Math

The goal of the mathematics curriculum is to develop a sound understanding of mathematical concepts and foster the ability to apply them creatively to new situations. A major objective is for all students to gain confidence in their mathematical abilities and develop them to the fullest.

Courses are designed to provide students with a solid foundation in mathematical principles. By applying these principles in a variety of problem-solving situations, students become comfortable with mathematical techniques for evaluating problems presented in both practical and theoretical contexts. The department recognizes that the ability to reason logically and analytically is a skill valued beyond the mathematics classroom. To support critical thinking skills, teachers emphasize the ability to assess new problems and determine how to proceed along a logical, organized path to a solution.

The use of technology, including the graphing calculator, is integrated throughout the curriculum. All Upper School students are required to own a TI-83 Plus or TI-84 Plus graphing calculator.

  • Advanced Studies Calculus AB

    2 semesters, 1 credit 
    Prerequisite: Math III AB with a minimum grade of B+ and department recommendation

    This rigorous course is equivalent to the first semester of a college-level calculus course. It begins with a study of limit theory and quickly moves on to differential calculus. The concept of the derivative is applied to related rates, extrema, optimization, and curve-sketching problems. The second half of the year is an in-depth study of integral calculus, which includes calculating the area under the curve and the volume of solids, as well as using differential equations in mathematical modeling problems.

  • Advanced Studies Calculus BC

    2 semesters, 1 credit
    Prerequisite: Math III BC Honors with a minimum grade of B+ and department recommendation

    This rigorous, fast-paced course is the equivalent of two semesters of college calculus. In addition to the work covered in the Advanced Studies Calculus AB course, the following topics are included: additional techniques and applications of integration, differential equations, the calculus of polar coordinates and vector-valued functions, the convergence and divergence of infinite series of constants, and Taylor polynomials.

  • Advanced Studies Linear Algebra

    2 semesters, 1 credit, offered in academic years with an even start (e.g., 2026–27)
    Prerequisite: AP Calculus BC with a minimum grade of B and department recommendation 
    This rigorous, college-level course explores various matrix methods for solving systems of equations and covers matrix algebra, determinants, vector geometry, vector spaces, eigenvalues, and linear transformations. Students examine the proofs of theorems and apply them to solve problems and create their own proofs. Students are also introduced to computer programming in C++.

  • Advanced Studies Statistics

    2 semesters, 1 credit
    Prerequisite: Math III with a minimum grade of A- or Math III AB with a minimum grade of B and department recommendation

    This course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. It introduces statistical methods for business, health science, and social science statistics. The course introduces students to the major concepts and tools for collecting, summarizing, analyzing, and drawing conclusions from data. There are four broad themes in this course: collecting data by sampling and experimentation, summarizing quantitative and categorical data, an introduction to probability, and statistical inference. Students use technology, investigations, problem-solving, and writing to build conceptual understanding.

  • Calculus

    2 semesters, 1 credit
    Prerequisite: Math III with a minimum grade of A- or Math III AB with a minimum grade of C+ and department recommendation. Grade 12 only.

    Students begin this year-long class by reviewing precalculus concepts, including polynomial functions, trigonometric functions, inverses of functions, graphs of functions, and trigonometric identities. They learn about limits, rates of change, the definition of a derivative, and basic differentiation rules, including the product, quotient, and chain rules. Next, students explore the various applications of derivatives, namely tangent lines, linear approximation, velocity and acceleration, related rates, and optimization. Then, they turn their attention to integral calculus, including antiderivatives, indefinite integrals, the basic integration rules, u-substitution, definite integrals, and the fundamental theorems of calculus. Students close out the year with a study of the applications of integrals, including areas of irregular regions in the coordinate plane, the average value of a function on a closed interval, displacement, and separable differential equations.

  • Data Science and Statistics

    2 semesters, 1 credit
    Prerequisite: Math III with a minimum grade of C. Concurrent enrollment in Math III AB or Math III BC Honors may be considered.

    This introductory data science course emphasizes a modeling approach with the General Linear Model. Students work with authentic datasets, investigate relevant and timely questions, and build coding skills. Throughout the course, data analyses and visualizations are conducted using R, a statistical programming language widely used in college and industry for data science applications. Additionally, students learn to find and clean data sets, store their work in Jupyter notebooks, apply critical thinking to interpret their observations, and provide statistical support for their conclusions. No prior experience with coding is necessary.

  • Math I

    2 semesters, 1 credit
    Prerequisite: Math B or Math 8

    Math I is the first of a three-year sequence of courses. Students solidify and extend their understanding of functions, solving equations, geometric relationships, and data analysis. Students continue to establish their understanding of linear and exponential sequences and functions. They expand their algebraic skills by focusing on solving equations and inequalities, including systems of linear equations and inequalities. Students develop explanations of geometric relationships of similarity and congruence through transformations and formal constructions. Students formulate and present mathematical arguments. Students build on their eighth-grade work, using linear models and linear regression equations. Additionally, students employ histograms, dot plots, and box plots to describe and compare the shape, center, and spread of univariate data. Students will be introduced to quadratic relationships and the skills needed to solve quadratic equations.

  • Math I (Honors)

    2 semesters, 1 credit
    Prerequisite: Department recommendation by current math teacher

    Math I Honors is the first of a three-year sequence of compacted courses. In this course, the Math I curriculum is regularly expanded through enrichment topics in each unit. Students expand their knowledge of sequences to series formulas and sigma notation and focus on topics related to matrices. They explore matrix addition and multiplication and use matrices to solve systems of linear equations with elementary row operations and the multiplicative inverse. Matrices are also used to represent vector transformations. Students build proficiency in moving between different forms of quadratic equations, identifying characteristics of the function from its equation, and using factoring and completing-the-square techniques. Students develop strategies to solve quadratic equations using various methods and are introduced to complex numbers as solutions.

