Why We Developed AP Precalculus
For thousands of new college students every year, introductory math is a disappointing barrier to success. Without strong preparation in high school, students struggle to complete remedial or introductory college math classes that are often taught in large lectures with minimal student support.
More than half of students enrolling at public two-year colleges and nearly a third of students at public four-year colleges are assigned to remedial math, and more than 40 percent of those students fail to complete their remedial coursework. That creates a huge barrier to college success, and it forces many aspiring STEM majors to abandon their intended field of study.
Offering a college-level precalculus course in high school will give students a new and valuable option for improving math readiness and staying on track for college.
The Advanced Placement® Program worked with college faculty to build a precalculus course that invites a more diverse group of students to prepare for college mathematics, encourages more students to complete four years of mathematics in high school, and improves student readiness to succeed in STEM courses and majors in college.
AP Precalculus will:
- Prepare more students for the rigors of college-level math.
- Address one of the biggest barriers to college completion, especially among underrepresented students.
- Create a new college credit opportunity for the many students who do not begin high school on an accelerated math track.
- Create a much broader pipeline for STEM majors by setting a strong foundation for further math coursework, including calculus, in college.
- Motivate, encourage, and reward high school students to develop the math proficiency needed for a variety of majors and careers.
An AP course in precalculus not only strengthens students’ preparation for calculus, but it also provides a bridge to college-level mathematics regardless of a student’s grade 9 starting point. The goal is to establish a path for more students to succeed in college-level mathematics and high-growth fields such as engineering, science, and medicine.
“AP Precalculus will open the door for many students to advanced course studies in mathematics and will bring a college-level course to students who may not have access to other AP math classes. It will level the playing field for underserved students, and all students who have completed an Algebra II course (or equivalent class) will be able to succeed in this course.” Brendan Murphy, John Bapst Memorial High School, Development Committee Member
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, Pacific University, Chief Reader
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 understanding of functions and their graphs as embodying dynamic covariation of quantities prepares students to tame 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.
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. AP Precalculus Exam scores can also be used by colleges for math and science course placement for newly enrolling students.
Teachers can enroll in an AP Summer Institute (APSI) for 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, free, digital instructional resources and through-course supports that include instructional videos, formative assessments, and personalized feedback reports.
Educators have an influential voice in 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. 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.