Mathematics

The Math Department emphasizes both applied and conceptual mathematics, both understanding and memorization. Occasionally using calculators to help with the mechanics, students are encouraged to concentrate on the ideas they are studying. The Math Department teaches students that if they know how to ask the right questions, they can find the right answers. Classes in algebra, geometry and calculus all emphasize an understanding of concepts prior to the memorization of formulas. Small classes allow teachers to track students so they are encouraged to take on the challenge of advanced math.

Algebra I

Using the language of algebra, students perform operations with real numbers, study algebraic expressions, solve equations and inequalities with one variable; students add, subtract, multiply, divide, and factor polynomials. In later lessons, students manipulate rational expressions; graph and use linear equations and inequalities; study relations, functions, and variation; and graph and solve systems of linear equations and inequalities. Finally, students consider radicals and solve quadratic equations. Students also apply concepts to solving word problems.

Geometry (Regular and Honors)

During this study of plane and solid geometry, students learn and use the concepts of point, line, and plane in several dimensions. Through deductive reasoning, students learn to write valid proofs and solve problems, using critical thinking supported by definitions, postulates, and theorems as they study parallel lines, congruent triangles, quadrilaterals, similar polygons, right triangles, and circles. Students investigate constructions, area, volume, and coordinate geometry. Algebra skills are reinforced throughout the course. The computer program Geometer's Sketchpad is used as a supplement to the course.

Advanced Algebra and Geometry (Honors)

The Advanced Algebra and Geometry course is designed for our most mathematically-inclined and gifted students. The course is offered for a select group of rising third formers with outstanding mathematical abilities, as demonstrated though excellent achievement in previous math courses and high SSAT Quantitative scores (usually 90th percentile or above). Algebra and geometry concepts will be explored in a fashion where students must explore relationships and look at unique possibilities for solutions. The course allows students to develop general problem-solving and communication skills through exploration and discussion. Texts for this course will be provided by the instructor.

Algebra II and Trigonometry (Regular and Honors)

This course teaches the principles of intermediate algebra. Students learn to solve, graph, and use equations and inequalities, as well as systems of equations and inequalities. Students also use polynomials, rational expressions, quadratic equations and inequalities, and analytic geometry to solve problems and perform mathematical operations. Other topics studied include logarithmic and exponential functions, trigonometric and circular functions, and applications of trigonometry to right triangles. In the Honors course, students also study trigonometric identities and applications of trigonometry to the general triangle.

Finite Mathematics

In this half-year course, students survey topics including single-variable and bivariate data, matrices, linear programming, basic finance, counting problems, and probability. A clear emphasis is placed on application to real-world problems. Students apply the concepts of annuities to mortgages and retirement funds, and use a linear model to detect trends and to make predictions. Students use programmable graphing calculators to assist in data analysis.

Introduction to Statistics

This half-year course is usually taken by students in the spring term, following the Finite Mathematics course. Students study four main areas of beginning statistics: producing data, organizing data, chance, and inference. Activities and applications give students an opportunity to investigate, discuss, and make use of statistical ideas and methods. Abundant examples from a variety of fields are used to illustrate important statistical ideas. Students use the graphing calculator and software programs such as Microsoft Excel and StatCrunch throughout the course.

Precalculus (Regular, Honors, and Advanced)

The material of the course includes review of second-year algebra; first- and second-degree equations with applications; inequalities including absolute values with applications; functions; graphs; polynomial and rational functions with applications; exponential and logarithmic functions with applications; and trigonometric functions with applications. At the regular level, students do several mathematical modeling projects using some of the functions that have been studied, including the linear function, exponential function, logistic function, and simple harmonic function. At the Honors and Advanced levels, students also study graphing in polar coordinates, vectors and their applications, mathematical induction, sequences and series, permutations, combinations, and probability. Programmable graphing calculators are used extensively in the course.

Calculus AB (Regular and Advanced Placement)

Students learn how to solve problems using analytical, graphical, and numerical methods. The material covered in this course includes limits; continuity; differentiation; applications of differentiation to increasing/decreasing functions, relative extrema, applications of extrema, concavity, inflection points, related rates, differentials, and local linearity; Rolle's theorem; mean value theorem for derivatives; indefinite and definite integration; the fundamental theorems of calculus; mean value of a function; mean value theorem for integrals; applications of integration to areas and volumes; definite integral as an accumulator; logarithmic and exponential functions including differentiation and integration; trigonometric functions including differentiation and integration; techniques of integration including algebraic and trigonometric substitutions, partial fractions (non-repeating linear factors) and integration by parts; solutions and applications of simple separable differential equations; numerical integration using Riemann sums and the trapezoidal rule; and L'Hopital's rule. Programmable graphing calculators are used extensively in the course.

Calculus BC (Advanced Placement)

Students in this course study the topics listed above, plus more. The additional material includes arc length and surfaces of revolution; applications of integration to work and to fluid pressure and fluid force; improper integrals; infinite series and the question of convergence; Taylor and Maclaurin series; power series, application of the ideas of calculus to functions given in parametric, polar and vector form; slope fields; numerical solution of differential equations using Euler's method; and solution of logistic differential equations and their use in modeling. Programmable graphing calculators are used extensively.

Linear Algebra

Linear Algebra is a course taught at the undergraduate level and at top-tier college preparatory schools throughout the nation. This half credit course is for students who've completed AP Calculus AB and/or BC, though, technically, it can be taught to strong students who have not completed Calculus. The main topics covered are systems of linear equations, matrices, Gaussian elimination, Gram-Schmidt orthogonalization, determinants, vector spaces, eigenvalues, and eigenvectors. Students explore a wide range of applications and may use computer software.

Statistics (Advanced Placement)

This course introduces students to the major concepts and tools for collecting, displaying, analyzing, and drawing conclusions from data. Students are exposed to the following four conceptual themes: (1) exploring data; (2) sampling and experimentation; (3) anticipating patterns through probability and simulation; and (4) statistical inference. Real experimental studies are used extensively throughout the course, and students design, conduct, and analyze their own experiments. All students are required to take the College Board AP examination near the end of the academic year.