## An Overview

The Advanced Placement program offers courses to high school students that are taught on a college level. After successfully completing the curricular requirements of an advanced placement course in calculus, students are given an opportunity to take an exam administered by the College Board to assess their knowledge of, but more importantly their understanding, of calculus.

Though the Advanced Placement program is an open enrollment program, students must have taken the correct sequence of courses leading up to enrollment in calculus to be successful. A solid, fast-paced, intense and rigorous foundation must be laid in algebra, geometry and trigonometry for students to be successful in AP Calculus. Specifically, students must have a firm understanding of functions and their properties, algebraic manipulations, and graphs. Important concepts of functions such as domain and range, even and odd, periodic, symmetry, zeros, and intercepts must be understood. Additionally, students need to know values of the trigonometric functions of 0, π/6, π/4, π/2 and their multiples. Part of your summer work is to write a paper in which you demonstrate your understanding of these basic algebraic and trigonometric concepts of functions.

Though the Advanced Placement program is an open enrollment program, students must have taken the correct sequence of courses leading up to enrollment in calculus to be successful. A solid, fast-paced, intense and rigorous foundation must be laid in algebra, geometry and trigonometry for students to be successful in AP Calculus. Specifically, students must have a firm understanding of functions and their properties, algebraic manipulations, and graphs. Important concepts of functions such as domain and range, even and odd, periodic, symmetry, zeros, and intercepts must be understood. Additionally, students need to know values of the trigonometric functions of 0, π/6, π/4, π/2 and their multiples. Part of your summer work is to write a paper in which you demonstrate your understanding of these basic algebraic and trigonometric concepts of functions.

## Instructional Methodology

The concepts covered in the AP Calculus AB course are listed throughout this syllabus. Attention is paid to helping students understand concepts from a variety of different avenues. Students discover numerical, graphical, and analytical methods of understanding concepts and are required to express their understanding through both the spoken word through in class presentations and in papers that will be presented that parallel their presentations. During the last one to four weeks of the course, each student is assigned a free response problem from one of the AP Exams from 2004 – 2007. They will be required to write a detailed paper in which they discuss the calculus involved in the problem, independent from the problem and then explain how they applied the calculus to solve the problem. They will present these papers in class.

Much learning and understanding can be gained from having a classroom that is student-centered in structure. For the first three or four units, learning activities are very teacher directed. Calculus skills are taught and practiced building a foundation for the application of calculus. During the latter two-thirds of the course, in class activities become more focused on the student-centered learning. Many times, students are given free response problems from past AP exams that emphasize the different methods of thinking according to the rule of four. Free response problems from exams from 1998 – 2003 are used extensively in class discussions to show students the many ways that concepts in calculus can be applied according to the rule of four. Students are given a notebook containing every free response problem from 1998 – 2007 that have been released in a notebook at the beginning of the year. As the time arises for reference to these problems, we discuss these in class. Typically, the teacher introduces the problem and then students discuss how to solve the problems in small groups for a few minutes and then share their ideas to the larger group for discussion. Many times, we only do one or two parts of the free response item at a time to show students that just because you do not have the answer to part a of a free response does not mean you cannot solve subsequent parts of the problem.

Much learning and understanding can be gained from having a classroom that is student-centered in structure. For the first three or four units, learning activities are very teacher directed. Calculus skills are taught and practiced building a foundation for the application of calculus. During the latter two-thirds of the course, in class activities become more focused on the student-centered learning. Many times, students are given free response problems from past AP exams that emphasize the different methods of thinking according to the rule of four. Free response problems from exams from 1998 – 2003 are used extensively in class discussions to show students the many ways that concepts in calculus can be applied according to the rule of four. Students are given a notebook containing every free response problem from 1998 – 2007 that have been released in a notebook at the beginning of the year. As the time arises for reference to these problems, we discuss these in class. Typically, the teacher introduces the problem and then students discuss how to solve the problems in small groups for a few minutes and then share their ideas to the larger group for discussion. Many times, we only do one or two parts of the free response item at a time to show students that just because you do not have the answer to part a of a free response does not mean you cannot solve subsequent parts of the problem.

## Role of Technology

The graphing calculator plays an integral role in both developing and applying concepts of calculus. Thus, it is required that all students enrolled in AP Calculus AB have access to a graphing calculator both in class and at home. Instruction during class activities and lectures will be using the TI-84 Silver Edition. Any calculator from the TI family (TI-84 plus) will be the best.

Students

Students

*also be required to write papers which must be typed using an equation editor of some type so that all papers can be submitted by email.*__may__