# Mathematics Courses

**Supervisor:** Robert Cole, 908-284-7190 rcole@hcrhs.org

The Mathematics department is proud to offer a wide range of learning experiences through courses that align with the charge that all students can and should develop the mathematical practices needed to best prepare for post-secondary schools or trades. The rigor of a student's academic schedule, the content understanding and skills attained, and the student's course performance are all key aspects considered by college admissions officers. Program level sequencing need not be constant; students may move between levels, based on student performance and department recommendation. Prerequisite requirements for all courses are listed in the course descriptions. Certain Algebra 1, Geometry and Algebra 2 courses require that students take the associated New Jersey Student Learning Assessment (NJSLA). Please read course descriptions carefully, to ensure that all prerequisite courses have been taken before selecting a course. We encourage students to challenge themselves in their course selection, finding a “best fit” course level which matches to their passion and enthusiasm for mathematics, meets specific educational needs, and recognizes math as a growth subject that takes time and effort to learn. Please speak to your current teacher and counselor, if you are considering a change in program level.

Students are encouraged to own a graphing calculator. The district recommends the use of TI-84, TI-84+, or silver editions.

There are three different curricular levels in the mathematics program:

- College Preparatory Level
- STEM Level
- Honors/Advanced Placement Level.

The following information will clarify the reasons for each level:

- The College Preparatory (CP) Level is designed to facilitate the mastery of the New Jersey Student Learning Standards (NJSLS), as well as content beyond the NJSLS at a level of rigor appropriate for students planning on attending four-year college programs, but not in the areas of Science, Technology, Engineering, and Mathematics (STEM).
- The STEM Level is designed to facilitate the mastery of the New Jersey Student Learning Standards, as well as content beyond the NJSLS, at a level of rigor appropriate for students planning to pursue careers in the areas of Science, Technology, Engineering, and Mathematics (STEM).
- The Honors/Advanced Placement Level is designed to facilitate the mastery of the New Jersey Student Learning Standards, as well as content beyond, at the most rigorous level for students planning on taking Advanced Placement math course, including AP Calculus and/or AP Statistics.

Click on the link to view Mr. Cole discussing course selections in the program:

## 2022-2023 Mathematics Course Descriptions

ALGEBRA 1 COURSES

#304 – ALGEBRA 1A - 5 Elective Credits**

Recommendation: Score of 1 on 8th grade NJSLA

This course is designed for students who did not meet proficiency on the Grade 8 NJSLA assessment and/or are in need of furthering their Algebra 1 readiness skills. Topics include: Relationships between quantities; Linear and exponential functions; Reasoning with equations; Descriptive statistics; Connecting algebra and geometry through coordinates. Successful mastery will enable students to take Algebra 1 (334).**Denotes that this course receives elective credit and does not meet HCRHS Math graduation requirements.

#334 – ALGEBRA 1B - 5 CREDITS

Prerequisite: #304 Algebra 1A

This course covers all of the core topics taught in a full-year college preparatory Algebra 1 course. Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take Geometry (324). Students enrolled in this course must take the NJSLA Algebra 1 Assessment.

#313 - ALGEBRA 1 CP - 5 CREDITS

Recommendation: Score of at least Level 3 on the 8th grade NJSLA

This course covers all of the topics taught in a full-year college preparatory NJSLA Standards’ Algebra 1 course, but not at the rigor of the STEM level Algebra 1 (312). Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take Geometry CP (323). Students enrolled in this course must take the NJSLA Algebra 1 Assessment.

#313F - FINANCIAL ALGEBRA - 5 CREDITS

Prerequisite: Concurrent enrollment in Algebra 1 CP 313 or Algebra 1B 334, based on departmental recommendation

This course is to be paired with either Algebra 1 313 or Algebra 1B 334. It is designed for students to get valuable and needed support for the concurrently running Algebra 1 course, while also gaining knowledge and skills to be educated citizens in an increasingly complex financial world. This course meets the Financial Literacy requirements as part of the NJ Student Learning Standards.

#312 - ALGEBRA 1 STEM - 5 CREDITS

Recommendation: Score of Level 4 or 5 on the Grade 8 NJSLA mathematics assessment, or score of 1 or 2 on the Grade 8 Algebra 1 NJSLA and recommendation from 8th grade school.

This course covers all of the topics in a traditional NJSLA Standards’ Algebra 1 course at a level of rigor designed to meet the needs of students interested in careers in Science, Technology, Engineering and Math (STEM). Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take Geometry (322). Students enrolled in this course must take the NJSLA Algebra 1 Assessment.

