Mathematics

Philosophy

The philosophy of the mathematics program in the Upper School is reflected in its goals, which are to provide the student with the information and skills necessary for advanced work in mathematics and the sciences, real world problem solving, critical thinking, and making sensible, responsible decisions in a highly technological society.

Course offerings include Geometry in Form III, Algebra II in Form IV, Precalculus in Form V, and Advanced Placement Calculus AB and Applied Calculus in Form VI, although some students may take a different sequence of courses because of acceleration. Courses are generally offered at two levels: a standard (B) level and an accelerated (A) level.

Geometry
This is a standard course in Euclidean geometry covering the following topics: parallelism and perpendicularity, triangle properties and congruence, similarity, right triangles (including right-triangle trigonometry), circles, and surface areas and volumes (plane figures and solids). Proofs of different types are introduced and used extensively. Geometer’s Sketchpad (a computer software program) is utilized on a regular basis to let students develop conjectures about various properties of geometric figures. Coordinate geometry is integrated into all topics. Text: Geometry, McGraw Hill Education.

Algebra II
The skills and concepts learned in Algebra I are refined and expanded in Algebra II. Linear and quadratic functions, complex numbers, radical functions, polynomial functions, rational functions, exponential/logarithmic functions, matrices, sequences, series, and probability, combinatorics are among the topics studied. Real-world applications receive considerable attention within each topic. Graphing calculators are required for this course. Text: Rockswold: Algebra and Trigonometry 6th edition in the advanced group and Sullivan: Intermediate Algebra in the standard group.

Precalculus
This course is a rigorous study of exponential/logarithmic functions, trigonometric functions (including graphical, analytical, and triangle-based representations), polar and parametrically defined functions, vectors, conic sections (time permitting in the standard group), combinatorics and probability, and some statistical analysis. The academic year culminates with the study of limits and an introduction to calculus. Extensive applications to real-world phenomena are covered within each topic of study. Graphing calculators are required for this course. Text: Sullivan: Precalculus: Enhanced with Graphing Utilities, 7th Edition, Pearson.

Finite Mathematics
Applying the mathematics from Algebra I and Algebra II, Finite explores problem solving using numerical, symbolic (algebraic), and graphical approaches. Current domestic and world issues provide relevant context for analysis and discussion. Group work and participation is emphasized. Texts: Pirnot: Mathematics All Around, and Mathematics in Action, A Guide to Algebraic, Graphical, and Numerical Problem Solving, 5th ed; Pearson.

Applied Calculus
This course is designed for students who are interested in pursuing a math, science, or business-related field of study after high school, or for those individuals who appreciate the world of functions and want to further challenge themselves. After a very brief review of exponential, logarithmic, polynomial, rational, and trigonometric functions, the course offers a detailed study of the concepts of calculus: limits, derivatives, and integrals. Some real-world applications, including those in business, physics, and other sciences, are emphasized throughout the course. Graphing calculators are required for this course. Text (ebook) Lial, Calculus with Applications, 11th Edition, Pearson.n.

Calculus AB
This is a standard first-term college course in differential and integral calculus that follows the Advanced Placement curriculum. Limits are investigated, leading to a study of differentiation and integration. Application problems from physics, engineering, business and economics are an essential part of the course. Graphing calculators (Ti-84 Plus), the use of which is essential to the course work, are required of all students. Text (Pearson ebook): Calculus: Graphical, Algebraic, Numerical by Demana & Finney

Statistics
Topics in this course include collecting data, constructing and interpreting graphical displays, counting techniques, probability, the normal distribution, confidence intervals, measures of spread, correlation and regression, and the mathematics of voting. Text: Elementary Statistics; Pearson Prentice Hall