Mathematics
	Algebra 1 This course is a standard first-year high school introductory algebra course. While most of the focus is on assuring proficiency in basic algebraic skills and processes, considerable time will be devoted to solving realistic and interesting applications. Topics include solving equations, inequalities and systems, factoring, polynomials, rational expressions, irrational numbers, radicals, and quadratic equations. It is in Algebra 1 that students acquire an appreciation for the value and power of their new algebraic and graphing tools. (1 credit; full year) Algebra 2 This course is a study of functions -- linear, quadratic, exponential, logarithmic, rational, and polynomial -- and an introduction to matrices, sequences and series, and basic probability concepts, among others. These topics are studied algebraically, graphically, and numerically, and through this triplex approach, students will continue to acquire an understanding of algebraic structure and how algebra can be used to model various situations. The graphing calculator becomes an integral element used not only as a tool for numerical manipulation but also for visualization and verification. (1 credit; full year) Algebra 2H This Honors-level course explores similar content and themes as presented in Algebra 2, with additional rigor. Supplementary topics may be introduced at the discretion of the instructor, but as stated in the Algebra 2 description above, this course is a study of functions -- linear, quadratic, exponential, logarithmic, rational, and polynomial -- and an introduction to topics including matrices, sequences and series, and basic probability concepts. These topics are studied algebraically, graphically, and numerically, and through this triplex approach, students will continue to acquire an understanding of algebraic structure and how algebra can be used to model various situations. The graphing calculator becomes an integral element used not only as a tool for numerical manipulation but also for visualization and verification. Department permission is required for admission into this course. (1credit; full year) Geometry & Trigonometry For two-thirds of the year, students focus on geometric properties and relationships of parallel and perpendicular lines, of symmetry and congruency, of quadrilaterals and polygons, of right triangles, of circles and of areas and volumes of various shapes. Occasional investigation utilizing the software The Geometer's Sketchpad will be introduced, while rigorous proof of geometric properties will be emphasized. The last third of the year is dedicated primarily to Trigonometry, an intensive study of a topic both algebraic and geometric in nature. (1 credit; full year) Geometry & Trigonometry H This is an Honors-level course that explores similar content and themes as presented in Geometry & Trigonometry, with additional rigor. Supplementary topics may be introduced at the discretion of the instructor, but as stated in the Geometry & Trigonometry description aforementioned, two-thirds of the year focuses on geometric properties and relationships of parallel and perpendicular lines, of symmetry and congruency, of quadrilaterals and polygons, of right triangles, of circles, and of areas and volumes of various shapes. Occasional investigation utilizing the software The Geometer's Sketchpad will be introduced, while rigorous proof of geometric properties is emphasized. The last third of the year is dedicated primarily to Trigonometry, an intensive study of a topic both algebraic and geometric in nature. Department permission is required for admission into this course. (1 credit; full year) Pre-Calculus This course is designed to provide the essential mathematical background needed in Calculus or AP Calculus. Topics in this course are prerequisites for Calculus, and their presentation develops both an intuitive base and some of the working tools for the study of more advanced mathematics. The curriculum consists of studying in depth algebraic topics, elementary and trigonometric functions with applications, matrices, parametric and polar equations, vectors, analytic geometry, and sequences and series. The TI Graphing Calculator is used extensively in this course as a means of exploration and investigation of applications. (1 credit; full year) Pre-Calculus H This is an Honors-level course that explores similar content and themes as presented in Pre-Calculus, with additional rigor. No textbook is utilized in this course, and the topics are addressed almost entirely from a problem-solving standpoint. Supplementary topics may be introduced at the discretion of the instructor, but as stated in the Pre-Calculus description aforementioned, topics in this course are prerequisites for Calculus, and their presentation develops both an intuitive base and some of the working tools for the study of more advanced mathematics. The curriculum consists of studying in-depth algebraic topics, elementary and trigonometric functions with applications, matrices, parametric and polar equations, vectors, analytic geometry, and sequences and series. The TI Graphing Calculator is used extensively in this course as a means of exploration and investigation of applications. Department permission is required for admission into this course. (1 credit; full year) AP Calculus This Advanced Placement course in Calculus is intensive and rigorous, covering the calculus of functions of a single variable. All topics of the AP Calculus curriculum, differential and integral, are included, as are some others. Applications are at the forefront of the course, and students are required to take the AP Calculus AB exam. Department Head permission is required for admission into this course, and successful completion of Pre-Calculus with a grade of 90 or Honors Pre-Calculus with a grade of 85 is a prerequisite. (1 credit; full year) AP Statistics This Advanced Placement course in statistics is designed to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusion from data. The topics are divided into four major themes: exploratory analysis; planning a project; probability; and statistical inference. Working within these themes, students learn to identify important variables, observe patterns in order to detect and form conjectures about relationships among variables, anticipate and reasonably model these relationships, form hypotheses, and draw valid conclusions based upon analytical methods. Department Head permission is required for admission into this course, and successful completion of Pre-Calculus is a prerequisite.     (1 credit; full year) AP Calculus 2 (BC+) This course reviews the AP Calculus AB course and studies the additional topics of the AP Calculus BC course -- methods of integration, convergence of series, Taylor and Power Series, and Calculus of polar and parametric functions. Additional topics may include hyperbolic functions, vector calculus, multivariable functions, and partial differentiation. Students enrolled in this course are required to take the AP Calculus BC exam. Department Head permission is required for admission into this course, and successful completion of AP Calculus is a prerequisite.  (1 credit; full year)

	11th & 12th Grade Mathematics Electives
	Fundamentals of Calculus This semester elective course is an introduction to the study of differential and integral calculus at an elementary level. Students will learn to find limits, derivatives, and integrals and acquire the ability to apply those concepts to problem-solving situations. With the exposure of the "big picture" of Calculus in this course, students will receive a firm foundation for future college calculus courses and for fields requiring calculus-related concepts. It is anticipated, though not required, that students enrolled in the Fundamentals of Calculus course will enroll in the Fundamentals of Probability and Statistics course during the second semester. Successful completion of Pre-Calculus is a prerequisite (1/2 credit; 1st semester) Introduction to Logic, Proof, and Reasoning This semester elective course is designed to introduce students to the structure underlying mathematical and logical proof while examining the type of reasoning that forms the backbone of mathematical thought. By examining the foundations and methods of proof, students will sharpen their ability to analyze arguments and draw valid conclusions -- skills that will carry over to every discipline. Course content will include: propositional logic, logical arguments, and logical constructions; proofs by contradiction, contrapositive, counterexample, and mathematical induction; set operations, subsets and equality; DeMorgan's laws; infinite unions and intersections; cardinality, countability and uncountability of infinite sets; relations and congruence; and equivalence of statements. Examples from set theory, algebra, logic, and number theory will be used to emphasize proof techniques and to expose students to the richness of mathematical topics not typically encountered in a high school course. Puzzles including Sudoku, Kakuro, and Nurikabe will be utilized to promote the type of logical thinking that permeates game theory. Completion of the core curriculum (Algebra 1, Algebra 2, and Geometry & Trigonometry) is prerequisite, though completion of Pre-Calculus is recommended. The course may be taken concurrently with a mathematics course at a level of Pre-Calculus or above. (1/2 credit; 1st semester) Introduction to Number Theory The study and use of numbers and their inherent patterns is one of the oldest intellectual pursuits of humankind. This semester elective course will help unlock some of the mysteries behind the "structure" of numbers. Topics explored in the course may include: number sequences, including the beautiful Fibonacci sequence; factorization and divisibility; the Chinese remainder theorem; figurate and perfect numbers; the Golden Ratio; Pascal's triangle; historical systems of numeration; systems with bases other than 10; modular arithmetic; and an introduction to group theory. Completion of the Mathematics curriculum (Algebra 1, 2, and Geometry & Trigonometry) is prerequisite, though completion of Pre-Calculus is recommended. This course may be taken concurrently with a mathematics course at the level of Pre-Calculus or above. (1/2 credit; 2nd semester) Fundamentals of Probability and Statistics This semester course is an introduction to the field of probability and statistics at an elementary level. Students will work with simulated and real data sets to study the central concepts of statistics -- data analysis, probability, and inference. Course content will include, though not exclusively: exploring data arguments, probability distributions, estimation and error, and sampling methods. Students enrolled in this course will receive a firm foundation for future college statistics courses and for fields requiring statistics-related concepts. Completion of the Mathematics core (Algebra 1, 2, and Geometry & Trigonometry) is prerequisite. This course may be taken concurrently with a mathematics course at a level of Pre-Calculus or above, excluding AP Statistics. (1/2 credit; 2nd semester) Independent Study in Mathematics This course is offered only on an as-needed basis to students who have completed GFA's entire mathematics curriculum (through AP Calculus 2). In the past, Independent Study has been offered in Linear Algebra, and the course content is mutually decided by the teacher and student(s). (1/2 credit; either semester)