SUMMER OF CODE (Jun 8 - Aug 21) Make your summer count.

AP® Precalculus

  9-12 graders

  Credits awarded on transcript  

  Algebra II completed with B- or better

  UC A-G approval pending

  2 hours per day (summer)  

  8-10 students per class

  4 days per week 2, 4, or 6 weeks

  669 per student, per week  

  Self paced instructor-guided  

  Personalized 1-1 support

  Office hours 1 hour per week

  1799 per student, per semester  

  90 minutes per class

  4-8 students per class

  Twice per week over 36 weeks

  1799 per student, per semester  

AP® Precalculus is a college-level course designed to prepare students for the AP® Precalculus exam and future Calculus coursework. Aligned with the College Board's AP Precalculus framework, this course provides a comprehensive exploration of mathematical functions and their applications through algebraic, numerical, and graphical analysis. By shifting the focus from computational fluency to deep conceptual understanding, students master the behavior of functions across multiple representations and develop the mathematical reasoning needed for success in advanced mathematics and science.

The course covers four major mathematical domains aligned to the AP exam: polynomial and rational functions, exponential and logarithmic functions, trigonometric and polar functions, and parametric equations with vectors and matrices. Students will develop proficiency in:

  • Modeling real-world phenomena using diverse function families including linear, polynomial, rational, exponential, logarithmic, and trigonometric functions
  • Analyzing function behavior through multiple representations—algebraic, graphical, numerical, and verbal
  • Applying procedural and symbolic fluency to manipulate functions and solve complex equations
  • Constructing mathematical arguments using precise language and logical reasoning
  • Connecting periodic and circular motion to trigonometric concepts through the unit circle

Students build advanced mathematical thinking as they explore how different function families describe the world around them—from exponential growth in population dynamics to trigonometric models of periodic phenomena. The course emphasizes the interconnections between representations, helping students see how a table, graph, equation, and verbal description all capture different facets of the same mathematical relationship.

Students should have successfully completed Algebra II with a grade of B- or higher before enrolling. The highest performing students enjoy working with abstract mathematical structures, are comfortable with multi-step problem solving, and have strong algebraic manipulation skills. AP® Precalculus provides a direct bridge to AP Calculus and serves as essential preparation for college-level mathematics and the quantitative demands of fields such as engineering, physics, economics, and data science.

Students will be provided access to lessons and practice AP exams through AP Classroom.
  Authorized by the College Board to use the AP® designation.
   University of California A-G approved for [C] Mathematics credits.

