## Full Year Mathematics Courses

### Math 9

#### Grade: 9

Mathematics courses in the 9th Grade explore algebra, geometry, and the connections between the two.Throughout, there is an emphasis on problem solving, reasoning, and proof. **Students are sectioned by interest and ability, **with the different classes varying in pace and level of abstraction.

### Math 9-1

This course explores advanced algebraic and geometric content through an emphasis on problem solving, reasoning, and proof. Topics include graph theory, laws of exponents and radicals, the algebra of rational expressions, quadratic equations, Euclidean and coordinate geometry, and unit-circle trigonometry.

### Math 9-2, 9-3, 9-4

These courses explore algebra, geometry, and the connections between the two, with an emphasis on developing students' ability to solve problems through a variety of approaches. Topics include algebra, coordinate geometry, systems of equations, trigonometry, quadratic functions, and combinatorics, with a consistent focus throughout on reasoning and proof.

### Math 10

#### Grade 10 - Required

This course is required at one of three levels: Math 10-1, Math 10-2, or Math 10-3.

### Math 10-1

Students expand upon the understanding of algebra and geometry gained in Math 9-1. They explore exponential and logarithmic functions, combinatorics, sequences and series, graphical transformations, polynomials and rational functions, circular motion and the trigonometric functions, trigonometric identities, complex numbers, and begin the study of infinitesimal processes.

### Math 10-2 and 10-3

These courses examine algebra, geometry, and discrete mathematics but in greater depth than the previous year, with a continuing emphasis on developing students’ ability to solve problems through a variety of approaches. Topics may include graph theory, geometric sequences and series, radicals and laws of exponents, the algebra of rational expressions, exponential functions, further study of quadratic equations, polynomial functions and complex numbers, statistics, and Euclidean geometry.

### Math 11C, Math 11D

#### Grade 11

These courses emphasize applications of mathematics and may include the following areas: algorithms, exponential functions, logarithms, trigonometric functions, transformations of functions, polynomial functions, combinatorics and probability, and further topics in geometry.

### Advanced Calculus (Accelerated)

#### Grade 12

In Calculus, students are introduced to the concepts surrounding limits, and learn how they can be applied to develop the theory of differentiation (rates of change) and integration (accumulation), which culminates in the fundamental theorems of calculus. Advanced Calculus continues to develop the techniques of differentiation and integration. In our curriculum, the class plans to cover indeterminate forms; logarithmic and implicit differentiation; related rates; integration by parts; partial fraction decomposition; improper integrals; parametric and polar equations; vector calculus as it applies to position, velocity, and acceleration; differential equations and population models; sequences; Taylor and power series. These topics should cover the vast majority of the Advanced Placement (AP) Calculus BC exam, and will provide a strong foundation for students interested in taking it. In addition to the aforementioned core topics, the class may often take occasional tangents into other areas of higher mathematical study. These topics may include different systems of numbers; different sizes of infinity; mathematical physics; multivariable calculus; and Fourier series.

*Prerequisite: Calculus*

### Advanced Elective: Mathematical Modeling

#### Grades 9-12

In this course, students will learn and use advanced mathematical topics and methods such as difference equations, dynamical systems, geometric similarity, model fitting and assessment, graph theory, dimensional analysis, probabilistic modeling, linear algebra, and linear programming. They will study problems motivated by population biology, chemistry, finance, economics, and physics, and through these problems will develop mathematical tools that are both beautiful and useful.

*Prerequisite: Permission of the department*

### Calculus (Accelerated)

#### Grades 11-12

Concepts and applications of differential and integral calculus are presented. For juniors, a month-long final project, requiring considerable independent work, concludes the course. Students who complete the course successfully are prepared to take the Advanced Placement (AP) Calculus AB exam.

*Prerequisite: Math 10-1 or permission of current math teacher*

### Calculus and Modeling

#### Grade 11

This course emphasizes mathematical modeling in a wide variety of contexts, introducing the major concepts of differential and integral calculus as tools. Students who complete this course will be ready for an accelerated senior-year course in which they complete the content in a typical first-semester calculus course.

*Prerequisite: Math 10B*