Larson & Edwards. Calculus of a Single Variable. AP Edition. Ninth Edition. Belmont: Brooks & Cole, Cengage Learning, 2010.

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1 AP Calculus BC Course Syllabus Course Overview The primary goal of AP Calculus is to develop students understandings of calculus concepts, methods and applications. There will be an emphasis on multiple representations throughout the course which will include graphical, numerical, analytical, and verbal representations and making connections between them. Technology will be used regularly in order to facilitate this emphasis. The four big ideas in AP Calculus are limits, integrals, derivatives, and series. Throughout the year, we will focus on calculating, approximating, modeling, and applications involving each of these big ideas. Textbook Larson & Edwards. Calculus of a Single Variable. AP Edition. Ninth Edition. Belmont: Brooks & Cole, Cengage Learning, 2010.

2 Course Outline Unit 1 Limits and Their Properties (3 weeks) 1. A Preview of Calculus 2. Finding Limits Graphically and Numerically 3. Evaluating Limits Analytically 4. Continuity and One-Sided Limits 5. Infinite Limits Unit 2 Differentiation (3 weeks) 1. The Derivative and the Tangent Line Problem (Defining the Derivative) 2. Basic Differentiation Rules and Rates of Changes 3. Product and Quotient Rules and Higher-Order Derivatives 4. The Chain Rule 5. Implicit Differentiation 6. Related Rates Unit 3 Applications of Differentiation (3 weeks) 1. Extrema on an Interval 2. Rolle s Theorem and the Mean Value Theorem 3. Increasing and Decreasing Functions and the First Derivative Test 4. Concavity and the Second Derivative Test 5. Limits at Infinity 6. A Summary of Curve Sketching 7. Optimization Problems 8. Newton s Method Unit 4 Integration (3 weeks) 1. Antiderivatives and Indefinite Integration 2. Area 3. Riemann Sums and Definite Integrals (Defining the Definite Integral) 4. The Fundamental Theorem of Calculus Part 1 If f is continuous on [a,b] then antiderivative of f(x). b a f ( x) dx F( b) F( a) where F(x) is any Part 2 If f is continuous on [a,b] then the function g defined by antiderivative of f. That is, g (x) = f(x) for a < x < b. 5. Integration by Substitution 6. Numerical Integration x g ( x) f ( t) dt is an a

3 Unit 5 Logarithmic, Exponential, and Other Transcendental Functions (3 weeks) 1. The Natural Logarithmic Function: Differentiation 2. The Natural Logarithmic Function: Integration 3. Inverse Fuctions 4. Exponential Functions: Differentiation and Integration 5. Bases Other Than e and Applications 6. Inverse Trigonometric Functions: Differentiation 7. Inverse Trigonometric Function: Integration Unit 6 Differential Equations (2 weeks) 1. Slope Fields and Euler s Method 2. Differential Equations: Growth and Decay 3. Separation of Variables and the Logistic Equation 4. First-Order Linear Differential Equations Unit 7 Applications of Integration (2 weeks) 1. Area of a Region Between Two Curves 2. Volume: The Disk Method 3. Volume: The Shell Method Unit 8 Integration Techniques, L Hopital s Rule, and Improper Integrals (3 weeks) 1. Basic Integration Rules 2. Integration by Parts 3. Trigonometric Integrals 4. Trigonometric Substitution 5. Partial Fractions 6. Integration by Tables and Other Integration Techniques 7. Indeterminate Forms and L Hopital s Rule 8. Improper Integrals Unit 9 Infinite Series (3 weeks) 1. Sequences 2. Series and Convergence 3. The Integral Test and p-series 4. Comparison and Series 5. Alternating Series 6. The Ratio and Root Tests 7. Taylor Polynomials and Approximations 8. Power Series

4 9. Representations of Functions by Power Series 10. Taylor and Maclaurin Series Unit 10 Conics, Parametric Equations, and Polar Coordinates (3 weeks) 1. Conics and Calculus 2. Plane Curves and Parametric Equations 3. Parametric Equations and Calculus 4. Polar Coordinates and Polar Graphs 5. Area and Arc Length in Polar Coordinates 6. Polar Equations of Conics and Kepler s Laws Unit 11 Vectors and the Geometry of Space (3 weeks) 1. Vectors in a Plane 2. Space Coordinates and Vectors in Space 3. The Dot Product of Two Vectors 4. The Cross Product of Two Vectors in Space 5. Lines and Planes in Space 6. Surfaces in Space 7. Cylindrical and Spherical Coordinates

