# COURSE CATALOG: MATHEMATICS DEPARTMENT

### FACULTY DIRECTORY: MATHEMATICS DEPARTMENT

### Graduation Requirements:

Three Years (includes 1 year Algebra I + 1 year Geometry)

Four Years are recommended by UC.

### Courses Offered:

#### Pre-Algebra

## Pre-Algebra

##### Grade 9

One-year course

##### Prerequisite:

Placement depends upon the results of the Math placement test and recommendation of 8th grade school.

##### Description:

This course is an introduction to Algebra, covering operations with fractions, decimals, and integers, the concept of variables and their application in equations and problem solving. Operations with exponents and polynomials are also studied.

#### Algebra I

## Algebra I

##### Grades 9-12

One-year course

##### Prerequisite:

Placement depends upon the results of the Math Placement Test and recommendations of 8th grade Instructor. For grades 10-12: Grade of “C” or better in Pre Algebra.

##### Description:

The course presents the language and symbolism of Algebra and the properties of the real number system used in solving equations and inequalities. Students are introduced to functions, graphing, and problem solving involving systems of equations. Operations with polynomials, rational expressions, and radicals are explored with an emphasis on problem solving techniques.

#### Algebra I - Advanced

## Algebra I - Advanced

##### Grade 9

One-year course

##### Prerequisite:

Placement depends upon the results of the Math Placement Test and 8th grade Math progress.

This course is designed to accommodate those students who have completed Algebra in 8th grade, but have not qualified for direct enrollment in Geometry 9.

##### Description:

This course is a more rigorous class than the regular Algebra I. More time is spent on the foundations (the “why”), and the mathematical applications of, the basic algebraic concepts, than in introducing them, since the assumption is that these students already possess a certain level of algebra knowledge. Most concepts involve the use of more complex examples and problems than in regular Algebra I, and are discussed/investigated to more depth with an emphasis on the fundamental properties and theorems that justify/prove them. Topics and concepts include, but are not limited to. The properties and number sets of the real number system, equations, inequalities, graphs and functions, absolute value, exponents and polynomials, quadratic equations, functions, and inequalities, operations involving rational expressions and equations, systems of equations and inequalities, and radicals.

#### Geometry

## Geometry

##### Grades 9-12

One-year course

##### Prerequisite:

Grade 9 students will be assessed to determine placement. Grade of “C” or better in Algebra I and/or instructor recommendation.

##### Description:

This course is designed for the average to above average student. Deductive and inductive reasoning is developed using concepts of parallel lines, triangle relationships and other geometric figures. Concepts of space geometry are integrated with plane geometry throughout the course. Algebraic skills are reviewed and strengthened through application in solving problems. The course includes: right triangle trigonometry, constructions, and loci, coordinate geometry, and transformations.

#### Algebra II

## Algebra II

##### Grades 9-12

One-year course

##### Prerequisite:

Grade 9 students will be assessed to determine placement.

Grade of “C” or better in Geometry.

##### Description:

This course includes graphing, solving, and applying systems of inequalities, linear equations, and quadratic and polynomial functions, powers, roots, radicals, exponential and logarithmic functions, quadratic relations and conic sections, the complex number system, polynomials of higher order, logarithms, and other selected topics. Multiple problem solving techniques are explored.

#### Algebra II Honors

## Algebra II Honors

##### Grades 9-12

One-year course

##### Prerequisite:

Grade 9 students will be assessed to determine placement.

Grade of “B” or better in previous courses and by Department selection.

##### Description:

This course includes the real number system, equations and inequalities of the first and second degree, functions, the complex number system, conic sections, polynomials of higher order, logarithms and other selected topics. The course will emphasize problem-solving techniques, and more challenging word problems will be done on each topic.

#### Trigonometry-PreCalculus

## Trigonometry - PreCalculus

##### Grades 9-12

One-year course

##### Prerequisite:

Grade 9 students will be assessed to determine placement.

Grade of “B” or better in Algebra II and Geometry and by Department selection.

##### Description:

This course is a study of pre-calculus mathematics. The first semester stresses the language of functions with an emphasis on circular and trigonometric functions. Properties of algebraic, exponential and logarithmic functions, conic sections, and an introduction to the concept of limits through sequences and series are covered in the second half of the course.

