Major Concepts/Content: The concepts and content for AP Calculus course incorporate the syllabus of the College Board.  Students are engaged in authentic applications involving limits and continuity, derivatives, integrals, transcendental functions, and infinite series.  The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally.  The standards develop the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling.  Graphing calculators are required for this course as mandated by the College Board.  Students should be encouraged to talk about the mathematics of change in calculus, to use the language and symbols of calculus to communicate, and to discuss problems and methods of solutions.

Major Instructional Activities: Instructional activities will focus on developing the students understanding of the concepts of calculus and providing experience with its methods and applications.  Activities will be structured to allow students to work in cooperative groups.  Appropriate technology will be utilized throughout the course.  Students should have access to a graphing calculators at all times.

Major Evaluative Techniques: Many evaluative processes will be used to assess students written and oral work.  These may include multiple choice, short answer, discussions, projects, quizzes, chapter tests, cumulative tests, or open ended questions.  Calculator should be available in assessment situations.  Students may take the AP College Board exam to qualify for college credit.

Essential Expectations: Upon completion of this course, students should be able to:

• Analyze functions and graphs emphasizing the relation between the geometric and analytic information on the use of calculus to predict and to explain the observed local and global behavior
• Demonstrate an intuitive understanding of the limiting process to include calculating limits using algebra and estimating limits from graphs or tables of data
• Understand the concept of continuity in terms of limits
• Define the derivative as the limit of the difference quotient
• Use the derivative at a point to determine the tangent line to a curve
• Use equations involving derivatives and provides verbal descriptions translated into equations involving derivatives and vice versa
• Understand the relationship between the increasing and decreasing behavior of f and the sign of f'
• Model rates of change, including related rates problems
• Makes and use rough sketches to understand the situation in related rates and maxima minima problems and solve the problems using appropriate methods
• Use basic rules for the derivative of sums, products, and quotients of functions
• Use the chain rule
• Use the Fundamental Theorem to evaluate definite integrals
• Solve anti derivatives following directly from derivatives of basic functions
• Solve anti derivatives by substitution of variables
• Compute volume from rotations of plane figures around axes
• Organize, analyze, and display one and two variable data including appropriate sorting methods
• Determines the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement

Last Revised: July 18, 2005