Math Courses


ALGEBRA I

This course provides a thorough introduction to the language of algebra, including its symbols and the axioms and laws which govern its structure. Emphasis is given to the understanding and manipulation of all manner of algebraic expressions, from performing standard operations to factoring polynomials and simplifying radical expressions. Among the primary goals are competence in solving linear equations and inequalities in one variable, systems of linear equations in two variables, and simple quadratic equations. Experience is provided in graphing in the Cartesian plane and in applying algebraic methods to the solution of practical problems.

 

GEOMETRY (REGULAR AND ADVANCED)

Devoted to plane Euclidian geometry, this course also extends into solid geometry. The subject is treated as a structured system and emphasizes deductive reasoning and mathematical proofs, whereby intuition and proofs are blended. Topics such as congruence, perpendicularity, geometric inequalities, parallelism, quadrilaterals, geometric proportions and similarity, circles, spheres, and surface areas and volumes of solids are studied.

 

ALGEBRA II

This course begins with a brief review of Algebra I and extends to include number systems, polynomials, rational expressions, linear equations and inequalities, systems of equations, elementary exponential and logarithmic functions, right-triangle trigonometry, and elementary probability and statistics. A graphing calculator is required.

 

ADVANCED ALGEBRA II AND TRIGONOMETRY

Advanced Algebra II and Trigonometry includes all the topics in Algebra II as well as binomial theorem, trigonometric functions, analytic trigonometry, the concept of function, and a detailed examination of the logarithmic and exponential functions. A graphing calculator is required.

Prerequisite: Permission of the Department

 

PRECALCULUS (REGULAR AND ADVANCED)

This course reviews the concepts from Algebra II that are central to calculus and explores several discrete math topics. Calculus topics focus on the study of functions: polynomial, trigonometric, logarithmic, and exponential. Discrete topics include polar coordinates, sequences and series, permutations and combinations, the Binomial Theorem, and conic sections. Throughout the course, students are expected to use the graphing calculator to solve problems in each topic area. The advanced section extends the curriculum and explores topics in greater depth. An additional study of vectors and probability is included, and a TI-89 graphing calculator is required.

 

ADVANCED PRECALCULUS ACCELERATED

The course is intended for students who have demonstrated an exceptional commitment and aptitude in mathematics. Topics are explored more rapidly, challenging students to apply concepts and skills at the highest level. The first three chapters of the AP Calculus BC curriculum are covered in the fourth quarter. A TI-89 graphing calculator is required.

Prerequisite: Permission of the Department

 

CALCULUS

This course is an introduction to the fundamental concepts of calculus. The first semester consists of a review of analytic geometry and trigonometry, and the study of the derivative, continuity and limits, and differentials. The second semester includes a study of integration, logarithmic and exponential functions, techniques of integration, and applications of integration. A graphing calculator is required.

Prerequisite: Precalculus

 

STATISTICS

Topics for study in this course include the organization of data into patterns and the interpretation of them using regression and correlation. Emphasis is on designing experiments and utilizing probability and randomness to establish inference. Students explore confidence testing in both distributions and proportions and employ modern technology to achieve these ends. A graphing calculator is required.

Prerequisite: Algebra II or Precalculus

 

ADVANCED PLACEMENT STATISTICS 

The AP Statistics course is built around four main topics: exploring data, planning a study, probability as a foundation for the procedures of statistics, and inferential reasoning. These four broad conceptual themes are studied in depth to prepare students for the Advanced Placement Exam given by the College Board. Students use the computer and a TI-84 Plus graphing calculator to examine distributions, to plan studies, to make conjectures, to study random behaviors, and to analyze and draw conclusions from data. This course is more theoretical, more demanding, and requires a higher level of conceptual understanding than the Statistics course. This course may be taken concurrently with any of the calculus courses.

Prerequisites: Advanced Precalculus and permission of the Department

 

ADVANCED PLACEMENT CALCULUS AB

This is a college-level course that follows the syllabus of the College Board and is for students who intend to take the Advanced Placement Examination in Calculus AB. Included are the rate of change of a function, limits, derivatives, integration, applications of the definite integral, transcendental functions and their derivatives and integrals, further methods of integration, and applications. A TI-89 graphing calculator is required.

Prerequisite: Precalculus and permission of the Department

 

ADVANCED PLACEMENT CALCULUS BC

This is a college-level course that prepares students to take the Advanced Placement Examination in Calculus BC. It follows the syllabus of the College Board and is for students who have successfully completed the first year of Calculus, Calculus AB, or who have completed Precalculus and have their instructor’s approval. Topics covered include a review of basic integral and differential calculus and techniques of integration, applications of the definite integral, polar coordinates, indeterminate forms and improper integrals, Taylor polynomials, approximation and interpolation, sequences and series, vectors, differentiation and integration of vector functions, and ordinary differential equations. A TI-89 graphing calculator is required.

Prerequisite: Advanced Placement Calculus AB or permission of the Department

 

MULTIVARIABLE CALCULUS AND DIFFERENTIAL EQUATIONS

This course in advanced mathematics includes core components of multivariable calculus, linear algebra, differential equations, and statistics. The use of mathematical software (Matlab), as well as TI-89 graphing calculators, is emphasized. Satisfactory completion of an assigned final project is required. The course is also designed to complement the Advanced Math/Science Research course; for those students enrolled in both, the two

courses can be interdisciplinary, if so desired, focusing on the area of mathematics that students often encounter in their research projects. The most common area is statistics, but other mathematical strands can be developed as needed. Completion of an individualized curriculum satisfies the project requirement of this course. A TI-89 graphing calculator is required.

Prerequisite: Advanced Placement Calculus BC and permission of the Department

 

LINEAR ALGEBRA

This course in advanced mathematics includes the core components of linear algebra. Topics covered include matrices, rank, determinants, linear equations, vector spaces, linear independence, eigenvectors, and linear transformations. Part of the course is proof-based and students hone their mathematical reasoning and logic skills. Sixth formers recommended for Linear Algebra or Multivariable Calculus may choose to take both concurrently.

Prerequisite: Advanced Placement Calculus BC and permission of the Department

 

Berkshire School

245 North Undermountain Road
 |  Sheffield, MA 01257
 |  T: 413 229 8511

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