# Mathematics & Computer Science

The Mathematics and Computer Science Department at Tappan Zee High School follows the recommendations set forth by the New York State Education Department and the National Council of Teachers of Mathematics by offering courses in Mathematics and Computer Science for all students. Regents examinations are the final examinations in each of the following courses: Algebra I, Geometry, and Algebra II.

**Algebra IA**

Full Year, 1 credit

This course is the first half of the Common Core Algebra course, the first high school math course in a three year sequence required for a Regents diploma. This course will cover solving linear equations and inequalities, descriptive statistics, exploring functions (linear, quadratic, exponential, absolute value, piecewise). This course is designed for students who were not successful in Pre-Algebra in Grade 8. (May be taken with an attached lab period that meets on a cycle basis.)

**Algebra IB**

Full Year, 1 credit

Prerequisite: Algebra 1A

This course is the second half of Common Core Algebra course, the first high school math course in a three year sequence required for a Regents diploma. This course will cover systems of equations, operations with polynomials, factoring, and problem solving. This course is designed for students who were not successful in Pre-Algebra in Grade 8. This course is expected to culminate with the New York State Common Core Algebra Regents Examination.

**Algebra I Regents**

Full Year, 1 credit

Prerequisite: Pre-Algebra

This is the first year of a three-year Regents sequence. This course will cover: Solving linear equations and inequalities, descriptive statistics, exploring functions (linear, quadratic, exponential, absolute value, piecewise), systems of equations, operations with polynomials, factoring, and problem solving. This course is expected to culminate with the New York State Common Core Algebra Regents Examination in June.

**Geometry Regents**

Full Year, 1 credit

Prerequisite: Algebra

This is the second year of a three-year Regents sequence. This course will cover Euclidean geometry with deductive proof, transformational proofs, Analytic geometry, Constructions, Linear equations and inequalities, systems of equations. This course is expected to culminate with the New York State Common Core Geometry Regents Examination in June.

**Geometry Regents Honors**

Full Year, 1 credit

Prerequisite: Algebra Honors or Departmental Approval

This is the second year of a three-year Regents sequence. This course will cover Euclidean geometry with deductive proof, transformational proofs, Analytic geometry, Constructions, Linear equations and inequalities, systems of equations. In addition to studying the regular Regents material in more depth, extra topics will be included and additional projects given. This course is expected to culminate with the New York State Common Core Geometry Regents Examination in June.

**Applications in Geometry**

Full Year, 1 credit

Prerequisite: Algebra

This course will cover the topics of Euclidean Geometry from a “hands on” investigative approach. Students will be using Geometer SketchPad, Patty Paper Geometry, Mira’s, Geoboards, etc. This course will focus on applications of theorems and concepts. This course will focus on applications of geometric theorems and concepts. It will be a heavily applied Algebra course, without the traditional focus on Geometric Proof. This course will culminate with a local final exam.

**Algebra II Regents**

Full Year, 1 credit

Prerequisite: Geometry, Algebra II NR

This is the third year of a three-year Regents sequence. This course will cover Absolute value, quadratic and radical equations, Polynomial and trigonometric equations, exponential and logarithmic equations, advanced factoring, trig graphs, logarithmic and natural logarithmic graphs, probability and statistics, standard deviation and regression analysis. This course is expected to culminate with the New York State Common Core Algebra 2 Regents Examination in June.

**Algebra II Regents Honors**

Full Year, 1 credit

Prerequisite: Geometry Honors or Departmental Approval

This is the third year of a three-year Regents sequence. This course will cover Absolute value, quadratic and radical equations, Polynomial and trigonometric equations, exponential and logarithmic equations, advanced factoring, trig graphs, logarithmic and natural logarithmic graphs, probability and statistics, standard deviation and regression analysis. In addition to studying the regular Regents material in more depth, extra topics will be included and additional projects given. This course is expected to culminate with the New York State Common Core Algebra 2 Regents Examination in June.

**Algebra II Non-Regents**

Full Year, 1 credit

Prerequisite: Applications in Geometry, Geometry or Departmental Approval

This course is offered after the completion of Geometry and is intended as a preparatory class for the Common Core Algebra 2 course which is required for a Regents diploma with advanced designation. This course will cover models, linear relationships and functions, exponential and logarithmic functions, rational functions, quadratic relations, radicals and complex numbers.

