Mathematics

AP Calculus AB is an introductory college-level calculus course. Students develop an understanding of the mathematics of change through their study of limits, derivatives, and integrals. Students approach applications and real-world problems involving differentiation and integration numerically, graphically, analytically, and verbally.

AP Calculus BC is an introductory college-level calculus course. Students develop an understanding of the mathematics of change through their study of limits, derivatives, and integrals. Students approach applications and real-world problems involving differentiation and integration numerically, graphically, analytically, and verbally. The content of the AP Calculus BC course extends one college-level semester beyond that of AP Calculus AB.

AP Statistics students explore four themes throughout the year: exploring data; sampling and experimentation; anticipating patterns; and statistical inference. Skills emphasized in the course include reading and understanding statistical content, communicating their understanding in writing, and using graphing calculators with fluency. These skills will help them learn to think and act like statisticians.

Advanced Algebra is a comprehensive course covering quadratic functions and equations, exponential and logarithmic functions, patterns and sequences, triangle trigonometry, trigonometric functions, and function transformations. Throughout the course, students will develop strong analytical and problem-solving skills by analyzing and interpreting graphs, making connections between the four different representations of mathematics–verbal, numerical, algebraic, and graphical–applying transformations, identifying and extending patterns, and using mathematical reasoning to solve complex problems. The course aims to provide students with a solid foundation in advanced algebraic concepts and equip them with the skills necessary for success in higher-level mathematics.

The Honors Advanced Algebra course is designed to develop “higher-order” thinking. The context students will use to explore this level of thinking is algebra. The learning methods revolve around investigation and exploration of patterns and will not focus solely on the generation of answers. In collaboration with learning partners, students will investigate, collect data, make conjectures, and search for models. The Honors Advanced Algebra course provides a strong foundation in concepts including functions, transformations, polynomials, trigonometry, vectors, logarithms, matrices, sequences and series and probability. The instruction is student-centered with open-end investigations and discovery learning. Critical thinking and problem-solving strategies are greatly emphasized.

In Algebra 1, students study the foundations of algebra and learn the tools to approach and solve problems logically. Students use various approaches to support their learning, including individual and group work, investigations, discussion, and technology integration whenever appropriate.

In Applied Statistics, students build statistical understanding through inquiry and student-driven, project-based methods. Students will make connections across curricular topics, including criminal justice, public health, and climate change. Students will be able to learn skills and vocabulary to support their analysis of that data. The course will encourage collaboration and communication as a means to both learn and share topics.

This Calculus course aims to give students a comprehensive understanding of differential and integral calculus principles. Through a combination of theory, practical exercises, and problem-solving techniques, students will develop a deep appreciation for the foundational concepts of calculus. They will explore limits and derivatives, learning to solve mathematical problems involving change rates, optimization, and function analysis. Additionally, the course focuses on integral calculus, covering antiderivatives, definite integrals, and integration techniques. With a strong emphasis on practical applications in fields such as physics, economics, and engineering, students will be able to apply their knowledge to real-world problems. Students use technology to solve problems and draw conclusions. The course uses a multi-representative approach to calculus, with concepts and problems expressed numerically, graphically, verbally, and analytically to enhance the learning experience for students.

The Foundations of PreCalculus course further develops students’ proficiency and conceptual understanding of functions, algebra, probability, and statistics. This course is for students intending to study the arts, humanities, business, or other post-secondary programs not requiring calculus. Students who intend to go into math, sciences, or engineering should take PreCalculus instead of, or possibly after, this course. Students can take AP Statistics, PreCalculus, Applied Statistics, or any other math elective after completing this course.

In Geometry, students study a variety of geometrical investigations, problems, patterns, and relationships of Geometry. This course also strengthens students' algebra skills while developing new algebraic understandings required for future math courses. Reasoning and justifying conclusions are central to proof and emphasized throughout the course.

In addition to the goals of the Geometry course, the Honors course places greater emphasis on independent learning, problem solving skills, and the integration of Algebra. This allows for topics to be covered in greater depth and for the inclusion of additional topics. Students will use matrices to represent transformations on the coordinate plane, investigate properties of non-Euclidean geometry, use deductive reasoning and logic extensively to justify conclusions, and use the Laws of Sines and Cosines in real-world applications.

Math Advanced Topics is designed for students who have shown a particular aptitude and interest in mathematics and would like to study some wider and deeper aspects of mathematics. Students who are strongly inclined to major in engineering, computer science, and/or math-related areas in college are highly encouraged to take the course. There is a choice of applied and pure math subjects such as:

• Differential Equations/Multivariable Calculus/Advanced Calculus
• Linear Algebra
• Sets, Relations, Groups
• Discrete Mathematics

Students will be able to study at least one topic in greater depth so as to develop a more significant understanding of a college-level course.

Even though human behavior is extremely complex, there are aspects of it that can be understood quantitatively, via such disciplines as Game Theory, Market Mechanisms, Voting Paradoxes, Diffusion of Ideas, and Behavioral Economics. Such formalisms heighten our awareness of our relationships with those around us, of the dynamics of the society in which we live, and - ultimately - of our own internal biases. This course is targeted at students interested in pursuing humanities, social sciences or business. The course will adopt a “tone” that emphasizes mathematical intuition over needless formalism, and concepts will be with numerous real-world applications.

Models in Mathematics is designed to give the non-Advanced Algebra student a broader view of mathematics, through previously unexplored ideas, some involving real-world application and some involving challenge to the imagination. Selected topics from algebra and geometry will be reviewed and extended as reinforcement. Each semester will be comprised of four to six content modules.

PreCalculus is a comprehensive study of mathematical concepts and functions. This course aims to deepen the understanding of concepts learned in Advanced Algebra; many course topics start with previous learning and then deepened. The course revisits function concepts such as domain and range, concavity, function notation, and transformations of functions. The main themes are investigating relationships between variables and how changes in one variable may affect the change in another variable.

One of the main goals is to develop deep conceptual understanding and flexible thinking. The course focuses on the use of analytical skills, and students complete much of the work without a calculator. Students engage with various problem sets that require choosing appropriate solution methods.

The Honors PreCalculus course provides a rigorous foundation of the concepts and skills necessary for success in AP Calculus BC. The main focus of the course is a rigorous examination of the function concept, through verbal descriptions, algebraic formulae, numerical values, and graphs. As well, we will look at how functions are used in modeling both mathematical and dynamical real-world phenomena.