Course Outline

    hide details
  1. Functions
    This unit establishes the foundational language of functions that underpins the entire course. Students explore function notation, domain and range, and rates of change to describe graph behavior. They study composition of functions, transformations including shifts, reflections, and stretches, and absolute value functions. The unit culminates with inverse functions, building students' ability to analyze how functions relate to one another and setting the stage for deeper study of specific function families.
  2. Linear Functions
    Building on the foundation of general functions, this unit provides a focused study of linear relationships. Students analyze and graph linear functions, develop models from real-world data, and use linear regression to fit models to data sets. Through this unit, students strengthen their ability to interpret slope as a rate of change and to use linear functions as the simplest yet most fundamental tool for mathematical modeling.
  3. Polynomial and Rational Functions
    This unit extends students' understanding to higher-degree polynomials and rational functions. Students begin with complex numbers, then explore quadratic functions, power functions, and polynomial graphs including end behavior and the relationship between zeros and factors. Polynomial division and the Remainder Theorem provide tools for rewriting expressions, while rational functions introduce asymptotic behavior. The unit also covers inverses, radical functions, and modeling using variation.
  4. Exponential and Logarithmic Functions
    Students explore exponential functions and their graphs, then are introduced to logarithms as the inverse operation to exponentiation. The unit covers logarithmic properties, solving exponential and logarithmic equations, and building mathematical models for growth and decay. Students learn to fit exponential models to real-world data, developing the ability to recognize and quantify exponential patterns in fields ranging from finance to biology.
  5. Trigonometric Functions
    This unit introduces the trigonometric functions by beginning with angles and their measurement. Students study the unit circle and use it to define the sine, cosine, and tangent functions, then extend these definitions through right triangle trigonometry. The unit builds the conceptual foundation for understanding periodicity by connecting circular motion to function values, preparing students for the deeper exploration of trigonometric graphs and identities that follow.
  6. Periodic Functions
    Building directly on the trigonometric foundations, this unit focuses on the graphical behavior of periodic functions. Students graph the sine, cosine, and other trigonometric functions, analyzing amplitude, period, phase shift, and vertical translation. The unit also introduces inverse trigonometric functions, which allow students to determine angle measures from known ratios—a key tool applied in later units for solving trigonometric equations.
  7. Trigonometric Identities and Equations
    This unit deepens students' mastery of trigonometric relationships through identities and equation-solving techniques. Students work with fundamental identities, sum and difference formulas, double-angle and half-angle formulas, and the optional sum-to-product and product-to-sum formulas. They learn systematic approaches to solving trigonometric equations and apply trigonometric functions to model periodic real-world phenomena such as tides, temperatures, and sound waves.
  8. Further Applications of Trigonometry
    This unit extends into advanced topics including the Law of Sines and Law of Cosines for non-right triangles (optional), polar coordinates, polar graphs, and the polar form of complex numbers. Students explore parametric equations and their graphs, gaining a new way to describe curves and motion. The unit also introduces vectors and their operations, connecting algebraic and geometric perspectives and aligning with the AP Precalculus framework's emphasis on parameters, vectors, and non-Cartesian representations.
  9. Systems of Equations and Inequalities
    This unit covers methods for solving systems of linear equations in two and three variables, as well as systems of nonlinear equations and inequalities. Students explore partial fractions (optional) and are introduced to matrix operations, including solving systems using matrix inverses and Cramer's Rule. These algebraic tools provide powerful methods for handling multiple-variable problems encountered in science, engineering, and economics.
  10. Analytic Geometry
    Students study the conic sections—ellipses, hyperbolas, and parabolas—from an analytical perspective. By deriving and using the standard equations for each curve, students learn to identify key features such as foci, vertices, and asymptotes. This unit connects algebraic representations to geometric shapes, reinforcing the course's emphasis on multiple representations and providing applications in physics, engineering, and astronomy.
  11. Sequences and Counting Theory
    The course concludes with an exploration of sequences, series, and introductory combinatorics. Students study arithmetic and geometric sequences, their notations, and associated series formulas. The unit introduces counting principles and the Binomial Theorem, connecting patterns in algebra to foundational ideas in discrete mathematics that are essential for future coursework in calculus and statistics.
Summer of Code
    see detailed summer schedule

The course is 100% online. Students will have access to an online textbook. However, students must have access to a printer at home to print out worksheets and other materials.

Students should have access to a device with a camera to take photos of their work for submission.

In addition to the standard requirements, AP® Precalculus students will need:

A graphing calculator (required for the AP® exam) or access to Desmos
Graph paper
Pencil and paper for working through problems

To take any of our courses, students must be familiar with opening a browser, navigating to a website, and joining a Zoom meeting.

Students must have a quiet place to study and participate in the class for the duration of the class. Some students may prefer a headset to isolate any background noise and help them focus in class.

Most course lectures and content may be viewed on mobile devices but programming assignments and certain quizzes require a desktop or laptop computer.

Students are required to have their camera on at all times during the class, unless they have an explicit exception approved by their parent or legal guardian.

Our technology requirements are similar to that of most Online classes.

A desktop or laptop computer running Windows (PC), Mac OS (Mac), or Chrome OS (Chromebook).
Students must be able to run a Zoom Client.
A working microphone, speaker, webcam, and an external mouse.
A high-speed internet connection with at least 15mbps download speed (check your Internet speed).

We encourage (but do not require) students taking AP® courses to take the AP Exams administered in May by the College Board. Being an Online School, we do not conduct AP® Exams ourselves yet. See the College Board's website to find a local location near you, if your school doesn't offer these exams.

