Mathematics

Algebra 1 is the first mathematics course at the high school level. 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. 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. 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. Passing the NYS Algebra 1 Regents Examination is a graduation requirement.

Geometry
Geometry is intended to be the second mathematics course in high school. This course employs 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, including congruence of two figures as transformations of each other. A major emphasis of this course is to allow students to investigate geometric situations. Properties of triangles, quadrilaterals, and circles will receive enough attention that students will be able to utilize these properties to solve problems. 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. This course culminates in the Geometry Regents Examination and is intended for the Regents level student. Passing the NYS Geometry Regents Examination is one of the requirements for an Advanced Regents diploma.

Geometry Honors
As this is the advanced Geometry course, students will explore these geometrical relationships at greater depth than in the Regents-level Geometry course.

Algebra II
Algebra II is intended to be the third mathematics course in high school. It is expected that students will identify and justify mathematical relationships, formally and informally. Students will learn fractional and negative exponentiation, perform operations with radical and imaginary expressions including rationalizing denominators with radical or imaginary expressions, know and apply sigma notation, solve absolute value equations and inequalities, solve quadratic inequalities, evaluate logarithmic expressions, work with arithmetic and geometric sequences, explore functions and relations, determine if a function is invertible and determine the inverse function, perform transformations of functions in the plane, explore the concepts of domain and range, become proficient with exponential and logarithmic functions and expressions, scatter plots and linear, power, logarithmic and exponential regression and probability, including variance and decision making, permutations, combinations, binomial probabilities, empirical probabilities and using the normal distribution to approximate binomial probabilities.

Algebra II Honors
As this is the advanced Algebra II course, students will explore these geometrical relationships at greater depth than in the Regents-level Algebra II course.

Precalculus
This is a course designed for students who wish to extend their mathematical background beyond the topics needed for the Algebra 2 Regents Examination. The course progresses from the study of natural numbers through the real numbers and attempts to show the unified structure of mathematics. Such topics as functions, radicals, sequences, series, synthetic division, the factor and remainder theorems, the Fundamental Theorem of Algebra, complex numbers, conic sections, polar equations and their graphs, and matrices are studied, as well as topics outlined in New York State’s Common Core precalculus curriculum. This course may include an introduction to limits and the basics of differential Calculus. The course provides an excellent background for anyone who plans to take mathematics in college.

Precalculus Honors
This course includes applications of concepts, including topics such as future value and present value of annuities. The course may include an introduction to the concepts of differential Calculus. This course is designed for the advanced mathematics student who wishes to take one or more of the mathematics options or an Advanced Placement course in the senior year. Students are encouraged to take the SAT Level 2 Subject Test examination in June.

This senior-level course is open to students who have successfully completed Pre-Calculus, wish to have a college level learning experience and earn Advanced Placement credit for college. This course develops students’ understanding of the concepts of calculus and provides experience with its methods and applications. This course emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Students will be presented with the meaning of the derivative in terms of rate of change and local linear approximation as well as how to use derivatives to solve a variety of problems. The meaning of the definite integral, both as a limit of Riemann sums and as the net accumulation of a rate of change and the use of integrals to solve a variety of problems will be discussed. Students are encouraged to take the Advanced Placement Calculus (AB) examination in May. Those who successfully complete this examination could receive up to four college credits.

This senior level course is open to students who have successfully completed Pre-Calculus Honors, are seriously considering a career that uses mathematics, and wish to have a college level learning experience. It covers all of the topics and concepts from AP Calculus (AB) and also the following: parametric, polar, and vector functions, Eulerʼs Method, lʼHopitalʼs Rule, integration by parts and simple partial fractions, improper integrals, logistic differential equations, infinite series, including their convergence and divergence, Taylor series, Maclaurin series, and the Lagrange error bound for Taylor polynomials. Students are encouraged to take the Advanced Placement (BC) examination in May. Students who successfully complete this examination could receive up to eight college credits.

This course is designed for college-bound students and is built around four main topics: exploring data, planning a study, probability as it relates to distributions of data, and inferential reasoning. This course will blend the rigor, calculations, and deductive thinking of mathematics with the real-world examples and problems of the social sciences, the decision-making needs of business and medicine, and the laboratory method and experimental procedures of the natural sciences. Students will be able to design a study, collect the information, analyze their data and disseminate their results. Students are encouraged to take the Advanced Placement Statistics examination in May. Students who successfully complete this examination could receive up to three college credits.