Mathematics 18-19

## Mathematics Courses

Algebra I (Common Core)

This is the first course in the revised New York State Mathematics sequence which reflects the common core learning standards 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. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings. 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. Problem situations resulting in systems of equations will also be presented. Measurements 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. The graphing calculator will be used as a tool to enhance instruction. The New York State Integrated Algebra Regents exam will be administered in June.

Prerequisite(s): 8th Grade Mathematics
Grade(s):  9
Credit:  1
Meets:  5 Periods Weekly

Geometry (Common Core)

This is the second course in the revised New York State Mathematics sequence which reflects the Common Core Learning Standards at the high school level. Students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusion follows logically from their hypothesis. This course is meant to employ 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. A major emphasis of this course is to allow students to investigate geometric situations. Properties of triangles, quadrilaterals, and circles should receive particular attention. It is intended that students will use the traditional tools of compass and straightedge as well as dynamic geometry software that models these tools more efficiently and accurately, to assist in these investigations. 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. The New York State Geometry Regents exam will be administered in June.

Prerequisite(s): Algebra I (Common Core)
Grade(s):  9, 10
Credit:  1
Meets:  5 Periods Weekly

Algebra 2 (Common Core)

This is the third course in the revised New York State Mathematics sequence which reflects the Common Core Learning Standards. Students will build on their work with linear, quadratic, and exponential functions, and extend their repertoire of functions to include polynomial, rational and radical 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 and solving exponential equations using the properties of logarithms. The Algebra 2 Common Core Regents exam will be administered in June.

Prerequisite(s): Algebra I (Common Core) and Geometry Common Core
Grade(s):  10, 11
Credit:  1
Meets:  5 Periods Weekly

Precalculus

This course will focus on functions and their transformations including polynomial, rational, exponential, logarithmic, and trigonometric functions. Trigonometric identities, rates of change, limits, and sequences and series will be studied. This course is required for all students who intend to enroll in Advanced Placement Calculus.

Prerequisite(s): Algebra 2/Trigonometry
Grade(s):  11
Credit:  1
Meets:  5 Periods Weekly

Precalculus Research

This course will include topics in our current Precalculus syllabus, with students delving deeper into mathematical concepts. Additional topics such as three dimensional geometry, vectors, mathematical induction, and fields will be included. A research paper will be required.

Prerequisite(s): Algebra 2/Trigonometry (and a desire to explore research)
Grade(s):  11
Credit:  1
Meets:  5 Periods Weekly

Precalculus (C)

This course will build on the immediate and advanced algebraic skills of the students, having students apply these skills with a higher level of critical thinking. This course will focus on functions and their transformations, limits and derivatives.
This course may be taken for college credit through Molloy College.

Prerequisite(s): Algebra 2/Trigonometry
Grade(s):  12
Credit:  1
Meets:  5 Periods Weekly

Calculus (C)

This course affords students the opportunity to investigate calculus concepts through applications related to a variety of fields including business, science, engineering, and technology. Topics such as: limits and continuity, derivatives, maxima and minima, antiderivatives, definite integral, Fundamental Theorem of Calculus, and techniques for integration will be studied. The TI-84 graphing calculator will be used as a tool to enhance instruction.

Prerequisite(s): Precalculus recommended: Algebra 2/Trigonometry required
Grade(s):  12
Credit:  1
Meets:  5 Periods Weekly

Multivariable Calculus

Students will learn the calculus of multivariable functions and vector fields. Before they can study the calculus of multiple dimensions, students will need to learn some concepts in Linear Algebra, such as: linear systems, matrices, matrix multiplication, properties of matrix operations, matrix transformations, solutions of linear systems of equations, the inverse matrix, cross product, dot product, Gauss-Jordan Elimination, orthogonal matrices, and determinates. Topics in the calculus component of the course will include: multivariable functions and their derivatives, partial derivatives, vector fields, gradient, divergence, curl, double and triple integrals, parameterized curves, flows, line integrals, Green's theorem, and flux integrals. Additionally, students will study other topics from multivariable calculus, including: Stoke's Theorem and the Divergence Theorem.

Prerequisite(s): AP Calculus BC (Score of at least 3 on the Advanced Placement Exam)
Grade(s):  12
Credit:  1
Meets:  5 Periods Weekly

Exploratory Programming

This course is an introductory course to the computer science curriculum. The basic concepts of how a computer works and object oriented programming will be taught. Other topics that will be covered in the course include: output, input, constants, variables, expressions, decisions and basic looping structures. Structured programming will be stressed. Students will create simple 3-D movies and games using "Alice" - an interactive graphics programming environment.