This course includes several timed tests where you will be asked to complete a given number of questions within a 60-90 minutes limit. These tests are designed to keep you competitively prepared but you can take them as often as you like. We do not proctor these exams, neither do we require that you install special lockdown browser.

In today's environment, when students have access to multiple devices, most attempts to avoid cheating in online exams are symbolic. Our exams are meant to encourage you to learn and push yourself using an honor system.

We do assign a grade at the end of the year based on a number of criteria which includes class participation, completion of assignments, and performance in the tests. We do not reveal the exact formula to minimize students' incentive to optimize for a higher grade.

We believe that your grade in the course should reflect how well you have learnt the skills, and a couple of timed-tests, while traditional, aren't the best way to evaluate your learning.

Home      Apply     

FAQ

Your questions. Our answers.

2Sigma School offers three flexible enrollment formats so students can learn in the way that best fits their schedule:

Independent Study is our most popular format and is offered year round. An assigned instructor guides the student through the course with weekly 1-on-1 office hours for teaching new concepts, reviewing work, and giving personalized feedback. At a standard pace, students complete one semester in about 18 weeks or the full course in 36 weeks. Students who want to move faster can set an accelerated goal and their instructor will provide additional office hours to match. This format works well for students with busy schedules or those completing coursework started in another format.

Summer of Code is our accelerated summer program. Students meet 2 hours per day, 4 days per week in an intensive format that allows them to complete a full-year course in as few as 6 weeks. This is ideal for students who want to earn credits quickly or get ahead before the school year starts. It requires a significant time commitment and is best suited for students who can dedicate themselves fully to the program during the summer.

Live Classes are our year-round, cohort-based format. Students attend live online sessions (90 minutes, twice per week) over 36 weeks in small groups of 10–14 students. This format provides consistent interaction with instructors and peers throughout the academic year, with time between sessions to work on projects and assignments. These classes are subject to cohort formation and may have limited availability.

Independent Study offers the most flexibility. During the application process, students provide their availability and we match them with an instructor whose schedule aligns. Sessions are then scheduled directly between the student and their instructor.

Summer of Code and Live Classes are cohort-based. Students indicate all of their available time slots when applying, and we form cohorts based on the collective availability of enrolled students. This approach gives families flexibility while ensuring each cohort has a consistent meeting time that works for everyone in the group.

As an accredited institution, 2Sigma School can award high school credits for our courses on a transcript, just like your child's regular school. Some high schools may accept these credits as part of their graduation requirements, and even use them to calculate your child's GPA. This policy varies by school, so we recommend you check with your child's school counselor.

Regardless of your local school's decision, students can submit our transcript to colleges as college applications allow additional transcripts to be submitted. This can help your child stand out in the college application process.

We are accredited by Cognia and most of our courses are not only NCAA approved, they are also approved for A-G credits by the University of California. Our AP courses are approved by the College Board.

In addition, 2Sigma School is an approved online course provider in multiple states, including California, Washington, Oklahoma, and Florida. See our accreditations page for more details.

Our instructors vary by course as well as by availability. Some of our instructors are high school teachers with deep expertise in computer science, teaching credentials in multiple states, and years of classroom experience. Others are professionals with an undergraduate degree in Computer Science with deep experience in the subject matter and a demonstrated ability and aptitude to teach teenage students.

All of our instructors undergo a rigorous screening process for content and pedagogical expertise. They are background checked as per local and state regulations, and are trained in online instruction and classroom management.

Students need a desktop or laptop computer running Windows (PC), Mac OS (Mac), or Chrome OS (Chromebook), along with a working microphone, speaker, and webcam. A high-speed internet connection with at least 10 Mbps download speed is required.

Students should be familiar with opening a browser, navigating to a website, and joining a Zoom meeting. Most course content can be viewed on mobile devices, but programming assignments and certain quizzes require a desktop or laptop computer.

Yes. All formats include access to instructor support. In Live Classes and Summer of Code, students can ask questions during class and instructors are available to provide additional guidance. In Independent Study, students have dedicated weekly office hours with their assigned instructor.

If a student needs additional 1-on-1 support beyond what is included, we offer tutoring sessions that can be arranged through our team. Contact us at admissions@2sigma.school for details.