# Mathematics

## Introduction

Course Titles and Descriptions

The Mathematics Department offers a variety of courses at each grade level to maintain interest and to encourage students of all ability levels to continue their study of mathematics for four years. The courses are designed to prepare students for success in the future by developing mathematical problem-solving skills, knowledge, and critical thinking skills.

### Grouping

The mathematics courses are grouped according to ability and interest in mathematics. The Advanced or Honors level courses are for students with high interest and ability. For all courses, prerequisite grade performance and teacher recommendations are strictly adhered to.

### Graphing Calculators

Graphing calculators are required on the New York State Math Regents examinations, as well as on the Advanced Placement examinations. It is recommended that students purchase their own calculators. They will be used in daily lessons, assignments, and assessments throughout the year to develop students’ mathematical reasoning skills and to appropriately use technology to aid in problem solving. The TI-84 (Plus or Plus Silver Edition) is recommended for student use. The TI-84 will be used for classroom demonstrations.

## Course Titles and Descriptions

212 Algebra (P) – 215 Common Core Algebra 1A (P) – 216 Common Core Algebra 1B (P) – 213 Unified 1 Algebra (P) – 220 Applied Algebra & Geometry (P) – 221 Geometry Honors (P) – 222 Geometry (P) – 223 Unified 2 Algebra (P) – 231 Common Core Algebra 2 Honors (P) – 232 Common Core Algebra 2 (P) – 233 Unified 3 Intermediate Algebra (P) – 234 Common Core Algebra 2A (P) – 235 Common Core Algebra 2B (P) – 236 Intermediate Algebra 2 & Geometry (P) – 238 College Algebra with Trigonometry (P) – 241 AP Calculus AB (P) – 242 AP Calculus BC (P) – 243 Unified 4 Intermediate Algebra (P) – 244 Precalculus Honors (P) – 245 Precalculus (P) – 246 Topics in Advanced Math E (P) – 247 AP Statistics-Probability (P) – 248 Calculus (Non AP) (P) – 949 Computer Science 1E (P) – 951 Computer Science 2E (P) – 952 Advanced Placement Computer Science H (P) – 943R/943A Math AIS Lab

### 212 Algebra (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Math 8; C+ grade performance or better recommended.

This course is required for entrance into most colleges and is a prerequisite for further study in mathematics and science at the Regents level. While much of the curriculum is developed around algebra, topics such as geometry, probability, statistics, and trigonometry are studied. The final examination in this course is the NYS Common Core Algebra Regents exam.

### 215 Common Core Algebra 1A (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Math 8.

This course will serve as the first year of a two-year program covering the NYS Common Core Algebra curriculum. Students will address many of the same curriculum topics that students in Algebra 1 study, with a concentration on the first half of the Algebra 1 curriculum. Students are supported with smaller class sizes, and focus is placed on increasing relevance and applications of math concepts. This course, combined with Common Core Algebra 2B in the following year, culminates with the NYS Common Core Algebra Regents exam. The final examination in the course is a local departmental exam.

### 216 Common Core Algebra 1B (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Common Core Algebra 1A.

This course will serve as the second year of a two-year program covering the NYS Common Core Algebra Curriculum. Students will address many of the same curriculum topics that students in Algebra 1 study, with a concentration on the second half of the Algebra 1 curriculum. Students are supported with smaller class sizes, and focus is placed on increasing relevance and applications of math concepts. This course culminates with the NYS Common Core Algebra Regents exam.

### 213 Unified 1 Algebra (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Math 8.

This is the first year of a four-year program that is designed for our most challenged math learners. This program will allow students to satisfy the math requirements necessary for graduation. Students take the NYS Common Core Algebra Regents exam at the end of the second year. In this course, topics include equations and inequalities, polynomials, geometry, introduction to trigonometry, and graphing of lines. Problem solving and the use of math in real-life situations are integrated throughout the course. The final exam in this course is departmental.

### 220 Applied Algebra & Geometry (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Algebra 1. Recommended for students who achieve a 73 or lower in CC Algebra 1.

