## Summary

Students are required to complete three credits of study, four credits are highly recommended for college admission. The Mathematics Department encourages all students to pursue the study of mathematics throughout their school career so that their understanding and appreciation of the subject, in both its cultural and immediate aspects, can be raised to the highest level. Our program provides offerings that allow all students to realize a pace most suitable to their individual rates of learning. Mathematics courses should be selected according to interests and requirements determined by future educational needs or occupational plans. Summary of courses offered appears below, with specific course descriptions in the pages that follow.

**Course / Grade / Credit / Weight / Classification / Special Note**

Algebra 9 / 1.0 / 1.0 / Regents / Regents

Geometry / 10 / 1.0 / 1.0 / Regents / Regents

Geometry Honors / 9-10 / 1.0 / 1.05 / Regents / Must be selected for class

Algebra II / 10-11 / 1.0 / 1.05 / Regents / Regents

AP Calculus / 12 / 1.0 / 1.1 / AP / AP exam

College Algebra / 11-12 / 3.0 / 1.1 / CCHS / CCHS, prerequisites

College Trigonometry / 11-12 / 3.0 / 1.1 / CCHS / CCHS, prerequisites

Introduction to Statistics / 12 / 3.0 / 1.1 / CCHS / CCHS, prerequisites

Calculus I & II / 11-12 / 4.0 / 1.1 / CCHS / CCHS, prerequisites

Pre-calculus / 11-12 / 1.0 / 1.05

Elective High School Calculus / 11-12 / 1.0 / 1.05 / Elective

Advanced Algebra with Financial Applications / 11-12 / 1.0 / 1.0 / Elective

### Mathematics Course Descriptions

#### Algebra

##### Grades 8-9

1 (one credit)

This is the first mathematics course in the high school. The Common Core Algebra course set forth here is not the algebra of 30 years ago. The focal point of this course is the algebra content strand. Algebra provides tools and ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts, and technology. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings. This course culminates in a Regents examination in Common Core Algebra.

#### Geometry

##### Grades 9-10

1 credit

Geometry is intended to be the second course in mathematics for high school students. There is no other school mathematics course that offers students the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusion follows logically from their hypothesis. This course is meant to employ an integrated approach to the study of geometric relationships. A major emphasis of this course is to allow students to investigate geometric situations. Properties of triangles, quadrilaterals and circles should receive particular attention. Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences. This course culminates with the Regents examination in Geometry. A separate section of this course may be available that culminates with a local exam. Students taking the non-regents course would qualify for the Regents Diploma only. Successful completion of one math Regents exam is required, for graduation.

#### Honors Geometry

##### Grade 9-10

1 credit

This course is the second course of a three year sequence in Mathematics. The curriculum is similar to that of Geometry, except that the practice problems and homework will be done on a higher level. The expectation of a math student in the honors program is to eventually reach AP Calculus or College Calculus in their senior year. This course culminates with the Regents examination in Geometry.

#### Algebra II

##### Grade 11-12

1 credit

In implementing the Algebra II process and content performance indicators, it is expected that students will identify and justify mathematical relationships, formally and informally. The intent of both the process and content performance indicators is to provide a variety of ways for students to acquire and demonstrate mathematical reasoning ability when solving problems. This is an upper level mathematics course for those students pursuing an Advanced Regents Diploma, and requires a Regents examination. A separate section of this course may be available that culminates with a local exam. Students taking the non-regents course would qualify for the Regents Diploma only.

#### AP Calculus

##### Grade 12

1 credit

This course is the reformulation of elementary mathematics through the use of the limit process. The study of calculus is the mathematics of tangent lines, slopes, areas, volumes, and lengths, centroids, curvatures, and most importantly, velocity and acceleration. Each of these topics involves the reformation of pre-calculus through the use of the limit process. The student would be able to take an Advanced Placement Examination at the completion of the course to receive possible college credit.

#### College Algebra

##### Grade 11-12

Prerequisites:

- CCHS Seniors – Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 85 on the Algebra II Regents
- CCHS Juniors- Cumulative GPA of 90 or higher in all Regents Courses and a minimum of 90 on the Algebra II Regents
- The recommendation of the course teacher or the Principal for the student’s provisional placement in the course

3 credits College Algebra is the first of the two course pre-calculus sequence. It is a functional approach to algebra designed to provide (1) the necessary preparation for students who intend to study calculus or other specialized college mathematics courses, and (2) the opportunity for students in general education to investigate and understand the pre-calculus level of mathematics.

