Mathematics

The fundamental purpose of Algebra I is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear and exponential relationships by contrasting them with each other. Students will study descriptive statistics for both univariate and bivariate data. Students will engage in methods for analyzing, solving, and using quadratic functions. Algebra I is the foundation for all future mathematics courses.

Topics will include:

• Equations and Inequalities

• Functions

• Linear Functions

• Exponential Functions

• Sequences

• Systems of Linear Equations and Inequalities

• Polynomials

• Quadratic Equations

• Quadratic Functions

• Descriptive Statistics

This is a one-year course, for the student who has passed Algebra 1, but may have struggled with the pace and/or the more advanced topics. The purpose of this course is to formalize and extend students’ geometric experiences from the middle grades at a more suitable pace and level. Students will explore more complex geometric relationships and begin to develop logical reasoning skills to be ap-plied in introductory geometric proof as well as problem solving. A local final exam will be given at the end of the year. Students who excel at this course would also have the option to take the Geometry Regents.

In Geometry students will learn to identify and justify geometric relationships both formally and informally. Just as in Algebra 1, the Geometry course provides students the opportunity to acquire and demonstrate mathematical reasoning ability while solving problems that represent a wide array of mathematical relationships.

Topics will include:

• Constructions & Unknown Angles

• Transformations/Rigid Motions

• Congruence & Proofs

• Similarity & Proofs

• Applying Similarity of Triangles

• Introduction to Trigonometry

• Coordinate Geometry

• Extending to Three Dimensions

• Circles

Students in the Accelerated Geometry will be assigned additional topics as well as more advanced problems in existing topics.

Possible Unique Experiences for Geometry Accelerated

Indirect Proofs

SAT Prep Questions

Geometry Problems of the Week

TI-84 Graphing Calculator Labs

Problem Solving with Trigonometry

Independent Projects throughout the year

More rigorous homework assignments

More challenging tests

Regents Exam: Geometry

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are three major themes in the Introduction to Statistics course:

Topics will include:

• Exploring Data,

• Sampling and Experimentation

• Probability and Simulation

Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, trigonometric, exponential, and logarithmic functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers, exponential equations using the properties of logarithms, and rational and radical equations. The course ends by exploring conditional probability, independence, and how to make conclusions and inferences from data.

Topics will include:

• Polynomial Functions

• Rational and Radical Equations

• Systems of Equations

• Quadratic Functions and the Complex Numbers

• Trigonometric Functions

• Exponential Functions

• Logarithmic and Inverse Functions

• Sequences and Series

• Probability

• Inferential Statistics 

Students in the Accelerated Algebra II will be assigned additional topics as well as more advanced problems in existing topics.

Possible Unique Experiences for Algebra II Accelerated

Further investigation into special values for trigonometric functions

Extending the curriculum past Regents level to gain a deeper knowledge of each topic

Introducing Pre-Calculus topics within each chapter of study that are aligned with the topics in Algebra II

More rigorous homework problems

More challenging tests

Projects throughout the year

Regents Exam: Algebra II

This elective course is for students who have completed Algebra 2, Algebra 2A or are recommended by the mathematics department. It can be taken as an alternative to College Algebra or Algebra 2B. Algebra II w/ Financial Applications is a math course that is algebra-based and applications-oriented. The course addresses college preparatory mathematical topics from Advanced Algebra, Statistics, and Probability. It will apply this mathematics to the financial areas of: banking, investing, credit, taxes, loans, and budgeting.  

Students in 11th and 12th grade may take this course with proper prerequisites.

AP Precalculus is an exploration of functions designed to better prepare students for college-level calculus and provides grounding for other mathematics and science courses. All students are required to take the AP exam in May and are responsible for the cost of the exam.

Throughout the course, students will explore polynomial, rational, exponential, logarithmic, and trigonometric functions. For each type of function, as well as general functions, students will

·         solve equations and inequalities

·         manipulate algebraic expressions representing functions

·         Construct and analyze graphical representations of functions

·         explore rates of change, compositions, inverses, and transformations

·         create, analyze and use models related to a context

Course content is taught with a focus on developing the following mathematical practices:

·         Procedural and Symbolic Fluency

·         Multiple Representations

·         Communication and Reasoning

As an advanced course, course content will be covered at a faster pace and with a higher level or rigor. Once required content is covered, students will be introduced to limits, continuity, and differentiation to further prepare them for their study of calculus.

AP Precalculus is an exploration of functions designed to better prepare students for college-level calculus and provides grounding for other mathematics and science courses. Furthermore, as AP Precalculus may be the last mathematics course of a student’s secondary education, the course is structured to provide a coherent capstone experience rather than exclusively focusing on preparation for future courses. All students are required to take the AP exam in May and are responsible for the cost of the exam.

Throughout the course, students will explore polynomial, rational, exponential, logarithmic, and trigonometric functions. For each type of function, as well as general functions, students will

·         solve equations and inequalities

·         manipulate algebraic expressions representing functions

·         Construct and analyze graphical representations of functions

·         explore rates of change, compositions, inverses, and transformations

·         create, analyze and use models related to a context

Course content is taught with a focus on developing the following mathematical practices:

·         Procedural and Symbolic Fluency

·         Multiple Representations

·         Communication and Reasoning

Advanced Placement Calculus AB consists of a full high school academic year of work and is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning.

Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes 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.  All students are required to take the AP exam in May and are responsible for the cost of the exam.

Topics will include:

• Functions, Graphs, and Limits

• Derivatives

• Integrals

• End-of-Year Project

The purpose of the Advanced Placement course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.

Students are exposed to four broad conceptual themes:

• Exploring Data: Describing patterns and departures from patterns

• Sampling and Experimentation: Planning and conducting a study

• Anticipating Patterns: Exploring random phenomena using probability and simulation

• Statistical Inference: Estimating population parameters and testing hypotheses

Students who successfully complete the course and exam may receive credit, advanced placement, or both for a one-semester introductory college statistics course. All students are required to take the AP exam in May and are responsible for the cost of the exam.