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COURSE DESCRIPTIONS — MATHEMATICS

The Mathematics curriculum is designed to ensure that all students have an opportunity to become successful in the learning of mathematics. The various courses allow students to value mathematics, become confident in their ability to do mathematics and become real problem solvers. Students should also learn to communicate effectively and to reason mathematically. The opportunity for all students to experience these goals is the integral part of the mathematics program. As a result, students should be mathematically trained to function well in today’s and tomorrow’s society in which students are capable of extending their learning to become informed citizens capable of understanding issues in a technological society.

This is a course designed to strengthen basic concepts of arithmetic and to expose students to the concepts of algebra. The topics are presented in a less rigorous manner and at a slower pace than in the Fundamentals of Algebra course. Included topics are: basic algebra, integers and exponents, rational and real numbers, statistics, plane geometry (perimeter, area and volume), ratios and percents, probability and sequences.

This course is designed to help students meet the Pennsylvania State Standards for eleventh grade.  Topics include number theory, concepts from Algebra I and II, Geometry, Statistics, and Probability.  After the PSSA test, the focus of the course will shift to mathematical applications of the topics learned earlier. Students who need a third math credit toward graduation should take this course.

The major purpose of this course is to expose students to all of the fundamental concepts of Algebra I. However, these topics are presented in a less rigorous manner and at a slower pace than the regular Algebra I. This course meets the graduation requirement for an Algebra credit.

An active hands-on approach is used to develop concepts and to explore theorems. Formal two-column proofs are not presented. It is less rigorous than Geometry but exposes students to the integral components of the subject. The course is a follow up course for students enrolled in Fundamentals of Algebra.

Prerequisite: Algebra I or Fundamentals of Algebra

Algebra I extends the properties of arithmetic to real numbers. The focus of Algebra I is to help students understand how mathematics relates to the real world. Specific topics include: linear equations and inequalities, polynomials, functions, graphs, factoring, radicals, and quadratic equations.

This course combines plane, solid and coordinate geometries and includes formal two-column proofs and paragraph proofs. This is a more rigorous course than Fundamentals of Geometry and will require strong algebra skills. Topics of study include: points, lines, planes, perpendicular lines, parallel lines, polygons, congruence, similarity, right triangles, circles, area and volume. Constructions using compass and straightedge and/or using “The Geometer’s Sketchpad” computer software are included.

Pre-requisites: Algebra I with a final grade of “C” or better OR Fundamentals of Algebra with a final grade of “A” and the approval of the Mathematics Department.

All of the material of Algebra II will be covered in addition to the following topics in Trigonometry: Trigonometric functions, complex numbers, trigonometric identities and equations, formulae involving triangles, and circular and inverse functions.

Prerequisites: A “B” or better in Algebra I and Geometry, and good work and study habits.

This course will review and extend the concepts of elementary algebra. Topics included are: functions and relations, systems of linear equations, graphs, factoring, rational and irrational numbers, inequalities, and complex numbers.

Prerequisites: Algebra I and Geometry, or Fundamentals of Algebra and Fundamentals of Geometry.

This course is the study of polynomial, exponential, logarithmic, and trigonometric functions, including their graphs and applications. Additional topics include: analytic geometry, polar representations of curves, matrices, and determinants.

Prerequisites:Algebra I, Geometry, and Algebra II or Algebra II-Trig.

This course exposes college bound students to the numerous components of Trigonometry. The topics will be trigonometric functions and their graphs, and applications of right and oblique triangles, and trigonometric equations. Use of the graphing calculator will be extensive throughout the course. Students who want to learn a higher-level math with more time devoted to the single topic of trigonometry should elect this course. This course may be taken in Semester Two or sequentially after Statistics.

Prerequisite: A “C” or better in Algebra II-Trig or Algebra II.

This is a course designed to give students a working knowledge of probability, statistics, and their applications.  Topics include organizing, summarizing, and reporting data, and certain theoretical distributions.  For many students, this course will be their first experience with mathematics as an applied subject rather than a calculation-based subject Graphing calculators are utilized extensively . Students planning careers in education or the social sciences should elect this course.

This course is offered in Semester One and may be followed by Trigonometry.

Prerequisites: Open to juniors and seniors who have successfully completed a minimum of two courses in college preparatory mathematics with a C or better in Alg. II or Alg. II/Trig.

