Elizabethtown Area School District

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1 Advanced Placement Calculus BC Course Number: 233 Grade Level: Length of Course: School Year Total Clock Hours: 120 hours Length of Period: 80 minutes Date Written: Periods per Week/Cycle: Every other day Written By: Mark Elicker Credits (if app.): 1 Weighting: 1.20 Prerequisite: Advanced Placement Calculus AB Placement Criteria: Recommended minimum final average of 83% in AP Calculus AB Course Description: This weighted course is an extension of Advanced Placement Calculus. Students will continue to study advanced topics including techniques of integration, polynomial approximations, and series. Upon successful completion of this 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 will be required for this course. (A TI-83 or TI-84 is the recommended calculator.)

2 page 1 Overall Course/Grade Level Sts Students will KNOW and be able TO DO the following as a result of taking this course. A. Find the limits of various functions. B. Find the derivatives of various functions. C. Interpret the derivative as a rate of change and in various applied contexts. D. Find the antiderivatives using various techniques of integration. E. Interpret the definite integral in various applied contexts. Apply calculus to parametric, polar, and vector functions. G. Develop polynomial approximations for various functions. Evaluate series, including geometric, harmonic, alternating, Taylor, and Maclaurin series. Prepare for the Advanced Placement Exam.

3 page 2 I Content Major Areas of Study List all units of study below: Unit Estimated Time Materials 1. Limits and Continuity 2-3 weeks Textbook, Graphing 2. Derivatives 3-4 weeks Textbook, Graphing 3. Applications of the Derivative 3-4 weeks Textbook, Graphing 4. Parametric, Polar, and Vector Functions 4-5 weeks Textbook, Graphing 5. Techniques of Integration 3-4 weeks Textbook, Graphing 6. Applications of Integration 3-4 weeks Textbook, Graphing 7. Differential Equations and Slope Fields 2-3 weeks Textbook, Graphing 8. Series 2-3 weeks Textbook, Graphing 9. Polynomial Approximation 3-4 weeks Textbook, Graphing 10. Advanced Placement Test Preparation 3-4 weeks Textbook, Graphing page 3

4 Name of Course: AP Calculus II Name of Unit: Limits and Continuity Essential Question for the Unit: What information can you determine about a function by using limits? A. How do you evaluate a limit using a graph? E A 2.11 B. How do you evaluate a limit algebraically? E A 2.11 C. How do you evaluate a limit using technology? E A 2.11 D. How do you determine if a function is continuous? E A 2.11 E. G. page 4a

5 Name of Course: AP Calculus II Name of Unit: Derivatives Essential Question for the Unit: What is a derivative? A. How do you find a second or higher-order derivative? B. When are the various techniques of differentiation appropriate? C. How do you determine if a function is differentiable? D. How are the derivatives of inverse functions related? E B 2.11 E B, C 2.11 E A, B 2.11 E B 2.11 E. G. page 4b

6 Name of Course: AP Calculus II Name of Unit: Applications of the Derivative Essential Question for the Unit: How is a derivative useful? A. How do you use calculus to find the maximum or minimum value of a quantity? B. How do you find a numerical approximation for the solution to a differential equation? C. How do you apply L-Hopital s to calculating limits? D. How are derivatives used in the calculations of moving particles? E B, C 2.11 E B, C 2.11 E A, B, C 2.11 E B, C 2.11 E. G. page 4c

7 Name of Course: AP Calculus II Name of Unit: Parametric, Polar, and Vector Functions Essential Question for the Unit: Why would a function be written in notation other than Cartesian? A. How do you find the derivative of a parametricallydefined function? E A, B, C, F 2.11 B. How do you find the derivative of a polar function? E A, B, C, F 2.11 C. How do you find the derivative of a vector function? D. How do you apply calculus techniques to solve problems involving parametric, polar, and vector functions? E. E A, B, C, F 2.11 E B, C, D, E, F 2.11 G. page 4d

8 Name of Course: AP Calculus II Name of Unit: Techniques of Integration Essential Question for the Unit: How do you decide which technique to use when integrating a function? A. What is an anti-derivative? I F 2.11 B. How do you integrate a function using known derivatives? C. How do you use substitution to integrate a function? D. How do you use integration by parts to evaluate an integral? E. How do you use partial fractions to integrate a function? E F 2.11 E F 2.11 E F 2.11 E F 2.11 How do you evaulate in improper integral? E F 2.11 G. page 4e

9 Name of Course: AP Calculus II Name of Unit: Applications of Integration Essential Question for the Unit: How is integration useful? A. How do you calculate areas between curves? E E 2.11 B. How do you calculate volume? E E 2.11 C. How do you calculate the amount of work performed? E E 2.11 D. How do you calculate arc length and surface area? E E 2.11 E. G, page 4f

10 Name of Course: AP Calculus II Name of Unit: Differential Equations and Slope Fields Essential Question for the Unit: What information is presented by a differential equation and its solution? A. How do you solve a first-order differential equation? E D, E 2.11 B. How do you create a slope field? E D, E 2.11 C. How does a logistic growth problem compare to exponential growth/decay equations? E D, E 2.11 D. E. G, page 4g

11 Name of Course: AP Calculus II Name of Unit: Series Essential Question for the Unit: What is a series and how is it used? A. What is a geometric series? E H 2.11 B. What is a harmonic series? E H 2.11 C. What is an alternating series? E H 2.11 D. How do you test a series for convergence? E H 2.11 E. What is a power series? E H 2.11 G, page 4h

12 Name of Course: AP Calculus II Name of Unit: Approximation Essential Question for the Unit: Why would you approximate a function with a polynomial? A. How do you create a Taylor polynomial to approximate a given function? B. How do you create a Maclaurin series to approximate a function? C. How do you find the interval and radius of convergence for a power series? D. How do you apply calculus techniques to a power series? E. How do you calculate error bounds of a polynomial approximation? E G, H 2.11 E G, H 2.11 E G, H 2.11 E G, H 2.11 E G, H 2.11 G, page 4i

13 Name of Course: AP Calculus II Name of Unit: AP Test Preparation Essential Question for the Unit: How do you sufficiently prepare to perform well on the AP exam? A. What can you expect on the AP exam? E A, B, C, D, E, F, G, H, I B. How do you prepare for the exam? E A, B, C, D, E, F, G, H, I C. D. E. G, page 4j

14 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 Computer Simulations Research Papers Class Participation 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 sts 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. AP Calculus BC EXam May page 5

15 IV. Expected levels of achievement Current grading scale: A: % B: 83-91% C: 74-82% D: 65-73% F: 0-64% 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