Mathematics Department
FORM III GEOMETRY
This course offers a study of Euclidean geometry supplemented by topics in transformational, coordinate, and solid geometry and regular review of Algebra I concepts. Links between algebra and geometry are stressed throughout the course. Throughout the course, students use dynamic geometry software in addition to pencil-and-paper drawing techniques as well as graphing calculators in their investigations.
FORM IV ALGEBRA II
This course begins with a brief review and extension of the concepts and techniques of Algebra I. In particular, methods of modeling data and solving problems using equations and inequalities (linear, simultaneous, and quadratic) are emphasized. Principles of analytic geometry enhance the connection between algebraic and geometric concepts. Topics include polynomial equations, rational expressions, radicals and quadratic functions, irrational and complex numbers, variation (direct, inverse and joint), and conic sections.
FORM V ADVANCED ALGEBRA AND TRIGONOMETRY
The first half of this course extends topics in trigonometry developed in previous years to include circular trigonometric functions, trigonometric formulas and equations, and advanced graphing techniques for sinusoidal and related functions. Special emphasis is placed on the modeling of functions from real-world data, problem solving techniques, and applications to the physical and social sciences. The second half of the course reviews and extends topics from Algebra II and introduces units on exponential and logarithmic functions, sequences and series, and probability and statistics.
FORM V INTENSIVE PRECALCULUS V
This course extends topics in trigonometry developed in previous years and introduces new topics in algebra and geometry. Special emphasis is placed on the theoretical foundations of the course content as well as on applications to the sciences and social sciences. Topics include toolkit functions; parametric functions; exponential, logarithmic and logistic functions; circular trigonometric functions; trigonometric formulae and equation; advanced graphing; conic sections; sequences and series; matrices; and probability and statistics.
FORM VI TOPICS IN PRECALCULUS
The first half of the course includes the study of conics, polynomial functions, theory of equations, introduction to limits and derivatives, linear programming, and solving systems of equations using matrices. The second half of the course emphasizes probability and statistics. Topics include descriptive statistics using a computer program called Fathom, elementary probability, probability distributions, and mathematical expectation. Students make extensive use of graphic calculators throughout the course.
FORM VI INTRODUCTION TO CALCULUS
This course provides a non-rigorous introduction to the fundamental notions of calculus - limits, differentiation, and integration. The course is taught on an intuitive level, with emphasis placed on gaining proficiency in manipulative techniques. Additional topics include a review of linear functions and trigonometry, analytic geometry, applications of differentiation to curve sketching and maximum/minimum problems, and applications of integration to area, volume, and accelerated motion problems.
FORM VI ADVANCED TOPICS IN CALCULUS AB
This is a course in elementary functions and introductory calculus comparable to a college-level course. The emphasis in the course is on an intuitive understanding of the concepts presented and familiarity with a variety of their applications. Topics include functions, limits, analytic geometry, differentiation, applications of differentiation, integration, applications of integration, transcendental functions, and elementary differential equations.
FORM VI ADVANCED STATISTICS
Statistics consists of four major topics: studying methods of gathering information, designing mathematical models to explore patterns in data, developing methods to analyze and summarize data, and presenting inferences and conclusions from this analysis. This course will focus on applying these techniques to problems from the social and physical sciences and writing about the results in a non-technical manner. Computers and graphing calculators are used as tools in analysis, but no previous knowledge of computers is required.
THE ADVANCED MATHEMATICS PROGRAM
FORM III GEOMETRY / INTERMEDIATE ALGEBRA
Through a series of problems, investigations, projects, and real-world applications, students develop the methods and inductive and deductive skills of Euclidean, transformational, and coordinate geometry and learn to apply these skills in a variety of settings. Using a hands-on, investigative approach with graphing calculators and dynamic geometry software as well as pencil-and-paper sketching techniques, students explore properties of two- and three-dimensional objects. Links between geometry and algebra are emphasized throughout the course. Students will be introduced to mathematical concepts such as spherical geometry and fractals as they relate to standard course material, will use the Internet for mathematical explorations, and will work with manipulatives as well as software in their exploration of 3D objects.
FORM IV INTENSIVE PRECALCULUS
This course extends skills and concepts developed in previous years and introduces a variety of new topics to prepare students to begin a rigorous study of calculus in the following year. Emphasis is placed on the theoretical origins of the concepts presented as well as their applications to the sciences and social sciences. Topics include toolkit functions; parametric functions; circular trigonometric functions and their applications to triangles; trigonometric formulae and equations; complex numbers; exponential, logarithmic, and logistic functions; polynomial functions; advanced techniques of equation solving; conic sections; sequences and series; probability; and curve sketching. Students should plan to take the SAT II: Mathematics Level II Test at the conclusion of this course.
FORM V INTENSIVE CALCULUS
FORM VI ADVANCED TOPICS IN CALCULUS BC
(Departmental permission required)
This is a two-year sequence in functions and calculus including an analysis of theory that is comparable to that offered in an honors section of college calculus. Topics include functions (elementary, vector, parametric, polar), limits and continuity (including epsilon-delta proofs), the derivative including linear approximations to a function, applications of the derivative including velocity and acceleration vectors for motion on a plane curve, antiderivatives, applications of antiderivatives, techniques of integration, the definite integral, applications of the definite integral including improper integrals, infinite series, and first and second order differential equations with applications.
COMPUTER SCIENCE ELECTIVES
INTRO TO PROGRAMMING AND MULTIMEDIA I
In this course, students will be introduced to various multimedia creation tools and basic programming languages. Students will have an opportunity to create and publish animations and websites. Basic programming vocabulary and problem solving techniques will be introduced.
INTRO TO PROGRAMMING AND MULTIMEDIA II
This course will extend the material covered in Level I. Students will work on larger projects, with emphasis on organization, problem solving, and presentation. Students will be able to produce attractive, informative, and useful content. This course will include a long-term capstone-programming project.
PROGRAMMING BASICS
This class introduces students to the basics of computer programming. The first semester will be devoted to web based programming, beginning with HTML (HyperText markup language) and move onto the Javascript scripting language, which adds interactivity to web pages. In the second semester, students will explore the syntax of the object oriented programming languages Visual Basics and C++. No prior programming experience is necessary to take this class.
PROGRAMMING IN C++
This class is a continuation of the C++ programming language introduced in Computer Science I. Problem solving and structured design techniques are studied through “hands-on” programming examples. Topics covered include variable assignment, conditionals, loops, function calls, classes, objects, recursion and arrays.
PROGRAMMING IN JAVA
This course features the object oriented programming language Java. Topics include program design, class design, implementation techniques, programming constructs, Java library classes, programming analysis, standard data structures and standard algorithms.
ADVANCED PROJECTS IN COMPUTER PROGRAMMING
For those who wish to continue their proficiency in computer programming, this class can fulfill the advanced student’s desire to pursue an independent programming project. Possible projects would be programming of games, Lego robotics, or exploration of programming languages.
WEB PAGE DESIGN
In this course, students will learn the production skills necessary for designing pages on the World Wide Web. Students begin the course by learning basic HTML coding, and the tenets of good design. They soon migrate to designing with the Dreamweaver web-authoring suite.
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