CURRICULUM

Calculus 2

This comprehensive course covers advanced integration techniques and applications for single variable functions. Students will extend their knowledge of integration from Calculus I to include integration by parts, trigonometric substitution, and improper integrals. Applications of differentiation and integration will extend to parametric equations and equations defined in polar coordinates. An in-depth study of sequences and series will complete the course with emphasis placed on tests for convergence and divergence, power series, McLaurin and Taylor series, and the interval and radius of convergence. Successful completion of this class enables students to move on to more advanced mathematical coursework such as Multivariable Calculus, Differential Equations, or Linear Algebra.

Teacher: Britta Milks

Calculus

This course is equivalent to a first-semester, introductory college calculus course, covering differential and integral calculus. Students will study limits of functions, continuity, derivatives, and applications of the derivative. As part of integral calculus, students will examine the definite integral as a limit of Riemann sums, area under a curve, area between two curves, volume of solids, solutions to differential equations, and various real-life applications related to economics, biological, and physical situations. Throughout the course, students will build their understanding of mathematical modeling in order to use functions and data to model real-world situations. Successful completion of this class enables students to move on to more advanced coursework in calculus.

Teacher: Britta Milks

Precalculus

This course is designed to give students greater preparation for calculus by furthering their study of algebra, geometry, and trigonometry. Students will expand their knowledge of linear and quadratic functions, polynomials, exponential and logarithmic functions, as well as radical and rational functions. Additional topics include an in-depth analysis of trigonometry, an introduction to polar and parametric equations, as well as an exploration of sequences and series. Time permitting, additional topics may include conic sections and a brief introduction to calculus concepts. Successful completion of this course enables students to move on to a calculus course.

Teacher: Britta Milks

Algebra 2

This course is designed to advance students' understanding and application of algebra skills. Topics covered include a brief review of first-degree polynomials, followed by an in-depth study of higher-power polynomials, rational, radical, exponential, and logarithmic functions. Particular attention is given to the relationship between functions and their graphs. Central to the course is the development of mathematical modeling and problem-solving skills, where students learn how to craft conceptually and procedurally fluent responses to mathematical prompts. Successful completion of this course enables students to move on to Precalculus.

Teacher: Britta Milks

Geometry 

Geometry is a spatial mathematics class that aims to understand the dimensionality and representation of shapes in space. The concepts in class build over time, beginning with basic points and lines, progressing to angles and parallel lines, two-dimensional polygons, and ultimately three-dimensional shapes. Students will explore plane and solid geometric figures while investigating topics such as congruence, similarity, length, perimeter, and area. Constructions will enable students to travel between worded descriptions of problems, symbolic notation, and visual representations of ideas. As an intermediary class between Algebra 1 and Algebra 2, Geometry class also aims to keep algebraic skills fresh by interweaving concepts of algebra, including the slopes of parallel and perpendicular lines, working in a coordinate plane, equations of circles, factoring, and simplifying radicals. By working through formal proofs, students will use logic in order to understand the progression from postulates and definitions to complex theorems. 

Students will be assessed through nightly homework assignments, graded for completion. Daily homework discussions will allow students to share and explain their problem solutions in a collaborative discussion format. This component of class is essential in encouraging students not just to memorize concepts and solutions, but to experience mathematics as a process that requires communication, collaboration, discussion, and perseverance. Each chapter or unit will conclude with a summative test combining topics and gauging students’ mastery of the content. Units will also contain more physical, project-based assessments in order to demonstrate various practical applications of concepts.

Teacher: Kenyon Fatt

Sports Science 

“Every graduate from BMA should leave knowing enough about the sport of alpine skiing to be capable of training themselves.” Jesse Hunt. Ultimately, the Sport Science Senior Elective strives to provide students with the fundamental knowledge and skills required for training and competing in the sport of Alpine Skiing. The class will be based on the text “The Science of Alpine Ski Racing,” edited by James Pritchard and Jim Taylor. 

The first trimester will begin with a Sport Demand Analysis, giving the 30,000’ perspective before diving into biomechanics, physiology, and motor learning specifically related to the development of skiing skills. The second trimester picks up on skiing skills, emphasizing tactical skill development and equipment before moving back to the physical development of strength, power, and endurance capabilities. The third trimester begins with nutrition and mental training before focusing on program design, which leads to the final presentation of Comprehensive Annual Plans. Each trimester will include assessments based on demonstrations, presentations, research projects, quizzes, and tests.
 

Anatomy and Physiology

Anatomy and Physiology is an introduction to the anatomy or the structure, and physiology or the functions, of the human body.  Building on concepts from biology, students take a tour through the body, learning about the workings of each organ system.  Homeostasis, or the stable internal environment of the body, is the guiding theme of the course, and the class will investigate what homeostasis means for each organ system and what happens when that balance is lost.  Throughout the course, each body system will be assessed through a sports science lens, connecting the material learned in the course to the training demands of a ski racer. Assessments in this course include tests and quizzes, lab activities, and research projects.