**GEOMETRY COURSES**

#324 - GEOMETRY - 5 CREDITS

Prerequisite: #334 Algebra 1

This course covers all of the core topics taught in a full-year college preparatory Geometry course. Topics include: Congruence, measurement and construction; Similarity and trigonometry; Geometric measurement and dimension; Connecting algebra and geometry through coordinates; Circles with and without coordinates; Applications of probability. Successful mastery will enable students to take Algebra 2 (344). Students enrolled in this course must take the NJSLA Geometry Assessment.

#323 - GEOMETRY CP - 5 CREDITS

Prerequisite: #3137 ALGEBRA 1 CP

This course covers all of the topics taught in a full-year college preparatory Geometry course, but not at the rigors of the STEM level Geometry (322). Topics include: Congruence, measurement and construction; Similarity and trigonometry; Geometric measurement and dimension; Connecting algebra and geometry through coordinates; Circles with and without coordinates; Applications of probability. Successful mastery will enable students to take Algebra 2 CP (333). Students enrolled in this course must take the NJSLA Geometry Assessment.

#322 - GEOMETRY STEM- 5 CREDITS

Prerequisite: #312 Algebra 1 STEM

Recommendation: Score of Level 4 or 5 on the Algebra 1 or Algebra 2 NJSLA assessment.

This course covers all of the topics in a traditional full year college preparatory Geometry course at a level of rigor designed to meet the needs of students interested in careers in Science, Technology, Engineering and Math (STEM). Topics include: Congruence, measurement and construction; Similarity and trigonometry; Geometric measurement and dimension; Connecting algebra and geometry through coordinates; Circles with and without coordinates; Applications of probability. Successful mastery will enable students to take Algebra 2 (332), or PreCalculus (342) if Algebra 2 has already been taken. Students enrolled in this course must take the NJSLA Geometry Assessment.

#321 – HONORS GEOMETRY- 5 CREDITS

Prerequisite: #311 Honors Algebra 2

Recommendation: Score of Level 4 or 5 on the Algebra 2 NJSLA assessment.

Honors Geometry is a weighted course, which emphasizes topics inherent to Euclidean plane and solid geometry. Topics presented include: Congruence, measurement and construction; Similarity and trigonometry; Geometric measurement and dimension; Connecting algebra and geometry through coordinates; Circles with and without coordinates; Applications of Probability. Successful mastery will enable students to take Honors Pre-Calculus (341). The computer is used as a tool for investigation and discovery. Students enrolled in this course must take the NJSLA Geometry Assessment.

**ALGEBRA 2 COURSES**

#344 - ALGEBRA 2 - 5 CREDITS

Prerequisite: #334 Algebra 1 AND #324 Geometry

This course covers all of the core topics taught in a full-year college preparatory NJSLA Standards’ Algebra 2 course. Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take elective courses such as Discrete Mathematics (361), Number Systems (355), Probability & Statistics (356), Pre-Calculus CP (363) and SAT Prep. Students enrolled in this course may take the NJSLA Algebra 2 Assessment.

#333– ALGEBRA 2 CP – 5 CREDITS

Prerequisite: #313 ALGEBRA 1 CP and # 323 GEOMETRY CP

This course covers all of the topics taught in a full-year college preparatory Common Core State Standards’ Algebra 2 course, but not at the rigors of the STEM level Algebra 2 (332). Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take Pre-calculus CP (363). Students enrolled in this course must take the NJSLA Algebra 2 Assessment.

#332 - ALGEBRA 2 STEM - 5 CREDITS

Grades: 9 (indicated as #3329) or 11

9th Grade Prerequisite: 8th grade Algebra 1 and score of Level 3 or 4 on the NJSLA Algebra1 assessment

11th Grade Prerequisite: #312 Algebra 1 STEM

This course covers all of the topics in a traditional Common Core State Standards’ Algebra 2 course at a level of rigor designed to meet the needs of students interested in careers in Science, Technology, Engineering and Math (STEM). Topics include: Reasoning with equations; Linear and exponential relationships; Descriptive statistics; Expressions and equations; Quadratic functions and modeling. Successful mastery will enable students to take Geometry (322), or Pre-Calculus (342) if Geometry has already been taken. Students enrolled in this course must take the NJSLA Algebra 2 Assessment.

#311 - HONORS ALGEBRA 2 - 5 CREDITS

Prerequisite: Algebra 1 in 8th grade and score of Level 4 or 5 on the NJSLA Algebra 1 assessment.