5 Assessment Homework is extremely important to the success of this class. Homework will be given frequently. A short quiz will be given corresponding to each assignment at the beginning of the next class period. Students should focus on learning from homework assignment and have completion be a byproduct of trying to learn from them. Far too often, students focus on just completing the assignment and rarely focus on learning. The long term goal is learning not completing. (5 points per quiz) There will be a test at the end of every unit. Tests will typically have a multiple choice section and a free response section requiring explaining solutions to problems in written sentences much like the AP Exam. Students will be graded as they would be graded on an AP Exam. Test may also have a portion that is to be completed with a calculator and another portion that is to be completed without a calculator. This once again mimics the AP Exam. (30 points each) There will be projects assigned throughout the course. Details of each project will be provided when the project is assigned. Students will often work in groups to complete these projects. Project assessments will involve communicating mathematical ideas both orally during a project presentation and in written sentences with a report detailing the project. (30 points each) Problem solving problems will be assigned as an integrated part of the regular lesson plans. Problem solving problems will be completed in class as an organized group activity. Much like with the projects, assessment for problem solving problems will involve communicating mathematical ideas both orally during a presentation and in written sentences with a report. (5 points each) Example Problem Solving Activities: PS1 - The teacher will present the following scenario: At 2:51 PM a car goes through a tollbooth on the Pennsylvania Turnpike at mile marker 71. At 3:02 PM on the same day, the same car goes through another tollbooth at mile marker 85. The speed limit on the turnpike is 65 miles per hour. Could the police issue the driver a ticket based on the Mean Value Theorem? The class will discuss this situation. PS2 - Students will create examples (or state that no such example exists) of a function that is continuous but not differentiable, a function that is differentiable but not continuous, a functions that is neither differentiable nor continuous, and a function that is both differentiable and continuous. They will then discuss the results in small groups. PS3 Students will be given a worksheet with a variety of limit problems including indeterminate forms requiring L Hopital s Rule. The students will complete the worksheet independently then share and discuss the results as a whole group discussion.

6 PS4 Students will be given real-world physical situations, consistent with previously released free response questions, and asked to represent it as a differential equation involving variables, then solve the equation and graph the solution; students will present their results to the class for whole group discussion. PS5 Students will be asked to write definitions of basic calculus concepts in a variety of forms such as recognizing the limit definition of derivative as being the slope of the tangent line or representing a Riemann sum as a definite integral. Definitions will be discussed as a whole group activity. PS6 Students will be asked to summarize the main ideas of each chapter using well-written sentences. Students will then share their summaries in either small groups or as a class. PS7 Students will use graphing calculators to find points of intersection between two curves. The intersection points will then be used to evaluate definite integrals to find the area between the curves. PS8 Students will graph various functions and their derivatives on the calculator and make conjectures about the relationships between their characteristics. PS9 Students will work on an assignment where they are asked to graph a function given the formula and estimate the area of a region bounded by the function, the x-axis, x = 2, and x = 6 using the midpoint Riemann sums with four subintervals of equal length. PS10 Students will use a table of values of two functions and their derivatives to apply the chain rule to find the numerical value of the derivative of composite functions. Rules and Responsibilities Be on time. You must be in your assigned seat and ready to go when the bell rings. Assignments must be completed on time or you will receive a grade of zero. Be prepared. Bring materials such as pencil, textbook, notebook, journal, and homework to class. Use the restroom and fountain before and after class not during. Be informed. When you are absent it is your responsibility to get notes and ask for missed assignments. You will be given as many days as you have missed to complete missed assignments. You must follow all school and classroom rules at all times. Anyone caught cheating will receive a zero for the assignment. Be polite. Raise your hand and wait to be recognized before speaking. Do not interrupt someone else who is speaking. Name calling, profanity, and ridiculing will not be tolerated. Keep your hand and other objects to yourself.

7 Parents Please contact me if you have any concerns. My address is The school phone number is (724) Students are welcome to stay after school for additional instruction. Other Information Graphing calculators will be provided for student use during class and used frequently as an integral part of the class. These uses include students being taught how to use graphing calculators to help solve problems, to experiment, to interpret results, and to support conclusions. These aspects of graphing calculator use will be an important part of all forms of assessment previously mentioned as students will be expected to perform each use on homework, during quizzes, unit tests, group projects, and in problem solving tasks. It is recommended that students either purchase a graphing calculator of their own for home use or download one from the internet. Grades will be posted on a weekly basis. Typically grades are posted on Thursday morning so that they coincide with the weekly eligibility reports generated in the high school office. Lesson plans will also be posted on a weekly basis. Lesson plans for a given week will be available online by the end of school the Friday before. Please remember that all plans are tentative. For more information related to AP courses including AP Calculus, please refer to:

Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,