Upper School Course of Study: Mathematics

The mathematics department offers two different sequences of courses designed to meet the needs of students with diverse skills, interests, and career aspirations. Two Advanced Placement courses are available to students who desire to earn college credit: AB Calculus and Statistics. In all math courses, teachers incorporate extensive use of graphing calculators as well as instructional manipulatives. Students learn problem-solving techniques through real world and cross-curricular applications. Throughout their studies, students will use the proper language and symbols of mathematics. Additionally, students have the opportunity to participate in the Virginia Mathematics League contests.

COURSE OF STUDY 2009-10

(All courses are not offered every year.)

MATHEMATICS

Algebra 1 (full year) (one high school credit) (course number 101)
This is the traditional college preparatory course that serves as a foundation for subsequent math courses.  Arithmetic skills and reasoning skills are developed, including arithmetic with integers and rational numbers, and solving and graphing linear functions and inequalities.  Students master operations with monomials and polynomials, and they use that knowledge to factor polynomials and solve quadratic equations. The students are introduced to radical equations and probability.  Problem solving is integrated throughout the course as connections to other subject areas are made through practical applications.  Models, manipulatives, and technology, including the graphing calculator, are used when appropriate. Students are expected to use the language and symbols of mathematics.

Algebra 1, Part 2 (full year) (course number 118)
This class is intended for the student who has satisfactorily completed Algebra 1, Part 1.  It is an in-depth exploration of linear and non-linear equations, polynomials, and radical and rational functions.  It serves as a foundation for subsequent math courses.  Students are expected to use the language and symbols of mathematics.  Models, manipulatives and technology, including the graphing calculator, are used when appropriate.

Geometry (full year) (course number 105)
This is a traditional study of Euclidian geometry.  Students perform a study of geometric structures, their characteristics and relationships.  The students describe and investigate relationships within a geometric system using definitions, axioms and theorems in that system.  Formal proofs and practical applications are used.  This course is designed for students who have acquired the skills of Algebra I and includes an introduction to trigonometry.

Honors Geometry (with permission) (full year) (course number 109)
This course is a comprehensive study of Euclidean geometry.  Students perform an in-depth study of geometric structures, their characteristics and relationships.  The students describe and investigate relationships within a geometric system using definitions, axioms and theorems in that system.  Emphasis is placed on mathematical argumentation through formal proofs and practical applications.  This course is designed for students who have mastered the skills of Algebra I and includes an introduction to trigonometry.

Informal Geometry (full year) (course number 111)

The goal of this course is to teach students to think more analytically so that they can apply these skills to problems involving space. Students explore angles and shapes, particularly triangles and quadrilaterals, and identify characteristics of each shape. Finally, they learn to attack challenging SAT-style problems involving perimeter, circumference, area and volume.

Advanced Algebra (with permission) (full year) (offered to students who have completed Geometry) (course number 112)
This traditional algebra course includes a comprehensive study of advanced algebra topics including absolute value, rational, logarithmic, exponential and trigonometric functions, and trigonometry.  Modeling real world applications is a major component of this course.  This course moves at a rapid pace to prepare students for the rigors of Pre-Calculus. 

Algebra II (full year) (course number 102)
This course provides the mathematical base for higher levels of math.  This course is intended to introduce students to different approaches to solving equations and inequalities, including systems of equations and inequalities, and to help students get a deeper understanding of linear relations and elementary functions.  Throughout the course, the students explore quadratic and polynomial functions and develop skills in graphing those functions.  Modeling real world applications is a major component of this course.  Students in this class take Algebra III and Statistics the following year.

Algebra III (semester course) (course number 116)
This course is intended for students who have studied Algebra II through Quadratic Equations.  This one semester course is devoted to advanced algebra, beginning with a review of quadratic equations and their applications.  Students build on their knowledge of quadratic equations through study of polynomial and inverse functions.  They then progress to exponential and logarithmic functions and use their knowledge of these functions to solve growth and decay problems.  Students study triangle trigonometry and develop basic knowledge of the six basic trigonometric functions and their relationships.  They also tackle sequences and series, arithmetic and geometric, finite and infinite, their properties and their applications to problem resolution.   Throughout the course, students are encouraged to use the language and symbols of mathematics.

