# Mathematics

## מָתֶמָטִיקָה

## Department of Mathematics

The Mathematics curriculum provides a sequence of courses designed to meet graduation requirements and college admissions expectations for students of varying abilities and learning styles. Throughout the curriculum the following skills are developed and refined: oral and written communication skills, problem solving skills and reasoning skills. Emphasis is placed on an analytical, graphical, and numerical approach using graphing calculators as the central tool.

Each student should possess a TI-83 Plus or TI-84 graphing calculator for use in the mathematics courses. This graphing calculator will be the calculator used throughout the four-year high school sequence in mathematics.

The course offerings are broad in scope to ensure that each student is properly challenged and motivated to do his/her best. For freshman year, acceptance into honors or accelerated courses is based upon junior high recommendations and performance on high school entrance exams. Acceptance into courses following freshman year is based upon teacher recommendations and prior high school grades in mathematics.

Students are required to complete three years of a mathematics sequence for graduation. Students interested in pursuing math/science in college are encouraged to take a mathematics course their senior year.

## Courses Offered

Algebra 1 Modified is a highly structured introduction to algebra. Topics studied include: operations with variables, solving equations, positive and negative numbers, formulas, operations with polynomials, factoring, graphing, equations with two variables, working with algebraic fractions, decimals and percents, squares and square roots, and quadratic equations.

**Homework Requirement: 1-2 hours per week**

Algebra 1 is the first year or a college preparatory sequence. Topics studied include operations with variables, the number line, solving linear equations, writing and graphing linear equations, solving systems of equations, operations with polynomials, factoring, operations with algebraic fractions, functions, roots, radicals, and quadratic equations. Special emphasis is given to real life applications and connections to geometry.

**Homework Requirement: 2-3 hours per week**

Algebra 1 Honors is the first year of a college preparatory sequence, which includes advanced Placement Calculus. Topics studied include basic operations with real numbers, solving linear equations and inequalities, graphs and functions, polynomials and factoring, operations and equations with rational expressions, irrational numbers and radicals, quadratic equations and functions, absolute value, composite functions, permutations and combinations, and probability. Some topics are taken from advanced algebra.

**Homework Requirement: 3-4 hours per week**

Geometry 2 is the second year of a college preparatory sequence. It is proof-oriented to emphasize deductive reasoning. Topics covered include congruent triangles, perpendicularity, parallel lines, quadrilaterals, polygons, similar polygons, the Pythagorean Theorem, circles, area, volumes and constructions. In addition, students study Algebraic applications of the properties.

**Homework Requirement: 2-3 hours per week**

Geometry 2 Modified is a highly structured introduction to geometry. A review of algebraic concepts is stressed with special emphasis given to the solution of algebraic equations and their application to geometry. Topics studied include triangles, perpendicularity, parallel lines, quadrilaterals, similar polygons, the Pythagorean Theorem, circles, area, volumes and constructions.

**Homework Requirement: 3-4 hours per week**

Geometry 2 Honors is a fast paced, in-depth course, including some solid geometry. Topics covered include congruent triangles, perpendicularity, parallel lines, quadrilaterals, lines and planes in space, polygons, similar polygons, the Pythagorean Theorem, circles, area, volumes, locus, and constructions.

**Homework Requirement: 3-5 hours per week**

Algebra/Trigonometry 3 Modified is highly structured introduction to algebra and trigonometry. This course includes a review of real numbers, first degree equations and inequalities in one variable, special products, factoring, equations, fractions and fractional equations, graphs of linear equations, functions and relations, systems of linear equations and inequalities, exponents and radicals, quadratic equations, and the trigonometry of right triangles.

**Homework Requirement: 3-5 hours per week**

Algebra/Trigonometry 3 is the third year of a college preparatory sequence. Topics studied include the real numbers, first degree equations and inequalities in one variable, special products, factoring, algebraic fractions and fractional equations, graphs of linear equations, functions and relations, systems of linear equations and inequalities, exponents and radicals, quadratic equations, and circular and trigonometric functions.

**Homework Requirement: 3-4 hours per week**

Pre-Calculus 3 Honors studies the topics of linear and quadratic functions and inequalities, the conic sections, polynomials and rational functions, radical functions, composite and inverse functions, exponential and logarithmic functions, trigonometric functions, sequences and series, binomial expansion, mathematical induction, determinants, and polar coordinates.

**Homework Requirement: 3-5 hours per week**

Pre-Calculus 4 completes a four-year college prep core sequence, which gives a firm foundation for the study of college calculus. Topics studied include a review of the trigonometric functions and their graphs, applications of trigonometry, sequences and series, permutations, combinations, probability, topics from analytic geometry, the conic sections, systems of equations and inequalities, and polynomial and rational functions and limits.

**Homework Requirement: 3-4 hours per week**

Advanced Placement Calculus AB prepares students to take the AP Calculus AB examination. Topics studied include analytic geometry, limits, the derivative, integration, transcendental functions and applications of the derivative and of the integral.

**Homework Requirement: 3-5 hours per week**

Advanced Placement Calculus BC prepares students to take the AP Calculus BC examination. Following the College Board’s suggested curriculum designed to parallel college-level calculus courses, AP Calculus BC provides students with an intuitive understanding of the concepts of calculus and experience with its methods and applications, and also requires additional knowledge of the theoretical tools of calculus. This course assumes a thorough knowledge of elementary functions, and covers all of the calculus topics in AP Calculus AB as well as the following topics: vector functions, parametric equations, and polar coordinates; rigorous definitions of finite and nonexistent limits; derivatives of vector functions and parametrically defined functions; advanced techniques of integration and advanced applications of the definite integral; and sequences and series.

**Homework Requirement: 4-6 hours per week**

Following the College Board’s suggested curriculum designed to parallel college-level statistics courses, AP Statistics introduced students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference.

*Homework Requirement*: 4-6 hours per week

This course includes a study of vectors, matrices, and linear transformations and is typically intended for students who have completed AP Calculus. It explores extensively what one can do with these objects, both in a pure and applied sense. Throughout it builds on prior knowledge from geometry and algebra (and a smidge from calculus). The course fosters mathematical habits of mind (such as abstracting from computation, trying to make arguments general, and proof).

*Homework Requirement*: 3-4 hours per week

Students will explore the science of computational thinking, programming, modeling and simulation, problem solving and systems thinking. Students will design their own algorithms and take part in writing code.

**Homework Requirement: 4-6 hours per week**

Following the College Board’s suggested curriculum designed to mirror college-level computer science courses, AP Computer Science A courses provide students with the logical, mathematical, and problem-solving skills needed to design structured, well-documented computer programs that provide solutions to real-world problems. These courses cover such topics as programming methodology, features, and procedures; algorithms; data structures; computer systems; and programmer responsibilities.

**Homework Requirement: 4-6 hours per week.**

This course follows a year-long college sequence giving a rigorous treatment of multi-variable calculus and linear algebra, with an emphasis on theory and proofs. A proof-based course in differential and integral calculus is required as a prerequisite as well as knowledge of LaTeX.

**Homework Requirement: 4-6 hours per week.**

This course is an introduction to point-set topology; it covers manifolds, atlases, Lusternik-Schnirelmann categories, tangent spaces, compactness, and the Heine-Borel Theorem. Assignments include rigorous proofs of lemmas, so a proof-based course in mathematics is required as a prerequisite as well as knowledge of LaTeX.

**Homework Requirement: 4-6 hours per week.**