All schools that want to label a course “AP” must get authorization by going through the AP Course Audit. This means submitting two things:
- A subject-specific AP Course Audit Form
- A course syllabus
Teachers have the option to create their own syllabus or adopt one of the sample syllabi provided. A teacher-created syllabus is checked by our reviewers to ensure that the course fulfills the AP Program’s course-specific curricular and resource requirements.
We offer plenty of resources, below, to help teachers understand course requirements and create a syllabus that fulfills these.
Designing Your AP Calculus BC Course
The AP Calculus BC course should be designed by your school to provide students with a learning experience equivalent to that of a full-year college course in single-variable calculus. Your Calculus BC course needs to develop students’ concepts of calculus and provide experience with its methods and applications. The course should emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. In addition, the connections among these representations should be highlighted.
Before studying calculus, students should complete four years of secondary mathematics designed for college-bound students; in these courses, they should study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions of the numbers 0, π/6, π/4, π/3, π/2, and their multiples.
Getting to Know the Course and Exam
The key document for each AP course is the course and exam description. Start by reviewing it to understand the objectives and expectations of the AP course and exam.
- AP Calculus AB and AP Calculus BC Course and Exam Description (.pdf/3.72MB) - Describes in detail the AP Calculus course and exam. Includes the curriculum framework and a representative sample of exam questions.
Creating Your Syllabus
Use these resources to design your syllabus.
Download this document for more help creating your syllabus.
- Syllabus Development Guide: AP Calculus BC (.pdf/210KB) - Includes the guidelines reviewers use to evaluate syllabi along with three samples of evidence for each requirement. This guide also specifies the level of detail required in the syllabus to receive course authorization.
Your course must fulfill these requirements, and your syllabus should make it clear how the requirements will be addressed.
AP Calculus BC curricular requirements:
- The course is structured around the enduring understandings within the three big ideas described in the AP Calculus Course and Exam Description (.pdf/3.7MB).
- The course provides students opportunities to apply the six Mathematical Practices for AP Calculus as they engage in the learning objectives described in the AP Calculus Course and Exam Description (.pdf/3.7MB).
- Students have access to graphing calculators and opportunities to use them to solve problems and to explore and interpret calculus concepts.
- Students and teachers have access to a college-level calculus textbook.
AP Calculus BC resource requirements:
- The school ensures that each student has a college-level calculus textbook (supplemented when necessary to meet the curricular requirements) for individual use inside and outside of the classroom.
- The school ensures each student has a graphing calculator for individual use inside and outside of the classroom, with all required capabilities listed in the AP Calculus Course and Exam Description (.pdf/3.7MB).
The list below represents examples of textbooks that meet the resource requirements of AP Calculus BC and have met or exceed the required alignment to the learning objectives and skills in the course curriculum framework. The list below is not exhaustive and the texts listed should not be regarded as endorsed, authorized, recommended, or approved by the College Board. Not using a book from this list does not mean that a course will not receive authorization. Syllabi submitted as part of the AP Course Audit process will be evaluated holistically, with textbooks considered along with supplementary, supporting resources to confirm that the course as a whole provides students with the content delineated in the curricular requirements of the AP Course Audit.
- The Charles A. Dana Center. Agile Mind Calculus AB. Agile Mind.
- Anton, Howard, Irl Bivens, and Stephen Davis. Calculus: Early Transcendentals, Single Variable. 10th Edition. Wiley.
- Anton, Howard, et al. Calculus, AP® Edition - Calculus AB. 11th edition. Wiley.
- Anton, Howard, et al. Calculus. 10th edition. Wiley.
- Anton, Howard, et al. Calculus: Single Variable. 10th edition. Wiley.
- Dietiker, Kysh, Sallee, Hoey. Calculus. 2nd edition. CPM.
- Dietiker, Kysh, Sallee, Hoey. Calculus- AP Calculus AB. 3rd Edition. CPM Educational Program.
- Hughes-Hallett, Deborah, et al. Calculus: Single and Multivariable, AP® Edition. 7th edition. Wiley.
- Hughes-Hallett, Deborah, et al. Calculus: Single and Multivariable. 6th edition. Wiley.
- Hughes-Hallett, Deborah, et al. Calculus: Single Variable. 6th edition. Wiley.
- Larson, Ron, and Bruce H. Edwards. Calculus National Geographic/Cengage Learning.
- Larson, Ron, and Paul Battaglia. Calculus for AP®. 1st edition. National Geographic/Cengage Learning.
- Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable National Geographic/Cengage Learning.
- Larson, Ron, and Bruce H. Edwards. Calculus: Early Transcendental Functions National Geographic/Cengage Learning.
- Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable: Early Transcendental Functions. National Geographic/Cengage Learning.
- Rogawski, Jon. Rogawski’s Calculus for AP®. 2nd edition. Bedford, Freeman and Worth Publishing Group.
- Stewart, James. Calculus. National Geographic/Cengage Learning.
- Stewart, James. Calculus: Early Transcendentals. National Geographic/Cengage Learning.
- Stewart, James. Single Variable Calculus. National Geographic/Cengage Learning.
- Stewart, James. Single Variable Calculus: Early Transcendentals. National Geographic/Cengage Learning.
- Stewart, James and Stephen Kokoska, Calculus for AP®: A Complete Course 1st edition. National Geographic/Cengage Learning.
- Sullivan, Michael, and Kathleen Miranda. Calculus for the AP® Course. 2nd edition. Bedford, Freeman and Worth Publishing Group.