Algebra II and Trigonometry
The course expands the syllabus outlined in the New York State MATH B curriculum while exploring and mastering the concepts of Intermediate Algebra and Advanced Trigonometry. The course is aimed at increasing the depth of understanding of advanced topics in Geometry, Logarithmic Functions, Exponential Functions, Statistics and Probability.
AP Calculus AB
AB Calculus is a college level course comparable to first semester college calculus. Appropriate credit and placement are granted by each college or university in accordance with their policies. AB Calculus is designed to develop students' conceptual understanding of calculus with a multi-representational approach. Material is presented graphically, numerically, analytically, and verbally with an emphasis on problem solving. Graphing calculators are used regularly to experiment, confirm written work, and interpret results.
AP Calculus BC
AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.
In AP Statistics, we will explore three conceptual themes: Exploring Data, Anticipating Patterns, and Statistical Inferences. Statistical methods are derived to summarize, analyze and interpret numerical information. We then incorporate these methods with Probability to develop The Central Limit Theorem. This forms the basis on which we calculate confidence intervals and perform hypothesis testing. These statistical tools are used to make inferences and draw conclusion about data.
In Calculus, we will go beyond the study of the relationship between quantities and explore how quantities change with respect to each other. Our knowledge of Algebra, geometry and function are applied to solve two problems: The Tangent Line Problem and the Area Problem. We are introduced to Limits, Differentiation and Integration. These concepts become the analytic tools that are used to describe real world phenomena.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
Foundations of Mathematics
Through the investigation of meaningful problems individually or in cooperative groups, while using appropriate technology, students will strengthen their foundations of mathematics. Students will prepare for success in future mathematics courses by building content knowledge to meet our standards in number and operations. Students will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.
In Geometry we will: (1) develop an understanding of geometric relationships in a plane in space, (2) develop an understanding of the meaning and nature of proof, (3) study the method of deductive proof in both mathematical and non-mathematical situations, (4) develop the ability to think creatively, and critically, in both mathematical and non-mathematical situations, and (5) integrate geometry with arithmetic, algebra, and numerical trigonometry.
Pre-Calculus is traditionally the 11th-year mathematics course. In addition to the topics provided in the syllabus, students will also be familiarized with SAT and ACT questions. The purpose of the course is to introduce students to college-level mathematics and to prepare them for study of the Calculus, both for engineering and business.
Topics included in the course are:
Functions and graphs; polynomial, power and rational functions; exponential, logistic and logarithmic functions; trigonometric functions; vectors, parametric equations, and polar equations; systems and matrices; sequences and series, mathematical induction; analytical geometry with conic sections; introduction to calculus introducing limits, derivatives and integrals.