Mathematics
College Preparatory Courses are designed to provide students with the knowledge and skills they need to succeed in college and careers as well as to be prepared to compete in a global marketplace.
Algebra I CP
Credits: 5
Course Length: Year
Grade Level: 9
This course is the first in the sequence of high school math classes. Students are introduced to the symbols, language, and concepts which form the basic foundation for later studies in both math and science. Major topics include: techniques for solving first and second degree equations in a single variable, solving linear equations and inequalities in two variables by graphing, solving systems of linear equations, functions, and operations on polynomials, rational expressions and radical expressions. Some students will be selected to take a ten-credit double period of Algebra I. This course must be taken for the first time during the regular school year in a Hillsborough Township Public School.
Geometry CP
Credits: 5
Course Length: Year
Grade Level: 9-10
Prerequisite: Algebra I
This course provides the student with the opportunity to develop the two modes of thought: inductive and deductive reasoning. The student studies the roles of definitions, axioms, and theorems in developing a deductive system often by writing proofs. Topics studied via this approach include: concepts of distance, perpendicularity and parallelism, congruence and similarity, circles, areas and volumes of figures in two and three dimensions. The techniques of algebra are employed throughout the course. This course must be taken for the first time during the regular school year in a Hillsborough Township Public School.
Algebra II CP
Credits: 5
Course Length: Year
Grade Level: 9-11
Prerequisite: Geometry
In this second year of algebra, the student extends the skills and concepts started in Algebra I but at a higher level of difficulty. Major topics included in the course are: the field properties of the real numbers; techniques of solving first and second degree equations and inequalities in one and two variables; techniques of simplifying and operating on polynomial, rational, and irrational expressions; linear and quadratic relations and functions; complex numbers; exponential functions; and logarithms; polynomial and radical equations; and introduction to trigonometry. This course must be taken for the first time during the regular school year in a Hillsborough Township Public School.
Selected Topics in College Math CP
Credits: 5
Course Length: Year
Grade Level: 12
Prerequisite: Algebra II and seniors only
This course is an introductory, non-calculus study of a variety of mathematical topics for seniors only. Students are introduced to major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will also explore topics including set theory, number theory, probability, and graph theory. Students will also study topics in Algebra, Functions, Modeling, and Statistics. Graphing calculators are not required but highly recommended. This is a college preparatory course designed for seniors intending to major in liberal arts, education, or communications.
Statistics CP
Credits: 5
Course Length: Year
Grade Level: 12
Prerequisite: Algebra III/Trig CP or Math Analysis CP/Pre-Calculus CP or AP PreCalculus
This course is an introductory, non-calculus based study of statistics for seniors only. Students are introduced to major concepts and tools for collecting, analyzing, and drawing conclusions from data. Graphing calculators are not required but highly recommended. This course does not count as a 3rd year of required mathematics, but rather, an elective.
Algebra III and Trigonometry CP
Credits: 5
Course Length: Year
Grade Level: 11-12
Prerequisite: Algebra II
The objective of this course is to strengthen the student’s algebra skills and then give a detailed introduction to trigonometry with the goal of preparation for Pre-Calculus. This course includes a review of fundamental concepts of algebra, including real numbers, exponents and radicals, algebraic expressions, fractional expressions, factoring polynomials, complex numbers, and solving systems of equations and inequalities. Particular attention will be given to the concept of a function, including general properties, notation, graphing, transformation, and inverses. Students will also revisit and expand on their understanding of linear, polynomial, exponential, and logarithmic functions. The course will also include an introduction to trigonometric functions and their inverses. If time permits, students will also learn about sequences and series. This course builds an understanding of “real-world” problems, establishing a firm foundation for future work in mathematics and its applications.
Pre-Calculus CP
Course Title through 2022-23: Math Analysis CP
Credits: 5
Course Length: Year
Grade Level: 10-12
Prerequisite: Successful completion of Algebra II CP with a final grade of 80% or higher.
This challenging course provides a sound transition to college-level mathematics. The major topics studied include the elementary functions, which consist of: polynomial, trigonometric, exponential and logarithmic functions. Students also learn how to transform these functions. Sequences, series, conic sections, limits and an introduction to calculus are also studied.
Calculus CP
Credits: 5
Course Length: Year
Grade Level: 11-12
Prerequisite: Successful completion of Pre-Calculus CP with a final grade of 80% or higher or a passing grade in AP Pre-Calculus.
This course is intended for those students who accelerated their math studies in the previous three years and who are ready to begin the study of calculus. It is especially valuable to students who plan to major in business, engineering, mathematics or in the social and life sciences in college. Major emphasis is given to derivatives; curve sketching, exponential and logarithmic functions, integration, trigonometric functions, and differential equations. Extensive applications to biology, medicine, business economics, ecology, social sciences, and physical sciences occur throughout the course.
Honors Courses & Advanced Placement
Admission to these courses requires departmental approval in advance. These courses are designed to challenge students to the limits of their abilities. In addition to possessing an appropriate mathematical background and demonstrating a consistently solid work ethic, students must possess innate mathematical curiosity while combining multiple mathematics concepts to solve non-routine problems.
Geometry H
Credits: 5
Course Length: Year
Grade Level: 9-10
Prerequisite: Successful completion of Algebra I CP with a final grade of 93% or higher and department approval.
This course provides the student with the opportunity to develop the two modes of thought: inductive and deductive reasoning. The student studies the roles of definitions, axioms, and theorems in developing a deductive system often by writing proofs. Topics studied via this approach include: concepts of distance, perpendicularity and parallelism, congruence and similarity, circles, areas and volumes of figures in two and three dimensions, as well as coordinate methods. The techniques of algebra are employed throughout the course. This course must be taken for the first time during the regular school year in a Hillsborough Township Public School.