**Pre-Calculus**

Full Year, 1 credit

Prerequisite: Algebra II Regents

This course would follow after successful completion of three years of Regents math courses. This course covers real number systems, analytic geometry, trigonometric functions, conics and transformations, parametric equations, functions, theory of polynomial equations including complex numbers, polar coordinates, exponential and logarithmic functions, matrices and determinants, partial fractions, and sequence series including proof by mathematical induction and an introduction to differential calculus and applications. College credit will be available through SUNY New Paltz for this course.

**Pre-Calculus Honors**

Full Year, 1 credit

Prerequisite: Algebra II Honors and/or Departmental Approval

This course would follow after successful completion of three years of Regents math courses. This course covers real number systems, analytic geometry, trigonometric functions, conics and transformations, parametric equations, functions, theory of polynomial equations including complex numbers, polar coordinates, exponential and logarithmic functions, matrices and determinants, partial fractions, and sequences and series including proof by mathematical induction and an introduction to differential calculus and applications. Approximately 20% of the course will cover the material in more depth or include additional topics or more in-depth proof. College credit will be available through SUNY New Paltz for this course.

**Math Analysis**

Full Year, 1 credit

Prerequisite: Algebra II

This course provides a fourth year of mathematics for seniors who have completed the Algebra II Regents course or the Algebra II Non-Regents course. It provides an opportunity for students to develop and maintain college level math skills in their senior year. The topics include real number analysis, quadratic equations, inequalities and absolute value equations and polynomials. Students will use applications of trigonometry, systems of equations, the laws of exponents and logarithms. Additional topics include SAT review and real-life financial math.

**Linear Algebra**

One Semester, 1/2 credit

Prerequisite: Pre-Calculus H or Departmental Approval

Linear Algebra is a challenging college level course that introduces the students to a variety of topics: matrix operations, systems of linear equations, determinants, Euclidean vector spaces, general vector spaces, inner product spaces, eigenvalues, eigenvectors, and linear transformations. An emphasis will be placed on exploring the practical aspects and uses of Linear Algebra in relation to the real world and careers. Students will experience a sample of the type of math that they will experience as a math major in college.

**Calculus**

Full Year, 1 credit

Prerequisite: Pre-Calculus and Departmental Approval

Topics include limits, continuity, derivatives and applications, integrals and applications, differential equations and slope fields. Students will solve problems dealing with rectilinear motion, related rates, optimization, area, and volume using polynomial, trigonometric, exponential, and logarithmic functions. This course does not prepare the student for the Advanced Placement Calculus examination and culminates in a local final examination. This course is recommended for students who desire an introduction to college level Calculus.

**Advanced Placement Calculus AB**

Full Year, 1 credit

Prerequisite: Pre-Calculus or Pre-Calculus Honors and Departmental Approval

This is a rigorous and demanding college-level course in Calculus. All students enrolled are expected to take the AP Calculus AB examination in May. This course covers: limits, continuity, in-depth study of the derivative including techniques of differentiation and applications; the concept of the integral and applications of integration; the Fundamental Theorem of Calculus; differential equations, and slope fields. This course includes an additional 3 periods per cycle lab. College credit will be available through SUNY New Paltz for this course.

**Advanced Placement Calculus BC**

Full Year, 1 credit

Prerequisite: Pre-Calculus Honors and Departmental Approval

All students enrolled are expected to take the AP Calculus BC examination in May. This course covers: completely ordered field, vectors, limits including the epsilon-delta differentiation, differentials, parametric representation, continuity, fundamental theorems in analysis to include Rolle’s Theorem and the Mean Value Theorem, applications to include velocity/acceleration problems, related rate problems, maxima/minima problems, etc., curve sketching, conics and transformation, integral concept, fundamental theorem of the calculus, area volume, work, trigonometric and inverse trigonometric functions, exponential and logarithmic functions, methods of integration, approximating integrals, more on polar coordinates, applications of course material, infinite series. This course includes an additional 3 periods per cycle lab. Students are expected to take the AP examination in May. College credit will be available through SUNY New Paltz for this course.

**Advanced Placement Statistics**

Full Year, 1 credit

Prerequisite: Algebra II Honors, Pre-Calculus (H) or department approval

This course introduces students to major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data through observing patterns and departures from patterns, planning a study, anticipating patterns in advance, producing models using probability and simulation, statistical inference, and confirming models. All students enrolled are expected to take the Advanced Placement Statistical Examination in May. It is recommended that those students enrolled in the Science Research Course take the AP Statistics course. College credit will be available through SUNY New Paltz for this course.

