Class XII Math Course Descriptions

CALCULUS: This course covers the fundamental concepts, techniques, and applications of differential and integral calculus, with an emphasis on polynomial and algebraic functions, including exponential and logarithmic functions. Content is flexibly paced to allow both in-depth examination of central principles and student-centered exploration of topics of interest. This course provides a solid foundation for Calculus I-level college study, but does not aim to prepare students for the Advanced Placement (AP) exam.

CALCULUS A: This course continues the differential calculus begun in Class XI and also covers integral calculus of functions of one variable with applications. Topics in the differential calculus component of the course include techniques of differentiation, differentials, related rates, curve sketching, optimization, and rectilinear motion. Topics in the integral section include area between two curves, volume of solids of revolution, and differential equations. Students wishing to prepare for the College Board Advanced Placement (AP) AB Calculus exam will find this a suitable course.

CALCULUS B: Students may enroll in this course with the department’s permission. This course, which covers differential and integral calculus and infinite series, prepares students for the College Board Advanced Placement (AP) BC Calculus exam. Topics covered in Calculus B, but not in Calculus, include additional methods of integration and applications involving polar coordinates, vectors, and parametric equations. After the AP exam, the course covers additional topics, which may include combinatorics, probability, and/or statistics.

LINEAR ALGEBRA: Prerequisite: Advanced Calculus at Brearley. Topics covered in this course include vectors, the algebra of matrices, linear transformations, eigenvalues and eigenvectors, general vector spaces, and applications of all of the above. The course is designed to develop an appreciation for and facility with mathematical abstraction and to serve as an introduction to writing mathematical proofs.

STATISTICS AND STATISTICAL MODELING: Introduction to the practice of statistics. Topics include organization of data with graphs and summary statistics; an examination of how data is produced through samples, experiments, and simulations; probability and random variables; and drawing inferences from data through confidence intervals and hypothesis tests. Computers and calculators are used extensively.