Mathematics Department

of three units: fiction, poetry, and creative non-fiction. Students will analyze published works and produce their own writing in each of these genres. Writing skills will be developed through pre- writing, editing, revising, and critiquing. Upon completion of the course, students will be able to identify successful elements of an effective piece of creative writing, participate in a writing community, and express themselves with originality and clarity in stories, poetry, and personal essays.

All students are required to enroll in a math course each of their four years in high school. Students must complete a minimum of four units: Algebra I, Algebra II, Geometry, and Pre-Calculus or Trigonometry and Analysis. Those students who successfully complete Algebra I in grade 8 must still complete four years of mathematics during upper school. A teacher recommendation, high averages in prerequisite courses, and a strong performance on standardized tests are required for all Honors and AP courses.

MATHEMATICS (4 CREDITS REQUIRED)

The mathematics curriculum is designed so that students learn to: • Read, write, and orally communicate mathematical concepts. • Organize, analyze, depict, and interpret data to make decisions and predictions related to real-world situations. • Solve theoretical and practical problems using essential concepts of algebra, geometry, probability, and statistics. • Comprehend the relationships between mathematics, sciences, and technology. Topics in each class are presented numerically, graphically, analytically, and verbally to enhance the learning experience. AP courses in calculus and statistics follow the topic outlines set by the College Board for their respective disciplines. Graphing calculator competencies increase with each grade level, and students are exposed to the latest math software each year.

COURSE OPTIONS:

Algebra I Algebra II or Algebra II (H) Geometry or Geometry (H) Pre-Calculus or Pre-Calculus (H) Calculus or AP Calculus (AB & BC) AP Statistics Trigonometry and Analysis (12th grade only)

ALGEBRA I

1 Credit

This introductory course is intended to build the foundation for further study in symbolic mathematics. The major concepts introduced will be simplifying expressions; solving equations, inequalities, and systems of equations in two or more variables; factoring polynomials; simplifying rational expressions; problem solving; defining, graphing, and exploring domains and ranges of functions; and simplifying radical expressions. Students will explore data using regression analysis and use their regression equation to make predictions. Graphing calculators will be used to solve problems, experiment with data, and verify conclusions. Trigonometry and geometry are also explored on an introductory level.

ALGEBRA II

1 Credit

A thorough review of topics from Algebra I comprises the first part of this course. More extensive study is given to the topics of radicals and complex numbers, linear and quadratic equations, and problem solving. New concepts studied include conic sections, logarithmic and exponential functions, sequences and series, matrices, probability, and statistics. Mathematical modeling through regression analysis will be explored on a deeper level than in Algebra I. Trigonometry will also be explored in a more formal and extended fashion including graphs of the trigonometric functions with transformations.

ALGEBRA II (H)

1 Credit

Algebra II Honors covers much of the same material as the regular Algebra II class with a more rigorous approach to the study of those topics as well as further topics from geometry and trigonometry. Specifically, students will look more closely at functions defined by tables, graphs, and equations, and utilize mathematical modeling more extensively. New concepts will be introduced numerically, graphically, analytically, and verbally whenever possible. Additional graphing calculator competencies will include solving systems of linear equations using matrices, finding roots of equations, solving non-linear systems of equations, and maximizing/minimizing graphs of functions.

GEOMETRY

1 Credit

This course is designed to emphasize the study of the properties and applications of common geometric figures in two and three dimensions (plane and solid geometry). It includes the study of transformations of plane figures and right triangle trigonometry. Inductive and deductive thinking skills are used in problem solving situations, and applications to the real world are stressed. This course also emphasizes writing proofs in various forms to solve (prove) properties of geometric figures.

GEOMETRY (H)

1 Credit

Honors Geometry covers the curriculum of the college preparatory geometry course, but the scope is much broader. In addition to the familiar topics, students will explore more challenging logic problems and write more extensive proofs. Analytic geometry will be explored in depth in preparation for more advanced math courses. Advanced mathematical concepts from Pre-Calculus and Calculus will also be introduced at an introductory level.

