MATHEMATICS DEPARTMENT
Upper School Math Honors Courses: All students are required to finish Algebra 2 in their mathematics study. Based on prior achievement, students will be placed in Regular or Honors sections. The Honors student may remain a member of that program by maintaining a B minimum grade annually. The Regular student is required to achieve a minimum grade of C- for the year-end grade in order to proceed in the sequence courses. Honors level courses differ from Regular in terms of depth of coverage, difficulty of problem material and number of topics covered as well as supplementary topics.
ALGEBRA I
This is a one-year upper school course in the structure and method of elementary algebra. This course emphasizes the reading and writing of mathematics, providing a wide variety of meaningful problem-solving opportunities. Four dimensions of understanding are emphasized to maximize performance: skill in carrying out various algorithms; developing and using mathematics properties and relationships; applying mathematics in realistic situations; and representing or picturing mathematical concepts. The content of the course addresses algebraic equations, inequalities, and coordinate geometry. It includes detailed work on the mechanics of polynomials, rational expressions and factoring.
GEOMETRY
This course combines algebra with the study of transformations, shapes, and logical deduction. Using a hands-on approach, students apply geometric tools throughout the course in discovering the theorems relating to reflections, rotations, and dilations of geometric figures. Formal proofs are introduced at midyear and primarily involve isometries, congruence, and symmetry relations. Area and volume receives special emphasis in the spring quarter.
Eligibility: C or better in Algebra I.
GEOMETRY HONORS
This is a one-year course in the basic figures of geometry and the nature of proofs, including work with points, lines, angles, polygons, and circles. Algebraic skills will be applied to solving problems in plane and space geometry, trigonometry, area, and volume. Emphasis will be on problem solving and applications. The course will also include development of conjectures into theorems.
Eligibility: Recommendation of middle school teacher or successful completion of freshman Algebra 1 with a minimum grade of B+ and recommendation of the teacher.
ALGEBRA II
This course extends the ideas and skills covered in Algebra I, introducing the key concept of functions and independent/dependent variables. During the year, the students learn to use sequences, linear systems, quadratic functions, matrices, exponential and logarithmic functions, and basic trigonometry. Throughout the course, there is an emphasis not only on conceptual understanding of the material, but also on its practical use and representational power.
Eligibility: A grade of C or better in Algebra I or recommendation of the Upper School Head.
ALGEBRA II HONORS
This course includes the topics in Algebra II but also adds geometric and arithmetic series, conic sections, trigonometric graphs, probability, and combinatorics. The course is designed for motivated students who seek a challenging course and who are able to learn mathematics at a higher than average rate.
Eligibility: B or better in Algebra I and Honors Geometry or the recommendation of the teacher.
ALGEBRA III
This course integrates ideas of functions and trigonometry with statistics, probability theory, and data analysis. The course begins with statistical analysis, a branch of mathematics that is relatively new and increasingly important in this age of information and computers. Then, concepts typically associated with functions, such as linear and quadratic modeling, transformations, compositions, inverses, polynomials, and exponential/logarithmic modeling are extended beyond what is covered in Algebra 2. Many of these extensions are done with the aid of a calculator having graphics and statistical capabilities. Once functions are mastered, students are ready to extend their knowledge of sequences and series, which ties in directly to probability concepts such as permutations, probability distributions, combinations and binomial probabilities. Amidst the statistics and functions, students are for the first time exposed to trigonometry and its many practical applications.
Eligibility: Successful completion of Algebra 2 with a minimum grade of "C" or recommendation from the Upper School Head
PRECALCULUS HONORS
This course lays the groundwork for the further study of mathematics by building a strong foundation of standard precalculus topics. These topics include functions and their properties, graphs, polynomials, exponents and logarithms, trigonometry, complex numbers/polar coordinates, vectors, sequences and series, and combinations. The course is fast paced and as such, designed for those students who are motivated in mathematics and seek a challenge. Successful completion of this course will set the stage for a smooth transition into the Advanced Placement Calculus program.
Eligibility: Successful completion of Algebra 2 Honors with a minimum grade of "B-" or successful completion of Algebra 3 with a minimum grade of "B+" and the consent of the instructor.
PRECALCULUS
This course is a gentler version of Precalculus Honors, covering much of the same material, but at a gentler pace and with less rigor and depth than the Honors version.
Eligibility: C+ or better in either Algebra III or Algebra II Honors.
CALCULUS AB ADVANCED PLACEMENT
This course follows the AB Calculus syllabus recommend by the Advanced Placement Program. It is primarily concerned with developing an understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Through the use of the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated
topics. The mastery of the cohesive whole will be assessed through the Advanced Placement exam in May. Students enrolled in this course are required to take the Advanced Placement exam.
Eligibility: Successful completion of Precalculus Honors with a minimum grade of "B" and the instructor's consent.
FINITE MATHEMATICS
This course is a one-year elective for students who have completed Algebra III and want a mathematics course that involves topics not generally covered in pre-calculus. The course includes (1) geometric constructions leading into sacred geometry, graphic design, and geometric patterns, (2) musical harmony, (3) game theory, (4) graph circuits and their relation to planning and travel, (5) voting, (6) apportionment, and (7) the applications of matrices. This course is not heavy in abstract mathematics and should be accessible to any student who has a C or better in Algebra III. Much of the work consists of hands-on exploration and projects.
Prerequisite: C or better in Algebra III
ENGINEERING CONCEPTS AND DESIGN
This course aims to expose students to introductory engineering concepts through the design and construction of a mini-electric vehicle. Academic disciplines including applied mathematics, physics, technical writing, vocational technology, and business economics will be integral requirements of the course. This year-long course will culminate with an endurance race in competition against other participating high school teams.
Prerequisite: Algebra II
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