# Course Catalog: Mathematics Department

INTRODUCTION

In keeping with the Jesuit tradition of education at St. Ignatius College Preparatory and in accordance with our school's statement of philosophy, the mission of the* Mathematics Department* is to develop “men and women for and with others” through a comprehensive and structured mathematics program. We strive to prepare 90% or more of the student body, over the course of four years, for success in a college calculus and/or statistics course. We instill a fundamental appreciation of the techniques of algebra in solution of problems and of logic through the study of geometry. Though only three years of math are required for graduation, we encourage students to continue math through their senior year in order to have the greatest flexibility in choosing courses of study in college.

CRITERIA FOR HONORS ENROLLMENT:

Qualifications for honors, accelerated and AP courses includes analysis of the student’s grade in his/her current math course, an evaluation by the current and previous teachers (if applicable) of the student’s grasp and application of concepts, participation, written work, motivation and interest in advanced mathematics study, overall recommendation, and various standardized tests (HSPT and PSAT). In addition, certain grade minimums must be met in order to be considered for an honors or AP course. Final enrollment in an honors or AP course is always contingent upon successful completion of current coursework, even if a student is provisionally admitted to an honors or AP course in the spring.

COURSES* *

#### ALGEBRA 1 (2100)

**Grade Level —** 9**Length** **—** One Year**Type of Course —** Core lower division course required for graduation**Prerequisite —** None**Criteria for Enrollment –** Algebra Placement Examination, Entrance Examination **UC/CSU Subject C Approval**

**Course Description —** Algebra 1 is a traditional course in elementary algebra with an emphasis on solving problems. The course falls into four basic parts: 1) the four operations on real numbers and their use in the solution of simple equations and related problems; 2) polynomials, factoring, and fractions, leading to the solution of more complicated problems; 3) inequalities, functions and relations, and systems of open sentences; and 4) irrational numbers and quadratic functions and equations. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### ALGEBRA 1 ACCELERATED (2104)

**Grade Level —** 9**Length** **—** One Year**Type of Course —** Core lower division course required for graduation**Prerequisite —** Some experience with Algebra concepts in 8th grade**Criteria for Enrollment –** Approval of Department Chair; entrance examination; recommending performance on departmental placement exam in April, prior to enrollment**UC/CSU Subject C Approval**

**Course Description — **The course follows the general goals and objectives of the regular Algebra 1 course. In addition, advanced topics of algebra are introduced: absolute value equations and inequalities, linear programming, polynomial functions and their graphs, analytic techniques to explore various curves, and an introduction to topics of geometry and trigonometry. Finally, students will be given challenge problems designed for curricular enrichment and requiring independent study and research on a regular basis. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### ALGEBRA 2 HONORS (2110)

**Grade Level —** 9**Length** **—** One Year**Type of Course —** Core lower division course required for graduation**Prerequisite —** Algebra 1 or equivalent in 8th grade**Criteria for Enrollment –** Approval of Department Chair; entrance examination; recommending performance on departmental placement exam in April, prior to enrollment **UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA calculations*

**Course Description —** This course is offered to entering freshman who have demonstrated mastery of Algebra 1 content. The course follows the general goals and objectives of the regular Algebra 2 course offered to juniors. The course includes in depth analysis of higher degree polynomials; analysis, interpretation and graphing of rational functions, including asymptotic behavior; an in-depth consideration of the conic sections, including transformations. Students who successfully complete Algebra 2 Honors typically enroll in Precalculus Honors after the completion of their Geometry course. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### GEOMETRY (2201)

**Grade Level —** 10**Length** **—** One Year**Type of Course —** Core lower division course required for graduation**Prerequisite —** Algebra 1 or Higher**Criteria for Enrollment –** Sophomore standing**UC/CSU Subject C Approval**

**Course Description —** The course reviews the basic concepts, terminology, and notation involved in geometry, and is designed for the student who successfully completed Algebra 1 as a freshman, though any student may apply. Both abstract and practical aspects are covered. Conditional statements, conjectures, theorems, and written justifications are systematically brought into the course, along with the subjects to which they pertain, in the context of problem solving as well as in the context of the preparation of formal proofs. Students construct an understanding by spending some of their class time working in collaborative learning groups. Review of algebraic and geometric concepts is employed throughout the course. In this way, algebra skills are maintained and the students are better prepared to enter into the geometric aspects of advanced algebra, math analysis, precalculus, and calculus courses. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### GEOMETRY ACCELERATED (2202)