Algebra II H
Credits: 5
Course Length: Year
Grade Level: 9-11
Prerequisite: Successful completion of Geometry H with a final grade of 80% or higher and department approval.
Successful completion of Geometry CP with a final grade of 93% or higher and departmental approval.
In this second year of algebra, the student extends the skills and concepts started in Algebra I but at a higher level of difficulty and with greater emphasis on derivation and proof. Major topics included in the course are: the field properties of the real numbers; techniques of solving first and second degree equations and inequalities in one and two variables; techniques of simplifying and operations on polynomial, rational, and irrational expressions; linear and quadratic relations and functions; complex numbers; exponential functions; and logarithms. This enriched course includes graphing equations in three variables and determinants. This course must be taken for the first time during the regular school year in a Hillsborough Township Public School.
AP Pre-Calculus
This course replaces Math Analysis H, beginning in the 2023-24 school year.
Credits: 5
Course Length: Year
Grade Level: 10-12
Prerequisite: Successful completion of Algebra II H with a final grade of 85% or higher and departmental approval.
Successful completion of Algebra II CP with a final grade of 95% or higher and departmental approval.
This challenging course provides a sound transition to college-level mathematics. The major topics studied include the elementary functions which consist of: polynomial, trigonometric, exponential, logarithmic, and parametric functions. Students also learn how to transform these functions. Sequences, series, conic sections, matrices, limits and an introduction to calculus are also studied.
AP Statistics
Credits: 5
Course Length: Year
Grade Level: 11-12
Prerequisite: Successful completion of AP Pre-Calculus with a final grade of 80% or higher and departmental approval.
Successful completion of Pre-Calculus CP with a final grade of 95% or higher and departmental approval.
Successful completion of Calculus CP with a final grade of 85% or higher and departmental approval.
Successful completion of AP Calculus AB with a final grade of 80% or higher and departmental approval.
The purpose of Advanced Placement Statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes: exploratory analysis, planning a study, probability, and statistical inference. The AP Statistics course is an excellent option for any student who has successfully completed Pre-Calculus, regardless of the student’s intended college major. Students who successfully complete the course and AP examination may receive college credit and/or advanced placement for an introductory college statistics course. Depending upon the specific college, this course may not satisfy the college’s math requirement for admission. Concurrent enrollment is available with Raritan Valley Community College for a fee. Further information will be available later in the Spring.
AP Calculus (AB)
Credits: 5
Course Length: Year
Grade Level: 11-12
Prerequisite: Successful completion of AP Pre-Calculus with a final grade of 80% or higher and departmental approval.
Successful completion of Pre-Calculus CP with a final grade of 95% or higher and departmental approval.
Successful completion of Calculus CP with a final grade of 85% or higher and departmental approval.
This course is offered to the student who has had considerable success with previous studies in mathematics and who plans to pursue more advanced work in mathematics, business, engineering, or the physical sciences. Major emphasis is given to the concept of the derivative, the integral, and their applications. Successful completion of this course prepares the student for the Calculus AB Advanced Placement exam.
AP Calculus (BC)
Credits: 5
Course Length: Year
Grade Level: 11-12
Prerequisite: Successful completion of AP Calculus AB with a final grade of 80% or higher and departmental approval
This course is offered to the student who has successfully completed the AP Calculus (AB) course. Such a student plans further study in the areas of mathematical sciences, engineering, or physical sciences. The course quickly reviews derivatives, integrals, and their applications. This course also includes topics such as infinite series and differential equations. This course prepares the student for the Calculus BC Advanced Placement Exam.
Computer Programming Courses
Computer Programming I
Credits: 2.5
Course Length: 1 Semester
Grade Level: 10-12
Prerequisite: Successful completion of Algebra I CP with a final grade of 70% or higher.
Students taking this semester course will receive an introduction to computer science while learning the fundamentals of programming in Python. The material emphasizes computational thinking and helps develop the ability to solve complex problems. It provides a foundation in structured programming techniques, number calculations and data, making decisions, repetition and loops, graphics, functions, and programming for music.
Computer Programming II H
Credits: 2.5
Course Length: 1 Semester
Grade Level: 10-12
Prerequisite: Successful completion of Computer Programming I with a final grade of 80% or higher and departmental approval.
This honors level semester course is a continuation from Computer Programming 1. Students will expand their knowledge and skills using structured programming techniques and concepts by addressing more complex problems and developing comprehensive programming solutions. Additional topics in Python include advanced functions, 2D lists, nested iteration, files, dictionaries, handling exceptions, additional programming for music, and the internet. Students completing this course will be prepared to take AP Computer Science A.
AP Computer Science A
Credits: 5
Course Length: Year
Grade Level: 10-12
Prerequisite: Successful completion of Computer Programming II H with a final grade of 80% or higher and departmental approval.
AP Computer Science A is equivalent to an introductory college-level computer programming course in the Java language. Students are introduced to object-oriented programming and fundamental topics in computer science that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course is aligned to the College Board, contains 20 hours of required lab work and prepares students to take the AP Computer Science A exam in May.
AP Computer Science Principles
Credits: 5
Course Length: Year
Grade Level: 10-12
Prerequisite: Successful completion of Computer Programming I with a final grade of 80% or higher, Algebra 1 with a final grade of 85% or higher, and departmental approval.
AP Computer Science Principles is an introductory college-level computing course that introduces students to the breadth of the field of computer science. Students learn to design and evaluate solutions and to apply computer science to solve problems through the development of algorithms and programs. They incorporate abstraction into programs and use data to discover new knowledge. Students also explain how computing innovations and computing systems—including the internet—work, explore their potential impacts, and contribute to a computing culture that is collaborative and ethical. Students who complete the course will be prepared for the Advanced Placement Computer Science Exam (Principles).