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## High School Mathematics

**Math Philosophy:**We are witnesses to God's glory and his existence through the study of mathematics. "For his invisible attributes, namely, his eternal power and divine nature have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse" (Rom. 1:20). Mathematics is also a testament to God's creation and the order He has made for us in this universe, which only further proves his existence and divine nature. "For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or power. All things were created through Him and for Him. And He is before all things, and in Him all things consist" (Col. 1:16-17).**Algebra I:**The study of basic structure of real numbers, algebraic expressions, and functions. The topics studied are statistical organization and analysis, linear equations, inequalities, functions and systems, quadratic equations and functions, polynomial and radical expressions, and the elementary properties of functions. Mathematical modeling of real-life problems, problem solving, and the construction of appropriate linear models to fit data sets are the major themes of the course.**Geometry:**Geometry is a branch of mathematics that is concerned with the properties of geometric objects - points, (straight) lines, and circles being the most basic of these. Although there are many types of geometry, this course is primarily devoted to plane Euclidean geometry, studied both with and without the use of a coordinate system. During high school, students begin to formalize their geometric experiences from elementary and middle school, make definitions more precise, apply concepts from algebra, and develop careful proofs.**Algebra II:**The study of the complex number system, symbolic manipulation, and functions. Advanced algebraic and data analysis techniques incorporating the use of technology enable students to discuss, represent, and solve increasingly sophisticated real-world problems. Topics studied include the properties of functions, the algebra of functions, matrices, and systems of equations. Linear, quadratic, exponential, logarithmic, polynomial and rational functions are studied with an emphasis on making connections to other disciplines and as preparation for a multitude of careers. A principal goal is to apply advanced data analysis techniques to find the best fit model from all the important function models, justify the model, and us it to make predictions. Communication of the problem solving skills used and the conclusion reached is another major emphasis.**Pre-Calculus:**This course completes the formal study of the elementary functions begun in Algebra 1 and 2. Students use the mathematical and modeling skills previously developed to study and apply the trigonometric functions. The use of technology and problem solving are emphasized in units covering data analysis, circular functions, and trigonometric inverses and identities. Students will conduct research and write extensively as they prepare for higher levels of mathematics. The concepts of trigonometry are extended to the study of polar coordinates and complex numbers. conics and quadratic relations are introduced through a locus definition using polar representations. Discrete topics include the principals of mathematical induction, the Binomial Theorem, and sequences and series, where sequences are represented both explicitly and recursively. An oral and written modeling presentation by students provides culminating synthesis to the concept of function.**Calculus:**The introductory topics of this course include limits and continuity of functions, derivatives of functions, and their applications to problems. Students find derivatives numerically, represent derivatives graphically, and interpret the meaning of a derivative in real-world applications. Models of previously studied functions will be analyzed using calculus concepts. The topics developed include the relationship between the derivative and the definite integral. The understanding, properties, and applications of the definite integral are included as students learn to explain solutions to problems. Students will model real-world situations involving rates of change using difference or differential equations.