# Mathematics Courses

**Supervisor:** Edward Brandt,

908-284-7190,

ebrandt@hcrhs.org

The rigor of a student's academic schedule, the content understanding and skills attained, and the grades received are key aspects considered by college admissions officers. Please note: sequencing need not be constant; students may move between levels, based on department recommendation and as long as prerequisite courses are taken. Prerequisite requirements and recommendations for all courses are listed in the course descriptions. Please read these carefully, to ensure that all prerequisite courses have been taken before selecting a course. While we encourage students to challenge themselves in their course selection, the demands of higher level courses can be significant. If you are considering a change in level, talk to your current teacher and counselor for guidance.

## New for 2018-2019:

#3136 - FINANCIAL ALGEBRA - 5 CREDITS

#3537 - ADVANCED PLACEMENT CALCULUS BC -7.5 CREDIT

From Mr. Brandt: *"We are excited to be offering Financial Algebra #3136 as a new course. This course is only for students who are also taking Algebra 1 CP 3137 or Algebra 1B 334. Financial Algebra will help support the Algebra 1 students while also meeting New Jersey's graduation requirement of financial literacy. The combination of strengthening skills and applying them to various financial contexts will be a rewarding opportunity. Check your counselor for more information."*

## 2018-2019 Mathematics Course Descriptions

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 Common Core State Standards, as well as content beyond the CCSS, 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 Common Core State Standards, as well as content beyond the CCSS, at a level of rigor appropriate for students planning to pursue careers the areas of Science, Technology, Engineering, and Mathematics (STEM).
- The Honors/Advanced Placement Level is designed to facilitate the mastery of the Common Core State Standards, as well as content beyond, at the most rigorous level for students planning on taking AP Calculus.

**COLLEGE PREPARATORY LEVEL COURSES:**

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

Recommendation: Score of 1 on 8th grade PARCC assessment.

This course is designed for students who did not meet proficiency on the Grade 8 PARCC 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 Academic Algebra 1 (334).**Denotes that this course receives elective credit and does not meet an HCRHS Math graduation requirement.

#334 – ALGEBRA 1B - 5 CREDITS

Prerequisite: #304 Algebra 1A

This course covers all of the core topics taught in a full-year college preparatory Common Core State Standards’ 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 Academic Geometry (324). Students enrolled in this course must take the PARCC Algebra 1 Assessment.

#324 - GEOMETRY - 5 CREDITS

Prerequisite: #334 Algebra 1

This course covers all of the core topics taught in a full-year college preparatory Common Core State Standards’ 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 Academic Algebra 2 (344). Students enrolled in this course must take the PARCC Geometry Assessment.

#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 Common Core State 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 must take the PARCC Algebra 2 Assessment.

#3137 - ALGEBRA 1 CP– 5 CREDITS

Recommendation: Score of at least Level 3 on the 8th grade PARCC assessment.

This course covers all of the topics taught in a full-year college preparatory Common Core State 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 (3237). Students enrolled in this course must take the PARCC Algebra 1 Assessment.

#3136 - FINANCIAL ALGEBRA – 5 CREDITS

Prerequisite: Concurrent enrollment in Algebra 1 CP 3137 or Algebra 1B 334, based on departmental recommendation

This course is to be paired with either Algebra 1 3137 or Algebra 1B 334. The course 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.

#3237 – GEOMETRY CP - 5 CREDITS

Prerequisite: #3137 ALGEBRA 1

This course covers all of the topics taught in a full-year college preparatory Common Core State Standards’ 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 (3337). Students enrolled in this course must take the PARCC Geometry Assessment.

#3337 – ALGEBRA 2 CP – 5 CREDITS

Prerequisite: #3137 ALGEBRA 1 and # 3237 GEOMETRY

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 PARCC Algebra 2 Assessment.

#363 – PRECALCULUS CP - 5 CREDITS

Prerequisite: #3337 ALGEBRA 2

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.

