Mathematics


The Mathematics Department believes that problem-solving skills--analysis of a problem, plan for solution, completion, review and extension of solution--are essential to critical, logical thinking in all disciplines. Our program, therefore, presents students with opportunities to develop these skills along with basic mathematical concepts. Using various approaches, including the use of graphing calculators, the Department strives to develop students' curiosity, initiative, confidence, responsibility, enjoyment, and satisfaction in dealing with mathematics. While the required sequence ends with Algebra II and Trigonometry, nearly all students continue the traditional sequence through Precalculus and Calculus.

Requirements:
Algebra I
Geometry
Algebra II and Trigonometry


Required Courses

Algebra I and Problem Solving (311)
Meets five times per week
This is an Upper Division course designed for those students who have yet to master a full, rigorous Algebra I program. Horace Mann students who took Introduction to Algebra in grade 8 must take this course, and many ninth grade students new to Horace Mann are also appropriate candidates for this course. As in Algebra I, students will study such topics as functions, factoring, operations on rational expressions and on equations of degree 2 and greater. Special emphasis will be placed on creative problem-solving techniques needed for success with the more challenging problems in the Upper Division math courses.

Geometry (320)
Prerequisite: Algebra I
The course is designed to convey an appreciation of geometry as a deductive system. Accordingly, formal logic is studied early in the course and then used throughout. Starting with undefined terms, postulates, and definitions, the students follow the progressive development of theorems and their proofs to create a mathematical structure with rich aesthetic and practical value. In building this axiomatic structure, they improve their ability to recognize and organize the various relationships among points, lines, triangles, polygons, and circles in the plane. This course also includes the study of geometry with coordinates, the solid geometry of common shapes, and transformational geometry using a computerized dynamic geometry program.

Geometry Honors (321)
Prerequisites: Algebra I and departmental approval
The Honors sections cover the material of Geometry at a faster pace to allow time for greater depth and enrichment. Emphasis is placed on original proofs and abstract reasoning.

Algebra II & Trigonometry (330)
Prerequisites: Algebra I and Geometry
After a brief review of elementary algebra, this course proceeds to the study of linear functions and relations, systems of linear equations and inequalities, graphs, polynomials and rational algebraic expressions, radicals and irrational numbers, complex numbers and polynomial functions, quadratic relations and systems, exponents and logarithms, and a substantial treatment of trigonometry. Graphing calculators are used in the course to enhance understanding and to facilitate the investigation of more sophisticated problems.

Algebra II & Trigonometry Honors (331)
Prerequisites: Algebra I, Geometry, and departmental approval
The Honors sections cover the topics in Algebra II & Trigonometry in greater depth and also cover a number of additional topics such as advanced graphing techniques, matrices, analytic trigonometry, and graphing in three dimensions.



Elective Courses (Grades 11 and 12)

Precalculus Options
To accommodate the interests and abilities of individual students, the Department offers three levels
of precalculus to those who have earned at least a C- in Algebra II & Trigonometry. Students who wish to continue their study of traditional mathematics should elect a precalculus course to be taken in the year after Algebra II & Trigonometry. These courses may lead to a calculus elective in the senior year.

Precalculus (340)
Prerequisite: Algebra II and Trigonometry
Using a discovery approach and developing problem-solving skills, this course addresses such advanced topics as polynomial, trigonometric, exponential, and logarithmic functions, and transformations. The more abstract topics of a traditional precalculus course are omitted. With the help of graphing calculators, students gain insight into the concept of a function, exploring the relationship between algebraic and graphical representations of functions and investigating applications to real-life situations. Similar in pace to Algebra II and Trigonometry, this course leads to Contemporary Calculus in the senior year.

Precalculus AB (341)
Prerequisite: A minimum grade of B+ or better in Algebra II and Trigonometry, and departmental approval
This course presents a more theoretical study of the topics covered in Precalculus. Skills in mathematical analysis and mathematical notation to be used in calculus are emphasized. Topics in probability and data analysis are also included. This course, with departmental approval, may lead to Advanced Placement Calculus AB in the senior year.

Precalculus BC Honors (342)
Prerequisites: Algebra II and Trigonometry Honors or departmental approval
A highly theoretical, rigorous approach to the study of algebraic and transcendental functions, this course includes the study of differential calculus and leads, with departmental approval, to Advanced Placement Calculus BC. Topics in number theory, probability and vector analysis are also included. The computer and graphing calculators are used to encourage exploration and enhance problem solving.

Contemporary Calculus (350)
Prerequisite: Successful completion of any precalculus course and departmental approval
This course is based upon the curriculum developed by the North Carolina School for Science and Mathematics. The graphing calculator is used as a tool to explore the topics included in a traditional introductory calculus course: functions and their graphs; limits; the derivative and its applications; definite and indefinite integrals; and logarithmic, exponential, and trigonometric functions. In addition, students study topics not usually accessible in traditional calculus courses. Through calculator exercises the student analyzes problems and discovers underlying concepts. The calculator is also used in class to help students gain insight into the principles of calculus, appreciate the relationship between the geometric and algebraic representation of concepts, and take advantage of numerical methods.

Advanced Placement Calculus AB (351)
Prerequisites: A minimum grade of B+ in Precalculus AB, and departmental approval
Meets every day
This course in preparation for the Calculus AB examination of the College Board includes the concepts of differentiation and integration with applications to rates of change, optimization problems, area, and volume. One semester of college calculus credit may be earned from this course.

Advanced Placement Calculus BC Honors (352)
Prerequisites: Precalculus BC Honors and departmental approval.
Meets every day
The culmination of the honors sequence in mathematics, this course is taken in preparation for the Calculus BC examination of the College Board. All of the work covered in Calculus AB is included as well as additional topics in special methods of integration, infinite series, polar coordinates, arc lengths, applications to work problems, and vectors and parametric equations. Two semesters of college calculus credit may be earned from this course.

Probability, Statistics and Social Science (355)
Prerequisite: Algebra II and Trigonometry
In this course students explore a fascinating branch of mathematics as they use probability and
statistics to explain and predict the human condition in a broad range of social science applications. Using advanced statistical methods, they analyze data and draw conclusions about important contemporary topics.

Advanced Placement Statistics (356)
Prerequisite: Precalculus and departmental approval
This Advanced Placement course is more intensive and theoretical than Probability, Statistics and Social Science, while providing significant applications to the biological and physical sciences. The purpose of the course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will use the computer as the fundamental tool of data analysis.