Mathematics

The mathematics curriculum aims to instill habits of mathematical thinking that will prepare students for further inquiry in math and for using quantitative reasoning throughout life. The department helps students recognize the relationships represented by the language of mathematics and learn essential problem-solving skills such as conjecturing, sense-making, and analyzing strategies and solutions.

Through appropriately challenging experiences, students have the opportunity to puzzle over relationships and to develop the habit of questioning. Discovery is recognized as a valuable tool in the learning of math; this discovery takes place in teacher-led classes, individual explorations, and in learning groups that offer a natural context for practicing mathematical communication. At all levels, technology is used to relieve the constraints of tedious computation and to help students conjecture about the mathematics they are studying. Graphing calculators and personal computers enable students to solve problems utilizing rapidly evolving modern methods. Students are taught to approach mathematics from multiple perspectives, including numerical, graphical, and symbolic.

Taking direction from the NCTM Standards and the College Entrance Examination Board, the Math Department strives to engage all students with the challenge, excitement, and relevance of math.

Courses

Algebra I: Topics in this standard introductory algebra course include equations, systems of equations, graphing, polynomials, rational expressions, radicals, quadratics, and problem solving.

Algebra II: After a review and a more in-depth approach of many topics from Algebra I, new topics include data analysis, polynomial functions, sequences and series, exponential functions, matrices, and transformation of functions. Additional topics in the honors section may include linear programming, probability, and combinatorics.

Geometry: Geometry approaches plane Euclidean Geometry through proof and discovery. All classes will include conic sections, solid geometry, and coordinate geometry. Other topics may include transformations, fractals, and non-Euclidean geometries such as Taxi Cab or spherical. Coordinate geometry is studied through units in trigonometry and the conic sections. The honors section often includes other assorted units, such as vectors, proof by induction, and computer programming.

Precalculus Topics (Grades 11-12): Students will study modeling, polynomial functions, sequences and series, trigonometric functions, and logarithmic functions. Other topics are rational functions, transformations, and statistics. This course has a pace and depth designed for students with a fair foundation in algebra (generally students who earned a C+ or B- in BB&N’s Algebra II course). Successful completion of this course could prepare 12th Grade students for an advanced college precalculus course or a humanities level college calculus course. 11th Grade students completing this course would be prepared for Statistics in Grade 12.

Precalculus (Grades 10-12): Students study extended units on modeling, polynomial functions, sequences and series, trigonometry and logarithms. Other topics are rational functions, radical functions, transformations, symmetry, polar coordinates, and statistics.

Honors Precalculus AB and Honors Precalculus BC: The honors sections take a toolkit approach to a large variety of functions which can be transformed to model phenomena. Honors Precalculus AB studies precalculus topics for the entire year, while Honors Precalculus BC accelerates to include an introduction to differential calculus.

Calculus: Major topics of this calculus course are limits, differential calculus and integral calculus, and their applications.

AP Calculus AB: Major topics are limits, differential calculus and integral calculus, and their applications. This course covers, as a minimum, all topics stated in The College Board Advanced Placement Program Calculus AB syllabus.

AP Calculus BC: Major topics are limits, differential calculus and integral calculus, and their applications. Infinite series, vectors, and parametric equations are also covered. This syllabus includes, as a minimum, all topics stated in The College Board Advanced Placement Program Calculus BC syllabus.

AP Computer Science AB (Grades 10-12): This is an introductory college-level computer science course using the programming language Java. The emphasis is on programming methodology, algorithms, and data structures. Major topics include arrays, methods, classes, objects, linked lists, trees, recursion, and searching and sorting algorithms. Participating students are prepared to take the AP Computer Science AB exam. Permission of the instructor is required. Previous computing experience is not necessary.

Statistics (Grade 11-12): Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students work frequently on projects involving the hands-on gathering and analysis of real-world data. Ideas and computations presented in this course have immediate connections with actual events and future applications for study in the social sciences, natural sciences, or business. Computers and calculators allow students to focus deeply on the concepts involved in statistics. This course covers many of the topics taught in AP Statistics and uses a similar approach.

Advanced Placement Statistics (Grades 10-12): This course prepares students for the AP Exam in Statistics. Sophomores and juniors generally take AP Statistics in addition to a math course in the normal sequence. For seniors, this course is an appropriate college preparatory alternative to Pre-Calculus or Calculus.

Linear Algebra and Multivariable Calculus: This course is broken into semester-long segments. First, a semester of linear algebra will cover basic concepts involving vectors and matrices, including solving systems of linear equations by Gaussian elimination, Cramer’s Rule, and inverse matrices; the concepts of linear independence, spanning vectors, and basis vectors; the dot (inner) product and the cross product; eigenvalues, eigenvectors, and the diagronalization of matrices; abstract linear transformations and change of basis. The second semester focuses on multivariable calculus, covering the generalization of calculus concepts to two and three dimensions, including partial derivatives, multiple integrals, optimization problems (using Lagrange multipliers), other coordinate systems (cylindrical, spherical), and vector calculus (Green’s Theorem, Stokes’ Theorem, etc.). The course may also include some discussion of differential equations and Fourier series.