  • Math II

    2 semesters, 1 credit
    Prerequisite: Math I with a minimum grade of C-

    Math II is the second of a three-year sequence of courses. Students expand their knowledge of functions to include in-depth work with quadratics. They build proficiency in moving between different forms of quadratic equations and in identifying the function’s characteristics from its equation. Students develop strategies to solve quadratic equations using various methods and are introduced to complex numbers as solutions. They learn to distinguish among linear, exponential, absolute value, and quadratic functions and apply transformations to their graphs. Students explore inverse relationships, including domain restriction and logarithmic functions. Students extend their work with transformations to include dilations. They write formal proofs for similarity and congruence. Additional topics in geometry include right triangle trigonometry, angle-arc relationships, the development of formulas related to regular polygons, volume, radian measure, and parabolas as conic sections. Students broaden their understanding of probability by studying conditional probability using tree diagrams, Venn diagrams, and two-way tables.

  • Math II (Honors)

    2 semesters, 1 credit 
    Prerequisite: Math I Honors with a minimum grade of B+ and department recommendation
    Math II Honors is the second of a three-year sequence of compacted courses where students apply their existing knowledge to new and challenging situations. Students build upon their fluency with linear, exponential, and quadratic functions at the start of the course and quickly move on to a study of piecewise, inverse, and logarithmic functions. Throughout the course, students apply algebraic thinking and transformations of functions. They deepen their understanding of deductive reasoning and writing two-column proofs in their study of geometry topics, including triangle congruence and similarity, special angle pairs, parallel lines and transversals, characteristics of special polygons, right triangles, and circles. Students return to algebra topics, including conic sections, polynomials, and rational functions.

  • Math III

    2 semesters, 1 credit 
    Prerequisite: Math II with a minimum grade of C each semester

    Math III is the third course of a three-year sequence of courses. Students continue to develop skills working with linear, exponential, and quadratic functions while beginning to work with higher-order polynomial functions. They learn the Fundamental Theorem of Algebra, apply strategies of factoring and polynomial division for finding roots, and learn to graph polynomials. Students learn to interpret and explain the behavior of rational functions and their graphs, and to use strategies to simplify and solve rational expressions and equations. They visualize 3-dimensional solids of revolution and practice using areas of cross sections to find an object’s volume. Students extend their skills with trigonometry by deriving and applying the Law of Sines and the Law of Cosines. Then, they learn to apply the sine, cosine, and tangent functions to any angle, use sine and cosine to model periodic behavior and explore fundamental trigonometric identities. Students also explore statistics using the Central Limit Theorem, the normal distribution, and basic inferences about means and proportions.

  • Math III AB

    2 semesters, 1 credit 
    Prerequisite: Math II with a minimum grade of B+ and department recommendation

    Math III AB is the third of a three-year sequence of courses. This course is designed to prepare students for Advanced Studies Calculus AB. The integration of ideas from previous mathematics courses is emphasized. This course covers the content of Math III at a faster pace and with more depth on some topics, including a strong emphasis on algebraic manipulation, polynomials, inverses, and trigonometry. Additionally, students complete extensive work with trigonometric functions and identities important to calculus. Students are introduced to the concept of limits. 

  • Math III BC (Honors)

    2 semesters, 1 credit 
    Prerequisite: Math II Honors with a minimum grade of B+ and department recommendation
    Math III BC Honors is the third course of a three-year compacted curriculum and is designed to prepare students for Advanced Studies Calculus BC. Students build on their understanding and facility with polynomial, rational, logarithmic, and exponential functions by exploring these topics in greater depth. The integration of ideas from previous mathematics courses is emphasized, including work with matrices and vectors. Students have the opportunity to expand their abstract reasoning. They visualize 3-dimensional solids of revolution and practice using areas of cross sections to find an object’s volume. Students connect trigonometric ratios to trigonometric functions of angles of rotation, both analytically and graphically. They extend their trigonometry skills by exploring and applying trigonometric identities important in calculus. Additionally, students study polar and parametric equations, limit theory, differentiation rules, applications of derivatives, sequences, series, and probability.

  • Math IV: Topics in Precalculus

    2 semesters, 1 credit 
    Prerequisite: Math III with a minimum grade of C+ and department recommendation
     
    This course is designed to prepare students for a college calculus course. Students are exposed to deeper levels of algebraic manipulation than seen in previous courses, learning strategies and techniques to master these crucial skills. They will review, expand upon, and apply their knowledge of polynomial, rational, exponential, and logarithmic functions, sequences and series, and probability. This course deepens and extends the study of trigonometric relationships introduced in Math III by emphasizing graphing functions, solving equations, and verifying identities. Students are introduced to vectors and their applications, matrix operations, and limits.

  • Mathematics of Finance

    2 semesters, 1 credit 
    Prerequisite: Math III with a minimum grade of C. Grade 12 only. 

    This course is a 12th-grade elective covering a wide variety of mathematical concepts with an emphasis on finance. During the first quarter, students review algebraic and geometric concepts in preparation for standardized testing, providing a firm foundation for the finance segment. During the remainder of the year, students will cover the basics of investment in stocks and bonds, business modeling, loans (especially car loans and mortgages), tax calculations and retirement planning, all emphasizing the underlying mathematics. The year concludes with students preparing a budget in an Excel spreadsheet that incorporates many of the concepts covered in previous segments of the course.

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