Elizabethtown Area School District

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1 Advanced Placement Calculus AB Name of Course Course Number: 232 Grade Level: Length of Course: 1 year Total Clock Hours: 180 hours Length of Period: 80 minutes Date Written: Periods per Week/Cycle: Every other day Written By: Mark Elicker Credits (if app.): 1 Prerequisite: Pre Calculus Course Description: This weighted course will cover the topics of a regular calculus course but will include a more in-depth study of the material. Upon successful completion of the course, students choosing to take the advanced placement exam, scoring three or above, may receive college credit from participating colleges and universities. A graphing calculator is required for this course. (A TI- 83 or TI-84 is the recommended calculator. page 1

2 Overall Course/Grade Level s Students will KNOW and be able TO DO the following as a result of taking this course. A. Graph a function using paper and pencil and technology. B. Analyze functions, their inverses, and their graphs. C. Find the limits of various functions. D. Find the derivatives of various functions. E. Use the derivative to analyze graphs of functions. F. Interpret the derivative as a rate of change and in various applied contexts. G. Find the integrals of various functions. Find the area under a curve using various approximation techniques including Reimann Sums of rectangles and trapezoids. Use integrals to model appropriate physical, social, or economic problems. Solve differential equations. K. Prepare for the Advvanced Placement exam. page 2

3 I Content Major Areas of Study List all units of study below: Unit Estimated Time Materials 1. Functions and Graphs 2-3 weeks Textbook, 2. Limits and Continuity 3-4 weeks Textbook, 3. Derivatives 4-5 weeks Textbook, 4. Applications of the Derivative 4-5 weeks Textbook, 5. Integration 4-5 weeks Textbook, 6. Applications of Integration 4-5 weeks Textbook, 7. Differential Equations 2-3 weeks Textbook, 8. Advanced Placement Test Preparation 3-4 weeks Textbook, College Board AP Materials, page 3

4 Name of Course: AP Calculus Name of Unit: Functions and Graphs Essential Question for the Unit: How are various functions solved and graphed? A. How do you find the domain and range of a function? B. When should you graph a function on paper versus using technology? I B E A C. What is a function composition? I B D. What are the properties of the following function families: constant, linear, polynomial, exponential, logarithmic, and trigonometric? E. E B F. G. page 4a

5 Name of Course: AP Calculus Name of Unit: Limits and Continuity Essential Question for the Unit: What does the limit tell us about a function? A. How do you evaluate a limit using a graph? E A, B, C 2.11 B. How do you evaluate a limit algebraically? E C 2.11 C. How do you evaluate a limit using technology? E C 2.11 D. How do you determine if a function is continuous? E A, C E. F G. page 4b

6 Name of Course: AP Calculus Name of Unit: Derivatives Essential Question for the Unit: How do you find the derivative of a function? A. What is the relationship between the slopes of tangent lines and rates of change? B. How do you use the definition and limits to calculate a derivative? C. How do graphing calculators calculate the value of a derivative at a point? D. How do you find a second or higher-order derivative? E. What is the difference between average and instantaneous rates of change? F. When are the various techniques of differentiation appropriate? G. How do you determine if a function is differentiable? E A, D E C, D 2.11 E D 2.11 E D 2.11 E A, D, E E B, D 2.11 E A, B, D 2.11 page 4c

7 Name of Course: AP Calculus Name of Unit: Applications of the Derivative Essential Question for the Unit: What information does the derivative provide? A. How do you determine a rate of change from other related rates? E F B. What does the first derivative tell about a function? E B, D, E, F 2.11 C. What does the second derivative tell about a function? D. How do you identify the extreme values of a function? E B, D, E, F 2.11 E B, E, F E. How do you solve optimization problems? E F F. How are position, velocity, and acceleration related? G. How does the mean value theorem apply to derivatives? E D, F 2.11 E D, F 2.11 page 4d

8 Name of Course: AP Calculus Name of Unit: Integration Essential Question for the Unit: How do you reverse differentiation? A. How do you find an anti-derivative? E G 2.11 B. What is the limit of a summation? E G 2.11 C. How do you find the area under a curve? E B, G, H D. What is a Riemann sum? E G, H E. What is the Fundamental Theorem of Calculus? E G 2.11 F. How does a graphing calculator evaluate a definite integral? E G, H 2.11 G. What is a definite integral? E G, H 2.11 page 4e

9 Name of Course: AP Calculus Name of Unit: Applications of Integration Essential Question for the Unit: What information does integration provide? A. How do you calculate the average value of a function over a specified interval? B. How do you find the displacement of a particle over time? C. How do you calculate the area between two curves? D. How do you find the volume of a solid of revolution? E. How do you calculate the surface area of a solid of revolution? E B, G 2.11 E G, I 2.11 E A, G, H E G, I 2.11 E G, I 2.11 F. How is work calculated? E G, I 2.11 G. page 4f

10 Name of Course: AP Calculus Name of Unit: Differential Equations Essential Question for the Unit: What is a differential equation and how do you solve one? A. What is a first-order differential equation? E F, G, I, J 2.11 B. What physical problems can be solved with differential equations? C. How do you solve exponential growth and decay problems? D. What is a slope field and what information does it provide? E G, I, J 2.11 E G, I, J E A, B, G, I, J 2.11 E. F G. page 4g

11 Name of Course: AP Calculus Name of Unit: Advanced Placement Test Preparation Essential Question for the Unit: How is the advanced placement exam set up? A. What can you expect on the AP exam? E A, B, C, D, E, F, G, H, I, J, K 2.11 B. Are you prepared for the exam? E A, B, C, D, E, F, G, H, I, J, K 2.11 C. D. E. F G. page 4h

12 II Course Assessments Check types of assessments to be used in the teaching of the course. (Provide examples of each type.) _X Objective Tests/Quizzes Constructed Responses Essays Reports _X_ Projects Portfolios Presentations Performance tasks Response Journals Logs _X_ Computer Simulations Research Papers Class Participation X_Notetaking X_Daily Assignments Writing Samples Provide copies of common assessments that will be utilized for all students taking this course. Overall course/grade level standards will be measured by a common course assessment. Unit objectives will be measured on an ongoing basis as needed by the classroom teacher to assess learning and plan for instruction. List common assessements below and recommended date/time frame for administration (at least quarterly). Name of Common Assessment When given? 1. Advanced Placement Calculus AB Exam May page 5

13 IV. Expected levels of achievement Current grading scale: PA Proficiency Levels Advanced Proficient Basic Below Basic Attach rubrics, checklists, or other documentation noting how levels of proficiency will be determined for common assessments. The following scoring documents have been developed for this course: page 6