Course of Studies

MATHEMATICS

In order to graduate from Summit High School, students must successfully complete three full-year mathematics courses.

Students who have not met the minimum proficiency level on the mathematics section of the state test - NJAsk 8 - will be assigned to the Mathematics Strategies course, in addition to their regularly scheduled mathematics class.

MATHEMATICS STRATEGIES

Grades 9-10

1 - 5 Credits

Students identified as partially proficient on the Mathematics section of the NJAsk 8 will be assigned to this course.

This program is designed to help prepare students to perform successfully on the upcoming PARCC End of Course Exams. Course content is based on the proficiencies and performance objectives described within the Common Core State Standards in Mathematics.

MATHEMATICS FOR PERSONAL FINANCE

Grades 11-12

5 Credits

This course is for students who demonstrate proficiency in basic skills, yet evidence a need for practical rather than abstract mathematics, and seek an alternative to the college preparatory mathematics options. The course is intended to further develop mathematical skills, to increase one’s ability to make personal decisions based on mathematical or business concepts, and to increase one’s ability to manage personal business (consumer) affairs. Enrollment in this course will fulfill the State of New Jersey financial literacy requirement for graduation.

FINANCIAL LITERACY AND PERSONAL FINANCE

Grades 11-12                                                                          

2.5 Credits

This course is designed for students who are interested in exploring a wide range of topics in financial literacy as they pertain to personal finances. Enrollment in this course will fulfill the State of New Jersey financial literacy requirement for graduation.

Using project-based instruction and real-world simulations, this course will provide students the opportunity to explore the key aspects of personal finances necessary to be successful now and throughout their adult lives. The primary structure of this class will focus on the examination of real-world situations. Through these experiences, students will develop skills, gather data, and formulate strategies needed to gain personal and financial responsibility related to financial planning, savings, investments, and charitable giving in the global community. By exploring the relationships among income and careers, money management, credit and debt management, risk management and investing, insurance, and taxes the student will become an educated and critical consumer.
 
FOUNDATIONS OF ALGEBRA

Grades 9-10

5 Credits

This first course in algebra is based on the properties of the real number system, the number line and the simpler language of sets. Inequalities are treated along with equations. Topics include: fundamental operations with real numbers and variables; functions and relations;algebraic manipulations; equations, graphs, and solutions of linear equations, and solutions of systems of equations. Probability provides a context for algebraic fractions, functions, and set ideas. Students will complete an introductory unit on Geometry topics including surface area, volume, and similar and congruent polygons. There is much work with graphing linear relationships and applications motivate all topics. Students will use calculators and other technology at appropriate times.

ALGEBRA 1 - MODELING WITH FUNCTIONS

Grades 9 – 10 – 11 – 12                                                                                               

5 Credits

PREREQUISITE: Foundations of Algebra

This course will focus on the solving systems of equations, exploring linear, quadratic, exponential, and rational functions, and manipulating radical, polynomial, and rational expressions. Emphasis will be placed on the application of these concepts in real world settings and methods for modeling real world scenarios using these functions. Graphing calculators will be used appropriately throughout this course to further develop each concept.

GEOMETRY

Grades 9-10-11-12

5 Credits

PREREQUISITE: Algebra 1

This course is for the successful Algebra 1 student who wishes to continue his study of college preparatory mathematics.

The course is Euclidean geometry and includes congruence, similarity, parallelism, perpendicularity, area, volume, and circles. Coordinates and transformations in both two and three dimensions are integrated throughout the course. There is a main sequence of proved theorems with many "originals" for the student to prove.

GEOMETRY HONORS

Grades 9-10

5 Credits

PREREQUISITE:  Algebra l, performance on a placement test, and acceptance through the written application process outlined on page v of the Course of Study booklet.


The course is Euclidean geometry and includes congruence, similarity, parallelism, perpendicularity, area, and volume. Coordinates and transformations in both two and three dimensions are integrated throughout the course. There is a main sequence of proved theorems with many "originals" for the student to prove. The content includes that of the regular Geometry course but with an increased degree of rigor and greater depth of coverage.

ALGEBRA 2

Grades 10-11-12

5 Credits

PREREQUISITE: Geometry

This course is for the college-preparatory student with average mathematical ability who has successfully completed Algebra 1 and Geometry. Students with above average mathematical ability who have an interest in mathematics (or science related careers) should consider the Algebra 2/Trigonometry course.

This course is a continuation of work begun in Algebra l. It emphasizes facility with algebraic expressions and forms, especially linear and quadratic forms, powers and roots, and functions based on these concepts. Students study exponential, logarithmic, polynomial, and other special functions, both for their abstract properties and as tools for modeling real-world situations. Geometric ideas are utilized throughout, and matrices are examined conceptually and applied.

ALGEBRA 2/TRIGONOMETRY

Grades 10-11-12

5 Credits

PREREQUISITE: Geometry

This course is for the student with above-average mathematical ability who has maintained a "B" average or better in mathematics and who wishes to continue his study of more advanced work in mathematics.

