Mathematics

9th grade
Required
Yearlong

Students develop skills and concepts in order to learn how to solve problems using variables. Learning occurs through discussion, exploration, and group work, with the teacher acting as a guide. Topics include real, rational, and irrational numbers; solving linear and quadratic equations; graphing linear and quadratic equations; systems of linear equations; factoring polynomials; properties of exponents; properties of radicals; and simplifying rational expressions. There is an emphasis on solving problems algebraically, as well as through other methods, including modeling and graphing. Developing communication skills is essential to the progression of the students’ mathematical competence. 

Upper School
Required
Yearlong

The first semester of this full-year course familiarizes students with the language and notation of Euclidean geometry. Formal proof is introduced, which opens up opportunities to investigate parallel lines, triangles, constructions, transformations, triangles, quadrilaterals, and circles. The second semester introduces righttriangle trigonometry, functions and transformations, area/perimeter/volume problems, and conic sections. Prerequisite: Algebra I.

Upper School
Required
Yearlong

The first semester of this full-year course emphasizes the role of algebra as the foundation for further mathematics study. It stresses the structure of algebra, the development of algebraic problem-solving skills, and the use of functions as models of real-world situations. This course concentrates on the application of linear equations through matrices, functions and transformations, number series, and rational expressions and equations. In the second semester, students explore the characteristics of polynomial, rational, exponential, and logarithmic functions, including an introduction to complex numbers. Prerequisite: Algebra I and Geometry. 

10th, 11th, or 12th grade
Required
One semester or intensive

Collecting, representing, analyzing, and interpreting data are of major importance in contemporary society. This statistics course emphasizes that learning to interpret data correctly is a means of developing increased awareness of social, political, and scientific issues. Students learn to create unbiased surveys and experiments; describe data objectively with graphs, tables, and numerical statistics; determine correlation between variables; and understand the concept of a statistically significant result. Prerequisite: Algebra II.

10th, 11th, or 12th grade
Elective
One semester
This semester-long course begins with a significant emphasis on trigonometry. Students explore concepts and applications from a circular function approach and then proceed to graphing trigonometric functions, using identities to transform expressions, and using trigonometric functions as mathematical models. Properties of elementary functions are reviewed, expanded upon, and applied to data analysis. Prerequisite: Algebra II.

12th grade
Elective
Yearlong

This yearlong course develops and applies the concepts of differential and integral calculus. Concepts related to limits, derivatives, and integrals are explored and understood through contextualized application and analysis. This is often accomplished by first starting with the application of a concept in a real-world situation, such as business calculus or physics. These concepts are then used in a variety of applications, such as optimization, related rates of change, and volumes of revolution. Students interpret, analyze, and apply single-variable calculus concepts graphically, numerically, algebraically, and analytically. Prerequisite: Pre-Calculus.

11th or 12th grade
Elective
Yearlong

This yearlong course develops and applies the concepts of differential and integral calculus. An in-depth exploration of the underlying concepts is used to develop a foundation and understanding of limits, derivatives, and integrals. These concepts are then used in a variety of applications, such as optimization, related rates of change, and volumes of revolution. Students learn to interpret the calculus concepts from several frames of reference: graphically, numerically, algebraically, and verbally. Clear communication of ideas and process is emphasized. Material in this course is a subset of the material on the AB Calculus AP exam. Prerequisite: Completion of Pre-Calculus with at least a B- or math teacher recommendation. 

12th grade
Elective
Yearlong

This yearlong course initially revisits the fundamental concepts of calculus, emphasizing rigorous analysis. It continues with a dual approach: exercising the application of course topics and visiting their logical, conceptual basis. The application side may consist of short exercises and more involved projects. The logical, conceptual side introduces and explores the idea of rigorous derivation and proof. In both approaches, students look at the derivative and the integral as they relate to the following topics: infinite series, non-Cartesian coordinate systems, differential equations, vector-valued functions, and multivariable functions. Prerequisite: Completion of Calculus I with at least a B- or math teacher recommendation. 

10th–12th grade  
Elective
One semester

A continuation of Introduction to Statistics, this course concentrates on statistical inference procedures. In the first half of this semester-long course, students analyze and interpret data. Topics include confidence intervals, tests of significance, and power and errors analysis associated with tests of significance. In the second half of the course, students design and implement a data collection method for a project of their choosing. Students then analyze and interpret the collected data and present their processes and findings. Prerequisite: Introduction to Statistics.

Upper School
Elective
One semester

Is the geometry learned in high school adequate for describing the physical world in which we live? How does an online business such as eBay or Amazon ensure the safety of a customer’s credit information? In this seminar, students try to answer questions such as these. Topics might include non-Euclidean geometry, Markov chains, discrete mathematics, number theory, matrix algebra, abstract algebra, fractals, and chaos theory. Students will research a topic of interest and present their findings to the class. This course is designed for students with strong preparation who would like to develop a broader understanding of the field of mathematics. Students may repeat this course for credit. Prerequisite: Completion or concurrent enrollment in Pre-Calculus.

Upper School
Elective
One semester

Students use mathematical thinking and skills to build an understanding of personal finance, as well as a broader knowledge of the financial world. Students learn about saving for short- and long-term goals for college, a home, and retirement, and about investing in stocks, bonds, and funds. Students study taxes and the differences between progressive and regressive taxation from a mathematical perspective. Each student develops and works on a mock financial portfolio for the semester and stays current on financial news  and developments through blogging and online discussion. Prerequisite: Algebra II (may take concurrently). 

Upper School

Collecting, representing, analyzing, and interpreting data are of major importance in contemporary society. This statistics course emphasizes that learning to interpret data correctly is a means of developing increased awareness of social, political, and scientific issues. Students learn to create unbiased surveys and experiments; describe data objectively with graphs, tables, and numerical statistics; determine correlation between variables; and understand the concept of a statistically significant result. Prerequisite: Algebra II.

10th–12th grade

This course is designed for students who are interested in an accelerated curriculum that covers the yearlong Algebra 2 curriculum in the first semester and first intensive, with the intention of taking Pre-Calculus in Semester 2. The course emphasizes the role of algebra as the foundation for further mathematics study. It stresses the structure of algebra, the development of algebraic problem-solving skills, and the use of functions as models of real-world situations. This course concentrates on the application of linear equations through matrices, functions and transformations, number series, and rational expressions and equations. Students explore the characteristics of polynomial, rational, exponential, and logarithmic functions, including an introduction to complex numbers. Prerequisite: Algebra I, Geometry, and approval by the Math Department.