# About AP Precalculus

## About the Course

In AP Precalculus, students explore everyday situations and phenomena using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, an important practice for thriving in an ever-changing world.

AP Precalculus prepares students for other college-level mathematics and science courses. The framework delineates content and skills common to college precalculus courses that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. Students study each function type through their graphical, numerical, verbal, and analytical representations and their applications in a variety of contexts. Furthermore, students apply their understanding of functions by constructing and validating appropriate function models for scenarios, sets of conditions, and data sets, thereby gaining a deeper understanding of the nature and behavior of each function type.

Modeling is also a key feature of the course. Students select, construct, and validate function models using transformations of functions and regressions. Students learn to select mathematical models-based characteristics of a bivariate data set; characteristics of covarying quantities and their relative rates of change; or a set of characteristics such as zeros, asymptotes, and extrema. Students also identify, interpret, and apply information from a function model for a given context or data set, subject to assumptions and limitations related to the context.

Through the course, students strengthen their procedural and symbolic fluency skills needed for higher level mathematics. While studying each function type, students solve equations and construct equivalent analytic representations in both contextual and purely mathematical settings.

"AP Precalculus has the potential to change the landscape of high school mathematics and the transition to college. The course provides an excellent foundation for calculus but also serves as an appropriate capstone mathematics course that will open pathways to success in STEM fields. The curriculum, while remaining true to traditional precalculus topics such as logarithmic and trigonometric functions, includes additional tools and skills such as the use of logarithmic scales, and modeling discrete dynamical systems with matrices. These together with an emphasis on rates of change and applications provide students the mathematical knowledge and skills that will prove tremendously beneficial in biology, chemistry, environmental science, kinesiology, and other sciences." Michael Boardman, Chief Reader

See how AP Precalculus fits into students' mathematics pathways.

## What Will Students Experience in AP Precalculus?

Modeling Real-World Data: Students will apply the mathematical tools they acquire in real-world modeling situations. By examining scenarios, conditions, and data sets and determining and validating an appropriate function model, students gain a deeper understanding of the nature and behavior of each function type.

Exploring Multiple Representations: Students will examine functions through multiple representations. Students will gain a deeper understanding of functions by examining them graphically, numerically, verbally, and analytically.

Mastering Symbolic Manipulation: Students will develop rigorous symbolic manipulation skills needed for future mathematics courses. Students learn that a single mathematical object can have different analytical representations depending on the function type or coordinate system, and that the different analytical representations reveal different attributes of the mathematical object.

Harnessing a Dynamic World: Students will engage in function building that does not reflect a static view of things but embodies how things change. Every function representation characterizes the way in which values of one variable simultaneously change as the values in another variable change. This study of functions and their graphs as embodying dynamic covariation of quantities prepares students to understand an ever-changing world.

“The AP Precalculus course content leverages research on learning calculus that calls for precalculus to include a focus on students conceptualizing quantities' values and considering how they are related and vary together. Including a focus on exploring how quantities change together allows students to understand and define growth patterns described in applied problems using function formulas and graphs.” Marilyn Carlson, Arizona State University, Development Committee Member

## How We Developed AP Precalculus

Every AP course is designed—and regularly updated—in consultation with college faculty and experienced high school teachers. In an ongoing effort to maintain alignment with best practices in college-level learning, AP courses and exams emphasize research-based curricula aligned with higher education expectations. College faculty and experienced high school teachers guide the development of the AP course framework, which defines what students must know and be able to do to earn a qualifying score on the AP Exam, thus conferring college credit or placement.

Throughout 2021, the AP Program gathered course research through examination of college syllabi, analysis of textbooks and pedagogical research, and content advisory sessions with college faculty. Then, an advisory board and writing team collaborated on the course framework based on these research inputs.

See the course framework.

## Credit and Placement

Precalculus fulfills a math requirement at a diverse range of colleges and universities, including the majority of public institutions. However, most highly selective colleges do not treat precalculus as a college-level course, and thus college credit for AP Precalculus will not be available at such institutions; instead, AP Precalculus will provide students attending such colleges with superb preparation for AP Calculus in high school or college calculus when they matriculate. The course also offers a valuable tool for guiding math and science placement for newly enrolling students. College Board is working with colleges and universities to expand credit policies and ensure that AP Precalculus sets a strong foundation for college success.

## Supporting Teachers

Teachers can enroll in an AP Summer Institute (APSI) for AP Precalculus, a four-day professional learning experience that equips teachers with a deep understanding of the course framework, exam, and instructional supports. Additional one-day professional learning workshops will also be available. APSI scholarships will be available to teachers who qualify.

AP students and teachers receive access to AP Classroom, which has free, digital instructional resources and through-course supports that include instructional videos, formative assessments, and personalized feedback reports.

## Recruiting Students

You have an influential voice in your students’ decisions about AP courses and college aspirations. AP Precalculus is for any student seeking a rigorous third- or fourth-year mathematics course following completion of Algebra 2. This course prepares students for calculus and prepares students to succeed in both STEM and non-STEM majors. AP Precalculus helps students interested in STEM majors develop an exceptionally strong foundation for calculus, the launchpad for most STEM majors. Students interested in non-STEM majors that do not require calculus can use AP Precalculus as a capstone math course, earning college credits that clear the way to focus in college on courses most relevant to their major and career. Moreover, AP Precalculus will have given such students the language and ideas surrounding the deep study of functions—used in the visual arts and music—or the ability to model complex systems that social and behavioral science students can use to examine the complexity of human individual and group interactions.

Given the benefits of AP Precalculus, teachers, counselors, and administrators should do everything possible to ensure the demographic representation in the AP Precalculus course mirrors their school’s population, eliminating all barriers that discourage students traditionally underrepresented in advanced math courses from participating.