The department’s mission is to develop in each student a love of mathematics, confidence in his/her abilities, and a sense of responsibility for his/her academic achievement.
While preparing students for the most rigorous college programs, the curriculum also exposes them to the history and beauty of mathematics. The wide range of course offerings enables students to complete four years of mathematics at the Upper School.
Ability grouping allows students to be successful as well as challenged. The pace of the course and the depth of study of various topics differ between courses offered at multiple levels.
5
Credits
-
Semester
Full Year
Course Description
This course provides the core of the general concepts and theorems of Geometry. While formal two-column and coordinate proofs are introduced, emphasis is placed on the development of logical and evidence-based thinking.The traditional concepts concerning lines, angles, planes, polygons, congruence, and similarity are connected to real-world applications and careers. The course also covers topics such as areas, surface areas and volumes of solids. Practice in applying concepts is strengthened by spiral review and occasional references to SAT-formattedquestions. The goal of the course is to build a solid understanding of the fundamentals of Geometry.
5
Credits
-
Semester
Full Year
Course Description
This course begins with an introduction to the terms and fundamental concepts in the field of Euclidean Geometry. Using these building blocks throughout the year, students derive powerful theorems and develop an understanding of geometric concepts. They learn to compose formal proofs for the first time. Composing formal proofs promotes an understanding of the rigor required when working in a deductive system. Students apply Algebra 1 skills to solve challenging problems in a geometric context. Topics studied include parallel and perpendicular lines; triangles, quadrilaterals, and other polygons; congruent and similar figures; circles; area, surface area and volume; and trigonometry
5
Credits
-
Semester
Full Year
Course Description
This course begins with a review of Algebra I topics, including linear equations, functions, and inequalities. Students solve systems of equations using graphing, substitution, and linear combinations. Focus then turns to the study of quadratic equations and the various methods of solving them, as well as an in-depth study ofquadratic functions and their graphs. Students learn about properties of rational exponents and radicals, rational expressions, and solving algebraic equations that use these various expressions. Students then explore the properties of logarithms and apply them to solving exponential and logarithmic equations. Finally, students are introduced to right triangle trigonometry, radian measure, and trigonometric functions.
5
Credits
-
Semester
Full Year
Course Description
This course includes the study of linear equations, linear data models, and linear relations. Students explore techniques of factoring, graphing parabolas, solutions of quadratic equations, and the algebraic properties of powers, roots, and exponents. Other topics of study include synthetic division, the zeros of higher degree polynomials, rational functions, exponentials, and logarithms. Fundamental counting principles, probability, conic sections, and trigonometry are introduced. Emphasis is placed on learning how to graph equations by finding x and y intercepts and by understanding how coefficients and other constants transform parent functions into the given function.
5
Credits
-
Semester
Full Year
Course Description
This course focuses on the interconnectedness between a function, its graph, and its relationship to relevant everyday topics. The course begins with an in-depth study of trigonometric functions and their inverses, including verifying identities, solving general triangles, and solving trigonometric equations. In the second semester, topics include the study of analytic geometry, parametric equations, vectors, and polar coordinates.
5
Credits
-
Semester
Full Year
Course Description
In this course, students complete a summer assignment review of Algebra 2 Honors topics in preparation for the various topics in math analysis that are required for learning calculus. The course begins with an in-depth study of trigonometric functions and their inverses, including verifying identities, solving general triangles, and solving trigonometric equations. In the second semester, topics include the study of analytic geometry, parametric equations, vectors, and polar coordinates. Students also study the concept of a limit using mathematical sequences and series, before introducing the definition of the derivative.
5
Credits
-
Semester
Full Year
Course Description
AP Precalculus prepares students for other college-level mathematics and science courses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. The course framework delineates content and skills common to college precalculus courses that are foundational for careers in mathematics, physics, biology, health science, social science, and data science.
5
Credits
-
Semester
Full Year
Course Description
This course is intended for students who want to learn some of the practical applications of calculus while increasing their understanding of the underlying mathematical concepts. Topics include limits, differentiation, and integration. Functions studied during the year include polynomial, rational, trigonometric, exponential, and logarithmic. This course will provide students the opportunity to refine their algebra skills and to develop a deeper understanding of functions.
5
Credits
-
Semester
Full Year
Course Description
This course is intended for students who want to learn the practical applications of traditional calculus while understanding the mathematical concepts underlying the techniques they have acquired. Students study nearly all the topics covered in a one-semester, college-level calculus course in a non-AP setting. First semester topics include limits at a point, derivatives, differentiation techniques, and the application of derivatives. Second semester topics include antiderivative, definite and indefinite integrals, integration techniques, area bounded by curves, and the volume of rotating solids. Functions studied during the year include polynomials, rational functions,exponentials, logarithms, and trigonometric functions.
Advanced Placement Calculus AB
5
Credits
-
Semester
Full Year
Course Description
A formal study of limits and continuity provides the foundation for the study of differential and integral calculus. The major emphasis is on clear, intuitive understanding of the concepts. Students develop facilities with the elementary techniques of calculating derivatives and integrals of frequently encountered algebraic and transcendental functions. Applications include curve-sketching techniques; motion along a straight path; related rates; extreme value problems; and the computation of area and volume.
Advanced Placement Calculus BC
5
Credits
-
Semester
Full Year
Course Description
This course covers all topics listed in the current Advanced Placement BC Calculus syllabus. In conjunction with Advanced Placement Calculus AB, it is equivalent to two semesters of first-year college calculus. Major topics include limits, integrals and their applications, techniques of integration, improper integrals, infinite series and convergence tests, Taylor and Maclaurin polynomials/series, parametric and polar functions, vector-valued functions, and linear differential equations. In addition, students will be introduced to a variety of proofs using William Dunham’s Journey Through Genius.
5
Credits
-
Semester
Full Year
Course Description
Statistics is a field that has applications in many academic disciplines. This introductory course in statistics provides students with a strong statistical base that is applicable to many courses of study in college. Throughout the course, students will apply their knowledge through self-selected projects that highlight the concepts they have learned. Students will begin by focusing on the different methods of collecting data. After data is collected, students will study the advantages and disadvantages of the numerous ways to analyze and display their data. In addition, the majority of time will be spent interpreting student data in many meaningful ways using statistical language.*Students may not take both Statistics and AP Statistics
Advanced Placement Statistics
5
Credits
-
Semester
Full Year
Course Description
In this course, students are introduced to the processes of designing experiments and statistical studies, as well as the tools for appropriately displaying and describing one-variable and two-variable data. Students will learn how to use the rules and laws of probability, normal distributions, and other statistical models to evaluate and interpret probabilities. The second semester of the course focuses on a rigorous in-depth study of the field of statistical inference including the concepts of using sampling distributions, confidence intervals, and hypothesis testing in to analyze sample data.
5
Credits
-
Semester
Full Year
Course Description
Apply previously developed skills learned in Calculus to learn Multivariable Calculus and Vectors. ● Cover Vectors, Partial Derivatives, Multiple Integrals and Vector Fields to prepare students for further study in technological disciplines and more advanced mathematics courses. ● Cover relevant applications in science and engineering to illustrate the utility of learning these topics. Use mathematical software, in problem solving, to allow the solution of more complex problems and provide visualization of the mathematical concepts in three dimensions.