The emphasis in Honors Algebra 2, which is a weighted course, is placed on the critical thinking skills necessary to understanding mathematical theory as well as the concrete manipulative and graphing skills necessary to mastery of content. Topics include: Polynomial, rational, and radical relationships; Trigonometric functions; Modeling with functions; Inferences and conclusions from data. Successful mastery will enable students to take Honors Geometry (321). Students enrolled in this course must take the NJSLAC Algebra 2 Assessment.

**PRE-CALCULUS COURSES**

#363 – PRECALCULUS CP - 5 CREDITS

Prerequisite: #333 Algebra 2 CP

This course is designed to allow a student to extend his or her preparation for college mathematics. It provides an exciting and rich learning experience that is a broad introduction to mathematical strategies used in the social sciences, business and non-technical careers. Sequences and Series, exponential and logarithmic functions, trigonometry, curve fitting, algebraic modeling, recursion, and a rigorous review of algebraic skills are included. Applications are stressed throughout the course.

#342 - PRECALCULUS STEM - 5 CREDITS

Prerequisite: #332 Algebra 2 STEM and #322 Geometry STEM

Recommendation: Score of Level 4 or 5 on the Algebra 1 or Algebra 2 NJSLA assessments.

This course Covers topics that extend beyond the Common Core State Standards’ at a level of rigor designed to meet the needs of students interested in careers in Science, Technology, Engineering and Math (STEM). Topics include: Trigonometry; Sequences and series; Mathematical induction; Limits; Polynomial functions and graphing; Quadratic relations; Exponential and logarithmic functions. The computer and the graphing calculator are used for investigations.

#341 – HONORS PRE-CALCULUS – 5 CREDITS

Prerequisite: #311 Honors Algebra 2 and #321 Honors Geometry.

This weighted course is designed to help prepare the student for Advanced Placement Calculus AB. Topics include: unit circle trigonometry; trigonometric identities; sinusoidal functions and modeling; complex numbers; polynomial functions and inequalities; exponential and logarithmic functions, and limits and derivates by definition. Successful mastery will enable students to take AP Calculus AB. The computer and graphing calculator are used as tools for analysis of functions and their characteristics. This course has a dual enrollment agreement with Raritan Valley Community College. Eligible students can earn 3 credits for RVCC’s course, MATH 112, Precalculus I, and 3 credits for RVCC’s course, MATH 113, Precalculus II. Visit the HCRHS dual enrollment webpage for more information.

CALCULUS COURSES

#367 – CALCULUS 1 CP - 5 CREDITS

Prerequisites: #363 PRECALCULUS CP

Calculus 1 is a college preparatory course that is not at the rigor of the other Calculus courses, but serves as an excellent foundational course of Calculus concepts for students not interested in STEM fields. Topics include: Rate of change; Differentiation; Integration; Applications; Analytic geometry. The TI-83 or TI-84 graphing calculator is used in this course.

#347 - HONORS CALCULUS 1 - 5 CREDITS

Prerequisites: #342 PreCalculus STEM

Honors Calculus 1 is a weighted course similar in nature to Advanced Placement Calculus, but not as extensive as the College Board's prescribed syllabus. Topics include: Rate of change; Differentiation; Integration; Applications; Analytic geometry. The TI-83 or TI-84 graphing calculator is used in this course.

#352 - ADVANCED PLACEMENT CALCULUS AB - 5 CREDITS

Prerequisites: #341 Honors PreCalculus

This is a weighted course designed for the mathematically mature student who plans to enter a profession where a technical or scientific background is desirable. The AB course is equivalent to a college-level Calculus offering and consists of the following topics: Rate of change; Differentiation; Integration; Applications; Transcendental functions; Analytic geometry; and Parametric equations. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply.

#353 - ADVANCED PLACEMENT CALCULUS BC - 5 CREDITS

Prerequisites: #341 Honors PreCalculus, departmental recommendation AND #353SI AP Calculus A 2.5 Credits

This is a weighted course designed for the mathematically mature student who plans to enter a profession where a technical or scientific background is desirable. The pace of the course is most challenging. The BC course may be equivalent to a two-semester college-level Calculus offering and consists of the following topics: rate of change; Differentiation; Integration; Advanced applications; Transcendental functions; Analytic geometry; Parametric equations; Differential equations; Taylor series; Maclaurin series; Power series; Analysis of polar curves. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply.

#353SI - ADVANCED PLACEMENT CALCULUS A - 2.5 CREDITS

Prerequisites: #341 Honors Pre-Calculus and teacher recommendation.

