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:
All students interested in honors and AP courses in the Mathematics Department must apply to the Mathematics Department Chair for admission. This process analyzes the student’s grade in his/her current math course, and an evaluation by the current teacher 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, UC Diagnostic, PSAT). Applications for the desired course are made available to the students well in advance of the registration period. 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
- Course Description - Algebra 1 is a traditional course in elementary algebra with an emphasis on solving everyday 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 May, prior to enrollment.
- 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 2H (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 May, prior to enrollment.
- Course Description - This course is offered to entering freshman who have demonstrated the necessary 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 and an introduction to trigonometry. Students who successfully complete Algebra 2H typically enroll in Honors Precalculus B 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
- Course Description - The course reviews the basic concepts, terminology, and notation involved in geometry. 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. 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 H (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 and Foreign Language, as well as Math; standardized test scores (math, language, reading).
- 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. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
ADVANCED ALGEBRA (9910)
- Grade Level - Entering 11
- Length - Five weeks in Summer
- Type of Course - Elective OFFERED IN SUMMER ONLY
- Prerequisite - Algebra 1 or Algebra Accelerated, Geometry
- Requirements - Graphing Calculator (TI-83 or TI-84 series)
- Criteria for Enrollment - Approval of Department Chair
- Course Description - This is a fast-paced course designed for the motivated student who desires to advance from the regular level math course into the accelerated level, or from Algebra 1 Accelerated into the AP Calculus BC class as a senior. The material consists of Algebra 2 topics which fall between Algebra 1 and Precalculus Honors. Topics include general use of a graphing calculator (TI-83 or TI-84 series required), exploring polynomial functions and their graphs, complex numbers, solving 2 and 3 dimensional linear systems using determinants and matrices, radicals, rational and irrational functions, conic sections, exponential and logarithmic functions, sequences and series. The class will also include an introduction to Trigonometry. Level of performance will dictate placement in Algebra 2, Precalculus Accelerated or Precalculus Honors for the coming Fall semester. The purpose of this class is to accelerate students. Thus it does not fulfill a requirement to graduate nor will units be granted.
ALGEBRA 2 (2300)
- Grade Level - 11
- Length - One Year
- Type of Course - Core upper division course required for graduation.
- Prerequisite - Algebra 1, Geometry
- Criteria for Enrollment - None
- 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, 12
- Length - One Year
- Type of Course - Elective for seniors. Elective for juniors fulfilling six semester graduation requirement in lieu of Algebra 2.
- Prerequisite - Algebra 1 Accelerated, Geometry OR Algebra 1, Geometry, Advanced Algebra OR Algebra 1, Geometry, grade of A in Algebra 2, recommendation of Algebra 2 teacher
- Criteria for Enrollment - Approval of Department Chair, based on: teacher recommendation; satisfactory national test scores; past performance in Math, especially Algebra 1.
- 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. Traditional topics of algebra are reviewed at the beginning of the course. The course then proceeds to an intense study of trigonometry (both right and oblique triangles), its applications to vector and complex numbers, circular functions, and trigonometric identities. The rest of the course is an analysis of families of functions and relations -- polynomials, rational functions, radical functions, trigonometric functions, logarithmic functions, exponential functions, and conic sections -- 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 fulfilling six semester graduation requirement
- Prerequisite - Algebra 2H (or Algebra 1 Accelerated and Advanced Algebra), Geometry
- Criteria for Enrollment - Approval of Department Chair, based on: teacher recommendation; satisfactory national test scores; past performance in Math, esp. Algebra 2H.
- Course Description - The student who has taken Algebra 2H as a freshman or Advanced Algebra in the summer between sophomore and junior year will, on meeting the Criteria for Enrollment, take Precalculus Honors as a preparation for Calculus. Most of the first semester consists of an intense study of trigonometry (both right and oblique triangles), its applications to vector and complex numbers, circular functions, and trig identities. The rest of the course is an analysis of families of functions and relations -- polynomials, rationals, radicals, trig, log and exponentials, and the conics -- 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 (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 2.0; Department 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. The first semester consists of an intense study of trigonometry (both right and oblique triangles), its applications to vector and complex numbers, circular functions, and trig identities. The second semester is an analysis of families of functions and relations -- polynomials, rationals, radicals, trig, log and exponentials, and the conics -- and their graphs both algebraically and through the graphing calculator, including 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, Grade of B- or better in Algebra 2
- Criteria for Enrollment - Department 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.
PROBLEM SOLVING STRATEGIES (2475)
- Grade Level - 12
- Length - One Semester (Fall only)
- Type of Course - Elective
- Prerequisite - Algebra 1, Geometry, Algebra 2
- Criteria for Enrollment - Senior standing; teacher recommendation; approval of department chair.
- Course Description - The basis of this course is the teaching and learning of a wide range of strategies which people in the real world use when solving problems; additionally, the student will develop improved communication skills through regular small-group work in the solution of progressively more challenging problems. It is expected that students, through persistence and serious effort enhanced by a spirit of cooperation, will learn to experience pleasure in solving mathematical problems, and come to appreciate the validity of diverse approaches to individual problems. (NOTE: students who enroll in this course are strongly encouraged, though not required, to enroll in Introduction to Trigonometry for the Spring semester.) A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
INTRODUCTION TO TRIGONOMETRY (2476)
- Grade Level - 12
- Length - One Semester (Spring only)
- Type of Course - Elective
- Prerequisite - Problem Solving Strategies (see above)
- Criteria for Enrollment - Senior standing; teacher recommendation; approval of department chair; successful completion of the Problem Solving Strategies course during the preceding fall semester.
- Course Description - A sequel to the Problem Solving Strategies course, designed for the motivated student who desires to develop and reinforce precalculus mathematics skills in the area of Trigonometry; topics include: trigonometric and circular functions and their graphs; solving right triangles; Law of Sines and Law of Cosines solutions of general triangles; identities; inverse relations and functions; solution of trigonometric equations. 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.
- 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 extrema and related rates of change; anti differentiation and its application to the solution of diffenential 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.
ADVANCED PLACEMENT 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, satisfactory national test scores, math department GPA of 3.6, overall GPA of 3.4. Students are required to take the Advanced Placement test in the last month of the course.
- 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.
ADVANCED PLACEMENT CALCULUS BC (2423)
- Grade Level - 12
- Length - One Year
- Type of Course - Elective
- Prerequisite - Precalculus Honors
- Criteria for Enrollment - Approval of Department Chairperson, teacher recommendation, satisfactory national test scores, Math Department GPA of 3.6, overall GPA of 3.4. Students are required to take the Advanced Placement test in the last month of the course.
- 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.
ADVANCED PLACEMENT STATISTICS (2470)
- Grade Level - 12
- Length - One Year
- Type of Course - Elective
- Prerequisite - Algebra 2, Precalculus Acceleated or Precalculus Honors
- Criteria for Enrollment - Grade of B- or better in Algebra 2, and Department Chair approval.
- 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 noncalculus 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.