**Intro to Personal Financing (12)**

Fall Semester, 1/2 credit

Pre-requisite: Passed the Algebra Regents or teacher recommendation

This one-semester course will present to students the essential knowledge and skills to make informed decisions about real world financial issues. Students will learn how: choices influence occupational options and future earning potential, to apply decision-making skills to evaluate career choices and set personal goals, to analyze their personal financial decisions, to evaluate the costs and benefits of their decisions, to recognize their rights and responsibilities as consumers, and to apply the knowledge learned in school to financial situations encountered later in life. The course content is designed to help the student make wise spending, saving, and credit decisions and to make effective use of income to achieve personal financial success.

**Computer Science: Intro to Gaming**

Full year, 1 credit

Prerequisite/Co-requisite: Algebra (No prior coding experience is necessary)

This course will give students an introduction to coding and gaming through experiences with a variety of programs such as Scratch, Construct3 and Unity. Students will learn from hands on experience the process of coding for games and apps.

**Computer Science I**

Fall Semester, 1/2 credit

Prerequisite: Algebra, No Coding Experience Necessary

This introductory course will implement significant language features, programming practices and application programs using Python programming language. Topics covered include developing programs, logic, debugging code, graphics, variables, looping structures, lists, and dictionaries. Sophomores, juniors and seniors may elect to earn 3 college credits at reduced tuition rates from STAC.

**Computer Science II**

Spring Semester, 1/2 credit

Prerequisite: Computer Science I

This course expands the programming practices explored in Computer Science I. Students write programs using the Java programming language. Topics covered include variables, conditional control statements, loops, Strings, methods, classes and arrays. Sophomores, juniors and seniors may elect to earn 3 college credits at reduced tuition rates from STAC.

**Advanced Placement Computer Science Principles**

Full year, I credit

Prerequisite: Algebra, No prior coding experience necessary

AP Computer Science Principles (CSP) curriculum is a full-year, rigorous, entry-level course that introduces high school students to the foundations of modern computing. The course covers a broad range of foundational topics such as programming, algorithms, the Internet, big data, digital privacy and security, and the societal impacts of computing. Computing affects almost all aspects of modern life and all students deserve access to a computing education that prepares them to pursue the wide array of intellectual and career opportunities that computing has made possible. This course seeks to provide students with a “future proof” foundation in computing principles so that they are adequately prepared with both the knowledge and skills to live and meaningfully participate in our increasingly digital society, economy, and culture.

**Advanced Placement Computer Science A (Java)**

Full Year, 1 credit

Prerequisite: Computer Science Visual Basic, Computer Science Java, Algebra II

Advanced Placement Computer Science A is equivalent to a first semester, college level course in computer science. This course continues with key Java programming concepts including loop structures, strings, methods, classes, inheritance, constructors, encapsulation, polymorphism and instantiation. The course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data, algorithms and social implications of computing. The AP Computer Science A course includes a minimum of 20 hours of hands on structured lab experiences to engage students in individual or group problem solving.

**Computer Science Capstone (Honors)**

Full Year, 1 credit, 11th or 12th grade

Prerequisite: AP Computer Science Principles or AP Computer Science Java can be repeated

The focus of this course is to provide a broad range of programming experience in the exciting field of Computer Science. Students will produce a portfolio of projects. The course will be project based and include applications to design computer programs that solve practical computational problems by programming the Web and writing data analysis programs in a modern high-level languages. Students will learn languages, tools, and techniques for developing interactive, dynamic web content. Throughout the course you will learn many fundamental concepts vital in the study of computer science through learning multiple languages including Python, web programming, data programming, iOS, Android and Swift.

**Learning Center Math**

Cycled, 0 credit

A lab-based extra help class where students have time to work on any problems they might have in their regular math class.

The following semester courses are also available through Virtual High School (VHS):

Mathematical Reasoning and Logic

Mathematics of Electricity

Number Theory

## Faculty Sites

Ms. Marisa Premus Team Leader

Mrs. Doreen Braunagel PreCalculus H | Algebra II | AP Calculus AB

Ms. Karen Connell Computer Science | Maker Space

Mr. Dino Doremus

Ms. Lisa Jacobs

Mr. Dave Marino

Ms. Kayleigh Marmion

Ms. Barbara Murphy Computer Science | Math

Ms. Christine O’Brien