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Basic introductions to limits, derivatives, and integrals
- Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / BC, AB / BC Calc or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. AP Calculus AB covers basic introductions to limits, derivatives, and integrals.
en.wikipedia.org/wiki/AP_Calculus
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What is AP Calculus AB & BC?
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What is AP Calculus?
AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore ...
- The Exam
The AP Calculus AB Exam has consistent question types,...
- Classroom Resources
AP Classroom is a free and flexible online platform that...
- Course Audit
AP Calculus AB resource requirements: The school ensures...
- Professional Learning
Sign in to the AP Calculus Community. Share real-time...
- AP Calculus Development Committee
AP Calculus AB; Active Page: AP Calculus Development...
- AP Classroom
AP Classroom is an online platform that provides...
- Course and Exam Description
AP Calculus AB and BC: Course and Exam Description. Drag up...
- AP Calculus BC Course
AP Calculus BC is an introductory college-level calculus...
- The Exam
AP Calculus AB is an Advanced Placement calculus course. It is traditionally taken after precalculus and is the first calculus course offered at most schools except for possibly a regular or honors calculus class. The Pre-Advanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams.
PREPARING FOR AP CALCULUS AB ap-calc.github.io 1 Introduction 1.1 About The following notes aim to provide a discussion and summary of selected pre-requisite topics for students interested in enrolling in a full-year Advanced Placement Calculus AB course. The content spans a number of topics that my students have found challenging in recent years.
- Limits and Continuity. You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.
- Differentiation: Definition and Fundamental Properties. You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
- Differentiation: Composite, Implicit, and Inverse Functions. You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
- Contextual Applications of Differentiation. You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
- INCLUDES
- AP COURSE AND EXAM DESCRIPTIONS ARE UPDATED PERIODICALLY
- AP Equity and Access Policy
- Acknowledgments
- College Board Staf
- AP Course Development
- Enrolling Students: Equity and Access
- Ofering AP Courses: The AP Course Audit
- How the AP Program Is Developed
- Using and Interpreting AP Scores
- BECOMING AN AP READER
- How to Apply
- AP Resources and Supports
- AP Classroom
- UNIT GUIDES
- PERSONAL PROGRESS CHECKS
- PROGRESS DASHBOARD
- Digital Activation
- Instructional Model
- Plan
- Teach
- Assess
- About the AP Calculus AB and BC Courses
- College Course Equivalent
- Prerequisites
- Introduction
- Overview
- 1 MATHEMATICAL PRACTICES
- 2 COURSE CONTENT
- Mathematical Practices
- Course Content
- Big Ideas
- BIG IDEA 1: CHANGE (CHA)
- BIG IDEA 2: LIMITS (LIM)
- BIG IDEA 3: ANALYSIS OF FUNCTIONS (FUN)
- UNITS
- Spiraling the Big Ideas
- MATHEMATICAL PRACTICES
- BIG IDEAS
- Introduction
- REQUIRED COURSE CONTENT LABELING SYSTEM
Course framework Instructional section Sample exam questions
Please visit AP Central (apcentral.collegeboard.org) to determine whether a more recent course and exam description is available.
College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been tr...
College Board would like to acknowledge the following committee members, consultants, and reviewers for their assistance with and commitment to the development of this course. All individuals and their afiliations were current at the time of contribution. Gabe Anderson, Valor Christian High School, Highlands Ranch, CO Gail Burrill, Michigan State U...
Sara Hunter, Associate Director, AP Curricular Publications Tifany Judkins, Director, AP Instructional Design and PD Resource Development Claire Lorenz, Senior Director, AP Instructional Design and PD Resource Development Daniel McDonough, Senior Director, AP Content Integration Stephanie Ogden, Director, AP Mathematics Content Development SPEC...
In an ongoing efort to maintain alignment with best practices in college-level learning, AP courses and exams emphasize challenging, research-based curricula aligned with higher education expectations. Individual teachers are responsible for designing their own curriculum for AP courses, selecting appropriate college-level readings, assignments, an...
College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been tr...
The AP Program unequivocally supports the principle that each school implements its own curriculum that will enable students to develop the content understandings and skills described in the course framework. While the unit sequence represented in this publication is optional, the AP Program does have a short list of curricular and resource require...
