MATHEMATICS. Mathematics is required through the completion of pre-calculus or a full year of statistics as recommended by the math department.

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1 MATHEMATICS The mathematics curriculum is a sequential study of basic concepts from algebra through calculus. All students are expected to study mathematics until they can demonstrate a satisfactory mastery of algebra, plane geometry, trigonometry, and coordinate geometry. Each student is strongly encouraged to continue the study of mathematics, specifically calculus, in the senior year in preparation for college. Graphing calculators are required in all upper school mathematics courses except geometry. Entering students will be recommended for the correct level of mathematics following a placement examination and if necessary, consultation with the department head. Mathematics is required through the completion of pre-calculus or a full year of statistics as recommended by the math department. Algebra I MA09000 This course is designed to present the structure of algebra and to improve computational skills. Problem solving techniques are developed to deal with the many and varied types of mathematical situations which include properties of real numbers, rational numbers, polynomials, factoring, radicals, inequalities, fractional equations, as well as equations through the roots of the quadratic equation. (Grade 9) Plane Geometry MA09001 Gr. 9 MA10003 Gr. 10 This course presents a formal approach to Euclidean plane geometry with an extension to three dimensions. Balancing theory and application, students learn to correlate plane and solid geometry with the environment. The idea of proof is presented early in the course; students begin to write them as soon as they are able. The process of understanding and writing proofs is supported through lessons on deductive and inductive reasoning. Concepts of space geometry and construction are integrated throughout the course, and algebraic skills are reviewed by applying them to various geometric situations. (Grades 9-10) Prerequisite: Completion of Algebra I Geometry and Algebra With Transformations MA09002 This course offers a unique study of geometry and its relationship to algebra. The focus of the course will be on transformations of geometric shapes and graphs and their corresponding algebraic equations. The study of reflections, rotations, translations and scale changes will result in creative insights into congruency, similarity, slope and other traditional geometric concepts. Students will make use of technology to illustrate and analyze the effects of transformations on geometric shapes and algebraic equations.

2 (Grade 9) Prerequisites: Completion of Algebra and departmental approval Algebra II MA10001 Gr. 10 MA11003 Gr. 11 This course continues the exploration of algebra begun in Algebra I. Its focus will be on the analysis, manipulation, and application of functions. Students will be expected to discover how to create a mathematical model for real world problems as a viable method for problem solving. (Grades 10-11) Prerequisite: Completion of Plane Geometry Functions, Statistics, and Trigonometry MA10002 This course entails a systematic survey of common elementary functions: polynomial, exponential, logarithmic, and trigonometric. Each major type of function is introduced to serve as a model for data arising from one or more real world phenomena. Students will also learn some of the traditional and contemporary techniques for organizing and describing data for the purpose of making comparisons. (Grade 10) Prerequisites: Geometry and Algebra with Transformations and departmental approval Pre-Calculus MA11001 Gr. 11 MA12004 Gr. 12 This course covers topics necessary for the study of calculus and other advanced courses in science and mathematics. A unifying theme in the course is the use of functions to model real world phenomena. Specific math topic areas covered include linear and other types of regression, trigonometry, polynomial functions with an introduction to maximization/minimization questions, exponential and logarithmic functions and their role in linearizing data sets, an introduction to combinatorics and probability, and a brief introduction to instantaneous velocity and the slope of a tangent line to a curve. We also study two-dimensional projectile motion, which involves a blend of trig with quadratic functions. If time permits, complex numbers, sequences and series or conic sections may also be studied. (Grades 11-12) Prerequisite: Completion of Algebra II Advanced Pre-Calculus MA11002 The main theme of this course is the mathematical analysis of change. Students will experiment and gather data that will lead to a study of various algebraic, trigonometric, exponential, and logarithmic models. Their study will include a brief introduction to the concept of the derivation. Additional topics will include conic sections, vectors, combinatorics and probability. The graphing calculator and computer software will be integral tools in this course. (Grade 11) Prerequisite: Completion of Functions, Statistics, and Trigonometry or completion of Algebra II and departmental approval.

3 Calculus MA12001 This course is an introduction to calculus for students who do not plan to continue their study of abstract mathematics beyond calculus or who expect to take beginning calculus in college. It is not designed to place students out of the first level of college calculus. Rather than delve into proofs, students concentrate on concepts and techniques in order to experience calculus. (Grades 11-12) Prerequisite: Completion of Pre-Calculus or FST and departmental approval. Statistics I MA12102 This course introduces students to data analysis, data collection, and experimental design. Students will often collect and analyze their own data, and the class will frequently discuss and analyze articles in the popular media. Students will use calculators and computers extensively for the numerical and graphical work, learning to interpret the results in context. (Grades 11-12) Prerequisite: Completion of Algebra II First Semester Statistics II MA12203 This is a one-semester course in inferential statistics, which follows Stat I. In this course we will investigate how hypotheses should be formed and tested with statistics. After studying the theory, students will devise their own experiments and carry them out. Computers and calculators will be used extensively. (Grades 11-12) Prerequisite: Completion of Statistics I or departmental approval Second Semester Note: A student may take Stat I and Stat II or just Stat I. These courses are designed for those students who have successfully completed Algebra II. They can come between Algebra II and Pre-calculus or they can be taken after Pre-Calculus instead of Calculus. If a current student in Algebra II chooses to take Statistics, both semesters must be taken to fulfill the MICDS math requirement.

