • The Chain Rule
  • Implicit Differentiation and Derivatives of Inverse Functions
  • Derivatives of Logarithmic Functions
  • Applications of the Derivative
  • Related Rates
  • Local Linearity

Chapter 4: Applications of Differentiation

  • Maximum and Minimum Values
  • The Mean Value Theorem
  • How Derivatives Affect the Shape of a Graph
  • Indeterminate Forms and L’Hospital’s Rule
  • Summary of Curve Sketching
  • Optimization Problems

Chapter 5: Integration

  • Antiderivatives

  • Riemann Sums
  • The Definite Integral
  • The Fundamental Theorem of Calculus
  • Indefinite Integrals
  • The Method of Substitution

Chapter 6: Applications of Integration

  • Area Between Curves
  • Average Value of a Function
  • The Definite Integral as an Accumulation Function
  • Rectilinear Motion Revisited
  • Volumes
  • Arc Length

Chapter 7: Techniques of Integration

  • Integration by Parts
  • Trigonometric Integrals
  • Trigonometric Substitution
  • Integration of Rational Functions by Partial Fractions
  • Strategy for Integration
  • Improper Integrals

Chapter 8: Differential Equations

  • Slope Fields and Euler’s Method
  • Separable Equations
  • Models for Population Growth

Chapter 9: Infinite Sequences and Series

  • Sequences
  • Series
  • The Integral Test and Estimates of Sums
  • The Comparison Tests
  • Alternating Series
  • Absolute Convergence and the Ratio and Root Tests
  • Strategy for Testing Series
  • Power Series
  • Representations of Functions as Power Series
  • Taylor and Maclaurin Series

Chapter 10: Parametric Equations and Polar Coordinates

  • Curves Defined by Parametric Equations
  • Calculus with Parametric Curves
  • Polar Coordinates and Derivatives
  • Areas and Lengths in Polar Coordinates

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Sample Video

Sample Video

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

Zoom online virtual classroom
This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.

Electronic Texbook (eBook) and WebAssign Online Homework System: This course requires the use of WebAssign for online homework and access to the electronic textbook. Visit the WebAssign website for system requirements.