The algebraic properties of the real number system are reviewed, as are equations and inequalities of the first and second degree. The real number system is extended to the complex number system. Conic sections are given geometric application. Coordinate geometry, systems of equations, and logarithmic, exponential, trigonometric, and polynomial functions are covered in detail.

ALGEBRA 2/TRIGONOMETRY HONORS

Grades 10-11

5 Credits

PREREQUISITE:  Geometry and acceptance through the written application process outlined on page v of the Course of Study booklet.

The algebraic properties of the real number system are reviewed, as are equations and inequalities of the first and second degree. The real number system is extended to the complex number system. Conic sections are given geometric application. Coordinate geometry, systems of equations, exponential, logarithmic, polynomial, trigonometric, and circular functions are studied in detail. Matrices and probability are covered as time permits.

TRIGONOMETRY/ALGEBRA 3

Grades 11-12

5 Credits

PREREQUISITE: Algebra 2

This course is for the college-preparatory student with average mathematical ability who has successfully completed Algebra 2. It is designed for students who want and need to continue taking mathematics but who are not ready for the demands of Pre-Calculus.

The course integrates ideas of functions and trigonometry with statistics and data analysis. It reviews and extends ideas about polynomial, exponential, logarithmic, and trigonometric functions. Statistical and algebraic concepts are integrated as students display, describe, transform, interpret, and model numerical data. The study of counting, probability, and simulation is also included.

PRECALCULUS

Grades 11-12

5 Credits

PREREQUISITE: Algebra 2/Trigonometry, Trigonometry/Algebra 3

This course is for the student who has successfully completed Algebra 2/Trigonometry, maintained at least a "C" average, and wishes to continue his study of mathematics at a more demanding level. Students who have taken the Trigonometry/Algebra 3 course and have maintained a B average may also enroll in this course.

The course develops the ideas associated with circular, polynomial, exponential, logarithmic, and trigonometric functions. The various functions are applied to real world situations. Additional topics are polar coordinates, sequences and series, and an introduction to matrices.

PRECALCULUS HONORS

Grades 10-11-12

5 Credits

PREREQUISITE:   Algebra2/Trigonometry and acceptance through the written application process outlined on page v. Algebra2/Trigonometry students must seek acceptance through the written application process outlined on page v of the Course of Study booklet and obtain the recommendation of their current teacher.

This course is designed for the student who has successfully completed Algebra2/Trigonometry Honors, maintained at least a "C" average, and wishes to continue his study of mathematics at a challenging level. Students who have completed Algebra2/Trigonometry and have maintained at least an "A-" average may apply for the course through the application process outlined on page v.

This course will prepare students for the rigorous AP Calculus AB curriculum. It will develop Precalculus topics in greater depth and at a challenging level that will expose students to the future demands of an Advanced Placement course. Topics that will be explored include circular, trigonometric, parametric, exponential, and logarithmic functions, vectors, polar coordinates, sequences and series, and an introduction to limits and derivatives.

INTRODUCTION TO ANALYSIS HONORS

Grades 11-12

5 Credits

PREREQUISITE: Algebra 2/Trigonometry honors and acceptance through the written application process outlined on page v of the Course of Study booklet.

This course is for the student who has successfully completed Algebra 2/Trigonometry Honors and ultimately wishes to continue his studies of mathematics in the Advanced Placement Calculus BC with Advanced Placement Physics C course. The first semester of this course explores precalculus topics such as polynomial functions, trigonometry, conic sections, exponents and logarithms, mathematical induction, and miscellaneous topics from advanced algebra and analytic geometry. The second semester includes a rigorous exploration of topics in calculus and includes limits, continuity, definition of derivative, derivatives of algebraic functions, and applications of derivatives. The calculus in this course is continued in the BC Calculus course. This course may require a summer assignment.

CALCULUS

Grade 12

5 Credits

PREREQUISITE: Precalculus

This course is designed for those students who have completed a course in Precalculus and would like to continue their study of advanced mathematics. This course is offered as an alternative to the rigors of the Advanced Placement Calculus AB course. Topics will include a study of advanced topics in Precalculus as well as topics in a formal Calculus course. Graphing calculators will be used throughout the course.

ADVANCED PLACEMENT CALCULUS AB

Grade 12

5 Credits

PREREQUISITE:  Precalculus and acceptance through the written application process outlined on page v of the Course of Studies booklet.

The work in this course is developed in conjunction with the syllabus of the Advanced Placement program. It includes the concepts of limit, differentiation of algebraic and transcendental functions, differentials, Mean Value Theorem, Rolle's Theorem, integration of standard elementary forms, and transcendental functions. Geometric and physical applications include the area under a curve, volume of revolution, and velocity. Additional topics include differential equations and hyperbolic functions.

All students’ enrolled in this class will be required to complete a summer curriculum assignment. This assignment is designed to review key mathematical topics that will be utilized throughout the course. Additionally, all students enrolled in an AP course will be required to prepare for and take the AP exam in May.

ADVANCED PLACEMENT CALCULUS BC

Grades 11-12

5 Credits Math 6 Credits Science

PREREQUISITES: Introduction to Analysis Honors, acceptance through the written application process outlined on page v of the Course of Study booklet, and approval of the department supervisors.