Prerequisite(s): None
Grade(s):  9, 10, 11, 12
Credit:  1
Meets:  5 Periods Weekly

Advanced Placement Calculus AB

In this course, students study topics from analytic geometry and calculus. They study lines, conic sections, limits, derivatives, related rates, maxima and minima, curve sketching, slope fields, Mean Value Theorem, differentiation of trigonometric, exponential, and logarithmic functions, differential equations, area under a curve, volumes of revolution and volumes of cross sections, integration, and differential equations. Students are required to take the Advanced Placement Examination in Calculus (AB level) in May.

Prerequisite(s): Pre-Calculus
Grade(s):  12
Credit:  1
Meets:  5 Periods Weekly

Advanced Placement Calculus BC

This course consists of a full academic year of work in calculus. In addition to the topics studied in Calculus AB, the BC course includes additional topics such as infinite series, logistic growth, vector functions, L’Hospital Rule, polar coordinates, improper integrals, partial fractions and arc length. Students are required to take the Advanced Placement Examination (BC level) in May. The AP exam will have both a BC score and an AB subscore.

Prerequisite(s): Precalculus or Precalculus Research
Grade(s):  12
Credit:  1
Meets:  7.5 Periods Weekly

Advanced Placement Statistics

This course is designed to be comparable to a typical non-calculus-based-technology introductory statistics course taught in a college/university. The course emphasizes (1) exploring data, (2) planning a study, (3) anticipating patterns and (4) statistical inference. The TI-84 graphing calculator will be the chief tool for data analysis. Students are required to take the Advanced Placement Examination in Statistics in May.

Prerequisite(s): Geometry
Grade(s):  10, 11, 12
Credit:  1
Meets:  5 Periods Weekly

Advanced Placement Computer Science A

This is a college level course in programming using the Java language. The course emphasizes object-oriented programming methodology with a concentration on problem-solving and algorithm development. This includes important concepts such as inheritance and data structures. Students will complete hands-on structured labs throughout the curriculum as required by the College Board..

Prerequisite(s): Algebra 2/Trigonometry
Grade(s):  10, 11, 12
Credit:  1
Meets:  5 Periods Weekly

Advanced Computer Programming

The first semester of the course will have a major focus on abstract data types and data structures that these students will understand and implement. These include Linked lists (singly, doubly, circular), Stacks, Queues, Priority queues, Sets, Maps, Trees, Heaps and Hash Tables. Additional Java topics that will be covered include: Big-Oh notation, Worst-case and average-case time, space analysis, Quick Sort and Heap Sort. The second semester of the course will introduce the basics of the Python Language. Students will learn to read as well as write simply Python code.

Prerequisite(s): Advanced Placement Computer Science A
Grade(s):  11, 12
Credit:  1
Meets:  5 Periods Weekly

Mathematical Problem Solving

The goal of this course is to train students in math competition problems such as the ones found on the Nassau County Interscholastic Math League, American Math Competition (AMC), American Invitational Mathematics Exam (AIME), and the Math Olympiad Summer Program (MOSP). Students will learn the theory behind the mathematical concepts that these competitions address. This affords our students the opportunity to participate in additional mathematics competitions such as: Columbia Math, Purple Math, and Harvard/MIT. All of these are national mathematics competitions with Columbia and MIT being on site and Purple Math being remote. The level of competition is a step above the level of competition that takes place in Nassau County. Teams for these competitions are often formed with students from multiple schools. We would be unique in that our team would be just from Jericho. This would give us a chance to compete against schools like Stuyvesant High School from New York City. Class time would be used to prepare students for all experiences.

Prerequisite(s): Algebra 2
Grade(s):  10, 11, 12   (9th graders would need permission from the instructor)
Credit:  1
Meets:  5 Periods Weekly

AP Computer Science Principles

The AP Computer Science Principles course is designed to be equivalent to a first-semester introductory college computing course. In this course, students will develop computational thinking vital for success across all disciplines such as using computational tools to analyze and study data and working with large data sets to analyze, visualize and draw conclusions from trends. The course is unique in its focus on fostering student creativity. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using computer software and other technology to explore questions that interest them. They will also develop effective communications and collaboration skills working individually and collaboratively to solve problems, and discussing and writing about the importance of these problems and impacts to their community, society and the world.

Prerequisite(s): Strong Foundation in Algebra
Grade(s):  10, 11, 12
Credit:  1
Meets:  5 Periods Weekly

Concepts in Mathematics

Arithmetic and algebra will be integrated throughout the semester. Emphasis will be placed on fundamental operations of integers and rational numbers, ratio and proportion, percent, factoring, linear and fractional equations, exponents, radicals, quadratic equations, and right triangles. Mathematical functions will be represented numerically, algebraically, verbally, and graphically. Formal symbolic logic, arguments, and methods of proof will be explored.  This course will prepare students for an entrance level mathematics test for first semester college students.

Prerequisite(s): Algebra 2
Grade(s): 12
Credit:  1
Meets:  5 Periods Weekly