This course is offered to entering freshmen who have demonstrated mastery of Algebra 1 content. 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.
*Class receives honors weighting in SI weighted GPA
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 1Acc 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.
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
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
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)