#### College Trigonometry

##### Grade 11-12

Prerequisites:

- CCHS Seniors – Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 85 on the Algebra II Regents
- CCHS Juniors- Cumulative GPA of 90 or higher in all Regents Courses and a minimum of 90 on the Algebra II Regents
- Successful completion of College Algebra
- The recommendation of the course teacher or the Principal for the student’s provisional placement in the course

3 credits

College Trigonometry is the second course for students who plan to continue on toward the study of Calculus. Topics include trigonometric functions, graphing techniques, right triangle applications, trigonometric identities, inverse functions, oblique triangles, two-dimensional vectors and complex numbers in trigonometric form.

#### Introduction to Statistics

##### Grade 12

Prerequisites:

- CCHS Seniors – Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 85 on the Algebra II Regents
- CCHS Juniors – Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 90 on the Algebra II Regents
- The recommendation of the course teacher or the Principal for the student’s provisional placement in the course

3 credits

This course examines the general elements and principles of statistics used in the fields of education, consumerism, quality control, allied health, physical sciences and social science. The course is broken up into two parts: descriptive statistics and inferential statistics. Topics include methods of summarizing and presenting data, measures of center, spread, and position; probability; binominal probability distribution; normal probability distribution; t-test chi-square tests; confidence intervals, hypothesis testing; and linear regression.

#### Pre-Calculus

##### Grades 11 – 12

1 credit

This course is a high-level continuation of Algebra II. Topics include Advanced Algebra, Trigonometry, Interpretation and construction of Function Graphs, Logarithms, Sequences, and Series. This course is designed to prepare the students for Calculus and will include basic Calculus concepts.

#### Calculus I

##### Grade 11-12

Prerequisites

- CCHS Juniors- Cumulative GPA of 90 or higher in all Regents Courses and a minimum of 90 on the Algebra II Regents
- Successful completion of College Algebra and College Trigonometry with a GPA of 85 or higher

4 credits

Analytic geometry topics are introduced as needed to carry out the orderly development of calculus. Topics include algebraic functions and transformations, trigonometric functions and identities, limits, continuity, derivatives, implicit differentiation, related rate problems, Rolles’ Theorem and Mean Value Theorem, curve sketching (relative min/max, concavity, points of inflection, limits at infinity, horizontal asymptotes), applications of differentiation, differentials, antidifferentiation, the definite integral, sigma notation, and Fundamental Theorem of Calculus.

#### Calculus II

##### Grade 11-12

Prerequisites:

- CCHS Seniors – Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 85 on the Algebra 11 Regents

4 credits

A continuation of calculus which builds on the basic concepts of derivatives and integration to include calculus of exponentials, logarithms, trigonometric functions, inverse trigonometric functions and hyperbolics, the area of a region between two curves, solids of revolution, application problems, integration, Trapezoidal rule, Simpson’s Rule, L’Hopital’s Rule, Taylor and Maclurin polynomials, sequences and series, power series and conics and rotation formula.

#### High School Calculus

##### Grade 11–12

1 credit

This one year non-Regent’s course includes limits, differentiation, application of differentiation and basic integrals.

#### Advanced Algebra with Financial Applications

##### Grades 11–12

1 credit*

* This course can be counted as a third Math credit or Business credit

Advanced Algebra with Financial Applications is a college-preparatory course that will use sophisticated mathematics to give you the tools to become a financially responsible young adult. The course employs Algebra, Precalculus, Probability and Statistics, Calculus and Geometry to solve financial problems that occur in everyday life. Real-world problems in investing, credit, banking, auto insurance, mortgages, employment, income taxes, budgeting and planning for retirement are solved by applying the relevant mathematics. Field projects, computer spreadsheets, and graphing calculators are key components of the course The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. The mathematics topics contained in this course are introduced, developed, and applied in an as-needed format in the financial settings covered. Students are encouraged to use a variety of Problem-solving skills and strategies in real-world contexts, and to questions outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, questions, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future, and is thusly aligned with the recommendations of the Common Core State Standards.