Mathematics

ALGEBRA I  Grade 9, 10, 11, 12  (full year)
Prerequisite: 8th Grade Algebra or Pre-Algebra

Students who take this course will study a variety of topics throughout the year.  Equal emphasis is placed on understanding the theoretical properties of algebra and its practical applications.  Topics include: variables; order of operations; integers; solving, graphing, and writing linear equations; solving and graphing linear inequalities; solving systems of linear equations; powers and exponents; quadratic equations; polynomials; factoring; proportions and rational equations; functions; and radicals.

GEOMETRY  Grade 9, 10, 11, 12   (full year)
Prerequisite:  8th Grade Advanced Algebra or Algebra I with “C” or better

This course builds spatial reasoning and logical thinking skills.  The first semester topics include angle relationships, perpendicular lines, parallel lines, congruent triangles and quadrilaterals. Students are also first introduced to the two-column proof and are required to write proofs using their knowledge of the postulates and theorems. In the second semester, additional advanced concepts of polygons are introduced. Examples include similar polygons, right triangles with applications of the Pythagorean Theorem and trigonometry, and circles.  Students will also use properties of area and volume of two and three dimensional shapes, coordinate geometry, and transformations and mappings. 

ALGEBRA II Grade 10, 11, 12 (full year)
Prerequisite: Algebra I and Geometry with “C” or better.
Note: If you didn’t have C or better in Algebra I and Geometry, please register for Fundamental Algebra II.

This course builds upon the Algebra I and Geometry courses, providing greater depth in theory, calculation, and application.  It is a course that is necessary for students planning to attend a four-year college.  Topics will include linear and quadratic equations and inequalities, matrices, systems of equations, characteristics of functions, powers and roots, exponential and logarithmic functions, polynomials, rational functions, conic sections, sequences, series, probability and statistics.  Graphing calculators will be used extensively in this course.

FUNDAMENTAL ALGEBRA II Grade 11, 12 (full year)
Prerequisite:  Algebra I and Geometry.
Note:   If you plan on taking Math Analysis, you should not take Fundamental Algebra II, you should take Algebra II.

This course will provide a second year of algebra for those students who have difficulty with mathematics.  This class will fulfill the graduation requirement.  Topics to be covered include linear and quadratic equations and inequalities; systems of equations; polynomials; exponential and logarithmic functions; conic sections; and probability and statistics.  Graphing calculators will be used extensively in this course.

ANALYSIS Grade 11, 12  (full year)
Prerequisite: Algebra II with “C” or better

This course will prepare the college-bound student for calculus.  It will cover a variety of topics (some of which were introduced in Algebra II) to allow for a deeper understanding of properties and applications.  First semester will include the study of graphs and their transformations; in particular, polynomial, and rational functions, exponential and logarithmic functions and trigonometric functions.  The second semester will cover additional trigonometry, sequences and series, probability and statistics, conics, parametric equations and polar coordinates, vectors, and limits.  Graphing calculators will be used extensively in this course.

ANALYSIS HONORS Grade 11, 12 (full year)
Prerequisite: Algebra II with instructor’s approval.

This course is for our strongest Algebra II students.  There will be very little review of prerequisite material.  Students will be challenged to work at an accelerated pace through Analysis topics so that there will be plenty of time for Differential Calculus to be covered.  Analysis topics will include exponential and logarithmic functions/equations, analytic trigonometry, sequences and series, probability, conics, parametric equations/graphs, and polar coordinates/equations/graphs.  Calculus topics will include limits, differentiation rules, and applications of the derivative.  Juniors who are successful in this course should register for AP Calculus BC as a full-year course in their senior year.

AP CALCULUS AB Grade 11, 12 (full year)
Prerequisite: Analysis with “B” or better OR Honors Analysis with “C” or better

This course is designed for students who plan to continue their education with an emphasis on engineering, medicine, science or other four-year degrees requiring some knowledge of calculus.  First semester topics will include limits and differential calculus, with an emphasis on applications of the derivative.  The second semester will cover integral calculus.  In particular, students will learn how to work with logarithmic, exponential, and inverse trigonometric functions, and applications of the integral.  The course syllabus strictly adheres to topics that are in the Advanced Placement curriculum, and includes time for preparing for the AP test in May.

AP CALCULUS BC Grade 12 (full year)
Prerequisite: Honors Analysis with “A”

This course is designed for students who plan to continue their education with an emphasis on engineering, medicine, science or other four-year degrees requiring some knowledge of calculus.  First semester topics will include a review of limits and differential calculus and introduction of integral calculus.  In particular, students will learn how to work with logarithmic, exponential, and inverse trigonometric functions, and applications of the integral.  Second semester topics of study will concentrate on applying and extending topics of differential and integral calculus.  The list of topics will include analyzing parametric curves and vector functions, improper integrals, L’Hôpital’s Rule, numerical and analytic solutions to differential equations, sequences and series, tests for convergence or divergence, computation and analysis of Taylor polynomials and Taylor series.

STATISTICS Grade 11 or 12 (one semester)
Prerequisite: Successful completion of Geometry and Algebra II

This is a one semester course.  To earn a full year mathematics credit, sign up for this course and 5650 – PERSONAL FINANCE. This is a course primarily for the student who plans to pursue a college degree in an area outside of math and science.  It is designed to provide students with exposure to the study of statistics with possible topics including descriptive statistics, probability, probability distributions, confidence intervals, and hypothesis testing.  Stronger mathematics students are encouraged to take Analysis, AP Statistics, or AP Calculus AB.  Graphing calculators will be used extensively in this course.

PERSONAL FINANCE Grade 11 or 12 (one semester)
Prerequisite: Successful completion of Geometry and Algebra II

This is a one semester course.  To earn a full year mathematics credit, sign up for this course and 5600 – STATISTICS. This is a course primarily for the student who plans to pursue a college degree in an area outside of math and science.  It is designed to expose students to personal finance with possible topics including financial aid, credit cards, loans, budgets, and taxes.  Stronger mathematics students are encouraged to take Analysis, AP Statistics, or AP Calculus AB.

AP STATISTICS AND PROBABILITY  Grade 11, 12 (full year)
Prerequisite: Successful completion of Algebra II

The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  This is an excellent course for students who have successfully completed Algebra II and who possess sufficient mathematical maturity and quantitative reasoning ability.  Important components of the course include the use of technology, projects and lab activities, group problem solving, and writing.  Students are taught how to use technology (primarily calculators) to simulate randomness, calculate statistics, find probability, create confidence intervals, and to perform significance tests.  Students will be taught how to use tables and formulas, but will move quickly to the calculator to compute in a wide variety of settings. The focus shifts away from computation and more emphasis is placed on the conceptual understanding and thoughtfully communicating decisions based on the statistical computations. Students taking the AP Statistics course are well-prepared and expected take the AP Statistics examination in the spring, making it possible to earn college credit and/or advanced placement.