**Grade Level —** 10**Length** **—** One Year **Type of Course —** Core lower division course required for graduation**Prerequisite —** Algebra 1 or Higher**Criteria for Enrollment –** Approval of Department Chair, based on: teacher recommendation; past performance in English, Foreign Language, and Math; standardized test scores (math, language, reading**UC/CSU Subject C Approval**

**Course Description —** This course follows generally the description of the traditional geometry course but also includes more proof (direct and indirect; in two-column, flow, and paragraph form). This course is designed for the student who successfully completed Algebra 1 Accelerated as a freshman, but any student may apply. Within the context of Geometry, the Accelerated course includes more challenging algebraic applications, such as solving quadratic equations. It also includes an introduction to analytic geometry and trigonometry, helping to prepare students for Precalculus. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### GEOMETRY HONORS (2203)

**Grade Level —** 10**Length** **—** One Year **Type of Course —** Core lower division course required for graduation**Prerequisite —** Algebra 1 or Higher **Criteria for Enrollment –** Approval of Department Chair, based on: teacher recommendation; past performance in English, Foreign Language, and Math; standardized test scores (math, language, reading) **UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA***Course Description —** This course follows generally the description of the traditional geometry course but provides extensive experience from early stages with the devising, presentation, and defense of student proofs and the theoretical consideration of the nature of proof (direct and indirect; in two-column, flow, and analytical paragraph form). The Honors course includes a more extensive coverage of solid geometry, an introduction to analytic geometry and trigonometry, and opportunities for curricular enrichment in problem-solving. Additional topics include vectors, trigonometric identities, conic sections, and the study of trigonometric and circular functions. Within the context of Geometry, the Honors course includes more challenging algebraic applications, such as solving quadratic, rational, irrational, logarithmic, and exponential equations. This course is designed for the student who successfully completed Algebra 2H as a freshman, but any student may apply. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### ALGEBRA 2 (2300)

**Grade Level —** 11**Length** **—** One Year**Type of Course —** Core lower division course required for graduation**Prerequisite —** Algebra 1, Geometry**Criteria for Enrollment –** None**UC/CSU Subject C Approval**

**Course Description — **The first part of the course reviews basic terminology, notation, concepts, skills, and application of elementary algebra by examination of the real number system. This part includes real number concepts and skills involving operations with positive and negative numbers and zero, solution of linear equations and inequalities, one and two variable equations, solving verbal problems, properties of polynomials and rational expressions. Ideas such as set, variable, number line, open sentence, ordered pair, equivalent sentences, and Cartesian coordinate system are studied and the student is required to demonstrate ability to solve problems involving these concepts.

The course also includes the concepts of function and relation and emphasizes linear and quadratic relations and functions. The text chapters discussing this material employ symbols, concepts, and methods presented in the earlier chapters. Thus, the course continually grows and builds on learned material. The course also includes discussions on exponential functions and logarithms, and a short look at trigonometry. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### PRECALCULUS ACCELERATED (2304)

**Grade Level —** 11**Length** **—** One Year**Type of Course —** Elective for juniors fulfilling six-semester graduation requirement in lieu of Algebra 2**Prerequisite —** Grades of B or better in both semesters of Algebra 1 Accelerated (or B- or below in Algebra 1 Accelerated/successful completion of Algebra 1 and a successful petition to department chair given suitable grade and recommendation from Geometry Accelerated or Honors), Geometry, Geometry Honors, or Geometry Accelerated. At least one accelerated or honors mathematics course must be completed as a freshman or sophomore.**Criteria for Enrollment –** Approval of Department Chair, based on: teacher recommendation; satisfactory national test scores; past performance in Math, especially Algebra 1, Algebra 1 Accelerated, or Algebra 2 Honors**UC/CSU Subject C Approval**