This summer course is of a hybrid design with the expectation of both in-class and online learning, with an approximate total of 60 hours. This course is paired with AP Calculus BC #353 to complete the course with 7.5 credits. Only students who are scheduled to take AP Calculus BC #353 in the immediately following school year are permitted to take this course. Students will automatically be enrolled in this course when selecting the AP Calculus BC #353 course. This course has a fee and is part of the Summer Institute.

#3537 - ADVANCED PLACEMENT CALCULUS BC - 7.5 CREDITS

Prerequisites: #341 Honors PreCalculus and departmental recommendation

This is a weighted course designed for the mathematically mature student who plans to enter a profession where a technical or scientific background is desirable. The BC course is equivalent to two college-level Calculus offerings and consists of the following topics: rate of change; Differentiation; Integration; Advanced applications; Transcendental functions; Analytic geometry; Parametric equations; Differential equations; Taylor series; Maclaurin series; Power series; Analysis of polar curves. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply.

#354 - ADVANCED PLACEMENT CALCULUS BC - MULTIVARIABLE - 5 CREDITS

Prerequisites: #352 AP Calculus AB

Recommendation: A score of at least a 3 on the AP Calculus AB Exam.

This is a weighted course designed for the mathematically mature student who plans to enter a profession where a technical or scientific background is desirable. The pace of the course is challenging. This BC and Multivariable Calculus course is designed for students who have already successfully completed AP Calculus AB. It consists of the following topics: Rate of Change; Differentiation; Integration; Advanced applications; Transcendental functions; Analytic geometry; Parametric equations; Differential equations; Taylor series; Maclaurin series; Power series; Analysis of polar curves, and topics associated with Multivariable Calculus. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply.

#370 - HONORS LINEAR ALGEBRA - 2.5 CREDITS

Pre or Co-requisite: AP Calculus BC (either #353 or #3537)

This honors weighted math course will be a rigorous introduction to Linear Algebra which aims to bridge the gap between high school and college mathematics for advanced students who may begin their college careers in upper level science courses. Students will learn the theory of Linear Equations, and the theory and computational tools associated with Matrix Algebra. With this foundation, students will explore areas of Linear Algebra such as Vector Spaces, Eigenvalues & Eigenvectors and their applications, Orthogonality and its application to Quadratic Forms, and the Geometry of Vector Spaces. This course may qualify for dual enrollment.

**DATA SCIENCES COURSES**

#356 - PROBABILITY & STATISTICS - 2.5 CREDITS

Prerequisite: Algebra 2 (any level)

This course is designed for juniors and seniors who want a better background in probability and statistics. The course exposes students to topics regarding experimental and theoretical probability; numerical representations of data; graphical representations of data; and written and verbal interpretation of data using concepts from exploratory data analysis. Computer applications, to examine graphical representations of real data (and its subsequent analysis) will play a major role in enhancing the understanding of concepts.

#359 – ADVANCED PLACEMENT STATISTICS – 5 CREDITS

Prerequisite: #321 Honors Geometry or #342 PreCalculus STEM

This is a weighted course, which includes the following topics: exploring data; planning a study; anticipating patterns; and statistical inferences. Computers and/or calculators are used as frequent exploration tools. This course is excellent for students who intend to study business, economics, and/or social sciences where data analysis is required. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply.

#362 - INTERNET OF THINGS - 2.5 CREDITS

Prerequisites: Algebra 1

This course is intended to provide students with a fundamental understanding of three big concepts: 1) “Internet of Things”, 2) “Cloud Computing” and 3) “Web Services”. This will be achieved by hands on design and building of a network that integrates home devices such as lights, outlets and motion detectors. The student will integrate and manage devices through Home Automation Software, Cloud Computing on Amazon Web Services. Solutions will be developed to interact and control these devices through Alexa, web interfaces and mobile devices across the internet. Prior programming experience is not required for this course

#364 – COMPUTER SCIENCE 1– JAVA - 2.5 CREDITS

Corequisite: Algebra 2 (any level)

This is an in-depth course designed to teach the fundamentals of computer science and program design. The programming language used in the course to teach these concepts is Java. The course covers classes; operators; input and output; control statements and functions. It is recommended for the serious minded problem solver who is interested in a career in a computer-related field. Students should have good study skills and a strong interest in computers. Since this is a lab-oriented problem-solving course, good attendance and the ability to focus and stay on task is important. Students are expected to complete programming assignments outside of class.