This course is designed for students who experienced difficulty with Algebra 1 and who would benefit from gaining stronger foundational algebra skills to achieve success in future math courses. Algebra topics include: Linear Functions, Linear Inequalities, Quadratic Functions and Systems of Inequalities and Equations. Geometry topics include: Transformational Geometry, Triangular Relationships, Quadrilaterals, Polygons and Solids. Instructional strategies in the course will emphasize application style questions and interdisciplinary connections. The activities will utilize manipulatives, Chromebooks and Mathematical software to assist the students with a deeper understanding. If successful, students in this course will take #236 Intermediate Algebra 2 and Geometry in their junior year and then #238 College Algebra & Trigonometry in their senior year. The final exam in the course will be a departmental local final exam.

### 221 Geometry Honors (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 93 in Algebra 1 and acceptable performance on honors problem solving test.

In addition to an enriched version of the standard Geometry curriculum, honors students will be afforded the opportunity to more extensively study selected mathematical topics. Increased emphasis will be placed on explanations and justifications of procedures and thought processes. Students will complete honors assignments that will include non-routine problem sets. The final examination in this course is the NYS Common Core Geometry Regents exam.

### 222 Geometry (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 73 in Algebra 1 or 90 in Common Core Algebra 2B or teacher recommendation.

This course includes an extensive study of geometric relationships, informal and formal geometry proofs, coordinate geometry, transformational geometry, constructions and circles. The final exam in this course is the NYS Common Core Geometry Regents exam.

### 223 Unified 2 Algebra (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Unified 1 Algebra.

This is the second year of a four-year-program that is designed for students with weak math skills. This program will allow students to satisfy the math requirements necessary for graduation. In this course, topics include equation solving, statistics, probability, polynomials, geometry, and graphing. The final examination in this course is the NYS Common Core Algebra Regents exam.

### 231 Common Core Algebra 2 Honors (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 90 in Algebra 1 and a minimum final average of 95 in Geometry Regents with acceptable performance on the honors problem solving test or minimum final average of 88 in Geometry Honors.

In addition to the material offered in Common Core Algebra 2, the student will study selected enrichment topics such as cubic equations, even/odd functions, symmetry tests, natural logarithms, and the graphs of six trigonometric functions. Increased emphasis will be placed on explanations and justifications of procedures and thought processes. The final examination in this course is the NYS Common Core Algebra 2 Regents exam.

### 232 Common Core Algebra 2 (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 75 in both Algebra 1 and Geometry/Geometry Honors.

This course includes an in-depth study of the real and complex number systems, a review and extension of functions and transformations, work with exponents, logarithms, trigonometric relationships and probability, and an extensive unit on statistics. The final examination in this course is the NYS Common Core Algebra 2 Regents exam.

### 233 Unified 3 Intermediate Algebra (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Unified 2 Algebra.

This is the third course of a four-year program that is designed for students with weak math skills. This course will allow students to satisfy their math requirements necessary for graduation. In this class, students will extend their algebra skills beyond those included in the NYS Common Core Algebra curriculum. Topics covered will include factoring, quadratics, rational expressions, complex numbers, and a variety of consumer topics. The final examination in this course is a departmental exam.

### 234 Common Core Algebra 2A (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 65 in Geometry Regents.

This is the first year of a two-year extended Algebra 2 Regents program designed for the math student who has had academic difficulty in previous math courses and needs to satisfy the third year math requirement and/or meet the eligibility requirements for an Advanced Regents diploma. Students will study the same curriculum as that in Algebra 2 Regents course, but with less emphasis on the theory of trigonometry. This course will cover approximately two-thirds of the Algebra 2 Regents material, with the remainder covered in the second year, Common Core Algebra 2-B, of the program. The final examination in this course is a departmental exam.

### 235 Common Core Algebra 2B (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 75 in Common Core Algebra 2A.

This is the second year of a two-year extended Common Core Algebra 2 program. The course will cover the final one-third of the Algebra 2 Regents curriculum, including basic trigonometric functions, graphs, identities, and equations. The NYS Common Core Algebra 2 exam will be given in June. During second semester, students will investigate several precalculus topics and will prepare for the Common Core Algebra 2 Regents exam.

