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). Two-column proofs 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 of the aforementioned topics of study. Text (ebook): 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, relations and functions, variation, radicals, polynomial functions, rational functions, and exponential and logarithmic functions are among the topics studied. Word problems receive considerable attention within each topic. Graphing calculators (Ti-84 Plus), the use of which is integral to the course-work, are required of all students. Text (ebook): Rockswold: Algebra and Trigonometry 6th edition

Precalculus
This course is a rigorous study of algebraic and transcendental functions, including polynomial, rational, trigonometric, logarithmic, and exponential functions, all with extensive applications, and an introduction to limits. Additionally, conic sections, sequences and series, combinatorics, and probability are examined in great depth. Graphing calculators (Ti-84 Plus), the use of which is essential to the course-work, are required of all students. Text (ebook) Sullivan: Precalculus: Enhanced with Graphing Utilities; 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 (ebooks) Pirnot: Mathematics All Around, and Mathematics in Action, A Guide to Algebraic, Graphical, and Numerical Problem Solving, 5th ed; Pearson.

Applied Calculus
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, integrals, and and their uses. Some real-world applications, including those in business, physics, and other sciences, are emphasized throughout the course. Graphing calculators (TI-84 Plus), the use of which is essential to the course-work, are required of all students. Text (ebook) Lial, Calculus with Applications, 11th Edition, Pearson.

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 (ebook): Calculus: Graphical, Algebraic, Numerical; Pearson

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. This course may not be offered every year. Text: Elementary Statistics; Pearson Prentice Hall