# Mathematics

The Mathematics Department at Xavier High School strives to give all students the background and skills they need for college and life. Xavier's graduation requirement is four years of math, and all students will take courses at least through Algebra II.

- Pre-Algebra
- Algebra I
- Geometry
- Algebra II
- Pre-Calculus
- Calculus
- Trigonometry
- AP Calculus
- AP Statistics UCONN ECE
- SAT Review

## Pre-Algebra

*CP - Course #314, Full Year, 1 Credit, Freshmen*

Pre-Algebra is a course custom-fitted for freshmen who score substantially below average on the entrance exam. The aim of this course is to give the student sufficient enrichment and background to be able to complete successfully the mathematics curriculum (Algebra I, Geometry, Algebra II). **Placement based on placement exam and recommendation of summer school teacher.**

## Algebra I

*Honors - Course #311, Full Year, 1 Credit, Freshmen*

This course is a study of the foundation rules of higher mathematics. Topic include the real number system, its properties, linear equations in one variable, functions and graphs, systems of open sentences in two variables, factoring, operations on polynomial and rational expressions, and solutions of quadratic and radical equations. Topics are covered to a greater depth than in the accelerated course and are integrated with word problems and exercises adaptable to the graphing calculator, which is required.

*Accelerated - Course #312, Full Year, 1 Credit, Freshmen*

This course is a study of the foundation rules of higher mathematics. Topics include the real number system, its properties, solving equations in one variable, operations on polynomials, factoring, simplifying rational expressions, solving systems in two variables, functions and graphing linear equations, inequalities, and solving quadratic equations. Where appropriate, emphasis on solution of word problems and calculator applications are included.

*CP - Course #313, Full Year, 1 Credit, Freshmen*

This course introduces the student to the concepts and skills of Algebra to prepare him for future courses in Geometry, Algebra II, and Trigonometry. Topics include operations with real numbers, solving linear equations and inequalities, factoring, algebraic fractions, fractional equations and functions.

CP - Course #324, Full Year, 1 Credit, Sophomores

This course introduces the student to the concepts and skills of Algebra to prepare him for future courses in Geometry and Algebra II. Topics include operations with real numbers, solving linear equations and inequalities, factoring, algebraic fractions, fractional equations, and functions. **This course is offered for those sophomores who took pre-algebra as freshmen.**

## Geometry

*Honors - Course #310, Full Year, 1 Credit, Freshmen*

This course is intended as an exploration of the properties, measurement, and relations of lines, angles, surfaces, and solids. Topics included in the course are the study of logic through deductive proof, angle relationships, right triangles, circles, the concepts of area and volume, and parallel line relationships. The degree to which deductive proof is emphasized is determined by the needs and abilities of the students in the class. **Prerequisite: Algebra Placement Exam in May and approval by Department Chairperson.**

*Honors - Course #321, Full Year, 1 Credit, Sophomores*

This course is intended as an exploration of the properties, measurement, and relations of lines, angles, surfaces, and solids. Topics included in the course are the study of logic through deductive proof, angle relationships, right triangles, circles, the concepts of area and volume, and parallel lines relationships. The degree to which deductive proof is emphasized is determined by the needs and abilities of the students in the class.

*Accelerated - Course #322, Full Year, 1 Credit, Sophomores*

This course examines the properties, measurement, and relation of lines, angles, surfaces, and solids. Intuitive thought and the development of logical thought are emphasized and reinforced. Topics included are deductive proof, angle relationships, parallel lines, right triangles, congruent and similar triangles, circles, and area of volume. Emphasis on deductive proof is left to teacher discretion through evaluation of the class.

*CP - Course #323, Full Year, 1 Credit, Sophomores*

The principle objective of this course is to introduce the student to the basic concepts of geometry and correlate formal geometric theorems with the student's practical experience with the world around him. Students are introduced to formal logical reasoning. Emphasis is placed on working with diagrams such as parallel lines, right triangles, congruent and similar triangles and circles, and discovering the relationships involved. Algebraic skills are reviewed and used to solve problems on a regular basis.

*CP - Course #334, Full Year, 1 Credit, Juniors*

The principle objective of this course, offered to juniors who took algebra I as sophomores, is to introduce the student to the basic concepts of geometry and correlate formal geometric theorems with the student’s practical experience with the world around him. Students are introduced to formal logical reasoning. Emphasis is placed on working with diagrams such as parallel lines, right triangles, congruent and similar triangles and circles, and discovering the relationships involved. Algebraic skills are reviewed and used to solve problems on a regular basis.

## Algebra II

*Honors - Course #320, Full Year, 1 Credit, Sophomores*

The purpose of this course is two-fold: to expand and clarify the basic concepts of Algebra I and to introduce new topics which broaden the students' background in the field of algebra and more sophisticated functions. Topics covered include operations on polynomials, rational quadratic and radical expressions and equations, functions, systems of linear and quadratic equations, exponents, and complex numbers. The remainder of the course is devoted to new concepts and algebraic relations. A graphing calculator is required. **Prerequisite: Course # 310**

*Honors - Course #331, Full Year, 1 Credit, Sophomores & Juniors*

The purpose of this course is two-fold: to expand and clarify the basic concepts of Algebra I and to introduce new topics which broaden the students' background in the field of algebra and more sophisticated functions. Topics covered include operations on polynomials, rational, quadratic and radical expressions and equations, functions, systems of linear and quadratic equations, exponents, and complex numbers. The remainder of the course is devoted to new concepts and algebraic relations. If a sophomore has earned a grade of B or higher in Honors Algebra I and wants the opportunity to take Honors Calculus his senior year, he make take this course concurrently with Honors Geometry during his sophomore year.