Calculus instruction is based upon the College Board's Advanced Placement Calculus BC curriculum. It includes the concept of limit, differentiation of algebraic and transcendental functions, differentials, mean value theorem, Rolle's Theorem, integration of standard elementary forms, and transcendental functions. Geometric and physical applications include the area under a curve and between curves, volumes of revolution, length of a curve, surfaces of a revolution, and velocity. The BC syllabus covers the topics of the AB Calculus course in greater depth and with more rigor. Additional topics include polar graphs, infinite sequences and series, and differential equations.

All students in this course will be required to complete a summer curriculum assignment. This assignment is designed to review key mathematical topics that will be utilized throughout the course. Additionally, all students enrolled in this class are required to prepare for and take the Advanced Placement Calculus BC exam in May.

ADVANCED PLACEMENT STATISTICS

Grade 12

5 Credits

PREREQUISITE:  Precalculus and acceptance through the written application process outlined on page v of the Course of Study booklet.

Students who have completed Algebra 2/Trigonometry with the permission of the department chairperson may also take this course. The regular statistics course will take precedence should there be insufficient enrollment to run both of the statistics courses. The course will deal with many facets of data analysis. Topics will include descriptive statistics, probability, probability distributions, and inferential statistics. Examples will be taken from many fields. Technology will be used extensively. This course will require a summer assignment. All students enrolled in this class are required to prepare for and take the Advanced Placement Statistics exam in May.

DISCRETE MATHEMATICS and STATISTICS

Grade 12

5 Credits

PREREQUISITE: Trigonometry/Algebra 3

The course will deal with two very practical branches of mathematics: statistics and discrete mathematics. Statistics topics will include descriptive statistics, probability and probability distributions. Students will be exposed to discrete mathematics topics including graph theory, fair division, systematic counting, and codes and information storage. Real-world applications will be used to further student understanding of the covered topics. Technology will be used extensively.

MULTIVARIABLE CALCULUS

Grade 12

5 Credits

PREREQUISITES:  BC Calculus, acceptance through the written application process outlined on page v, and approval of the department supervisor.

This course is for the exceptional student who has successfully completed a course in single variable calculus (our BC Calculus course). The course will only be offered as an online experience. Details of the expectations for this course can be obtained through the department supervisor.

The course is a rigorous study of advanced topics in mathematics. Multivariable Calculus is a challenging exploration of functions of several variables and includes representations of such functions through the use of vectors, differentiation and integration, optimization, parametric curves and surfaces, and vector fields while exploring real world applications. Students will receive a graphing calculator for their use throughout the course.


INTRODUCTION TO COMPUTER PROGRAMMING

Grades 9 -10-11-12

2.5 Credits

PREREQUISITE:  Algebra 1

This elective course has been developed to simultaneously introduce students to computer programming and to prepare them for an introductory course in the formal JAVA language Students will learn to program stories and games in the Alice programming environment.

Students will learn the basics of programming languages with a focus on critical knowledge and skills that may be applied in future classes. Students will learn to create and manipulate object classes and to use these manipulations to develop program animations. As they progress, students will learn to program using a variety of diverse techniques including if/else statements, loops, while and for statements as well as techniques unique to the Alice program.

Completion of this class will prepare students to enroll in a follow up course that will introduce them to the Java programming language.



INTRODUCTION TO JAVA PROGRAMMING

Grades 9-10-11-12

2.5 Credits

PREREQUISITE: Introduction to Computer Programming

This course is for the student who has successfully completed Introduction to Computer Programming, maintained at least a "B-" average, and wishes to continue the study of computer programming at a more sophisticated level.

The course serves as a direct follow up to the “Introduction to Computer Programming” course and introduces to students the Java programming language. Over the course of the semester students will develop strong Java programming skills through a series of programming and written assignments.

Topics discussed in this class will mirror those taught in the “Introduction to Computer Programming” course. By building a studentís Java abilities in a fashion similar to their Alice experiences in the prerequisite course, students will develop a strong, core set of fundamental skills. Topics that will be taught include a wide variety of techniques such as if/elsestatements, loops, while and for  statements. In addition, students will learn about object-oriented programming and public and private classes.



ADVANCED PLACEMENT COMPUTER SCIENCE A

Grades 10-11-12

5 Credits

PREREQUISITE: Introduction to JAVA Programming and acceptance through the written application process outlined on page v

This course is for the student who has successfully completed Introduction to Programming in JAVA, maintained at least a "B-" average, and wishes to continue the study of computer programming at an advanced level.

The Advanced Placement Computer Science class is designed to prepare students for the AP Computer Science A examination. Instruction is based upon the College Board's Advanced Placement Computer Science A curriculum. In this class, students will learn how to develop and write Java programs utilizing object-oriented program design.

Topics include implementation techniques, programming constructs and programming analysis with an overall focus on top-down development. In addition, students will learn how to test and debug their programs as well as utilize error handling to address runtime errors.

This course is equivalent to a semester of college level computer programming.
All students enrolled in an AP course will be required to prepare for and take the AP exam in May.