AP Calculus BC Course Syllabus Course Overview Instructor: S. Atkins, Atkins.Storie.L@muscogee.k12.ga.us AP Exam: Thursday, May 5, 2016 (Morning 8 AM) AP Mock Exam: Friday, April 29 (4 PM 8:30 PM) AP Cram Sessions: Sunday, May 1, (2:00 4:00) Wednesday, May 4 (3:30 5:30 PM) AP Breakfast: Thursday, May 5 (7:00 AM) The development of students understanding for the fundamental concepts of calculus is the primary objective of our AP Calculus program. With this in mind, a key focus of instruction is students comprehension of how and why main concepts are developed. Once the foundational knowledge for key concepts is built, students apply their understanding in multiple representations of these calculus concepts. Using graphical, numerical, and analytical approaches to solving problems, students can offer a wide range of responses to various applications and extensions of calculus concepts. Along with minimal reviews of previous topics, the main areas of concentration include limits, continuity, differentiation, and integration. Additional explorations for applications of each topic are also incorporated. Appropriate tools such as calculators and computers will be utilized to effectively provide for mathematical learning and applications in problems solving. Teacher lecture and discussion, partner and group activities, hands-on experiences, and calculator /computer projects will be used to implement instruction of the course. Teaching Strategies Expectations for students are set at a high level. Delivery of the course objectives will involve the critical use of student investigations at a graphical, numerical and analytical level. Students must utilize all their prior knowledge at a deeper level and with the use of technology, such as calculator and computer programs like Geometer s Sketchpad. By expanding their experiences in this manner, students are forced to explain solutions in a variety of ways, while using proper terminology in their communicated responses. Throughout the course, students will continue to understand and apply concepts at a deeper level while engaging in exploratory and discovery activities. On a daily basis, instruction of the course is not limited to teacher lecture and class discussion. Sometimes students will work with a partner to solve problems, discover patterns and make conjectures about data. For other activities, students may work with a group to share ideas and illustrate their findings to the class. For demonstration purposes, visualization of key concepts, and integration of calculus application problems, students collaboratively engage in hands-on tasks that often use technology. With a course focus of AP exam preparation, students will frequently engage in applying their calculus knowledge to solving multiple-choice and free-response type questions on daily warm-up quizzes and AP style unit assessments. Used throughout the year, these strategies help set the tone for class and allow us to discuss strategies and calculator techniques that can be helpful on the exam. During fourth nine weeks, extensive review activities will be offered to better prepare students for the AP exam. In-class activities will rotate between selected calculator and non-calculator questions in both multiple-choice and freeresponse format. Using released AP questions, students will review problems together to collaborate solution methods, pinpoint weaknesses, and present alternate solution methods to the class. Students may also choose to take a full-length mock exam, which incorporates questions from recently released AP Exams. Technology Numerous technology based activities are incorporated into the course instruction. All students are required to have a Texas Instruments graphing calculator. Suggested models are the TI-84 Plus/Silver/CE, TI-89, or TINspire. The graphing calculator is used primarily for its graphing and analysis capabilities as students examine graph behavior and data values in the table feature. For some hands-on activities, the Texas Instruments Calculator-Based Laboratory equipment and probes are used to collect and analyze data. Geometer s Sketchpad is also used for student exploration and instructor demonstration purposes. Using this computer software, students explore such topics as limits, derivative, and area under the curve. Selected Geometer s Sketchpad activities from Calculus in Motion TM software are used for demonstration purposes and group problem-solving activities.
Prerequisites Before studying calculus, all students should complete four 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 linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewisedefined functions. 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 and so on) and know the values of the trigonometric functions at the numbers 0, π, π, π, π, and their multiples. 6 4 3 2 Topic Outline for Calculus BC I. Functions, Graphs and Limits Analysis of graphs. With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function. Limits of functions (including one-sided limits) An intuitive understanding of the limiting process. Calculating limits using algebra. Estimating limits from graphs or tables of data. Asymptotic and unbounded behavior Understanding asymptotes in terms of graphical behavior. Describing asymptotic behavior in terms of limits involving infinity. Comparing relative magnitudes of functions and their rates of change (for example, contrasting exponential growth, polynomial growth and logarithmic growth). Continuity as a property of functions An intuitive understanding of continuity. (The function values can be made as close as desired by taking sufficiently close values of the domain.) Understanding continuity in terms of limits Geometric understanding of graphs of continuous functions (Intermediate and Extreme Value Theorems). Parametric, polar and vector functions. The analysis of planar curves includes those given in parametric form, polar form and vector form. II. Derivatives Concept of the derivative Derivative presented graphically, numerically and analytically. Derivative interpreted as an instantaneous rate of change. Derivative defined as the limit of the difference quotient. Relationship between differentiability and continuity. Derivative at a Point Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents. Tangent line to a curve at a point and local linear approximation. Instantaneous rate of change as the limit of average rate of change. Approximate rate of change from graphs and tables of values. Derivative as a Function Corresponding characteristics of graphs of ƒ and ƒ. Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ. The Mean Value Theorem and its geometric interpretation. Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa.
