AP CALCULUS COURSE SYLLABUS School Year CEDAR GROVE HIGH SCHOOL. Phone Number: (678)
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1 AP CALCULUS COURSE SYLLABUS School Year CEDAR GROVE HIGH SCHOOL Teacher: Mrs. J. Showell Phone Number: (678) Room Number: 223 School Year: Textbook: Stewart Website: Tutorial Days: Thursdays 3:20-4:20 Textbook Price: Replacement Cost Tutorial Location: 223 Department Philosophy: We believe that all students can be successful in math. However, math is not a spectator class. You must actively solve problems in order to gain the skills to be successful in life. We are here not only to teach you math but also to teach you how to think analytically. Math is not only about numbers. Math is a tool to solve problems. Math is logical thinking applied to real world applications. Math is more a thought process than a way to manipulate numbers. Course Description: AP Calculus is a college-level course, with a demanding topic outline. Students need to be dedicated and conscientious in order to succeed in such a challenging course. Our emphasis is that students truly understand calculus and its application to the real world. Student discussions and explorations are a big part of the class. Students should be able to calculate, write about the content, along with the discussions that take place. The course begins with an in depth look at functions, then the limits and continuity of those functions are explored. Next, the concepts of the derivative are covered. Finally, applications of the derivative are studied. Further we go in depth looking at antiderivatives, and then integrals are explored. Next, the concept of the area between two curves is covered. Finally, applications of the integral including the volume of solids of revolution are studied. The time allotment in the outline is an estimate; the actual time varies depending on the students. Course Prerequisites: Before studying AP Calculus, all students should complete four (4) years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piece-wise defined. In particular, before studying Calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, etc.). A working knowledge of a graphing calculator is also necessary. 1
2 AP Calculus AB Course Outline: I. A Preview of Calculus/ Review (2 week) [C2] Review of Pre calculus (a)the Area Problem (b) The Tangent Problem (c) The Limit of a Sequence (d) The Sum of a Series (e) Graphing Calculator Review: graphing variety of functions - using features of calculator as trace, zoom, window. Polynomial, exponential, logarithmic, trigonometric, piece-wise. III. Limits and Rates of Change (3 weeks) (a) The Tangent and Velocity Problem (b) The Limit of a Function (c) Calculating Limits Using the Limit Laws (d) The Precise Definition of a Limit (e) Continuity (f) Tangents, Velocities, and Other Rates of Change V. Applications of Differentiation (5-6 weeks) (a) Maximum and minimum Values (b) The Mean Value Theorem (c) How Derivatives Affect the Shape of a Graph (d) Limits at Infinity (e) Horizontal Asymptotes (f) Summary of Curve Sketching (g) Graphing with Calculus and Calculators (h) Optimization Problems (i) Applications to Economics (j) Newton s Method (k) Anti-derivatives VII. Applications of Integration (4-5 weeks) (a) Areas between Curves (b) Volumes (c) Volumes of Cylindrical Shells (d) Work IX. Differential Equations (2-3 weeks) (a) Modeling with Differential Equations (b) Slope Fields (c) Exponential Growth and Decay (d) Predator-Prey Systems 2 II. Functions and Models (2week) (a) Four Ways to Represent a Function (b) Mathematical Models (c) New Functions from Old Functions (d) Principles of Problem Solving IV. Derivatives (5-6 weeks) (a) Derivatives Introduction (b) The Derivative as a Function (c) Differentiation Formulas (d) Rates of Change of the Natural and Social Sciences (e) Derivatives of Trigonometric Functions (f) The Chain Rule (g) Implicit Differentiation (h) Higher Derivatives (i) Related Rates (j) Linear Approximation and Differentials VI. Integrals (4-5 weeks) (a) Areas and Distances using Riemann Sum and Trapezoid Rule (b) The Definite Integral (c) The Fundamental theorem of Calculus (d) Indefinite Integrals (e) The Total Change Theorem (f) The Substitution Rule VIII. Transcendental Functions (3-4 weeks) (a) The Natural Logarithmic Function (b) The Natural Exponential Function (c) General Logarithmic and Exponential Functions (d) Inverse Functions (e) Inverse Trigonometric Functions
