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July 2007 AP Calculus AB Unit 1—Introduction to Calculus Page 1 Name of Course: AP & 8230; Encourage students to bring to class an English/native language dictionary. C. Present mathematical procedures and results clearly, systematically, succinctly and correctly. D. Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. 2.11.11 Concepts of Calculus A. Determine maximum and & 8230;

Find the slope of a line passing through two points. Write the equation of a line with a given point and slope. Interpret slope as both a ratio and as a rate in real-life applications. Sketch the graph of a linear equation in slope-intercept form. Write equations of lines that are parallel or perpendicular to a given line. Use function notation to represent and evaluate a function. Find the domain and range of a function. Sketch the graph of a function. Identify different types of transformations of functions. Classify functions and recognize different transformations of functions. Fit linear, quadratic, and trigonometric modes to real-life data sets. Understand what calculus is and how it compares with precalculus. Understand that the tangent line problem is basic to calculus. Understand that the area problem is basic to calculus. Estimate a limit using a numerical or graphical approach. Learn different ways that a limit can fail to exist. Study and use a formal definition of limit. Evaluate a limit using properties of limits. Develop and use a strategy for finding limits. Evaluate a limit using factoring and rationalizing techniques. Evaluate a limit using the Squeeze Theorem. Determine continuity at a point and on an open interval. Use properties of continuity on a closed interval. Use properties of continuity. Understand and use the Intermediate Value Theorem. Determine infinite limits from the left and left. Find and sketch the vertical asymptotes of the graph of a function. Text/Resource Materials: Larson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus of a Single Variable: Eighth Edition . Boston: Houghton Mifflin, 2006. Chapters P and 1 This course is explored through the interpretation of graphs and tables as well as analytic methods. The use of the graphing calculator is integrated throughout the course to provide a balanced approach to the teaching and learning of calculus that involves analytical, numerical, graphical, verbal, and written means. Students obtain solutions algebraically or analytically, support their results graphically or numerically with technology, and interpret results in the context of the problem. Students apply these methods to investigate and solve problems, to write about their conclusions, and to communicate orally with one another in small groups

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