Algebra and Geometry • Intermediate Electives • Advanced Electives • Teaching Assistants

Algebra and Geometry

Algebra I
This is a comprehensive course in which students master fundamental algebraic topics and techniques. These include evaluation and simplification of algebraic expressions, solving and graphing linear equations, linear systems, operations with polynomials, radical and rational expressions, and factoring. Throughout the course students encounter many opportunities to gain problem-solving skills and number sense. Students use manipulatives to gain an understanding of abstract concepts. Those who successfully complete this course enroll in Algebra II/Geometry, Year One, the following year.

Algebra II/Geometry, Year One
This course introduces and integrates concepts of geometry and intermediate algebra using an inductive approach. Geometer’s Sketchpad and Fathom computer programs, a graphing calculator, and manipulative tools such as patty paper, compass and straightedge are used to help students discover fundamental geometrical and algebraic relationships. Topics include properties of parallel and perpendicular lines, triangle, polygon, and circle properties, right triangle trigonometry, transformations, linear and quadratic functions, arithmetic sequences, variation, proportion, and similarity. Coordinate geometry is emphasized throughout. If time allows, students will also study some elementary statistics, including measures of central tendency and fitting data to a line. Prerequisite: Algebra I or the equivalent.

Accelerated Algebra II/Geometry, Year One (honors level)
This course will cover all of the topics of Algebra II/Geometry, Year One, at an accelerated pace and a greater level of depth. We will place extra emphasis on deductive reasoning and the role of proof in mathematics. Additional topics may be included. Prerequisite: Algebra I or the equivalent; consent of the instructor and the department chair.

Algebra II/Geometry, Year Two
This course is the second in a two-year sequence and continues to integrate geometry and intermediate algebra concepts, but now using deductive reasoning. Students write various forms of formal proofs in order to establish many of the geometrical and algebraic conjectures they formed in the previous course, as well as additional principles. New topics include congruent triangles, inequalities in triangles, solid geometry, real number exponents, inverse functions, higher degree polynomial functions, exponential and logarithmic functions, complex numbers, Pythagorean proofs, rational functions, and coordinate geometry proofs. Prerequisite: Algebra II/Geometry, Year One, or the equivalent.

Accelerated Algebra II/Geometry, Year Two (honors level)
This course will cover all of the topics of Algebra II/Geometry, Year Two, at an accelerated pace and a greater level of depth. Additional topics may be included. Prerequisite: Algebra II/Geometry, Year One, or the equivalent; consent of the instructor and the department chair.

Intermediate Electives

One intermediate elective is offered each year. The prerequisite for all intermediate electives is completion of Algebra II/Geometry, Year Two, or the equivalent.

Descriptive Statistics (offered 2012-2013)
This class covers many topics studied in an introductory non-calculus-based college-level statistics course. Students observe and describe patterns and departures from patterns through the exploration of data, select appropriate data and data-gathering techniques to create an effective study, and produce models of commonly occurring patterns through the use of probability and simulation. If time remains, the course introduces the topic of statistical inference. Students design their own studies, for which they collect and analyze data. Both calculator and computer are used extensively as tools in this course. Descriptive Statistics does not prepare students for the Advanced Placement Statistics exam, as it omits transformations and many hypothesis tests.

Discrete Mathematics
This course will cover a wide variety of mathematical topics and is designed for students who do not wish to continue their study of mathematics at the precalculus level. Sometimes the course is called “Finite Mathematics,” as little knowledge of continuous functions and their properties is required to do well in the course. Students need to be prepared to think carefully and be willing to engage in a substantial amount of problem solving.  The course will draw material from areas such as graph theory, probability and combinatorics, statistics, computer programming, game theory, set theory, logic, cryptography and number theory.

Probability and Statistics
This course is designed for students who do not wish to continue their study of mathematics at the precalculus level. Students learn to describe data, explore various probability distributions, and study issues concerning experimental design. Emphasis is placed on critiquing real-world statistical information.

Trigonometry
This course is designed for students who do not wish to continue their study of mathematics at the precalculus level. Students will focus on triangular and circular trigonometry and their applications. Topics include right-triangle relationships, laws of sines and cosines, vectors, real-valued trigonometric functions and their graphs, and elementary identities. Real-world applications are stressed.

Advanced Electives

Precalculus
A short review of the concepts of functions and their properties is followed by a thorough study of circular and triangular trigonometry. Students study conic sections, logarithmic and exponential functions, the graphs of rational functions, Binomial Theorem, arithmetic and geometric series and sequences, polar coordinates, 2-D vectors, polynomial graphs and functions, and parametric equations. Students use paper, pencil, and graphing calculators. Completion of this course prepares students to take Statistics and/or Calculus I. Prerequisite: Algebra II/Geometry, Year Two, or the equivalent.

Accelerated Precalculus (honors level)
Topics covered include all of those listed for Precalculus. In addition, Accelerated Precalculus includes three-dimensional vectors, DeMoivre’s Theorem, and mathematical induction. This course is for students who have a strong interest in mathematics and want to pursue advanced topics in great depth. Students are prepared to take Statistics and/or Calculus I upon successful completion of this course. Prerequisite: Algebra II/Geometry, Year Two, or the equivalent.

Honors Statistics (honors level)
This course is similar to an introductory non-calculus-based college-level statistics course. Students observe and describe patterns and departures from patterns through the exploration of data, select appropriate data and data-gathering techniques to create an effective study, produce models of commonly occurring patterns through the use of probability and simulation, and confirm models through statistical inference. Students design their own studies, for which they collect and analyze data. Both calculator and computer are used extensively as tools in this course. Students are prepared to take the Advanced Placement Statistics Examination in May. Prerequisite: Algebra II/Geometry, Year Two, or the equivalent.

Calculus I  (honors level)
Students enrolling in this course are assumed to have strong fundamental algebra and precalculus skills. Topics include limits, continuity, derivatives, integrals and their applications, slope fields, and separable differential equations. Concepts are approached through a three-step process: graphically, numerically, and analytically. Graphical analysis plays a major part in the development of many concepts. Students are prepared to take the Advanced Placement Calculus AB exam in May. Prerequisite: Precalculus or Accelerated Precalculus.

Calculus II (honors level)
This course is a continuation of Calculus I and includes infinite sequences and series; parametric, polar, and vector function calculus; slope fields; Euler’s method; L’Hôpital’s rule; improper integrals; integration techniques; and an introduction to differential equations. If time permits, multivariable calculus is introduced. Students are prepared to take the Advanced Placement Calculus BC exam in May. Prerequisite: Calculus I or the equivalent.

Multivariable Calculus (Global Online Academy; fall semester)
In this course, students will explore vector algebra and functions, matrices, curves in space, arc length and curvature, and velocity and acceleration. Further topics include partial differentiation, local extrema, exact differentials, the chain rule, directional derivatives, gradients, double and triple integration, line integrals, and volume. Students must have access to a computerized 3-D graphing utility, such as Grapher (a standard utility on Mac computers) or Autograph, and must be comfortable using learning to use new technology independently. Prerequisite: Calculus I. Note: This is an online course.

Teaching Assistants

Math Teaching Assistants
Teaching assistants are vital contributors to our algebra and geometry classes. TAs attend class each day, help students with practice problems and resolve homework difficulties, answer questions, and grade daily homework. In addition, they run review and extra-help sessions. As the year progresses, TAs plan and teach full lessons to the class. Upon completion of the year, students will receive one math credit. Prerequisite: Invitation of the department.