Statistics (semester course) (course number 114)
This course is intended for students who have completed Algebra II through Quadratic Equations.  This one semester course covers introductory statistics and probability.  Topics include experimental design, measures of central tendency, correlation and regression, and probability and chance variability.  Varied sampling methods are discussed as well as different graphing techniques.  Interpretation of data is stressed.  Statistical applications to a wide variety of subjects, such as the social sciences, economics, and business, are stressed.  Students perform a statistics project, including appropriate graphs and calculations for in-class presentation.  The graphing calculator is used extensively throughout the course while a balanced approach of numerical and logical methods is emphasized.  Throughout the course, students are encouraged to use the language and symbols of statistics.

Pre-Calculus (full year) (course number 110)
This course provides the mathematical background for a calculus class. It is a course intended for students who have a solid working knowledge of Algebra and have basic knowledge of Trigonometry. This rigorous course is intended to develop skills in graphing linear and non-linear function using different methods, get a deeper understanding of different kinds of functions and their applications, extend the understanding of trigonometry and master skills in solving equations and inequalities. The course focuses on skills and concepts and their applications in real life by using models, relating to other subjects, and conducting real life projects. This course enables students to approach a problem algebraically and graphically. Students develop their quantitative thinking, reasoning, algebraic and graphical skills.

Honors Pre-Calculus (with permission) (full year) (course number 103)
This course provides the mathematical background for the AP calculus class and is a prerequisite for AP Calculus.  It is intended for students who have mastered Algebra and have a working knowledge of Trigonometry.  Students explore all of the topics of Pre-Calculus, but at a faster pace and in more depth.  Students in the Honors class also learn to solve problems analytically by exploring analytical trigonometry and analytic geometry.

Differential Calculus (full year) (course number123)
This course is intended for students who have a solid working knowledge of algebra, geometry, trigonometry and elementary functions.  The purpose of the course is to prepare the student for college calculus.  The course covers differentiation of elementary functions as well as applications of calculus to problem solving.  The graphing calculator is used extensively throughout the course while a balanced approach of graphical, numerical and algebraic methods is stressed.  Problem solving is introduced early and integrated throughout as connections to other subject areas are made through practical applications.  Models and technology are used when appropriate.  Throughout the course, students are encouraged to use the language and symbols of calculus.

Advanced Placement Statistics (with permission) (full year) (offered to students who have satisfactorily completed Pre-Calculus or to those who are currently taking Honors Pre-Calculus) (course number 107)
This course is intended for students who have a thorough knowledge of algebra, geometry, trigonometry and elementary functions.  The purpose of the course is to prepare the student for advanced placement into college statistics.  The content of the course is driven by The College Board Advanced Placement Course Development Syllabus.  The graphing calculator is used extensively throughout the course while a balanced approach of graphical, numerical and algebraic methods is stressed.  Students are required to complete a summer reading and problem solution assignment prior to admission into the course.  The assignment is due on the first day of class. Problem solving is introduced early and integrated throughout as connections to other subject areas are made through practical applications.  Models and technology are used when appropriate.  Throughout the course, students are encouraged to use the language and symbols of statistics.

Advanced Placement Calculus AB (with permission) (full year) (course number 104)
This course is intended for students who have a thorough knowledge of algebra, geometry, trigonometry and elementary functions.  The purpose of the course is to prepare the student for advanced placement into college calculus.  The content of the course is driven by The College Board Advanced Placement Course Development Syllabus.  The graphing calculator is used extensively throughout the course while a balanced approach of graphical, numerical and algebraic methods is stressed.  Students are required to complete a summer reading and problem solution assignment prior to admission into the course.  The assignment is due on the first day of class.  Problem solving is introduced early and integrated throughout as connections to other subject areas are made through practical applications.  Models and technology are used when appropriate.  Throughout the course, students are encouraged to use the language and symbols of mathematics.

Advanced Placement Calculus BC (with permission) (full year) (course number 126)

BC Calculus is similar to AB Calculus except that it is more rigorous and covers three semesters of college calculus versus two.

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