Second derivatives Corresponding characteristics of the graphs of ƒ, ƒ and ƒ. Relationship between the concavity of ƒ and the sign of ƒ. Points of inflection as places where concavity changes. Applications of derivatives Analysis of curves, including the notions of monotonicity and concavity. Analysis of planar curves given in parametric form, polar form and vector form, including velocity and acceleration. Optimization, both absolute (global) and relative (local) extrema. Modeling rates of change, including related rates problems. Use of implicit differentiation to find the derivative of an inverse function. Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed and acceleration. Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations. Numerical solution of differential equations using Euler s method. L Hospital s Rule, including its use in determining limits and convergence of improper integrals and series. Computation of derivatives Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric and inverse trigonometric functions. Derivative rules for sums, products and quotients of functions. Chain rule and implicit differentiation. Derivatives of parametric, polar and vector functions. III. Integrals Interpretations and properties of definite integrals Definite integral as a limit of Riemann sums. Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: b f (x)dx = f(b) f(a) a Basic properties of definite integrals (examples include additivity and linearity). Applications of Integrals Appropriate integrals are used in a variety of applications to model physical, biological or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific applications should include finding the area of a region (including a region bounded by polar curves), the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, the length of a curve (including a curve given in parametric form),and accumulated change from a rate of change. Fundamental Theorem of Calculus Use of the Fundamental Theorem to evaluate definite integrals. Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined. Techniques of antidifferentiation Antiderivatives following directly from derivatives of basic functions. Antiderivatives by substitution of variables (including change of limits for definite integrals), parts, and simple partial fractions (nonrepeating linear factors only). Improper integrals (as limits of definite integrals). Applications of antidifferentiation Finding specific antiderivatives using initial conditions, including applications to motion along a line. Solving separable differential equations and using them in modeling (including the study of the equation y = ky and exponential growth). Solving logistic differential equations and using them in modeling.
Numerical approximations to definite integrals. Use of Riemann sums (using left, right and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically and by tables of values. IV. Polynomial Approximations and Series Concept of series. A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence. Series of constants Motivating examples, including decimal expansion. Geometric series with applications. The harmonic series. Alternating series with error bound. Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series. The ratio test for convergence and divergence. Comparing series to test for convergence or divergence. Taylor series Taylor polynomial approximation with graphical demonstration of convergence Maclaurin series and the general Taylor series centered at x = a. Maclaurin series for the functions e x 1, sin x, cos x, and Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation and the formation of new series from known series. Functions defined by power series. Radius and interval of convergence of power series. Lagrange error bound for Taylor polynomials. Student Evaluation Along with the daily warm-up quizzes, students are assigned homework problems from the textbook and project activities. These problems are used to reinforce students knowledge of key concepts and manipulation skills. Daily quizzes, homework, and writing assignments comprise 25 percent of the course evaluation. The remaining 75 percent is devoted to formal evaluations, with 60 percent for tests and 15 percent for exams. Formal evaluations are typically administered at the end of key concept instruction. Most evaluations are AP style, including calculator and non-calculator sections as well as multiplechoice and free-response type questions. Student evaluations are graded according to the published AP guidelines. Likewise, quarter exams and the mock AP exam follow the AP format, and questions from previous AP Exams are incorporated in the course as much as possible. The AP mock exam will be administered on Friday, April 29, from 4-8 PM. Students are strongly encouraged to take this full-length, mock exam because it provides valuable experience before the actual AP exam and the grade can be used in place of the final exam. Grades will be assigned based on the following percentages: 1. Daily Warm-up Quiz 5% 2. Homework/Quiz/Lab/Writing/Group Work 20% 3. Tests 60% 4. Quarter Exam 15% All assignments are graded out of 100 points. Tests and quizzes will be announced at least two days in advance. It is the student's responsibility to complete all homework assignments on an individual basis. The student's understanding of content may be evaluated by the following methods: grading for the correctness of all or simply a few of the problems, grading ½ correctness and ½ attempt, or grading for attempt alone, or student presentation/group work/board work. 1 x. *****Late assignments will NOT be accepted for any reason*****