4 Linear Algebra and Group Theory MA12104 During the first half of the course we will explore vector spaces, matrix representations of linear operators, inverse matrices, basis and dimension, change of basis, eigenvalues and eigenvectors, finding eigenvectors and diagonal matrices as a way to reveal hidden structure. The second half of the course will introduce groups, subgroups, quotient groups, group isomorphisms and homomorphisms. We will then briefly explore the theory of equations and the connection between algebraic solutions and field extensions of the rational numbers. Our goal will be to tie everything together with a study of the group of automorphisms of an extension field over a fixed subfield and to see the correspondence between the group structure and the tower of extension fields. (Grades 11-12) Co-requisite: AP BC Calculus First Semester Advanced Topics in Mathematics MA12005 This course is available to a student who has completed all the mathematics courses that the school offers. If a student wishes to continue his/her studies in mathematics s/he must contact the department chair who will, with the Head of the Upper School, determine the requirements and outline the procedure needed to secure approval for this course. This approval is required by May of the preceding year. (Grade 12) Criteria for Recommendation to Advanced Placement (AP) Courses The Mathematics Department will offer the following AP Calculus courses for the school year : AP AB Calculus, AP AB Calculus (Juniors), AP BC Calculus, and AP Computer Science. In addition, AP Statistics will be offered as a senior elective. We will, as a department, make our recommendations using the criteria below. 1. The department usually reserves its recommendation for students with the following grades: AP AB Calculus from Pre-Calculus, A- or better; AP AB Calculus (Juniors) from FST, B+ or better; AP AB Calculus from Introduction to Calculus, B or better; AP BC Calculus from AP AB Calculus (Juniors), B or better; and AP Statistics from Pre-Calculus, B or better. Students may also be recommended for AP Statistics if they have completed, or plan to enroll in an Advanced Placement Calculus course. 2. The department will also use the following criteria to determine a student's readiness to study an Advanced Placement Mathematics course: A facility with algebraic representations and manipulations; an ability to think critically; an ability to process new material and apply that material to new situations; a willingness to meet daily classroom expectations; and a strong interest in mathematics.

5 Advanced Placement AB Calculus (Juniors) MAAP001 The main theme of this course is the mathematical analysis of change. Students will study algebraic, trigonometric, exponential and logarithmic models leading to a discovery of the basic concepts of both differential and integral calculus. This course, which is the equivalent to the first course of college level calculus, prepares students to take the Advanced Placement AB Calculus examination in May. (Grade 11) Prerequisite: Completion of Functions, Statistics, and Trigonometry and departmental approval. Advanced Placement AB Calculus MAAP002 The main theme of this course is the mathematical analysis of change. Students will study algebraic, trigonometric, exponential and logarithmic models leading to a discovery of the basic concepts of both differential and integral calculus. This course, which is the equivalent to the first course of college level calculus, prepares students to take the Advanced Placement AB Calculus examination in May. (Grade 12) Prerequisites: Completion of Advanced Pre-Calculus and departmental approval. Advanced Placement BC Calculus MAAP004 This course, which is equivalent to the first two courses of college level calculus, prepares students to take the Advanced Placement BC Calculus examination in May. It encourages students to explore and to test their own ideas as they study theory, proofs and theorems and engage in active problem solving. (Grade 12) Prerequisites: Completion of MAAP001 and departmental approval. Advanced Placement Statistics MAAP005 This course is an in-depth study of the concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes: exploration of data, experimental design, probability models, and statistical inference. The course is open to juniors and seniors who have demonstrated a good mathematical mind and are willing to work diligently in an AP curriculum. The course may be taken concurrently with a calculus course. Students will use computers and calculators and will learn to write as statisticians. (Grades 11-12) Prerequisite: Completion of Algebra II. No recommendation needed.

6 AP Computer Science MAAP006 This course emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development and is meant to be the equivalent of a first-semester college-level course in Computer Science. It also includes the study of data structures, design, and abstraction, as well as a more formal and in-depth study of algorithms, data structures, design, and abstraction. At the end of this course students will be qualified to take either the Computer Science A or AB examination. (Grades 11-12) Prerequisite: Algebra II with a B or better

7 MATHEMATICS DEPARTMENT POLICY ON DEADLINES AND LATE WORK Late daily homework assignments are noted and if chronic, a note is sent to the advisor. If the assignment is graded, late papers will be assessed a 1/3 grade reduction. Major assignments and/or projects that are late are assessed a 1/3 grade reduction. If the assignment has been returned to the rest of the class, the assignment must be completed without credit. (Specific problems are dealt with on an individual basis.) MATHEMATICS DEPARTMENT POLICY ON PLAGIARISM AND CHEATING Plagiarism is defined in Webster s New World Dictionary as to take ideas or writings from another and offer them as one s own. If you give the impression that the thoughts or words you use are your own and they came from someone else, this is plagiarism. It is acceptable to use a person s ideas or words, but you must give them credit. Examples of cheating are as follows: 1. Looking at another student s paper during a test or quiz. 2. Having written material containing information about the test on your person or in view around your desk. Be sure notebooks and papers are under your desk and out of sight during tests. 3. Asking someone in a different section what was on the test or quiz. 4. Copying homework from another student. 5. Getting information from members of another group when working on a group project. Discussing homework with other students is not cheating. You are encouraged to work with other students on homework and it is not cheating to discuss the process for working a problem if you complete the problem yourself.

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in