#### Trigonometry - PreCalculus Honors

## Trigonometry - PreCalculus Honors

##### Grades 10-12

One-year course

##### Prerequisite:

Grade of “B” or better in previous classes and by Department selection.

##### Description:

This course is an in-depth preparation for Calculus. It concentrates on elementary functions, especially trigonometric functions and their applications, limits of sequences, series, and functions with several units on derivatives and their applications. Analytic geometry is studied using a vector approach. Problem solving techniques are emphasized and more challenging problems are explored.

#### Calculus

## Calculus

##### Grades 11-12

One-year course

##### Prerequisite:

By Department selection. Students must have a thorough knowledge of college preparatory algebra, geometry, trigonometry and analytical geometry.

##### Description:

This course includes review of analytical geometry, functions, formal differentiation, applications of the derivative, integration, applications of the definite integral, transcendental functions, methods and applications of integration, and elementary differential equations.

#### AP Calculus AB

## AP Calculus AB

##### Grades 11-12

One-year course

##### Prerequisite:

By Department selection.

##### Description:

This course is designed for the most advanced math student. The students must have a thorough knowledge of college preparatory algebra, geometry, trigonometry and analytical geometry. Topics include: review of analytical geometry, functions, formal differentiation, applications of the derivative, integration, applications of the definite integral, transcendental functions, methods and applications of integration, and elementary differential equations. All students are required to take the AP test in May.

#### AP Calculus BC

## AP Calculus BC

##### Grades 11-12

One-year course

##### Prerequisite:

By Department selection.

##### Description:

This course covers a full year of college calculus (the calculus of functions of a single variable). Included are all of the topics covered on the AP Calculus BC exam. Emphasis is on conceptual understanding. Students will develop the ability to express, interpret, and relate functions graphically, numerically, analytically and verbally, write and verbally communicate their mathematical results with justifications using correct notation and terminology. The graphing calculator can be used to solve a variety of problems and will recognize when a graphing calculator is necessary as well as when it is not the best approach. All students are required to take the AP test in May.

#### Finite Math

## Finite Math

##### Grade 12

One-year course

##### Prerequisite:

Grade of “C” or better in Algebra II and/or Geometry with instructor recommendation.

##### Description:

This is an advanced course for students who wish to continue the study of mathematics but do not plan to major in a discipline requiring calculus. The emphasis of the content of this course is on the use of mathematics to solve real world problems. Developing reasoning skills, rational, logical thought processes, and problem solving skills will be stressed. Areas of application include business and economics, biology and medicine, the social sciences and more. Course topics include: a variety of strategies to solve problems, a review of algebra, linear systems, linear programming: elementary matrix operations, set theory and Venn Diagrams, probability and statistics, financial math, including interest compounding and investment strategies.

#### Statistics

## Statistics

##### Grades 11-12

One-year course

##### Prerequisite:

Completion of Algebra II with a "C" or better.

##### Description:

This course is intended to provide an introduction to the fundamental concepts and methods of statistics and probability. The course consists of an introduction to data exploration, sampling, experimentation, pattern anticipation and statistical inference. Topical coverage includes basic data exploration, data modeling, correlation, regression, designing studies, probability, sampling distributions, estimating with confidence intervals, testing claims, comparing two groups and chi-square analysis.

#### AP Statistics

## AP Statistics

##### Grade 11-12

One-year course

##### Prerequisite:

Completion of Algebra II with a "C" or better.

##### Description:

This course is intended to provide an introduction to the fundamental concepts and methods of statistics and probability. The course consists of an introduction to data exploration, sampling, experimentation, pattern anticipation and statistical inference. Topical coverage includes basic data exploration, data modeling, correlation, regression, designing studies, probability, sampling distributions, estimating with confidence intervals, testing claims, comparing two groups and chi-square analysis.

The goal of this course is to assist students in developing statistical vocabulary and an understanding of statistical methodologies for the purpose of becoming better consumers and interpreters of statistical information. Additionally, students will be prepared to take the AP Statistics administered in May.

#### Computer Programming

## Computer Programming

##### Grades 10-12

One-year course, Elective

##### Prerequisite:

Algebra I & Geometry

##### Description:

This course introduces computer programming using the JAVA programming language with object-oriented programming principles. Emphasis is placed on event-driven programming methods, including creating and manipulating objects, classes, and using object-oriented tools such as the class debugger.

**This course meets the UC/CSU College-Preparatory Mathematics (c) course requirements.**