Math Department
Welcome to the Math Departments Website!
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The Math Department (from left to right): Terraferma, Basilio, Ko, Wilson |
Announcements:
- Study math!
Course Descriptions:
- Integrated Algebra is the first mathematics course in the high school. The integrated algebra course set forth here is not the algebra of 30 years ago. The focal point of this course is the algebra content strand. Algebra provides tools and ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts, and technology. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings. Problem situations may result in all types of linear equations in one variable, quadratic functions with integral coefficients and roots as well as absolute value and exponential functions. Coordinate geometry will be integrated into the investigation of these functions allowing students to make connections between their analytical and geometrical representations. Problem situations resulting in systems of equations will also be presented. Alternative solution methods should be given equal value within the strategies used for problem solving. For example, a matrix solution to a system of equations is just as valid as a graphical solution or an algebraic algorithm such as elimination. Measurement within a problem-solving context will include calculating rates using appropriate units and converting within measurement systems. Data analysis including measures of central tendency and visual representations of data will be studied. An understanding of correlation and causation will be developed and reasonable lines of best fit will be used to make predictions. Students will solve problem situations requiring right triangle trigonometry. Elementary probability theory will be used to determine the probability of events including independent, dependent and mutually exclusive events.
- Geometry is intended to be the second course in mathematics for high school students. There is no other school mathematics course that offers students the opportunity to act as mathematicians.Within this course, students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusion follows logically from their hypothesis. This course is meant to employ an integrated approach to the study of geometric relationships. Integrating synthetic, transformational, and coordinate approaches to geometry, students will justify geometric relationships and properties of geometric figures. Congruence and similarity of triangles will be established using appropriate theorems. Transformations including rotations, reflections, translations, and glide reflections and coordinate geometry will be used to establish and verify geometric relationships. A major emphasis of this course is to allow students to investigate geometric situations. Properties of triangles, quadrilaterals, and circles should receive particular attention. It is intended that students will use the traditional tools of compass and straightedge as well as dynamic geometry software that models these tools more efficiently and accurately, to assist in these investigations. Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences.
- Algebra 2 and Trigonometry is the capstone course of the three units of credit required for a Regents diploma. This course is a continuation and extension of the two courses that preceded it. While developing the algebraic techniques that will be required of those students that continue their study of mathematics, this course is also intended to continue developing alternative solution strategies and algorithms. For example, technology can provide to many students the means to address a problem situation to which they might not otherwise have access. Within this course, the number system will be extended to include imaginary and complex numbers. The families of functions to be studied will include polynomial, absolute value, radical, trigonometric, exponential, and logarithmic functions. Problem situations involving direct and indirect variation will be solved. Problems resulting in systems of equations will be solved graphically and algebraically. Algebraic techniques will be developed to facilitate rewriting mathematical expressions into multiple equivalent forms. Data analysis will be extended to include measures of dispersion and the analysis of regression that model functions studied throughout this course. Associated correlation coefficients will be determined, using technology tools and interpreted as a measure of strength of the relationship. Arithmetic and geometric sequences will be expressed in multiple forms, and arithmetic and geometric series will be evaluated. Binomial experiments will provide the basis for the study of probability theory and the normal probability distribution will be analyzed and used as an approximation for these binomial experiments. Right triangle trigonometry will be expanded to include the investigation of circular functions. Problem situations requiring the use of trigonometric equations and identities will also be investigated.
- Math B is the completion of the mathematics study begun with Math A. The Math B curriculum includes diverse topics such as complex numbers, relations and functions including exponential, logarithmic and circular functions. Students also further develop their understanding of probability and statistics. The last term of Math B involves an in depth study of the fundamentals of trigonometry. The graphing calculator is an integral part of the Mathematics B course and the Math B Regents examination is the culmination of the course. The last offering of the Math B exam will be June 2010.
- Pre-Calculus is a class that will teach you ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts, and technology. This course will assist students in developing skills and a range of techniques to successfully solve problems in a variety of settings. Some of the major topics will reinforce the material that was learned in Math B and several topics will prepare you with foundational skills that will be necessary for Calculus and future college courses. Students will have the chance to work with graphing calculators to explore many of the principles covered in class. In addition, an increased emphasis will be placed on writing and the ability to express mathematical ideas.
- AP Calculus AB students are introduced to the two major components of Calculus: differentiation and integration. After a brief review of Pre-Calculus topics related to functions, domains and restrictions, and graphs of functions, the concept of limits is introduced in order to develop the derivative as a measure of rate of change of a function. Limits are further used in relation to proof of continuity and differentiability of functions. Continued development of techniques of differentiation and analysis of function behavior of the first and second derivative leads to the study of minimization and maximization applications and linear approximation. Students will also work with derivatives of logarithmic and exponential functions, and learn implicit differentiation techniques for when explicit differentiation is not possible.
After estimating with finite sums, definite integration is introduced via Riemann sums and the Mean Value Theorem. After connecting differential and integral Calculus, the Fundamental Theorem of Calculus, parts I and II, is discovered. Integration techniques, including substitution and parts, are used as students explore various forms of mathematical modeling. The application of integration techniques is completed through assorted situations including exponential growth and decay, areas in the plane, and volumes, including those formed by washers rotated around an axis. Students will take the AP exam in May.