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
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.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Precalculus
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 functions; 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 and an introduction to limits, derivatives, and general curve sketching. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
Calculus
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 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
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 emphasizes conceptual understanding of derivatives, integrals, and limits, 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.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
AP Calculus BC
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 is required.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Honors Linear Algebra Multivariable Calculus
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.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations (UC/CSU Subject C Approval Pending)
Math Analysis
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
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.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Introduction to Finance
Students taking this elective 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.