#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 student 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.

**STEM LEVEL COURSES:**

#312 - ALGEBRA 1 STEM - 5 CREDITS

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

This course covers all of the topics in a traditional Common Core State 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 PARCC Algebra 1 Assessment.

#322 – GEOMETRY STEM- 5 CREDITS

Prerequisite: #312 Algebra 1

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

This course covers all of the topics in a traditional Common Core State Standards’ 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 PARCC Geometry Assessment.

#332 - ALGEBRA 2 STEM - 5 CREDITS

Grades: 9 (indicated as #3329) or 11

9th Grade Prerequisite: 8th grade Algebra 1

11th Grade Prerequisite: #312 Algebra 1

9th Grade Recommendation: Meet the district cut-off scores on the placement test provided to the sending districts in early June and score of at least Level 4 on the PARCC Algebra 1 assessment.

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 PARCC Algebra 2 Assessment.

#342 – PRECALCULUS STEM - 5 CREDITS

Prerequisite: #332 Algebra 2 and #322 Geometry.

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

#347 – HONORS CALCULUS 1 - 5 CREDITS

Prerequisites: #342 PreCalculus STEM

Honors Calculus 1 is a weighted course similar in nature to Advanced Placement Calculus 1, 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.

**HONORS AND ADVANCED PLACEMENT LEVEL COURSES:**

#311 - HONORS ALGEBRA 2 - 5 CREDITS

Prerequisite: Algebra 1 in 8th grade, completion of HC placement evaluation and score of Level 4 or 5 on the PARCC Algebra 1 assessment.

Recommendation: Teacher recommendation, and meeting district cut-off scores on an Honors Algebra evaluation administered in early June.

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 PARCC Algebra 2 Performance-Based and End-of-Year Assessments.

#321 – HONORS GEOMETRY- 5 CREDITS

Prerequisite: #311 Honors Algebra 2

Recommendation: Score of Level 4 or 5 on the Algebra 2 PARCC 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 PARCC Geometry Performance-Based and End-of-Year Assessments.

#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: mathematical induction; complex numbers; polynomial functions and inequalities; exponential and logarithmic functions, and mathematical modeling. 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.

#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.

**ELECTIVE COURSES IN MATHEMATICS PROGRAM:**

#035 – SAT PREPARATION - 2.5 Credits

Grades:10-12

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

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 – PARCC PREP – 2.5 CREDITS

Grade: 10,11, 12

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

#355 – NUMBER SYSTEMS – 5 CREDITS + 3 College Credits Prerequisite: Geometry and Algebra 2 of any level.

We are proud to offer this course in a Dual Enrollment capacity with Raritan Valley Community College. The 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. Course fee plus an application fee payable to RVCC are also required for students taking the class for RVCC credit.

#356 - PROBABILITY & STATISTICS - 2.5 CREDITS

Prerequisite: Algebra 2

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.

#360 – HONORS DISCRETE MATHEMATICS - 2.5 CREDITS

Prerequisites: #311 Honors Algebra 2 or #332 Algebra 2, and #321 Honors Geometry or #322 Geometry

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

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.

#364 – COMPUTER SCIENCE 1– JAVA - 2.5 CREDITS

Co-requisite: Algebra 2

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 – COMPUTER SCIENCE 2 – JAVA - 2.5 CREDITS

Prerequisite: #364 Computer Science 1 – Java

This is a continuation of Computer Science 1 that explores languages such as Python, apps design, and C++. It covers topics on arrays; searching and sorting; inheritance and polymorphism; graphics; files and applets. Students are expected to complete programming assignments outside of class.

#366 – ADVANCED PLACEMENT COMPUTER SCIENCE PRINCIPLES – 5 CREDITS

Prerequisite: Algebra 1 and score of at least a Level 4 on Algebra 1 PARCC assessment.

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. In addition, this is a course that students can take their freshman or sophomore year, if they would like to begin their high school career with an AP course. 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.

#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.