All AP style tests are scored using the AP guidelines; however, the raw, composite score is changed to a grade for the course using the following conversion: Make-up Work: Missed assignments due to an absence must be arranged for and made up within 3 days for students who have excused absences only. If your absence is unexcused or no excuse is submitted within 3 days, a grade of zero will be assigned for ALL missed work. Discussions of and arrangements for make-up work must be coordinated with me before or after class. It is the student s responsibility to ensure that all make-up work is completed. With regard to make-up work, the following procedures will be implemented: For make-up of tests or quizzes for which the student had prior knowledge of, the test or quiz will be taken in class on the day of return. At the teacher s discretion, the make-up test or quiz may or may not be the same version as the one administered the day given in class. For daily homework assignments that have not been graded and returned to all students, make-up work may be done at home and turned in for credit. If an assignment has been collected, graded, and returned to all students, missing daily homework assignments must be completed in my presence after school. Make-up of lab or group activities must be coordinated on a case-by-case basis. I reserve the right to administer a different version of tests or make-up assignments for any student who misses an assignment or test or for students who incur more than 7 absences. Cheating Policy: Blatant cheating on assignments will not be tolerated. This includes copying other student s work, having the exact content of another student s work for multiple problems, possessing another student s work, submitting another student s work as your own, or assisting others in cheating. During tests and quiz situations, students should refrain from looking anywhere other than down at the test paper. Cheating methods for tests and quizzes will be deterred with calculator vs. non-calculator sections, different versions of tests and quizzes, and strict monitoring. A grade of zero will be assigned as a consequence for all cheating incidences and for both parties involved, when the case warrants. Additionally, an incident report will be filed with the honor council. Group Work Policy: Students will often work cooperatively in groups. Participation within a group and rotation of responsibilities among group members is expected. When learning tasks or performance tasks are evaluated based on responses turned in collectively by a group, each member will receive the grade earned by the group, unless otherwise stated. If, however, any member disagrees with a response given by the group, that member may turn in his/her own response or solution, which will be graded on an individual basis. Credit Recovery Policy: Some assignments and tests may qualify for credit recovery for students who do not pass the initial assessment. When credit recovery is allowed, a student must attend tutoring sessions until all necessary skills are acquired to complete a re-assessment. The percent correct on the re-assessment will be used to determine the amount of credit added to the initial assessment grade, up to a score of 70.
Classroom Expectations Be on time and seated by the bell, with pencils sharpened and materials ready. 1 st tardy - warning 3 rd tardy - 45 minute detention 2 nd tardy - 30 minute detention 4 th tardy - administrative referral Students must raise their hand and wait to be recognized. Students must be respectful and courteous, both physically and verbally. Students hands must be visible at all times. Students must place all trash in appropriate containers. No food, drink, or gum will be allowed in class. No personal grooming in class will be allowed. Absolutely no strong perfume, cologne, lotion or spray should be worn or used in class due to medical conditions of the instructor. Above all, students are expected to follow school rules. Please note the following school policies as stated in the Student Handbook: attendance, conduct, cell phones, food, drinks, gum, and classroom expectations. Technology Occasionally, students will be allowed to use school laptops/netbooks as well as their personal laptops, netbooks, ipads, ipods, or other electronic devices in class to complete projects. Use of these devices is at the discretion of the teacher, and students may only use them for the assigned activities. Inappropriate use of the device will result in consequences outlined in the Student Handbook. MCSD and Columbus High School are not responsible for damaged, lost or stolen, personal devices. Student Assistance Each student may seek individualized assistance on Monday and Friday afternoons from 3:25 3:50. I have read and understand the policies and guidelines stated in Mrs. Atkins AP Calculus BC syllabus. Student Signature Date Parent/Guardian Signature Date