# Mathematics

Three years of mathematics are required for graduation. Students who have successfully completed Algebra I in the eighth grade complete PreCalculus in the junior year and then are eligible for the study of Calculus during their senior year. Students who take Pre-Algebra in the eighth grade will complete two years of Algebra and one year of Geometry by the end of the junior year. The department offers courses at different levels of difficulty, including Advanced Placement, so that each student receives a course of study suited to his or her background, interest, and ability. There are significant differences in the presentation, pace, content, and amount of independent work required in the different levels of each course. Therefore, it is important that students (with the advice and recommendation of the Math Department) carefully select the proper level of each course. The use of technology, especially the graphing calculator, will be integrated into the curriculum throughout the fouryear program, especially in the PreCalculus and Calculus courses.

## Required Courses

- Algebra I, Algebra I Fundamentals
- Algebra II Honors
- Algebra II
- Algebra II Fundamentals
- Geometry Honors, Geometry, Geometry Fundamentals

## Algebra I, Algebra I Fundamentals

Algebra I involves the study of the Real Number System. The properties and the basic operations of real numbers are introduced early in the curriculum, and the solution of linear equations is emphasized. In the latter half of the year, functions and relations are introduced, and the solution of rational equations and systems of equations are studied. If time permits, the solution of quadratic and radical equations is included. Algebra I meets 4 times per week, Algebra I Fundamentals meets 5 times per week.

## Algebra II Honors

Algebra II includes the study of linear equations in two and three variables, an introduction to functions, linear inequalities in two variables, polynomial operations, factoring of higher order polynomials, laws of exponents, radicals, solving quadratic equations and quadratic systems, complex numbers, conics, exponential and logarithmic functions and an introduction to sequences and series. Prerequisite: Algebra I. Meets 4 times per week.

## Algebra II

Algebra II includes the study of linear equations in two and three variables, an introduction to functions, linear and quadratic functions, linear inequalities in two variables, polynomial operations, rational expressions and functions, factoring of higher order polynomials, laws of exponents, radicals, solving quadratic equations and quadratic systems, complex numbers, exponential and logarithmic functions, matrices, and an introduction to sequences and series. Prerequisite: Algebra I. Meets 4 times per week

## Algebra II Fundamentals

Algebra II Fundamentals includes the study of linear equations in two and three variables, systems of equations, matrices, an introduction to functions, quadratic functions, linear inequalities in one and two variables, absolute value equations and inequalities, laws of exponents, polynomial operations, factoring of higher order polynomials, rational expressions and equations, radical expressions and equations, solving quadratic equations, logarithms, and sequences and series. This course is not recommended for those students who wish to take the “PreCalculus” course during their junior or senior years. Prerequisite: Algebra I or Algebra I Fundamentals. Meets 4 times per week.

## Geometry Honors, Geometry, Geometry Fundamentals

This course provides a thorough study of the main topics of plane and solid Euclidean geometry. Three-dimensional concepts are included in the curriculum. The course also emphasizes the meaning and use of deductive reasoning and the formal requirements of writing a logical geometric proof. In addition, numerical application problems from such topics as areas and volumes, measurement of angles and arcs, and proportions are studied. Upon completion of two years of algebra and one year of geometry, students will be prepared to take the SAT Subject Test, Math Level 1. Prerequisites: Algebra I, Algebra II recommended. Meets 4 times per week.

## Elective Courses

- Foundations of PreCalculus
- Functions and Statistics
- PreCalculus
- PreCalculus Honors
- AP Statistics
- Topics in Calculus
- Calculus
- AP Calculus AB
- AP Calculus BC
- Multivariable Calculus

## Foundations of PreCalculus

This course is designed for students who wish to continue their study of mathematics and plan to study math or math-related disciplines in college. The curriculum includes: linear, quadratic, polynomial, exponential and logarithmic functions, a thorough introduction to trigonometry (including right triangle and circle trigonometry), trigonometric equations, fundamental trigonometric identities, the Law of Sines, the Law of Cosines, and operations on complex numbers. Prerequisites: Algebra I, Algebra II, Geometry, and permission of the department. Meets 4 times per week.

## Functions and Statistics

This course is designed to strengthen students' algebraic background while, at the same time, introducing or extending the core functions of PreCalculus: linear, quadratic, polynomial, exponential, and logarithmic functions. Interspersed with the development of these functions will be an introduction to some of the major ideas of statistics, providing a head start to students who may be required to take a Statistics course in college. This course will introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Topics will include experimental design, sampling, graphing, summarizing data, and an introduction to probability. Meets 4 times per week.

