Upper School Mathematics

The Math department's goal is to give each student the very best mathematics education possible, taking into consideration ability, interest, and necessary preparation for success in college and in life. Each teacher strives to instill the confidence necessary to extend the students' horizons into new areas of mathematically related study such as science, and each hopes to foster independent study and continued interest in mathematics. Competent use of technology is taught throughout the curriculum. The TI-84 graphing calculator, in particular, is an integral tool at all levels of instruction. The minimum requirement for graduation is three years of mathematics in the Upper School, however, the department encourages students to take mathematics during all four years. 

 

ALGEBRA I
Full year, one credit
Algebra I introduces the student to the basic structure of algebra and the real number system. It helps her recognize how the techniques developed are used to formulate a mathematical system. Students will be introduced to the role of deductive reasoning and will appreciate the need for precision of language. Solutions of linear equations and inequalities in one and two variables, graphing of functions, products and factors, fractions and fractional equations, and quadratic equations are a few of the topics stressed. 

GEOMETRY
Full year, one credit, Prerequisites: Algebra I 
Geometry is the study of various plane figures, such as points, lines, angles, and circles as well as some simple three-dimensional interrelationships. The course emphasizes proof and deductive reasoning throughout, using a traditional development of geometry as a system of logical thought. Topics from Algebra I are reviewed continuously and applied in a wide variety of geometric settings.

HONORS GEOMETRY
Full year, one credit, Prerequisites: Algebra I and department approval
This course is designed for the student who is able to move at a faster pace and who desires to go into the subject in greater detail. The content of the course is the same as Geometry; however, many enrichment problems are provided.

ALGEBRA II
Full year, one credit, Prerequisites: Algebra I and Geometry
The purpose of the second-year algebra course is to offer the student a sound development of the structure of the real number system. Within this development, the skills from the first-year algebra course are reviewed, consolidated, and expanded to lay a solid foundation for future work in mathematics. Among the topics considered are linear and quadratic relations and functions, matrices, exponential and logarithmic functions, complex numbers and an introduction to trigonometric functions.

HONORS ALGEBRA II
Full year, one credit, Prerequisites: Algebra I, Geometry, and department approval
Honors Algebra II is an algebra course designed for students who desire an enriched and rapidly paced second year of algebra. In addition to topics covered in a regular algebra class, this class also includes sequences, series, and an in-depth study of trigonometry. Students in Honors Algebra II constantly make connections to topics covered in precalculus, thus seeing mathematics as a whole rather than as a collection of isolated topics.

PRECALCULUS
Full year, one credit, Prerequisite: Algebra II or Honors Algebra II
The precalculus course is designed for students who have completed Algebra II or Honors Algebra II. Various types of functions are studied, including polynomial, exponential, logarithmic and circular functions. In addition to trigonometry, analytic geometry with vectors is covered. Special attention is given to mathematical modeling of real world problems. Concepts are developed through the use of technology, especially graphing calculators. This course prepares a student for calculus.

HONORS PRECALCULUS
Full year, one credit, Prerequisites: Honors Algebra II and department approval
This course is designed for students who desire an enriched and rapidly paced course. The content is the same as Precalculus with some added topics. Additionally, students will begin the study of calculus, enabling them to take AP Calculus BC the following year.

STATISTICS
Full year, one credit, Prerequisites: Algebra II and department approval
Important topics in the study of statistics will be introduced, including exploratory data analysis and probability. Some work on statistical design of experiments and the use of statistical inference will be pursued through hands-on projects and research. Graphing calculators with their specific statistical functions will be used on a daily basis and the internet will provide many resources for data and critical analysis.

COLLEGE ALGEBRA AND TRIGONOMETRY
Full year, one credit, Prerequisites: Algebra II or Statistics and department approval
Designed to provide students with a further opportunity to refine and enhance their algebraic problem-solving skills prior to college math courses, College Algebra and Trigonometry will focus on functions, including exponential, logarithmic, and trigonometric functions. College Algebra and Trigonometry will be an additional choice for students in their junior or senior year following Algebra II or Statistics.

AP STATISTICS
Full year, one credit, Prerequisites: Algebra II and department approval
This course is equivalent to the one semester introductory statistics course offered by most colleges and required for many majors including psychology, sociology, health sciences, and business. Topics include exploratory data analysis, planning an experimental study, probability, and statistical inference. Graphing calculators are used daily and statistical software is introduced periodically. Open-ended problems, projects, and communication of results are emphasized. Students enrolled in the AP course are required to take the AP Statistics exam in May. 

CALCULUS
Full year, one credit, Prerequisites: Precalculus and department approval
Calculus covers the majority of the material in AP Calculus AB, but students do not take the AP exam. Students taking Calculus will be well prepared for a rigorous college-level calculus course.

AP CALCULUS AB
Full year, one credit, Prerequisites: Precalculus or Honors Precalculus and department approval
Calculus with analytic geometry follows Precalculus. Calculus gives methods of solving two large classes of problems: 1) finding the instantaneous rate of change of a variable quantity (differential calculus) and, 2) evaluating a product in which one factor varies (integral calculus). This course follows the AP Calculus AB curriculum. Students enrolled in the AP course are required to take the AP Calculus AB exam in May.

AP CALCULUS BC
Full year, one credit, Prerequisites: Honors Precalculus and department approval
This course includes all of the material covered in the AP Calculus AB curriculum with the addition of the calculus of variable factor products and the calculus of functions defined by power series. Students enrolled in the AP course are required to take the AP Calculus BC exam in May.

HONORS MULTIVARIABLE CALCULUS and DIFFERENTIAL EQUATIONS
Full year, one credit, Prerequisites: AP Calculus BC and department approval
These courses will be offered through the One Schoolhouse. The tuition for these courses will be covered by Harpeth Hall. Multivariable Calculus is offered in the fall; Differential Equations is offered in the spring.  Learn more about these courses.

INTRODUCTION to COMPUTER SCIENCE
One semester, one-half credit: open to sophomores, juniors, and seniors
This course is an introduction to coding and computer science. Students will learn how to create all kinds of computer graphics and visual effects using the Processing coding language. They will also study HTML (HyperText Markup Language) to understand how the web works and how to create their own web pages. Finally, they will explore how computers can interact with the physical world in a unit on robotics. By the end of the course, students should have a firm foundation in coding, HTML and web design, and simple robotics.

AP COMPUTER SCIENCE A
Full year, one credit; open to sophomores, juniors, and seniors 
Prerequisites: Introduction to Computer Science, enrollment in Honors Algebra II or higher, or departmental permission
This course follows the Advanced Placement course description for Computer Science A and is roughly equivalent to a one-semester college programming course. The course emphasizes object-oriented programming methodology with an emphasis on problem solving and algorithm development. It also includes the study of data structures and abstraction. Because the AP exam tests use of the Java programming language, this course will be taught using Java as the programming language. Students enrolled in this course are required to take the AP Computer Science A exam in May.

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