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### Mathematics

 ALGEBRA IAlgebra is the language of patterns and relationships, through which most of mathematics is communicated. It is a tool which people use to model real situations and answer questions about them. It is also a way of operating with concepts at an abstract level and then applying them, often leading to the development of generalizations and insights beyond the original context. The algebra which is appropriate for all students in the twenty-first century moves away from a tight focus on manipulating symbols to include a greater emphasis on conceptual understandings, on algebra as a means of representations and on algebraic methods as problem-solving tools. Algebra is the gatekeeper for the future study of mathematics as well as science, social sciences, business and a host of other areas. (New Jersey Mathematics Curriculum Framework 1995) 5 CreditsGEOMETRY This course is designed to incorporate all the conceptual aspects of geometry, e.g., visualization, analysis, informal reasoning and deduction. The study of geometry will be broken down into three components: Euclidean Geometry, Coordinate Geometry and Transformational Geometry. The primary objective of this course is to assist the students with the development, verification and application of geometric concepts. Technology will be implemented into several aspects of this course. This will allow student to formulate and test geometric conjectures, test patterns and further investigate mathematical ideas. 5 CreditsALGEBRA II/TRIGONOMETRY Prerequisite: Students will have successfully completed Algebra I and Geometry. This course is designed to extend the students’ previous knowledge of algebraic concepts and introduce trigonometric functions. In addition, the students will continue to develop their analytical and problem solving skills. This course will consist of two main topics. The first part of the semester will be an extension of algebra. The topics that will be covered include word problems, variables, the number line, properties of real numbers, equations and inequalities of first degree, systems of linear open sentences, multiplication, division, factoring, exponential functions and logarithms. The second half of the course deals with trigonometric functions, reference angles and their uses, the solutions to right and oblique triangles, graphs, equations involving trigonometric functions, probability and statistics. 5 CreditsPRECALCULUSPrerequisite: Students will have successfully completed Algebra I, Geometry and Algebra II/Trigonometry. This course is designed to extend the students’ previous knowledge of algebraic concepts and trigonometric functions, to help students truly understand the fundamental concepts of algebra, trigonometry and analytic geometry, to build an intuitive foundation for calculus, and to show how algebra and trigonometry can be used to model real – life problems. A principle feature is the balance among the algebraic, numerical and verbal methods of representing problems. In addition, the students will continue to develop their analytical and problem solving skills.  The course will integrate the use of the graphing calculator and other technologies to develop a deeper understanding of the mathematical concepts and make connections to real life phenomenon. 5 CreditsCALCULUSThis course will be divided into two main categories: Differential and Integral Calculus. It is extremely important that students be aware of the continuity of their education in mathematics. Therefore the focus of this course will be on graphical analysis of functions and solving application problems, which will incorporate both branches studied this year. The emphasis of the course will be on using derivatives and integrals to analyze real functions and their graphs. Students will apply the analysis to applications by using higher level thinking skills. A strong understanding of trigonometry is essential since it will be emphasized throughout the course. The course will focus on derivatives and their applications of modeling trigonometry and their related topics. It will also introduce definite integrals, differential equations and mathematical modeling. 5 Credits STATISTICSStatistics is the science of analyzing data. Much of this data will be numerical in nature. Statistics gives us the tools we need to describe important aspects of a data set and to present these results to others. These important aspects enable us to take the data and use it to make decisions. This course will give the students the skills to gather data in an accurate way. It will then show the students how to calculate important results from the data. From these results we will learn what conclusions can be drawn from the data. This course will seek to show students how numerical data is used throughout our modern society. It will show applications of numerical data from bar codes to cryptography to the Internet. It will apply statistical data to elections, voting systems, games, and in many other areas.5 CreditsADVANCED PLACEMENT CALCULUS AB This course will be divided into two main categories: Differential and Integral Calculus. It is extremely important that students be aware of the continuity of their education in mathematics. Therefore the focus of this course will be on graphical analysis of functions and solving application problems, which will incorporate both branches studied this year. The emphasis of the course will be on using derivatives and integrals to analyze real functions and their graphs. Students will apply the analysis to applications by using higher level thinking skills. A strong understanding of trigonometry is essential since it will be emphasized throughout the course. The first part of the course will focus on derivatives and their applications of modeling trigonometry and their related topics. It will also introduce definite integrals, differential equations and mathematical modeling. The second part will continue to show applications of integrals and go into more depth on the topics that will be covered on the Advanced Placement exam, if applicable. 10 CreditsADVANCED PLACEMENT CALCULUS BC Prerequisite: Students will have successfully completed Algebra I, Geometry, Algebra II/Trigonometry and Precalculus. Calculus BC is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multi-representational approach to calculus, with concepts, results and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Calculus BC is an extension of Calculus AB rather than an enhancement; common topics require a similar depth of understanding. Both courses are intended to be challenging and demanding. Broad concepts and widely applicable methods are emphasized. The focus of the courses is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, although facility with manipulation and computational competence are important outcomes, they are not the core of these courses. Technology should be used regularly by students and teachers to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. Through the use of the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. 10 Credits