AP Calculus BC Course Syllabus

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1 AP Calculus BC Course Syllabus Mr. Lonny Stearns Room B Course Overview This course will cover all topics included in the Calculus BC topic outline as it appears in the AP Calculus Course Description. The student will be able to work the problems from a graphical, numerical, and analytical point of view and will then be able to communicate their solutions both verbally and in written form. Students will use a graphing calculator to help them solve problems, experiment, interpret results, and support their conclusions. The purpose of this multiple approach is to foster a deeper understanding of calculus and prepare students to take and perform well on the AP exam this spring and in subsequent courses. The AP Exam in May is a requirement for this course. AB Course Outline This is a preliminary schedule for the course and may change based on student performance. Topic Outline: I. Limits and Derivatives a. The Tangent and Velocity Problems - Instantaneous Velocity - Average Velocity b. The Limit of a Function - One-sided Limits c. Calculating Limits Using the Limit Laws - Direct Substitution Property - Squeeze Theorem d. Continuity - Continuous Functions - Intermediate Value Theorem e. Limits Involving Infinity - Asymptotes Written as Limits f. Tangents, Velocities, and Other Rates of Change - Definition of a Limit g. Derivatives h. The Derivative as a Function - Other Notations to write Derivatives - Higher Derivatives i. What Does f Say About f? - Local Max/Min - Critical Values - Increasing/Decreasing Functions - Concavity - Inflection Points - Antiderivatives 1

2 II. Differentiation Rules a. Derivatives of Polynomials and Exponential Functions - Constant Rule - Power Rule - Constant Multiple Rule - Sum/Difference Rule - Definition of e as a Limit x - Derivative of e b. The Product and Quotient Rules c. Rates of Change in the Natural and Social Sciences d. Derivatives of Trig Functions sin cos - lim 0 1 and lim e. The Chain Rule - The Power Rule Combined with the Chain Rule - Derivatives of Parametric Equations f. Implicit Differentiation - Derivatives of Inverse Trig Functions g. Derivatives of Logarithmic Functions - Logarithmic Differentiation - The Number e as a Limit h. Linear Approximations and Differentials III. Applications of Differentiation a. Related Rates b. Maximum and Minimum Values - Local/Absolute Max/Min - Extreme Value Theorem - Fermat s Theorem c. Derivatives and the Shapes of Curves - Mean Value Theorem - Increasing/Decreasing Test - First Derivative Test - Concavity Test - Second Derivative Test d. Graphing with Calculus and Calculators e. Indeterminate Forms and L Hospital s Rule - Differences - Products - Powers f. Optimization Problems - First Derivative Test for Absolute Extreme Values g. Antiderivatives - Differential Equations - Direction Fields 2

3 IV. Integrals a. Areas and Distances - Left/Right Riemann Sums b. The Definite Integral - Link Limits of Riemans Sums to Integrals - Properties of Integrals - Comparison Properties c. Evaluating Definite Integrals - Evaluation Theorem - Net Change Theorem d. The Fundamental Theorem of Calculus e. The Substitution Rule f. Integration by Parts g. Additional Techniques of Integration - Trig Integrals - Trigonometric Substitutions - Partial Fractions h. Approximate Integration - Midpoint Rule - Trapezoidal Rule - Error Bounds i. Improper Integrals V. Applications of Integration a. More About Area b. Volumes - Cross Sections - Disk/Washer Method - Shell Method c. Arc Length - Parametric Arc Length d. Average Value of a Function - Mean Value Theorem for Integrals VI. Differential Equations a. Modeling With Differential Equations - Population Growth - Logistic Differential Equations - Motion of a Spring b. Direction Fields and Euler s Method c. Separable Equations d. Exponential Growth and Decay - Half Life - Newton s Law of Cooling e. The Logistic Equation VII. Infinite Sequences and Series a. Sequences b. Series c. The Integral and Comparison Tests; Estimating Sums d. Other Convergence Tests e. Power Series f. Representations of Functions as Power Series 3

4 g. Taylor and Maclaurin Series h. The Binomial Series i. Applications of Taylor Polynomials VIII. Vector Functions a. Vector Functions and Space Curves b. Derivatives and Integrals of Vector Functions c. Arc Length and Curvature d. Motion in Space IX. Polar Coordinates a. Curves in Polar Coordinates b. Areas and Lengths in Polar Coordinates X. Review for the AP Exam Teaching Strategies I will utilize a variety of activities with each class period. A typical class will consist of a combination of lecture, to introduce topics, and classroom / group work. We will have daily classroom work that will be collected, graded, and returned during the next class period. Students will work together on a regular basis, both formally and informally. Collaboration with classmates will be an invaluable tool. I will encourage different approaches to solving a problem and believe that we will learn through our mistakes. Emphasis is placed on students communicating their method of solution and a justification of their answer. Technology Each student is required to have a graphing calculator. All classroom work requiring the use of a calculator will be completed on a TI-84 Plus for this is the type of calculator utilized on our Smart board immolator. Calculators are used to assist in the understanding of topics, as well as for experimentation. There will be numerous assignments, quizzes and portions of exams in which a calculator will not be used. All classroom presentations will be done with the Smart Board. 4

5 Student Evaluation Evaluations are based on assignments, quizzes, and exams. Assignments: includes both in class work as well as homework. Class work and homework assignments are graded based on a scale of ten points. Included with class work will be a Problem of the Week in which free response questions will be assigned. DTQ s: (Do These Quickly) are warm-up activities at the beginning of the block. Most of these questions are multiple choice questions from previously released AP Exams. Quizzes: given each week and will be a combination of multiple choice questions and free response. Exams: exams will always be in two parts; Calculator and non-calculator. Exams will be comprised of questions that reflect questions found on the AP Exam as well as questions found on college-level Calculus exams. Take home exams may also be utilized. BONUS: Students will have the opportunity to make up points during the semester. A) Students may bring a progress report, signed by the parent, during the last week of each month. These progress reports can be printed off Infinite Campus. B) Students can earn points by coming in during access or any free period they have on their schedule. Access is from 7:00-7:30. Students may come in to my room during their free periods to work on assignments, study for exams or quizzes, or to work on notes. This opportunity is available even during periods in which I am teaching a different class. Students can come in, sign their name in the notebook, and sit in an empty desk and work as long as they need. Points are earned based on the time spent working on math only at the rate of 1 point for each 30 minutes. C) We will have extra problems / assignments during the semester. Absences Absences will be recorded as excused and unexcused for the purpose of makeup work. Work that is missed due to absences will receive credit if the student contacts teachers on the day he or she returns from any absence to arrange to complete all makeup work assigned and to establish when this makeup work is due. Makeup work for the first two unexcused absences will be allowed for credit with one grade reduction for all work completed. After the first two unexcused absences from a class, makeup work will be allowed for credit with two letter grade reductions for all work completed. Grade Breakdown A 90% or higher Exceptionally strong knowledge of content B 80% % Strong knowledge of content C 70% % A good knowledge of content D 60% % Some knowledge of content F Below 60% No evidence of knowledge of the content 5

6 Primary Textbooks We have created our own textbook for this academic year. These textbooks will be available on our first day of classes in August. Students will need to provide a 3-Ring binder to keep this textbook in. Supplementary Materials AP Calculus Multiple Choice Questions, AP Calculus Free Response Questions, , , AP Calculus AB Free Response Questions, Food & Drink As per Lakewood High School policy, no food or beverage, except water, is allowed in the academic wing. No exceptions! Cell Phones I will follow the policy set forth by Lakewood High School. I reserve the right to alter or change this syllabus without notice. 6

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a