### 236 Intermediate Algebra 2 & Geometry (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Common Core Algebra 1B or Applied Algebra & Geometry or following a placement evaluation, permission by the Department Supervisor.

This course is designed for students who have taken the two year stretched Common Core Algebra program or Applied Algebra & Geometry. The curriculum emphasizes intensive review of elementary algebra and its extension covering variations, exponents, logarithms, quadratic equations, functions and their graphs, and systems of equations. It also includes selected topics from probability and statistics. This course is a prerequisite to the HVCC UHS senior year math elective, College Algebra with Trigonometry. The final exam is a departmental exam.

### 238 College Algebra with Trigonometry (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of #236 Intermediate Algebra 2 and Geometry or following a placement evaluation or permission by the Department Supervisor.

Students in this course are eligible to enroll in the Hudson Valley Community College University in the High School program. This curriculum is aligned with HVCC Math 150 College Algebra with Trigonometry program and is instructed in the first semester of the school year. Students who enroll and successfully pass the course will earn four HVCC credits. The curriculum includes advanced algebra and trigonometry topics. For the second semester, students will cover selected Algebra 2 topics that will prepare them for taking a precalculus course at the collegiate level. The midterm exam is a HVCC departmental final and the final exam is a local departmental final exam. Students wishing to enroll in the University Program at HVCC will be responsible for paying the reduced course credit fee.

Advanced Placement Calculus H (P) Enrollment in this course is restricted to students who have displayed special effort and exceptional ability in mathematics and who are seeking advanced placement in college. The Advanced Placement examination is required of all students taking this course. Students who do not take the exam will not receive AP credit. A fee is charged by the College Board and must be paid or the student may be removed from the course.

### 241 AP Calculus AB (P)

Full Year – 1 Unit

Students electing this course are required to take the AP examination (AB) covering topics in differential and integral calculus. This course is equivalent to one semester of college calculus. Enrollment in Advanced Placement Calculus AB is based upon the student’s:

- Achievement of minimal final average of 90 in Common Core Algebra 2 and Precalculus or 85 in Algebra 2 Honors and Precalculus Honors.
- Problem solving and analytical abilities.
- Work habits and career plans.
- Math teachers’ recommendations.

### 242 AP Calculus BC (P)

Full Year – 1 Unit

Students electing this course are required to take the AP examination (BC) covering topics in differential and integral calculus, as well as topics in infinite series, advanced techniques of integration, polar and parametric equations, and vector functions. This course is equivalent to two semesters of college calculus.

- Achievement of minimum final average of 93 in Common Core Algebra 2 Honors and Precalculus Honors.
- Problem solving and analytical abilities.
- Work habits and career plans.
- Math teachers’ recommendations.

### 243 Unified 4 Intermediate Algebra (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Unified 3 Intermediate Algebra.

This is the final course of a four-year program that is designed for students with weak math skills. In this class, students will continue to focus primarily on intermediate algebra skills, along with selected geometry and trigonometry topics. The objective of this course is to strengthen a student’s math foundation and provide readiness for future math courses at the post-secondary education level. The final examination in this course is a departmental exam.

### 244 Precalculus Honors (P)

Full Year – 1 Unit

**Prerequisite:** Minimal final average of 93 in Common Core Algebra 2 and acceptable performance on honors problem solving test or 85 in Common Core Algebra 2 Honors.

In addition to an enriched version of the standard Precalculus curriculum, students in this course will be afforded the opportunity to more extensively study selected precalculus and calculus topics. Increased emphasis will be placed on explanations and justifications of procedures and thought processes. Topics included in this course include advanced algebra; exponential and logarithmic functions; advanced graphing techniques; limits; and extensive differential calculus. This course is not part of the University in the High School program. The final examination in this course is departmental.

### 245 Precalculus (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 75 in Common Core Algebra 2 Regents/Honors.

This college-level course is designed for the student who desires a strong background in math preparation for calculus at the college level or Advanced Placement Calculus AB. Topics in this course include advanced algebra, polynomial, trigonometric, exponential, and logarithmic functions; polar graphing, conic sections, matrices, limits and differential calculus. The final examination in this course is a departmental exam. If enrolled in the University in the High School program, students can earn three State University of New York credits upon successful completion of this course. Juniors enrolled in Precalculus must earn a grade of 90 to be eligible for AP calculus AB.

