# Mathematics

The core Mathematics program includes Algebra I, Geometry and Algebra II as required courses. The focus is on the symbolic language of algebra, geometric figures, sound arguments, and first exposures to functions, graphing, problem solving, and mathematical modeling. What lies beyond necessitates skill with computation, an intuition for sensible estimates, much practice with algebraic manipulations, and experience applying appropriate concepts and strategies, and appropriate use of technology in given situations.

### Courses & Descriptions

This is a logical development of a first course in algebra - the foundation - emphasizing basic concepts, understanding, and fundamental skills. The course content includes the real number system, algebraic symbolism and its application (translating from English to mathematical language), applied problem-solving, graphs, exponents, radicals, linear and quadratic relations, factoring, rational expressions, equations and inequalities.

In this course the students are introduced to Euclidean Geometry. The challenge of being able to solve problems using the components of deductive structure and employing traditional, coordinate, and transformational approaches makes the course both fun and rigorous. Additionally, the course strives to integrate algebra and geometry, as these disciplines are made richer by building on each other.

This is an intermediate course which redevelops the concepts of Algebra I and extends them to a more mature understanding of inequalities; polynomial functions; graphing techniques; rational, real, and complex number systems; and introductions to exponential and logarithmic functions. Algebra I and Geometry are thus blended together in the analytic geometry of Rene Descartes. Students will also apply these concepts and skills to the solution of real world applied problems. This course is appropriate for those students whose background indicates a need for a more in- depth review of algebra skills, and moves at a slower pace than MA 31-32. Students enrolled in this course will be required to take MA 39 Functions, Statistics and Trigonometry.

This accelerated course offers a faster pace and deeper coverage of the topics considered in MA 29-30 and introduces trigonometric functions. Students are likely to continue to MA 45-46 and MA 55-56; some will move to MA 39-40 or MA 41-42. Students are ready for the Math Level I SAT II Test after this course.

This honors course offers deeper coverage of the topics considered in MA 31-32 and introduces sequences, series, and probability. Students are likely to continue to MA 47-48 and MA 57-58; some will move to MA 45-46 and MA 55-56. Students are ready for the Math Level I SAT II Test after this course.

This course completes the Algebra II requirement for students who have taken MA 29-30. Algebra II skills are reinforced and new topics include trigonometry, sequences and series, as well as statistical analysis. Students are likely to continue on to MA 41-42, but will not be eligible for MA 45-46. Students are ready for the Math Level I SAT II Test if taken in December or later.

Through the study of elementary combinatorics, probability, and descriptive statistics, students will learn to deal with the plethora of data that confronts us daily.

- What part does chance play in our lives?
- What inferences can be drawn from masses of statistics?
- How valid are they?
- What do we mean when we say an occurrence is unexpected?
- What can be predicted? One outcome should be the recognition of the misuse of statistics by those advertisers, politicians, and the like who bombard us with "evidence" for taking their positions. (11
^{th} and 12^{th} graders only; can be taken concurrently with another mathematics course with department approval.)

The two Precalculus courses, MA 45-46 and MA 47-48, continue the traditional sequence from arithmetic through algebra and analysis to calculus, either in high school or college. Precalculus reviews and extends both algebraic skills with applications and the concept of a function and its applications. Students in these courses are ready for Math Level I SAT II Test if taken in December, and Math Level II SAT II Test at the June session.

The traditional sequence may include an extension of material from the first three courses: algebraic structure and proof, the elementary functions, conic sections, sequences, the binomial theorem and mathematical induction, and elementary probability. Some introduction to the ideas related to the calculus is also included. This first course beyond the academy's requirement is strongly encouraged as the goal of all students. It has fast become a necessary part of a fuller education, useful to those wishing to maximize their options for college majors and employment opportunities as well as those aspiring toward the sciences or mathematics.

This honors course offers deeper coverage of the material than the MA 45-46 Precalculus course.The elementary functions are completely explored with the assistance of a graphing calculator. Other areas such as limits, mathematical induction, polar coordinates, and vectors will be included in the course. In the last quarter of the course, students will start AP Calculus. (AP Calculus is the usual sequel.)

This is a year-long course with two major segments. The first portion of the course is an in-depth examination of ideas such as vectors, matrices, systems of linear and non-linear equations, sequences and series. The second portion of the course introduces students to the major themes of calculus, specifically the limit, the derivative, and the definite integral. This segment is designed to prepare students for a traditional college calculus course.

The goal of the course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusion from data. Students will be exposed to four main conceptual ideas: Exploring Data, Planning a Study, Anticipating Patterns, and Statistical Inference. (MA 45-46 is a prerequisite; Advanced Placement Exam administered in mid-May is required; can be taken concurrently with another mathematics course (including MA 47-48) with department approval.)

This introduction to The Calculus includes analytic geometry, introductory limit theory and continuity, differential and integral calculus of the elementary functions, geometric motivation and formalism, and applications to graphing and to economics, physical sciences, and life-sciences. (MA 47-48 is the usual prerequisite; Advanced Placement Exam administered in mid-May is required.)

In addition to the material covered in AB- Calculus not already covered in MA 48, topics include limit theory, continuity and convergence, power and Taylor series, elementary differential equations, methods of integration, approximation techniques, polars, vectors, and parametrics. (MA 47-48 or MA 55-56 is a prerequisite; Advanced Placement Exam administered in mid-May is required.)

This course will present the basic concepts of linear algebra. The course will cover both computational methods and more abstract concepts related to linear algebra. Topics will include systems of linear equations, vectors and matrices, vector spaces, determinants, eigenvalues and eigenvectors, linear transformations, and applications.