**Course Description —** Precalculus mathematics is a course designed for the student who intends to continue the study of mathematics in the direction of the natural or physical sciences and is a preparation for Calculus. Traditional analytic trigonometry is taught at the beginning of the course which includes an intense study of right triangle trigonometry, its applications to vectors, circular functions, and trigonometric identities, and solving trigonometric equations. The rest of the course is an analysis of families of functions and relations – polynomials, rational functions, radical functions, trigonometric functions, logarithmic functions, and exponential functions -- and their graphs both algebraically and through the graphing calculator, including an introduction to the fundamental aspects of Calculus. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### PRECALCULUS HONORS (2313)

**Grade Level —** 11**Length** **—** One Year**Type of Course –** Elective** **for juniors fulfilling six-semester graduation requirement**Prerequisite —** Grades of B or better in both semesters of Algebra 2H (or B- or below in Algebra 2H/successful completion of Algebra 1 Accelerated and a successful petition to department chair given suitable grade and recommendation from Geometry, Geometry Honors, or Geometry Accelerated**Criteria for Enrollment –** Approval of Department Chair, based on: teacher recommendation; satisfactory national test scores; past performance in Math, especially Algebra 2H**UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA and UC/CSU GPA*

*calculations*

**Course Description — **Precalculus mathematics is a course designed for the student who intends to continue the study of mathematics in the direction of the natural or physical sciences and is an intensive preparation for Calculus. Most of the course is an analysis of families of functions and relations – polynomials; rational function; radical functions; trigonometric functions, including an intense study of right triangle trigonometry, its applications to vectors, circular functions, and trigonometric identities; logarithmic functions; and exponential functions -- and their graphs both algebraically and through the graphing calculator, including an introduction to the fundamental aspects of Calculus. Significant independent work is considered a requirement for this course – students will be asked to perform independent study tasks, including (but not limited to) viewing and taking notes from screencasts, taking online quizzes, and collaborative learning. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### PRECALCULUS (2405)

**Grade Level —** 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite —** Algebra 1, Geometry, Grade of B or better in Algebra 2**Criteria for Enrollment –** Minimum Math GPA of 3.0; Approval of Department Chair**UC/CSU Subject C Approval**

**Course Description —** This course is designed to give a thorough preparation for college Calculus. The course content is the same as Precalculus Honors, but is presented at a slower rate and with additional algebra review. Most of the course is an analysis of families of functions and relations – polynomials; rational function; radical functions; trigonometric functions, including an intense study of right triangle trigonometry, its applications to vectors, circular functions, and trigonometric identities; logarithmic functions; exponential functions -- and their graphs both algebraically and through the graphing calculator, including an introduction to the fundamental aspects of Calculus and an introduction to limits, derivatives, and general curve sketching. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### MATH ANALYSIS (2460)

**Grade Level —** 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite – **Algebra 1, Geometry, Algebra 2**Criteria for Enrollment –** Approval of Department Chair**UC/CSU Subject C Approval**

**Course Description —** This course is designed to give each student thorough preparation in basic Trigonometry and Statistics. THIS COURSE IS NOT MEANT TO BE A PREPARATION FOR CALCULUS. Topics include the Trigonometric and Circular functions and their applications, Identities, Oblique Triangle Trig, and Vectors (in two dimensions) in rectangular and polar form. The course also includes an introduction to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### CALCULUS (2410)

**Grade Level —** 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite – **Precalculus, Accelerated or Precalculus Honors**Criteria for Enrollment –** Approval of Department Chair, based on teacher recommendation, satisfactory national test scores, past performance in Math, especially Precalculus**UC/CSU Subject C Approval**

**Course Description —** This course is designed for the student who is interested in pursuing a college major with a strong emphasis in mathematics. In the first part of the course, the elementary properties of functions and their inverses are reviewed, as well as specific types of functions (exponential, logarithmic, trigonometric). Subsequently, the student is introduced to the concepts of limits and continuity; differentiation and its applications to problems of extreme and related rates of change; anti differentiation and its application to the solution of differential equations; definite integrals and their application to finding areas, volumes, and length of curves. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### AP CALCULUS AB (2413)