PRE-CALCULUS

1 Credit

This course in advanced mathematics provides an extensive and extended study of both algebraic and geometric concepts, with major emphasis on trigonometry, conic sections, functions and

their graphs, and probability. The basic concepts of analytic geometry, including continuity and limits of functions, and the definition of the derivative are also introduced. Students will explore the representation of patterns using arithmetic and geometric sequences and series, including the use of sigma notation to represent series.

PRE-CALCULUS (H)

1 Credit

This course is designed for students who plan to take calculus, either during senior year or in college. Pre-Calculus Honors is a program of mathematical studies focusing on the development of the student’s ability to comprehend and apply the study of functions and advanced mathematics concepts to solve problems. The course will include an in-depth study of polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as an introduction to sequences and series, parametric and polar equations, probability, and limits. Emphasis is placed on active participation through modeling, group activities, and communication in mathematics.

CALCULUS

1 Credit

This mathematics course is ideally suited for students interested in business and economics, life sciences, and social sciences and who have met the prerequisites for a calculus course but do not choose to take AP Calculus. Limits, differentiation, and integration are studied in the same depth as most first semester college calculus courses. Students are also given a brief introduction to solving differential equations by separation of variables. Students are encouraged to investigate mathematical ideas and processes graphically, numerically, algebraically, and verbally. Mathematical modeling and making predictions from models will be further explored, and graphing calculator technology will continue to be utilized when appropriate.

AP CALCULUS AB

1 Credit

This course is intended for students who are preparing for the advanced placement calculus exam. The course begins with an extensive exploration of elementary functions with an emphasis on the relationships between functions and their graphs, and students will be introduced to the concept of families of functions. Both differential and integral calculus of a single variable are explored. Theory and application are emphasized equally. Students are encouraged to look at mathematical ideas and processes numerically, graphically, analytically, and verbally. Emphasis will be placed on both the mechanics and the interpretation of differential and integral calculus. Students will become proficient with the entire range of their graphing calculator’s capabilities. Students taking this course will be expected to take the advanced placement exam in calculus for the purpose of receiving college credit in calculus.

AP CALCULUS BC

1 Credit

Like Calculus AB, this course is intended for students who are preparing for the advanced placement exam. In addition to the topics covered in AP Calculus AB, students will also be introduced to analysis of planar curves given in parametric, polar, and vector form; slope fields; Euler’s method; antiderivatives by substitution, parts, and simple partial fractions; logistic equations; Taylor polynomial approximations; and Taylor and Maclaurin series. The content of Calculus BC is designed to qualify students for placement and credit in a course that is one level beyond that granted for Calculus AB.

AP STATISTICS

1 Credit

The purpose of this AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will explore data (describing patterns and departures from patterns), sample and experiment (planning and conducting a study), anticipate patterns (exploring random phenomena using probability and simulation) and statistical inference (estimating population parameters and testing hypotheses. Students may take AP Statistics as a second math course—with teacher recommendation—after successfully completing Algebra II. Students can also take AP Statistics as their only math course during their senior year.

TRIGONOMETRY AND ANALYSIS

1 Credit // Grade 12

This course provides a general overview of mathematics aimed at those seniors who will be majoring in the liberal arts, education, social sciences, business, nursing, and allied health fields. Students will study topics covered in a normal pre-calculus course with additional scaffolding in place. The core components of the course will center on evaluating all trigonometric functions in any radian measure using the unit circle, graphing and identifying key features of sinusoidal functions, and modeling using trigonometry. The analysis portion of the course will take the families of functions and explore features of each family. Other topics include the study of complex numbers, combinatorics, and sequences and series. Students who have had both Pre-Calculus and Trigonometry and Analysis will also be well-prepared for a college-level course in calculus should they choose to take it after entering college.