The scope of content for an AP course and exam is derived from an analysis of hundreds of syllabi and course o erings of colleges and universities. Using this research and data, a committee of college faculty and expert AP teachers work within the scope of the corresponding college course to articulate what students should know and be able to do up...
The extensive work done by college faculty and AP teachers in the development of the course and exam and throughout the scoring process ensures that AP Exam scores accurately represent students’ achievement in the equivalent college course. Frequent and regular research studies establish the validity of AP scores as follows: While colleges and univ...
Each June, thousands of AP teachers and college faculty members from around the world gather for seven days in multiple locations to evaluate and score the free-response sections of the AP Exams. Ninety-eight percent of surveyed educators who took part in the AP Reading say it was a positive experience. There are many reasons to consider becoming a...
Visit collegeboard.org/apreading for eligibility requirements and to start the application process.
By completing a simple activation process at the start of the school year, teachers and students receive access to a robust set of classroom resources.
AP Classroom is a dedicated online platform designed to support teachers and students throughout their AP experience. The platform provides a variety of powerful resources and tools to provide yearlong support to teachers and enable students to receive meaningful feedback on their progress.
Appearing in this publication and on AP Classroom, these planning guides outline all required course content and skills, organized into commonly taught units. Each unit guide suggests a sequence and pacing of content, scafolds skill instruction across units, organizes content into topics, and provides tips on taking the AP Exam.
Formative AP questions for every unit provide feedback to students on the areas where they need to focus. Available online, Personal Progress Checks measure knowledge and skills through multiple-choice questions with rationales to explain correct and incorrect answers, and free-response questions with scoring information. Because the Personal Progr...
This dashboard allows teachers to review class and individual student progress throughout the year. Teachers can view class trends and see where students struggle with content and skills that will be assessed on the AP Exam. Students can view their own progress over time to improve their performance before the AP Exam.
In order to teach an AP class and make sure students are registered to take the AP Exam, teachers must first complete the digital activation process. Digital activation gives students and teachers access to resources and gathers students’ exam registration information online, eliminating most of the answer sheet bubbling that has added to testing t...
Integrating AP resources throughout the course can help students develop skills and conceptual understandings. The instructional model outlined below shows possible ways to incorporate AP resources into the classroom.
Teachers may consider the following approaches as they plan their instruction before teaching each unit. Review the overview at the start of each unit guide to identify essential questions, conceptual understandings, and skills for each unit. Use the Unit at a Glance table to identify related topics that build toward a common understanding, and the...
When teaching, supporting resources could be used to build students’ conceptual understanding and their mastery of skills. Use the topic pages in the unit guides to identify the required content. Integrate the content with a skill, considering any appropriate scafolding. Employ any of the instructional strategies previously identified. Use the avai...
Teachers can measure student understanding of the content and skills covered in the unit and provide actionable feedback to students. At the end of each unit, use AP Classroom to assign students the online Personal Progress Checks, as homework or an in-class task. Provide question-level feedback to students through answer rationales; provide unit- ...
AP Calculus AB and AP Calculus BC focus on students’ understanding of calculus concepts and provide experience with methods and applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), each course becomes a cohesive whole, rather than a collection of unrelated topics. Both ...
AP Calculus AB is designed to be the equivalent of a first semester college calculus course devoted to topics in diferential and integral calculus. AP Calculus BC is designed to be the equivalent to both first and second semester college calculus courses. AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defi...
Before studying calculus, all students should complete the equivalent of four years of secondary mathematics designed for college-bound students: courses that should prepare them with a strong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculus students should take courses in which they study a...
The course frameworks for AP Calculus AB and AP Calculus BC define content students must know and skills students must master in order to earn transferable, long-term understandings of calculus. The frameworks reflect a commitment to what college faculty value and mirror the curricula in corresponding college courses. Teachers may adjust the framew...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
NOTE: Labels are used to distinguish each unique element of the required course content and are used throughout this course and exam description. Additionally, they are used in the AP Question Bank and other resources found in AP Classroom. Enduring understandings are labeled sequentially according to the big idea that they are related to. Learning...
About AP. College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses in 38 subjects, each culminating in a challenging
The AP Calculus AB Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted).
