# Mathematics

### Required Math Courses

Algebra I begins the study of functions. Functions represent the systematic dependence of one quantity on another. Students use functions to represent and model problem situations and to analyze and interpret relationships. Students work in many situations to set up equations and inequalities and use a variety of methods to solve them. Coursework concentrates on foundations for functions, linear functions, and quadratic and other nonlinear functions

After an in-depth study of the structure of the real number system, key topics to be covered will be of linear and quadratic equations, systems of equations, graphs of linear equations, and operations on rational expressions. Problem solving is stressed throughout the year, with a special focus on the mathematical modeling of real-world situations.

Geometry consists of the study of geometric figures of zero, one, two, and three dimensions and the relationships having to do with size, shape, location, direction, and orientation of these figures. The students will use a variety of representations, tools, and technology to solve meaningful problems by representing figures, transforming figures, analyzing relationships, and proving things about them. Topics will include congruency, reasoning/proof, trigonometry, similarity, dimensionality, and patterning of all geometric figures. The particular concepts studied are those that provide a background for advanced math-concepts. The course's guiding principle is to provide students opportunities to become adept problem solvers and clear thinkers.

The particular concepts studied are those that provide a background for advanced math-concepts. The course's guiding principle is to provide students opportunities to become adept problem solvers and clear thinkers. In addition, geometry consists of the study of geometric figures of zero, one, two, and three dimensions and the relationships having to do with size, shape, location, direction, and orientation of these figures. The students use a variety of representations, tools, and technology to solve meaningful problems by representing figures, transforming figures, analyzing relationships, and proving things about them. Topics will include congruency, similarity, dimensionality, and patterning of all geometric figures.

In Algebra II, students will broaden their knowledge of quadratic functions, exponential functions, and systems of equations. Students will study logarithmic, square root, cubic, cube root, absolute value, rational functions, and their related equations. Students will connect functions to their inverses and associated equations and solutions in both mathematical and real-world situations. In addition, students will extend their knowledge of data analysis and numeric and algebraic methods. Students will use technology, specifically the graphing calculator, to collect and explore data and analyze statistical relationships.

Algebra II Honors continues the study of functions that began in Algebra I, utilizing a more sophisticated approach. Students use functions and equations as a means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations. The course emphasizes the use of equations and functions to represent geometric curves and figures and the connections between algebra and geometry as tools of one to help solve problems in the other. Functions studied include quadratic and square root, rational, exponential and logarithmic. Conic sections (nonfunctions) are also studied. Graphing calculators will be used extensively.

### Math Elective Courses

Students will develop and apply skills necessary for college, careers, and life. Course content consists primarily of applications of high school mathematics concepts to prepare students to become well educated and highly informed 21st century citizens. Students will develop and apply reasoning, planning, and communication skills to make decisions and solve problems in applied situations involving numerical reasoning, probability, statistical analysis, finance, mathematical selection, and modeling with algebra, geometry, trigonometry, and discrete mathematics.

The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. The study of Pre-Calculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems.

Pre-Calculus Honors is the preparation for calculus. The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. The study of Pre-Calculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems. The PreCalculus Honors course goes into greater depth in the topics of analytic trigonometry, series, and probability. In addition, four weeks of the course are devoted to the first chapter of Calculus AB, including limits, the tangent line problem, and the area problem.

Pre-Calculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college.

This is a college-level calculus course designed to meet the Advanced Placement curricular requirements for Calculus AB (equivalent to a one-semester college course). The major topics of this course are limits, derivatives, integrals, and the Fundamental Theorem of Calculus. This course will investigate and analyze course topics using equations, graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. Applications, in particular to solid geometry and physics, will be studied where appropriate.

AP Calculus BC is roughly equivalent to both first and second semester college Calculus courses. It extends the content learned in AB to different types of equations (polar, parametric, vector-valued) and new topics (such as Euler's method, integration by parts, partial fraction decomposition, and improper integrals), and introduces the topic of sequences and series. The course covers topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, the Fundamental Theorem of Calculus, and series. Students are taught to approach Calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations.