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)
AP Physics C: Mechanics
The AP Physics (Physical Science) course is equivalent in content, depth, and complexity to an introductory physics course at the college level. This course is designed to prepare the student to excel on the AP Physics C: Mechanics exams offered in May. The course follows the AP curriculum closely. AP Physics is an in-depth, content-intensive study of physical principles that allows students the opportunity to engage hands-on in scientific experimentation. Core units of study include kinematics, Newton’s laws, conservation laws, harmonic motion, and rotational motion. Additional topics will vary but may include electricity & magnetism, relativity, quantum mechanics, particle physics, thermodynamics, and other advanced topics. Use of calculus in problem solving is expected to increase as the course progresses. Students are required to take the Advanced Placement exam in May. Students are required to complete an assignment over the summer due on the first day of school. This is a mathematically rigorous course which requires a solid foundation in both physics and math.
Corequisite – Students enrolling in this course must also enroll in the corresponding AP Science Laboratory course, which meets once per week for 50 minutes outside of the regular bell schedule. Meetings will occur before or after school.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Environmental Science: An Ecological Perspective
Environmental science is the study of our natural environment, with an emphasis on humanity’s impact on the environment. This is a project and inquiry-learning based course that investigates the science behind today’s environmental issues. Students will be immersed in hands-on science activities, group work, discussions of current scientific research, a long-term scientific investigation, decision-making based on their critical thinking skills, and the design of inquiry-based experiments. The course is arranged in independent modules that offer students a holistic approach towards environmental issues by exploring current environmental problems from a scientific interdisciplinary perspective. While topics will focus of life science related issues, we will also incorporate some basic geological, physical, chemical and technological components that directly impact living creatures.