3 Objectives: 1. Analyze the graph of a function and explain the observed local and global behavior of a function. 2. Calculate limits using algebra, and estimate limits from graphs or tables of data. 3. Describe asymptotic behavior in terms of limits involving infinity. 4. Compare relative magnitudes of functions and their rates of change. (For example, contrast exponential growth, polynomial growth, and logarithmic growth.) 5. Determine if a function is continuous in terms of limits or geometrically. 6. Find a derivative geometrically, numerically, and analytically. 7. Find the rate of change or instantaneous rate of change of a function using algebra, graphs, or a table of values. 8. Find the tangent line to a curve at a point and local linear approximation. 9. Find the derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions. 10. Find the derivatives of sums, products, and quotients of functions. 11. Find derivatives using the chain rule and implicit differentiation. 12. Describe the relationship between the increasing and decreasing behavior of a function and the sign of its derivative. 13. Describe the relationship between the concavity of a function and the sign of its second derivative, and find the points of inflection of the function. 14. Use implicit differentiation to find the derivative of an inverse function 15. Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration. 16. Find the ant derivative of a function. 17. Evaluate an integral using Riemann sums and Trapezoidal Rule. 18. Evaluate the definite integral using the Fundamental Theorem of Calculus. 19. Evaluate the definite integral using techniques of integration, including substitution. 20. Use integration techniques to solve problems involving the accumulation of area. 21. Solve problems using differentiable separable equations. 22. Find the area between two curves using techniques of integration. 23. Find the volumes of solids of revolution using integration techniques. Technology Requirement: Technology enables students to see what is being discussed. Topics are presented using the Rule of Four graphically, numerically, algebraically, and verbally. Teacher will use a Texas-Instruments 84 graphing calculator in class regularly. Students are requested to bring graphing calculator daily to class. We will use the calculator in a variety of ways including: (a) Conduct explorations. (b) Graph functions within arbitrary windows. (c) Solve equations numerically. (d) Analyze and interpret results. (e) Justify and explain results of graphs and equations. GRADING SYSTEM: The Dekalb County School District believes that the teachers shall conduct the most important assessment of student learning as they observe and evaluate students in the context of ongoing classroom instruction. A variety of approaches, methodologies, and resources shall be used to deliver educational services and to maximize each student s opportunity to succeed. Teachers shall evaluate student progress, report grades that represent the student s academic achievement, and communicate official academic progress to students and parents in a timely manner through the electronic grading portal. 3
4 GRADING CATEGORIES Pre-Assessments Prior to Learning 0% Assessment During Learning 25% Guided, Independent, or Group Practice 45% Summative Assessments 30% *GRADE PROTOCOL A B C D 70 F Below 70 CLASSROOM EXPECTATIONS MATERIALS AND SUPPLIES PARENTS AS PARTNERS SCHOOL EXPECTATIONS FOR SUCCESS 1. Follow Directions 2. Keep Hands, Feet and Objects to yourself 3. No Food, Drink, Headgear, Cellphones or any electronic devices 4. Be in your seat when the bell rings 5. No Yelling, Screaming and Profanity One 2 (2 inch) 3 ring binder & Loose leaf paper 6 dividers One pack of Expo Dry Erase Board Markers 2 Pencil Sharpener and 1 pack of pencil top Eraser (Dollar store items) Blue or Black Pens & Pencils 1 Box of Tissue TI- 84 plus Graphing Calculator Parents are welcome to Volunteer in class and school activities. If interested, kindly contact Mrs. Showell Make-up Policy: Students will be allowed to make up any work missed with an excused absence. Students must present an excused admit slip upon returning from an absence before getting any missed work. It is the responsibility of the students to make arrangements to get his/her work. Students has two (2) days after receiving work to return the make up work. Late Assignments: Students will be allowed to turn in no more than six late assignments. Students should use the attached cover slip (completely filled), stapled to the work to turn in the late assignments. No late assignments will be accepted without the cover slip. Homework Policy: Homework is assigned daily and collected on a regular basis. Assignments are designed to take about one hour and include not only problems from the current discussion, but almost always some problems from the last few days of class discussion as well. Re-do Policy: Any student can make up two test/quizzes. Please use the attached cover slip (completely filled), to sign up to retake immediately after receiving the original test back. Failure to show up counts toward their re-do testing opportunity. Must attend tutorials before re-do test. Must re-do test within five days. No re-do testing for cheating or disruptive behavior. 4
5 AP CALCULUS COURSE SYLLABUS School Year ACKNOWLEDGEMENT RECEIPT (Sign and return this sheet to Mrs. Showell by 08/12/16). This will count as a graded assignment) Student Name (Print) I have read, reviewed with my parents, and understand the guidelines and expectations for my AP Calculus AB class for school year Student Signature: Parent/Guardian Signature: Date: Date: Special Note: If you have an address, please place it on the line below or just me at my address on the first sheet and I will get it that way. Parents name Home # Cell # Work # address 5
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