This is a more rigorous course than Geometry and is intended for students possessing strong algebra skills, developed problem solving abilities, and good organization and study skills. All topics addressed in Geometry will be presented, but higher level thinking skills and algebraic proficiency will be required to solve geometric-based problems. Emphasis is placed on both oral and written communication skills needed to explain and support relationships, and on accessing and applying proper algebra concepts. Constructions and Geometer Sketchpad software will be presented, and out-of-class assignments using these techniques will be required throughout the course.

Prerequisites: A “B” or better in Algebra I or in 8th grade Algebra I is required.

Any student earning a “C” or “D” needs a teacher’s recommendation to enter or to continue in the Honors Program.

This is a rigorous course for accelerated math students. The course is based on problem-solving and functions. Graphs and applications of polynomial, exponential, and logarithmic functions will be studied. Matrices, sequences, series, and trigonometry will also be covered in this course.

Prerequisites: A “B” or better in Algebra I and Honors Geometry is expected.

Any student earning a “C” or “D” needs a teacher’s recommendation to continue in the Honors program.

This course is the study of polynomial, exponential, logarithmic, and trigonometric functions, including their graphs and applications. Additional topics include: analytic geometry, parametric and polar representations of curves, sequences, series, matrices, and determinants.

Prerequisites: A “B” or better in Algebra I, Honors Geometry and Honors Algebra II-Trigis expected. Any student earning a “C” or “D” needs a teacher’s recommendation to continue in the Honors program.

The topics in this course cover content areas not normally covered in any other mathematics course. Part I is the Mathematics of Social Choice: voting, weighted voting and power, fair division and apportionment methods. Part II is Management Science: Graph theory, shortest network problems and scheduling using directed graphs and critical paths. Part III topics are related to Growth and Symmetry: Fibonacci numbers, the Golden Ratio, Population Growth, Symmetry and transformational geometry, and Fractal Geometry. Part IV is an introduction to calculus that includes graphs of polynomial and rational functions, limits, the derivative and techniques of differentiation.

Prerequisites: A “B” or better in all previous Honors level courses.

This Advanced Placement course is offered to those students with high mathematical ability and interests. The topics are basically those outlined by the College Entrance Examination Board. The course entails detailed study of functions, graphs and limits, derivatives and their applications, integrals and their applications, as well as elementary differential equations. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally.

Prerequisites: Successful completion of Algebra I, Honors Geometry, Honors Algebra II-Trig, and Honors Pre-Calculus.

AP Calculus BC is primarily concerned with developing the students' understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results and problems being expressed graphically, numerically, analytically, and verbally. Calculus BC is an extension of Calculus AB rather than an enhancement; common topics require a similar depth of understanding. Primary topics of the course include the study of functions, graphs, and limits, derivatives, integrals, and polynomial approximations and series, as outlined by the Collegeboard Advanced Placement Program.

Prerequisites: Successful completion of Algebra I, Honors Geometry, Honors Allgebra II - Trig., Honors Pre-Calculus, and Honors Discrete Mathematics or teacher recommendation.

This advanced placement course is offered to those students with excellent problem solving ability and a keen interest in computer science as a career. The focus of this course is to provide students with a conceptual background in computer science. The major emphasis is on programming methodology, algorithm design, and object oriented programming in the Java language. This course prepares a student for advanced placement in a college computer science program by means of the A level of the Advanced Placement Exam of the College Entrance Board.

Prerequisites: Students must have previous programming experience in either the C++ or Java language. Students must also have the recommendation of the AP Compute Science Instructor and the Mathematics Department.

This advanced placement course is offered as an extension of the AP Computer Science A for students interested in pursuing a post-secondary degree in any field of computer science. The focus of this course is to develop and utilize advanced data structures in the Java programming language. This course prepares a student for advanced placement in a college computer science program by means of the AB level of the Computer Science Advanced Placement Exam of the College Entrance Board.

Prerequisites: Successful completion of AP Computer Science A with a "B" or better or approval of the AP Computer Science Instructor.

This Advanced Placement course is intended to introduce students to the major components of collecting, analyzing and drawing conclusions from data. Students will be exposed to exploring data, planning a study, conducting an experiment, anticipating patterns and statistical inference. Topics include descriptive statistics, probability and various probability distributions. Emphasis will also be placed on hypothesis testing and tests comparing two parameters. Other topics include correlation and regression and chi-square tests. Modern technology will be utilized in the form of the TI-84+ graphing calculator and computers. This course may be taken concurrently with Discrete Math, Pre-Calculus or Calculus.

Prerequisites: Students must have completed Algebra II or Algebra II/Trig with a “B” or better and have good written and oral communication skills.