### 246 Topics in Advanced Math E (P)

Full Year – 1 Unit

**Prerequisite:** Successful completion of Common Core Algebra 2.

This fourth-year math course is designed for the student who wishes to prepare for a noncalculus, college-level course as well as for students interested in the social sciences.

Topics studied in this course include polynomial, rational, and logarithmic functions; sequences and series; matrices and game theory; vectors; probability and statistics; set theory and logic. The final examination is departmental. If enrolled in the University in the High School program, students can earn three State University of New York credits upon successful completion of this course.

### 247 AP Statistics-Probability (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 80 in Precalculus.

Students electing this course are required to take the AP examination in Statistics. Students who do not take the exam will not receive AP credit. This full-year, college-level course will provide background and practice in the presentation and analysis of statistical data involving frequency distributions, measures of center and spread normal distribution, hypothesis testing, design of experiments and simulation, and linear regression. Students who are considering a major in psychology, sociology, education, medicine, as well as science and mathematical fields should consider electing this course. A fee is charged by the College Board and must be paid or the student may be removed from the course. Students in this course will have the opportunity to enroll in the University in the High School Program, and can earn three State University of New York credits upon successful completion of this course.

### 248 Calculus (Non AP) (P)

Full Year – 1 Unit

**Prerequisite:** Minimum average of 80 in Precalculus or 75 in Precalculus Honors.

This full-year, college-level course will provide background and practice in basic level calculus concepts. Topics in this course include limits and derivatives, differentiation rules, applications of differentiation, and integration. Students in this course will have the opportunity to enroll in the University in the High School Program and can earn three State University of New York credits upon successful completion of this course.

### 949 Computer Science 1E (P)

First Semester – 1/2 Unit

**Prerequisite:** Successful completion of Geometry.

This course will serve as an introduction to programming techniques using the Java language. Selecting algorithms will be stressed as students learn and apply computer commands dealing with variable and formula representation, formatting text, branching and looping techniques, one-dimensional arrays, and nested loop structures. The final examination in this course is departmental.

### 951 Computer Science 2E (P)

Second Semester – 1/2 Unit

**Prerequisite:** Computer Science 1 or, following a placement evaluation, permission of the Department Supervisor.

This course will extend Java programming skills previously learned in Computer Science 1. Topics that will be covered using the Java language include two-dimensional arrays, sorting and searching techniques, user-defined functions, subroutines, strings, graphics, gaming techniques, animation, and graphical user interfaces. The final examination in this course will be departmental.

### 952 Advanced Placement Computer Science H (P)

Full Year – 1 Unit

**Prerequisite:** Minimum final average of 88 in Computer Science 2 and a minimum final average of 75 in Common Core Algebra 2 R/H, or following a placement evaluation, permission of the Math Department Supervisor.

This full-year course will concentrate on advanced programming techniques and topics using the Java language. Such topics as data structures, classes, use of algorithms, and programming methodology will be explored. Enrollment in this course is restricted to students who have displayed special effort and exceptional ability in computer science and who are seeking advanced placement in college. The Advanced Placement Examination is required of all students taking this course. Students who do not take the exam will not receive AP course credit. A fee is charged by the College Board and must be paid or the student may be removed from the course.

### 943R/943A Math AIS Lab

No Credit

This lab will offer academic intervention services to two groups of students who will meet on separate rotations. The first group (Course #943R) are those students who have not yet taken or have not yet passed the New York State Common Core Algebra Regents examination and who will take the exam in January. The second group (Course #943A) are those students whose scores on the Eighth Grade state math assessment and/or teacher recommendation have indicated that they may require additional support in mastering the material in Algebra. Ninth graders enrolled in Algebra who are new to the district may also be scheduled for this lab. Students in this lab will prepare for the June Common Core Algebra Regents exam. Students in either lab will meet every other rotation.