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# Mathematics

*The Mathematics Department develops students' understanding of mathematics skills and practices to prepare them for college-level courses, future careers, and responsible consumer and civic participation. *

You will use mathematical practices such as pattern and data analysis, logical and qualitative reasoning, and the application of proofs and theorems to develop skills in problem solving and critical thinking. You will learn to demonstrate an understanding of the connection between mathematical topics and real-world situations, recognizing that mathematical understanding can influence decision-making in all areas of life. You and your teachers will incorporate technology into assignments, presentations, and demonstrations as appropriate.

Three years (30 units) of Mathematics are required for graduation. Unless otherwise noted, all Mathematics courses are UC-approved as college-preparatory core/elective courses.

Algebra 1 studies the fundamental skills and techniques that underlie all future work with mathematics. This course begins with computational skills, development of conceptual understanding, and problem solving strategies. The course covers order of operations with real numbers; number properties; real numbers on the number line and in the Cartesian plane; solving equations and proportions; functions; slope; solving and graphing linear equations and inequalities; solving systems of equations and inequalities; polynomials; factoring; powers and roots; rational expressions and equations; and radical expressions and equations.

This is a standard high school course in Euclidean Geometry. It emphasizes a deductive approach to the subject, studying its logical framework as well as its concepts. The topics include the study of two- and three-dimensional figures, their construction and characteristics, and their surface areas and volumes; deductive and inductive reasoning, which includes proofs; parallel and perpendicular lines and planes; similarity and congruence; right triangles and trigonometry; and the coordinate plane. In addition, it seeks to integrate algebra into the study of geometry.

This course is available to sophomore and qualified freshman students. In order to take this course, sophomores must have earned a C or higher in both semesters of Algebra 1, while freshman must demonstrate mastery performance on the Math Challenge Examination.

This is a faster-paced and more rigorous version of standard Geometry (see above). In addition to covering the topics of Geometry, this course will develop coordinate approaches to algebra and strategies for more advanced mathematical problem solving. Lectures, discussions, and assignments cover the topics and proofs in greater depth and with more theory than the standard Geometry course. Motivation on the part of the qualified student is assumed to be high.

This course is available to qualified sophomore and freshman students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average. In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), AND have earned an A- or higher in both semesters of Algebra 1 or by earning a qualifying score on the Math Placement Exam (freshmen only).

This course builds on the skills and concepts from Algebra 1 while utilizing the systematic approach and visualization skills learned in Geometry. The topics include manipulating linear and quadratic equations and inequalities; in-depth study of linear, quadratic, polynomial, absolute value, radical, rational, logarithmic, and exponential functions and their graphs; powers and roots; and exponents and roots.

The course is available to sophomore and junior students. In order to take this course, sophomores and juniors must have earned a C or higher in both semesters of Geometry.

This is an accelerated course that covers the material from Algebra 2 (see above) plus a substantial introduction to trigonometry. The development and applications for algebraic, exponential, logarithmic, and trigonometric functions are central to this course. Graphing calculators are used throughout this course. Motivation on the part of the qualified student is assumed to be high.

This course is available to qualified students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average (not applicable to the UC GPA). In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), AND have earned a B+ or higher in both semesters of Algebra 1 and A- or higher in both semesters of Geometry or B- or higher in both semesters of Honors Geometry.

This course covers the basic principles of probability, data analysis, and fundamental statistical problem solving. Topics include an introduction to statistics; data collection and presentation; descriptive statistics; correlation and regression; probability distributions; the standard Normal distribution; and the basics of inference. This course will integrate data analysis with graphing calculator technology, and gives students the opportunity to complete projects which demand they actively construct their own understanding of the concepts and techniques of statistics. Upon completion of this course, students will have met the high school probability and statistics Common Core standards.

This course is available to qualified students. In order to take this course, students must have earned a C- or higher in both semesters of any level of Algebra 2.

This course is designed as a bridge between Algebra Two and Pre-Calculus. Students will study the following topics: linear programming; systems of linear and non-linear equations and inequalities in two and three variables; solving systems by matrices; polynomial, radical, rational, exponential, and logarithmic functions and their graphs; conic sections; and applications of these functions. Emphasis will be placed on honing skills needed in future math courses as well as the ability to use these skills in a variety of application problems. This course will give students the opportunity to complete the foundation necessary for success in Pre-Calculus.

This course, which is equivalent to a one-semester introductory non-calculus-based college course in statistics, introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics include exploratory analysis of data, planning and conducting a study, probability, and statistical inference. Students will examine four major conceptual themes in this course, including: the exploration of data, sampling and experimentation, anticipating patterns, and statistical inference. This course seeks to integrate data analysis with technology, as well as projects which demand students to actively construct their own understanding of the concepts and techniques of statistics. Upon completion of this course, students will have a strong command of the statistical process, including design, analysis, and making conclusions.

This course is available to qualified students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average. Students who take this course must sit for the Advanced Placement examination in May. In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), attend the mandatory AP Information Night, receive a positive recommendation from the English Department to take this course, AND have earned a B- or higher in both semesters of Honors Algebra 2/Trigonometry).

This course includes a review and expansion of the study of linear and quadratic equations and inequalities, systems of equations and inequalities, and their graphs. It continues with the study of polynomial, radical, rational, exponential, and logarithmic functions, their graphs, and their inverses and applications; in-depth work on trigonometric functions, their graphs, and their applications; matrices and their applications; and complex numbers. Lastly, the concept of limits will be introduced. Graphing calculators are used intermittently in this course.

This course is available to qualified students. In order to take this course, students must have earned a B- or higher in both semesters of Algebra 2 or a C of higher in both semesters of Honors Algebra 2/Trigonometry.

This is an accelerated course designed to prepare students for Calculus. It begins with an overview of linear and quadratic functions, their graphs, and their applications. It proceeds with an in-depth study of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions, their graphs, inverses, and applications; matrices and determinants and their applications; complex numbers; conic sections; and an introduction to the fundamental concepts of limits. Graphing calculators are used in this course.

This course is available to qualified students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average. In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), AND have earned a B- or higher in both semesters of Honors Algebra 2/Trigonometry.

In this course, the student will acquire a sound understanding of limits, derivatives of elementary functions, and explore introductory differential equations. The curriculum includes al topics covered in the College Board’s description of AB Calculus material. The course is designed to prepare students for the Advanced Placement Exam in Calculus AB. Graphing calculators are used throughout the course. Preparation for this class begins with guided independent study during the summer.

This course is available to qualified students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average. Students who take this course must sit for the Advanced Placement examination in May. In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), attend the mandatory AP Information Night, AND have earned a B- or higher in both semesters of Honors Pre-Calculus.

In this course, the student will acquire an expanded understanding of techniques for integrating elementary functions and solving differential equations, including logistic differential equations. The student will develop a detailed understanding of infinite series, convergence/divergence of those series, and Taylor and Maclaurin series used to mimic the behavior of more complex functions. The curriculum includes all topics covered in the College Board’s description of Calculus BC material, including a review of material from the Calculus AB course. The course is designed to prepare students for the Advanced Placement Exam in Calculus BC. Graphing calculators are used throughout the course. Preparation for this class begins with guided independent study during the summer.

This course is available to qualified students. Students who earn a C- or higher in this course will earn an extra grade point toward their grade point average. Students who take this course must sit for the Advanced Placement examination in May. In order to be eligible to take this course, students must receive department approval (which may include a separate application and/or examination), attend the mandatory AP Information Night, have earned a B- or higher in both semesters of AP Calculus AB, AND have earned a 3 or higher on the Calculus AB Exam.