Mathematics

Algebra I introduces various topics that comprise elementary algebra. Students not only acquire important algebraic skills to simplify problems and solve equations, but they also gain an understanding of the concepts that lie at the heart of algebraic manipulations. In so doing, this course directly prepares the student for the questions concerning algebra on the mathematics sections of the SAT and ACT exams, as well as providing a solid foundation on which to build in subsequent mathematics courses such as Geometry, Algebra II, and Trigonometry. Major topics include the algebraic modeling of real-life problems, solving and graphing equations and inequalities, systems of equations; ratios, and proportions; properties and use of exponents; mathematical modeling using functions, tables, and graphs; number patterns, counting methods, and permutations; polynomials and factoring; radical expressions and equations.

This is a one-year college prep course that meets state graduation requirements. This course includes the following topics: An overview of functions (linear, quadratic, and exponential) in function form, graphs, and tables; Linear equations and inequalities in one and two variables; Geometric constructions; Congruence and rigid motions; Geometric relationships and properties of triangles, parallel lines, quadrilaterals, and circles; Analyzing and interpreting data in one and two variables.

This one-year course reinforces and extends the mathematical foundation established in an Algebra I course. It offers an in-­‐depth investigation of the topics of a yearlong course in Geometry while revisiting numerous algebraic topics from a geometric perspective.
Semester One is devoted to the study of basic principles, reasoning and proof, parallel and perpendicular lines, congruent triangle theory, and special relationships within triangles. Important theorems from semester one include the isosceles triangle theorem and the proof that all triangles have angles whose sum is 180 degrees.
Semester Two is devoted to a study of quadrilaterals, area, perimeter, and circumference, similarity theory, and right triangle trigonometry. The major objectives of this course are a thorough understanding of mathematical topics as tested in both the SAT and the ACT. By the end of this course, a student will have, among other things, complete familiarity with the x-­‐y plane, a facility with the Pythagorean Theorem, and the ability to find measurements indirectly using trigonometry and a calculator.

This is a one year college prep course that meets state graduation requirements. This course includes the following topics: Similarity; Coordinate geometry; Trigonometric ratios; Quadratic functions; Quadratic equations; Probability.

Prerequisite: Integrated Math 1/Algebra 1

This course reviews and extends the mathematical investigations of the previous two courses into the study of function theory, trigonometry, systems of equations and inequalities, and exponential and logarithmic functions. It constitutes the third-year course in the Mathematics Department Syllabus progression.

Prerequisite: Algebra I and Geometry.

The following units will be covered in Integrated Math 3: Statistics (Random Processes), Circles and Conics, Trigonometric Functions, Exponential Functions, Functions Capstone, Rational and Polynomial Expressions. This course will complete the 3-year Integrated Math series and includes remaining High School Common Core Math Standards that are not covered in Integrated Math 1 and Integrated Math 2.

Prerequisites: Integrated Math 2/Geometry Co-requisites: Integrated Math 2 equivalent (from middle school)

This course is designed for students who are interested in pursuing STEM fields in college. This course is an enhanced course and not an honors course and will cover topics above the Integrated Math 3 course, including vectors, complex numbers and advanced trigonometric function analysis. The following units will be covered in Integrated Math 3 STEM: Statistics (Random Processes), Circles and Conics, Trigonometric Functions, Vectors, Exponential Functions, Functions Capstone, Rational and Polynomial Expressions. This course will complete the 3-year Integrated Math series and includes the remaining High School Common Core Math Standards and a variety of the “plus” standards that are not covered in Integrated Math 1 and Integrated Math 2.

Prerequisites: Integrated Math 2/Geometry Co-requisites: Integrated Math 2 equivalent (from middle school)

This one semester elective is designed to introduce students to the environmental science aspect of ecology. A basic understanding of general biological processes such as photosynthesis and nutrient cycling is helpful, but not required. Topics covered throughout the semester include: analysis of biotic and abiotic factors in ecosystems; nutrient and energy cycling; food chains and food webs; the atmosphere; the greenhouse effect and global warming; water and air pollution; land use; food; waste; biodiversity and sustainability. Through participation in labs performed in class, students will acquire reasoning skills necessary in understanding and conducting scientific investigations, reinforce the topic currently being studied and develop skills in organizing information, making observations, recording scientific data and preparing lab reports.

This course is a rigorous one year introduction to the major topics of Precalculus. Students will learn about topics that are beyond the scope of both Algebra II and Trigonometry, but which are necessary to understand Calculus. This course is recommended for any student who is interested and proficient in mathematics and wishes to expand and extend his/her knowledge in this area by pursuing the subject beyond the framework of the basic algebra and geometry course offerings.

Prerequisite: Algebra II/Trigonometry (or permission of the instructor).

This course is designed for students who have a strong background in Precalculus, including equation theory and trigonometry, and wish to continue their study of higher-­‐level mathematics as well as take the AP Calculus AB exam in May. As such, this course is aimed at students who are hard workers and are looking for a challenge. Topics covered in past years include: functions, limits, differentiation, logarithmic & exponential functions, applications of differentiation, integration, applications of integration, and further techniques of integration. There is a heavy emphasis on problem-­‐solving, particularly in the form of word problems.

Prerequisite: Precalculus (or permission of the instructor).

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. Using 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. These themes are developed using all the functions listed in the Prerequisite.

Prerequisite: Calculus AB, Advanced Placement

The AP Statistics course lends itself naturally to a mode of teaching that engages students in constructing their own knowledge. For example, students working individually or in small groups can plan and perform data collection and analyses where the teacher serves in the role of a consultant, rather than a director. This approach gives students ample opportunity to think through problems, make decisions and share questions and conclusions with other students as well as with the teacher. Important components of the course should include the use of technology, projects and laboratories, cooperative group problem- solving, and writing, as a part of concept-oriented instruction and assessment. This approach to teaching AP Statistics will allow students to build interdisciplinary connections with other subjects and with their world outside school.

Prerequisite: Integrated Math 3, Integrated Math 3 STEM

This elective in Mathematics reinforces and extends the mathematical foundation comes from a year’s study of both Algebra and Geometry. One aim of Finite Mathematics is to strengthen a student’s basic mathematical skills in accordance with the standards of the NYS Mathematics Regents. A second basic aim is to enrich the student’s mathematical foundation with explorations of topics such as prime number theory, set theory, abstract group theory, and number theory which are not generally taught within the confines of syllabus math courses. Finite Mathematics is both practical in its emphasis on review, and interesting in its varied selection of intriguing mathematical topics.