**Grade Level —** 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite – **Precalculus Accelerated or Precalculus Honors**Criteria for Enrollment –** Approval of Department Chair based on teacher recommendations and satisfactory national test scores, minimum Math Dept. weighted GPA of 3.5 -- with accelerated courses counting as +0.5 to the GPA for the accelerated course(s), and honors courses counting as +1.0 to the GPA for the honors course(s). *Students are required to take the Advanced Placement exam in May.*

**UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations*

**Course Description —** This course is designed for the student who is interested in pursuing a college major with a strong emphasis in mathematics. The course will cover three main topics of Calculus: limits, derivatives, and integrals. The course will emphasize a multi-representational approach to calculus with concepts and solutions expressed graphically, numerically, and analytically. The course represents understanding of derivatives, integrals, and limits is a priority, as well as applications of these concepts. In order to develop these concepts, functions and graphs are a fundamental part of this course. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### AP CALCULUS BC (2423)

**Grade Level —** 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite – **Precalculus Honors**Criteria for Enrollment – **Approval of Department Chair, teacher recommendations and satisfactory national test scores, minimum Math Dept. GPA of 3.65 -- with accelerated courses counting as +0.5 to the GPA for the accelerated course(s), and honors courses counting as +1.0 to the GPA for the honors course(s). *Students are required to take the Advanced Placement exam in May.*

**UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations.*

**Course Description —** AP Calculus BC is an extension of AP Calculus AB rather than an enhancement. This course includes all topics covered in the AP Calculus AB course, with similar emphases and similar depth of understanding required. The course also presents intensive study of parametric, polar, and vector functions; sequences and series; and elementary differential equations. A Texas Instruments TI-83 or TI-84 series graphing calculator will be required.

#### AP STATISTICS (2470)

**Grade Level —** 12**Length** **—** One Year **Type of Course —** Elective**Prerequisite – **Algebra 2, Precalculus Accelerated or Precalculus Honors**Criteria for Enrollment –** Grade of B+ or better in Algebra 2, Approval of Department Chair, teacher recommendation. *Students are required to take the Advanced Placement exam in May.*

**UC/CSU Subject C Approval**

*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations.*

**Course Description —** This course is designed to give students a foundation for further studies in math while emphasizing preparation for majors in psychology, sociology, and other non-calculus fields. The course is intended for students wishing to complete the equivalent of a one-semester non-calculus based college course in statistics and will introduce them to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.

#### INTRODUCTION TO FINANCE (2474)

**Grade Level —** 11, 12**Length** **—** One Year**Type of Course —** Elective**Prerequisite – **Algebra 2, Precalculus Accelerated or Precalculus Honors**Criteria for Enrollment – **Grade of B+ or better in Algebra 2, Approval of Department Chair, teacher recommendation.**UC/CSU Subject C Approval**

**Course Description —** Students taking this class will develop the skills needed to make sound financial decisions. Topics will include planning your career, payroll and taxes, banking, credit, budgeting, purchasing, basic economics, an introduction to stats and business ethics. All of these topics will be taught through a lens of fiscal and ethical responsibility. This course is intended for students who want to pursue a business or finance sequence of studies in college and is intended to introduce students to a college level finance course.

#### MATHEMATICS TEACHING ASSISTANT

**Grade Level —** 10, 11, 12**Length** **—** One Semester or One Year**Type of Course —** Elective**Prerequisite – **None**Criteria for Enrollment –** Permission of instructor and approval of Department Chair. Enrollment is via roster submitted by instructor. Students should not list this course on their Schedule Request Forms.

**Course Description —** Math Teaching Assistants provide support for the math department (1 hour/week) either before school, after school, or during resource period in one or more of the following ways:

- Assist students taking courses in which the Teaching Assistant has demonstrated mastery.
- Assist with grading assignments that require no teacher interpretation.

Students interested in being a Teaching Assistant are required to fill out a short application available from their teacher or the math department chair. Teaching Assistants are typically supervised by an individual teacher, whose signature is required at the time of application. Students will be selected based on department needs and student qualifications. In some cases, students taking AP math courses will have priority in being a Teaching Assistant due to their qualifications in offering peer assistance.