AP Precalculus will bridge the gap between algebra and calculus by covering four major units. The first three units will cover content that colleges and universities typically expect students to be proficient in, in order to qualify for college credit and/or placement. Units one through three are a required part of this course and will be assessed on the AP Exam in May. Topics covered in units one through three include 1) Polynomial and Rational Functions, 2) Exponential and Logarithmic Functions, and 3) Trigonometric and Polar Functions. The fourth unit consists of additional topics that extend and deepen the function concepts developed in units one through three. These additional topics are excluded from the AP Exam and include parametric equations, vectors, and matrices.

Precalculus is not a required course for graduation from University High School; students who elect this course should understand that it is demanding. Precalculus goes beyond the ability to deal successfully with equations and formulas. It requires a commitment to exploring, understanding, and explaining the rationale of the topics covered.

AP Calculus AB is a college-level course. The curriculum is outlined by the College Board, which administers the Advanced Placement exam in May. This is a rigorous course, and students are expected to work at a rapid pace and to put in a significant amount of study time outside of class. Students need to work to understand the material conceptually, as they will be expected to apply the concepts in novel ways to unique problems. The course also includes a focus on learning how to properly justify mathematical statements.

Both differential and integral calculus are covered. Students will learn the processes of finding a derivative and integrating, as well as the conceptual underpinnings of both. Several applications will also be taught. Topics covered will include limits and their properties; finding derivatives of polynomials, trig functions, log function,s and exponential functions; definite and indefinite integrals; area between curves; accumulation functions; particle motion; volumes of solids; and differential equations.

AP Calculus BC is a college-level course that follows the guidelines and requirements provided by the College Board’s Advanced Placement program. This course is equivalent to a first-year collegiate calculus II course, and it will be taught with the academic expectations and rigor of a college-level course. This course will prepare students for advanced college-level math classes, and with a good score on the AP exam, a student can place out of the equivalent college course.

This course will continue to expand upon the three big ideas covered in AP Calculus AB. Topics include integration techniques, convergence, infinite sequence and series, parametric equations, polar coordinates, vector-valued functions, and logistic functions. Students will also use class time to practice AP-style questions to prepare for the AP exam in May.

Multivariate Calculus & Differential Equations investigates calculus with different coordinate systems and multiple variables, following a discussion-based format covering both analog and digital methods. The course explores topics that are studied in a typical college-level third-semester calculus course, including vectors and vector-valued functions, non-Cartesian coordinate systems, differentiation in several variables, optimization in several variables, multiple variable integration, and line and surface integrals. The course concludes with an introduction to differential equations. Topics may include solving exact first-order equations, solving second-order homogeneous and non-homogeneous linear equations, and exploring applications to various fields.

This course will create a bridge from calculus-based courses that involve mathematical calculations to theoretical upper-level mathematics courses where students work to prove theorems and grapple with mathematical abstractions. Topics can include, but are not limited to, proof and logic for coding and data science, higher-level probabilities, financial math, graph theory, number theory, and math history. Other topics may also include game theory, differential equations, and linear algebra. Students should take this course if they are interested in more mathematics after AP Calculus AB and if they are interested in exploring advanced mathematics in preparation for a math-heavy degree at the college level.

The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The students use computer-based statistics programs as well as a graphing calculator in this course; technology is an important part of mathematics at this level. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

-Exploring data: describing patterns and departures from patterns
-Sampling and experimentation: planning and conducting a study
-Anticipating patterns: exploring random phenomena using probability and simulation
-Statistical inference: estimating population parameters and testing hypotheses.

This course is rigorous but can be completed successfully with hard work and diligence.