## PreCalculus

This full-year course is intended for interested math students who may study introductory Calculus during their senior year or in college. The curriculum covers the elementary functions and their properties and a comprehensive study of trigonometry. In this course, students develop the tools that are necessary to succeed in a Calculus course. Prerequisites: Algebra I, Algebra II Honors or Algebra II, and Geometry. Meets 4 times per week.

## PreCalculus Honors

This course is intended for students who have demonstrated an aptitude and interest in mathematics and who are likely to study AP Calculus during the senior year. Since the concept of a function is crucial to the further study of mathematics, functions and their properties form part of the core curriculum. Polynomial, exponential, logarithmic and trigonometric equations and their applications, geometric sequences and series, and an introduction to differential Calculus complete the core. In addition, some or all of the following topics are included: polar coordinates and complex numbers, combinations, probability, and review for SAT Subject Tests, Math Level 2. Prerequisites: Algebra I, Algebra II, Geometry, and permission of the department. Meets 4 times per week.

## AP Statistics

This course follows the recommendations of the Committee on Mathematics of the Advanced Placement Program. It introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. First semester topics include interpreting, summarizing, comparing, and exploring distributions of data, and methods of data collection such as surveys, experimental, and observational study. Second semester topics explore statistical inference through confidence intervals and tests of significance. Course supplements include newspaper and magazine articles. Students are challenged to think beyond the equations to justify, explain, interpret, and infer from data and subsequently communicate an appropriate and complete conclusion. Students are prepared to take the Advanced Placement exam. This course is open to seniors. Prerequisites: Must have completed any level of PreCalculus or be concurrently enrolled in PreCalculus or higher. Must have strong reading/writing skills and permission of the department. Meets 4 times per week.

## Topics in Calculus

This course is intended for students who have successfully completed the Foundations of Precalculus course. It does not prepare students for either of the Calculus AP exams. It is appropriate for those who plan to continue the study of Calculus in college and/or who may need this background for courses in applied sciences. This course starts with a focused review of the major functions and concepts of Precalculus and then branches into the curriculum of the Calculus course (delineated below). The amount of the Calculus curriculum covered by this course in a given year will depend on the strength of the class in that year. Prerequisites: Algebra I, Algebra II, Geometry, Foundations of PreCalculus, and permission of the department. Meets 4 times per week.

## Calculus

This course is intended for students who have successfully completed the Precalculus course. It does not prepare students for either of the Calculus AP exams. It is appropriate for those who plan to continue the study of Calculus in college and/or who may need this background for courses in applied sciences. The curriculum introduces the fundamental concepts of Calculus, including the ideas of functions, limits, continuity and standard differentiation formulas and their applications. Other topics covered are the derivatives of trigonometric functions, the natural logarithm, the exponential functions, and basic methods of integration. Prerequisites: Algebra I, Algebra II, Geometry, PreCalculus, and permission of the department. Meets 4 times per week.

## AP Calculus AB

This course follows the recommendations of the Committee on Mathematics of the Advanced Placement Program. The ideas of intervals, neighborhoods, functions, and limits are carefully explored leading to rigorous development of the standard differentiation formulas. Through applications of derivatives to problems in maxima and minima, the student gains experience in the power of calculus. Students are prepared to take the Advanced Placement exam. Prerequisites: Algebra I, Algebra II, Geometry, PreCalculus, and permission of the department. Meets 5 times per week.

## AP Calculus BC

This course follows the recommendations of the Committee on Mathematics of the Advanced Placement program. This course covers all of the topics taught in the AP Calculus AB course as well as the following additional topics: parametric, polar and vector functions (and their derivatives), slope fields, Euler's method, convergence of improper integrals and series, applications of integrals, and Taylor and Maclaurin series. Prerequisites: Algebra I, Algebra II, Geometry, PreCalculus, and permission of the department. Meets 4 times per week.

## Multivariable Calculus

This course is intended for students who have successfully completed AP Calculus BC. Taught at an undergraduate college level, this full-year course provides a thorough study of the calculus of functions of several variables. Topics include lines, planes and surfaces in R3 , vector-valued functions and TNB frame, partial differentiation, Clairaut's Theorem, gradients, Lagrange multipliers, cylindrical and spherical coordinates, double and triple integrals and applications. The course continues with vector fields, line integrals, surface integrals, Green’s Theorem, Stokes’ Theorem and the Divergence Theorem. An introduction to Linear Algebra may also be included as time permits. Prerequisite: Successful completion of AP Calculus BC and permission of the department. Meets 4 times per week.