*Accelerated - Course #332, Full Year, 1 Credit, Juniors*

Beginning with an in-depth review of the techniques related to operations on polynomials, rational, quadratic and radical expressions and equations, this course proceeds to a deeper study of the fundamental ideas of functions and relations, analytic geometry, systems of linear and quadratic equations, exponents and logarithms, and complex numbers.

*CP - Course #333, Full Year, 1 Credit, Juniors*

After a thorough review of the topics covered in Algebra I, especially those related to the simplification of polynomial, rational, and radical expressions and the solution of polynomial, quadratic, rational, and radical equations, the course proceeds to a deeper look at the notions of functions and relations, analytic geometry, systems of linear and quadratic equations, exponents and logarithms and complex numbers. Elementary trigonometry is also included.

*CP - Course #343, Full Year, 1 Credit, Seniors*

After a thorough review of the topics covered in Algebra I, especially those related to the simplification of polynomial, rational, and radical expressions and the solution of polynomial, quadratic, rational, and rational equations, the course proceeds to a deeper look at the notions of functions and relations, analytic geometry, systems of linear and quadratic equations, exponents and logarithms and complex numbers. Elementary trigonometry is also included. This course is for students who took Geometry in Junior year.

## Pre-Calculus

*Honors - Course #330, Full Year, 1 Credit, Juniors*

This course is a preparation for the study of calculus. It is a study of functions including circular functions, trigonometric functions and their applications, algebraic functions, exponential functions and logarithmic functions. Limits are studied through the examination of sequences, series, and functions. This course also includes the study of analytic geometry.

*Course #341, Full Year, 1 Credit, Seniors*

This course is a preparation for the study of calculus. It is a study of functions including circular, algebraic, exponential, logarithmic, and trigonometric functions and applications. Limits are studied through the examination of sequences, series, and functions. A study of analytic geometry is included.

*Accelerated - Course # 344, Full Year, 1 Credit, Seniors*

This course is a preparation for the study of calculus by seniors in the Accelerated Program looking to take Calculus during their freshman year of college. It is the study of functions including circular, algebraic, exponential, logarithmic, and trigonometric functions and applications. Limits are studied through the examination of sequences, series, and functions. A study of analytic geometry is included. **Pre-requisite: Approval by Department Chairperson and a B average from Algebra 1, Geometry, and Algebra 2.**

## Calculus

*Course #345, Full Year, 1 Credit, Seniors*

Students cover the topics run through during a typical first semester of college Calculus. Topics include: Review of Functions, Limits, and Continuity; Higher and Lower order Derivatives; Exponential, Logarithmic, and Trigonometric Derivatives; and basic Integration. Heavy emphasis will be placed on solving application problems involving derivatives. A TI-83 calculator (or similar) is required.

## Trigonometry

*Accelerated - Course #342, Full Year, 1 Credit, Seniors*

This course is a preparation for the study of pre-calculus or calculus in college. It is a study of the trigonometric functions and their graphs, trigonometric identities, and the trigonometry of triangles. Inverse functions, circular functions, complex numbers, polar graphing, and vectors are also studied.

*CP - Course #3431, Full Year, 1 Credit, Seniors*

Basic Trigonometry begins with a review of Algebra I, Geometry, and Algebra II topics in preparation for the SAT. The course continues with the study of the trigonometric functions using coordinate geometry and right triangle relationships. Included in the course are the Law of Sines and the Law of Cosines, applications, and the graphs of the functions.

## AP Calculus

*Course #340, Full Year, 1 Credit, Seniors*

This course prepares the student to take the AB Advanced Placement Test in May. Special topics can be included to allow the students to take the BC Test. The course will require the student to be very familiar with the TI-83 graphing calculator, as the text reflects the most recent revisions to the calculus curriculum, integrating technology with traditional problems. Topics covered include functions and limits, derivatives and their applications, and integrals and their applications. Pre-requisite: Approval by Department Chairperson and Academic Dean.

## AP Statistics UCONN ECE

*Course #3455, Full Year, 1 Credit, Seniors*

AP Statistics involves the study of, exploratory analysis, probability, planning a study, and statistical inference. The AP Statistics course is taught with activity-based learning in which students actively construct their own understanding of the concepts and techniques of statistics through simulations and mathematical labs. The final assessment for the course will be the creation of an original study with the variable(s) clearly identified, the collection of pertinent data and appropriate statistical compilations. Students will also need to present the findings of the study in a clear and understandable manner. **This class currently earns 4 credits through the Early College Experience program at the University of Connecticut.**

## SAT Review

*Course #0301, Semester Course, .5 Credit, Juniors*

SAT Review is a one-semester course that provides juniors with opportunity to prepare intensively for both the verbal and math sections of the SAT. In the course, students are introduced to the content of the test, learn fundamental test-taking strategies and are provided with ample opportunity to implement these strategies by taking practice tests. The Math portion of the SAT course will provide test taking strategies for multiple choice problems as well as open answer questions. The four major topics covered in this course are: Numbers and Operations, Algebra and Functions, Geometry and Measurement, and Data Analysis, Statistics and Probability. Each unit of study includes instruction on the given topic, followed by guided practice and, finally, individual completion of practice tests. Grading is done on a pass-fail basis, based on a student’s effort, attentiveness and involvement during each class period.

## Math Department Faculty

### David Applegate

**Email:**

### Geoffrey Close

**Email:**

### Dan Deconti

**Email:**

### Andrew Gargano

**Email:**

### Andrew Mule

**Email:**

### Ryan Pipke

**Email:**