#365 - CYBERSECURITY - 2.5 CREDITS

Prerequisite: Algebra 1

This course is designed for students who are interested in exploring careers in Cybersecurity. The focus of instruction will include the implementation and monitoring of security on network and computer systems. Students will investigate strategies to identify and protect against security threats such as hackers, eavesdropping and network attacks. The basics of cryptography and logic reasoning will be explored. Hands-on labs in a cyber range provide practice in the configuration and mitigation of system vulnerabilities. Each unit integrates current events and related cyber ethics and law. *Ethics agreement must be signed by all students and parents during the first 2 weeks of class.

#366 – ADVANCED PLACEMENT COMPUTER SCIENCE PRINCIPLES – 5 CREDITS

Prerequisite: Algebra 1

This course is intended for students as an introduction to computer science aspects needed for our ever-growing, technology-based world. It is designed to give students foundational computing skills, an understanding of the real-world impact of computing applications, and programming literacy. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply. This course has a dual enrollment agreement with Raritan Valley Community College. Eligible students can earn 4 credits for RVCC’s course, CSIT 103, Computer Concepts and Programming. Visit the HCRHS dual enrollment webpage for more information.

#368- ADVANCED PLACEMENT COMPUTER SCIENCE – 5 CREDITS

Prerequisite: #364 Computer Science 1 Java or #366 AP Computer Science Principles

This course continues the study of Computer Science topics started with Computer Science 1. This is a lab course that gives extensive practice and emphasis on good programming design and technique. Students are expected to complete programming assignments outside of class. This is an AP course that follows the suggested course of studies for the Computer Science exam. It provides the students with the knowledge and the practice to help them with the AP exam and/or a career in Computer Science. Students enrolled in an AP course are expected to take the AP Exam. In addition, students enrolled in an AP course who take the AP Exam will receive full AP weight for the course. Otherwise, Honors weight will apply. This course has a dual enrollment agreement with Raritan Valley Community College. Eligible students can earn 4 credits for RVCC’s course, CSIT 105, Foundations of Computer Science. Visit the HCRHS dual enrollment webpage for more information.

GENERAL STUDIES

#035 – SAT PREPARATION - 2.5 Credits

Prerequisites: Prerequisites: Geometry (any level) and #022 English

Note: This course does not meet NCAA eligibility requirements and counts as a general elective credit only.

SAT Preparation is a course designed to help students prepare for the math and verbal sections of the SAT. Students will learn test taking strategies and improve their problem-solving skills, through exposure to reading, writing and qualitative and quantitative reasoning tasks. Students can expect to strengthen their repertoire of skills in arithmetic, algebra and geometry, as well as critical reading, the study of vocabulary through context, a review of compositional skills, and the ability to write unified and coherent timed essays. Students will receive informative feedback from practice SAT tests.

#326 – NJSLA PREP – 2.5 CREDITS

This is a compensatory basic skills course which emphasizes remediation and reinforcement of skills and concepts necessary to pass the NJSLA Assessment. Students will prepare for either the Algebra 1, Geometry, or Algebra 2 NJSLA Assessments, depending on their math history. Students are placed in this course based upon their performance on previous NJSLA Assessments, or by teacher recommendation.

#355 – NUMBER SYSTEMS – 5 CREDITS

Prerequisite: Geometry and Algebra 2 (any level)

This course is designed to serve the needs of future liberal arts majors. Topics include systems of enumeration, sets and set operations, logic, problem solving strategies, modular arithmetic, Euclidian geometry, and number theory. It is a wonderful opportunity for students who have gone through our Academic Level math courses to continue their learning in the area of mathematics in a college level course. Qualified students are able to earn 3 college credits from Raritan Valley Community College for MATH 101: Number Systems. This course has a dual enrollment agreement with Raritan Valley Community College. Eligible students can earn 3 credits for RVCC’s course, MATH 101, Number Systems. Visit the HCRHS dual enrollment webpage for more information.

#360 - HONORS DISCRETE MATHEMATICS - 2.5 CREDITS

Prerequisites: Honors Algebra 2 or PreCalculus STEM

This is a weighted course, which may be elected in addition to or in place of Analysis, Trigonometry, or Calculus. Topics offered include: Game theory; Matrices; Sets; Discrete functions and relations; Permutations and combinations; Discrete probability and statistics; Markov chains; Election theory, Apportionment; Bin packing, Coding theory; Fractals; Scheduling; Fair division.

#361 – DISCRETE MATHEMATICS – 5 CREDITS

Prerequisites: Geometry (any level)

This course is designed for juniors and seniors who want a better background in traditional discrete mathematics, along with online applications of mathematics in a project-based environment. The project-based course exposes students to topics that include matrices, graph theory, election theory, and digital technology. This course satisfies the 5 credits needed beyond Algebra 1 and Geometry.