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)

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)

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 honor 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.

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 CALCULUS BC 8˚(2424)

Grade Level — 12
Length — One Year (Day and time TBD)

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 — This section of AP Calculus BC will be offered in a flipped-teaching format with one night on-campus and two instances of open office hours. Students will complete all assignments through Canvas and will complete unit assignments in-person.

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.

*This class will be offered pending adequate enrollment.

HONORS LINEAR ALGEBRA AND MULTIVARIABLE CALCULUS (2430)

Grade Level — 12
Length — One Year

Type of Course — Elective
Prerequisite – AP Calculus BC or AP Calculus AB and the approval of the Department Chair
Criteria for Enrollment – Approval of Department Chair, teacher recommendations and satisfactory national test scores, minimum weighted 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).

UC/CSU Subject C Approval (Pending)
Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations.

Course Description — This course covers differential, integral, and vector calculus for functions or more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics. The course opens with a unit on vectors, which introduces students to this critical component of advanced calculus and will culminate in Green’s, Stokes’ and Gauss’ Theorems. We will study partial derivatives, double and triple integrals, and vector calculus in both two and three dimensions. Students are expected to develop fluency with vector and matrix operations. Understanding of parametric curves as a trajectory described by a position vector is an essential concept, and this allows us to break free from one-dimensional calculus and investigate paths, velocities, and other applications of science that exist in three-dimensional space. We study derivatives in multiple dimensions, we use the ideas of the gradient and partial derivatives to explore optimization problems with multiple variables, and we consider constrained optimization problems using Lagrangians. After our study of differentials in multiple dimensions, we move to integral calculus. We use line and surface integrals to calculate physical quantities especially relevant to mechanics and electricity and magnetism, such as work and flux, and we employ volume integrals for calculations of mass and moments of inertia.

The study of systems of linear equations, the algebra of matrices, determinants, vector spaces, linear transformations, the algebra of linear transformations with an introduction to dual spaces, eigenvalues and eigenvectors, and the applications of vectors and matrices to linear equations and linear transformations.

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.

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 also extends beyond personal finance to some topics more relevant to college level business and finance courses. Therefore, it can provide a stronger foundation for students considering that path of study in college.

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:

1. Assist students taking courses in which the Teaching Assistant has demonstrated mastery.
2. 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.