Teacher: Ida Sargent

Environmental Science

Environmental Science at Burke Mountain Academy is a seminar-style, discussion-driven exploration of how natural systems and human societies intertwine. Anchored in Socratic dialogue, the course blends ecology, economics, sociology, ethics, geology, chemistry, and data science to help students identify, analyze, and debate environmental challenges from our local watershed to the global climate. Through daily discussions and analytical writing, students learn to question assumptions, weigh risks, and communicate complex ideas with clarity.

The year unfolds in three thematic arcs: We begin the fall by “building our toolbox” with ecology and biodiversity foundations, then tackle the logistics and resource impacts of feeding a growing human population before analyzing the history and potential future of our energy systems throughout the winter. In the spring, our discussions turn to pollution science and environmental justice, asking students to connect air, water, soil, and waste issues to policy frameworks such as the Clean Air Act and ongoing executive actions. By the final AP-style assessment, students have progressed from curious observers to solution-oriented thinkers ready to participate in community, national, and global conversations about our shared environmental future.

Teacher: Duncan Barnes

Sports Science 

“Every graduate from BMA should leave knowing enough about the sport of alpine skiing to be capable of training themselves.” Jesse Hunt. Ultimately, the Sport Science Senior Elective strives to provide students with the fundamental knowledge and skills required for training and competing in the sport of Alpine Skiing. The class will be based on the text “The Science of Alpine Ski Racing,” edited by James Pritchard and Jim Taylor. 

The first trimester will begin with a Sport Demand Analysis, giving the 30,000’ perspective before diving into biomechanics, physiology, and motor learning specifically related to the development of skiing skills. The second trimester picks up on skiing skills, emphasizing tactical skill development and equipment before moving back to the physical development of strength, power, and endurance capabilities. The third trimester begins with nutrition and mental training before focusing on program design, which leads to the final presentation of Comprehensive Annual Plans. Each trimester will include assessments based on demonstrations, presentations, research projects, quizzes, and tests.
 

Physics
 

Physics at Burke Mountain Academy asks how we model, measure, and harness motion. Grounded in lively daily discussions, the course pairs classic mechanics with modern computation: students translate observations into mathematical models, test them through hands-on labs, and extend their analyses with Python-powered simulations. Along the way, Physics students cultivate resilience, learning to treat every setback as an invitation to iterate, troubleshoot, and refine their thinking.

In the fall, discussions focus on kinematics and dynamics with vector motion, Newton’s laws, free-fall, and projectile labs that let students move between graphs, equations, and real-world phenomena. Winter shifts to Python, where an online, university-level coding course teaches automation, data analysis, and, above all, how to manage a long-term project and persist through failure. Spring returns to classical physics theory, using the work-energy theorem, momentum, electrostatics, and magnetism as springboards for a capstone design project that fuses physics, creativity, and clear communication. By year’s end, students see physics not merely as a body of knowledge but as a powerful way of questioning and engaging with the world.

Teacher: Duncan Barnes

Chemistry

Chemistry is a foundational course that allows students to experience science in two important ways — as both a body of knowledge and a process of discovery. The beginning of the year aims to get students thinking at the atomic level and to gain a basic understanding of the intermolecular forces occurring all around us every day. Students learn about a breadth of topics, including atomic structure, periodic table trends, types of chemical bonds, intermolecular forces, chemical reactions, acids and bases, and an introduction to biochemistry. Mastery of these concepts and skills will be reinforced through discussions, worksheets, summative assessments, and ultimately put into application through lab demonstrations and practicals.

Throughout the year, the course will also give students experience implementing the scientific method through various labs and demonstrations. Though initially students will be given protocols to follow, they will eventually develop a protocol of their own design in order to exercise their critical thinking and research skills. Particular emphasis will be put on exploration that follows the steps of the scientific method in order to develop a process of discovery that can be applied to problem solving and analysis beyond the chemistry classroom. The practical side of class will be evaluated based on professionalism and comportment during lab times, creativity and innovation when designing protocols, and communication and writing skills via lab write-ups. Ultimately, the Chemistry class aims to provide students with both critical knowledge of basic scientific concepts as well as a sense of curiosity and excitement about scientific discovery.

Teacher: Kenyon Fatt

Biology

Biology at Burke Mountain Academy is an inquiry-driven, discussion-based journey from the molecular building blocks of life to the dazzling diversity of Earth’s organisms. Anchored in lively discussions and reinforced with hands-on labs, fieldwork, and mini-research projects, the course asks students to question what it means to be alive, trace how energy and information flow through cells and ecosystems, and communicate discoveries with clarity and confidence. By combining big-picture storytelling with microscopes, data sets, and a healthy dose of curiosity, students sharpen their critical thinking skills and see how biology underpins everything from human health to global sustainability. In the fall, discussions are focused on the molecular and cellular “toolbox”: macromolecules, cytology, and an introduction to evolution by natural selection. We begin to introduce our asynchronous format in the winter while journeying through the Tree of Life, comparing prokaryotes, viruses, and protists while working on research projects that spotlight life’s most surprising branches. By spring, we have turned to the kingdoms we meet every day - fungi, plants, and animals - through sourdough fermentation experiments, field ecology labs, and comparative dissections that prepare students for future BMA science coursework.

Teacher: Duncan Barnes