Mathematics

Starting August 2023:  All freshmen students take this course.

Prerequisite:  Successful completion of Algebra I by Sophomores and Juniors.

Pre-AP Geometry with Statistics provides students with a conceptual bridge between algebra and geometry that deepens their understanding of mathematics. The course includes a unit of statistics and probability to support students’ understanding of concepts essential to quantitative literacy. 

Throughout the course, students solve problems across the domains of algebra, geometry, and statistics.

The following big ideas are addressed across all units:  Measurement, Transformation, Comparison and Composition.

Pre-AP Geometry with Statistics has four main units:

Unit 1: Measurement in Data

Unit 2: Tools and Techniques of Geometric Measurement

Unit 3: Measurement in Congruent and Similar Figures 

Unit 4: Measurement in Two and Three Dimensions

Rising sophomores may place out this course as determined by a review of math placement exam scores, administered in the Spring of their freshmen year, or in the Fall prior to the start of their sophomore year.

This course is designed to provide students with a basic foundation in algebra. Topics include functions and their graphs, linear and quadratic equations, inequalities, factoring, polynomials, radicals and exponents, and systems. In addressing these topics, it is expected that the student will increase their Algebra specific vocabulary and be able to apply the math in modeling real-life situations.

Prerequisite:  Successful completion of Geometry and Algebra I (via enrollment or math placement exam)

In Pre-AP Algebra 2, students solidify and extend their understanding of functions and data analysis developed in prior courses.

Students build upon linear, quadratic, and exponential functions as they work to define logarithmic, polynomial, rational, square root, cube root, and trigonometric functions. Quantitative literacy is developed by weaving data sets, contextual scenarios, and mathematical modeling throughout the course.

The following big ideas are addressed across all units:  Functions, Operations with Functions, Inverse Functions.

Pre-AP Algebra II has four main units:

Unit 1: Modeling with Function

Unit 2: Algebra of Functions

Unit 3:  Function Families

Unit 4T: Trigonometric Functions 

Unit 4M: Matrices and their Applications

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

Advanced Algebra with Financial Applications is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent.  The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Precalculus, and Calculus under seven financial umbrellas: Banking, Investing, Credit, Employment, Income Taxes, Automobile Ownership, Independent Living, Retirement Planning, and Household Budgeting.  The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations.  The mathematics topics contained in this course are introduced, developed, and applied in an as-needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts and to question outcomes using mathematical analysis and data to support their findings.  The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations.   The use and development of critical thinking skills is crucial in this course.  

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

With the recent advent of massively powerful computers and artificial intelligence, game theory departed from the world of abstract concepts (pioneered by John von Neumann and John Nash) and entered into the world of practical realities. Today, for any “zero-sum” game, we can study computed solutions for the “Game Theory Optimal” strategy against which no player can win, but only stalemate. Using that knowledge as a foundation, players can learn how to maximally exploit weaknesses in imperfect strategies, thus discovering the mathematical limit of victory against any given opponent. Modeled after similar courses offered at UC Berkeley, MIT, and other universities, this course uses the game of Texas Hold’Em Poker as a framework for understanding these concepts. Making use of cutting-edge AI technology released to the public only this year, this course will use “GTO ‘Game Theory Optimal’ Wizard” node locking to compute solutions for study. By applying and mastering game-theoretical concepts for this specific game, students will learn how to see the world through a game-theoretical lens and apply their skills to a breadth of other fields such as economics, politics, social science, and more. (Note that this course treats poker academically and has no relationship with nor advocacy for gambling of any kind.)

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

Precalculus is a survey course in advanced mathematical concepts, designed for high school seniors. It is intended for those who do not qualify for Honors Pre-Calculus. The emphasis is on reinforcing algebraic techniques, functions, and logarithms, while also introducing trigonometry, sequences and series, probability, statistics, matrices, and vectors.

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

AP Precalculus serves as a rigorous prelude to AP Calculus AB.  The course framework includes two essential components:

MATHEMATICAL PRACTICES

The mathematical practices are central to the study and practice of precalculus.  Students should develop and apply the described skills on a regular basis over the span of the course.

AP Precalculus focuses on three main practices:

Practice 1: Procedural and Symbolic Fluency

Practice 2: Multiple Representations

Practice 3: Communication and Reasoning

COURSE CONTENT

The course content is organized into units of study that provide a suggested sequence for the course. These units comprise the content and conceptual understandings that colleges and universities typically expect students to master to qualify for college credit and/or placement.

AP Precalculus has four main units:

Unit 1: Polynomial and Rational Functions

Unit 2: Exponential and Logarithmic Functions

Unit 3: Trigonometric and Polar Functions

Additional Topics Available to Schools (Not Included on AP Precalculus Exam)

Unit 4: Functions Involving Parameters, Vectors, and Matrices

Prerequisite:  Successful completion of a Precalculus-level course.

This elective course offers students the opportunity to explore the fundamental principles of Calculus at a pace that provides students time to understand, appreciate and apply these concepts, ultimately preparing students for a first-year college calculus course. Topics include limits, some techniques of differentiation and integration, and applications.

Prerequisite:  Successful completion of a Precalculus-level course.

Designed in accordance to the Advanced Placement curriculum, this elective course is equivalent to the first part of a college-level calculus sequence. Attention focuses on preparing students for the AP examination. Topics include limits, the derivative, techniques of differentiation, the integral, integration, and applications.

Prerequisite:  Successful completion of a Calculus-level course.

Designed in accordance with the Advanced Placement curriculum, this elective course is equivalent to the first and second parts of a college-level calculus sequence. Attention focuses on preparing students for the AP examination. In addition to the topics listed in Calculus AB AP, students will study elementary differential equations, parametric equations, sequences and series, and applications.

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

This junior/senior elective course introduces the basic concepts of probability and statistics using real-world examples/data. Probability topics include counting techniques, odds, simple probability, and conditional probability. Statistics topics include graphical and numerical representations of distribution, sampling techniques, confidence intervals, and regression lines.

Prerequisite:  Successful completion of Algebra II/Trigonometry or Pre-AP Algebra II.

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, sampling and experimentation, anticipating patterns, and statistical inference.  The course will prepare students for the AP Exam in the Spring Semester and provide a solid foundation for collegiate Statistics courses.