AP CALCULUS AB - Weebly



AP Calculus AB Course Syllabus and GuideBaker High School Fall 2016Mrs. AgnewCOURSE OVERVIEWAP Calculus AB is a college-level mathematics course that is “primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.” This course is intended to be challenging and demanding. The focus of the course is not manipulation or memorization of functions, curves, theorems, or problem types. Though algebraic manipulation and computational competence are important skills, the true focus of the course is the development of problem solving strategies using the concepts and skills introduced in this course. Emphasis will be placed on the Six Mathematical Practices that will be embedded into all activities done throughout the course.COURSE RESOURCESPrimary TextbookLarson, Ron and Bruce Edwards. Calculus, AP Edition. 9th ed. Belmont, CA: Brooks/Cole Cengage Learning, 2010.Ancillary Textbooks and ResourcesAlbert, Benita and Phyllis Hillis. Calculus Calculator Labs. Andover, MA: Skylight Publishing, 2005.Anton, Howard, Irl Bivens, and Stephen Davis. Calculus. 10th ed. Hoboken, NJ: John Wiley & Sons, 2012.Finney, Ross, Franklin Demana, Bert Waits, and Dan Kennedy. Calculus: Graphical, Numerical, Algebraic, AP Edition. 4th ed. Boston, MA: Pearson Prentice Hall, 2012.Foerster, Paul. Calculus: Concepts and Applications. 2nd ed. Emeryville, CA: Key Curriculum Press, 2005.Rogawski, Jon and Ray Cannon. Calculus for AP. 2nd ed. New York: W.H. Freeman and Sons, 2012.Smith, Robert and Roland Minton. Calculus, Early Transcendentals. 4th ed. New York: McGraw-Hill, 2012.Stewart, James. Calculus, AP edition. 7th ed. Belmont, CA: Brooks/Cole Cengage Learning, 2012.TECHNOLOGY RESOURCESIn this course, technology will be used on a daily basis to enhance both teaching and learning. Several labs throughout the semester will focus on the use of the calculator to draw conclusions or discover connections to previously learned material. Therefore, all students are required to have a graphing calculator, specifically a TI-83, TI-84, TI-89, or TI-Nspire. In addition to the graphing calculator, the instructor will make use of the Geometer’s Sketchpad and Calculus in Motion software when presenting new material. Finally, all notes and lectures are presented using Microsoft Power Point and SmartBoard presentation software. These presentations will be posted on the instructor’s Moodle site for student access.EVALUATION AND ASSESSMENTThe grading procedures for this course will follow the procedures set forth by the school district. Each quarter grade will be computed using homework, lab activities, quizzes, class work grades, and tests. The percentage for each category in the pre-exam quarter grade is listed below:Class work/Homework/Quizzes30%Tests/Major Projects70%The quarter exam will account for 20% of the final quarter grade. The student’s final course grade will be the average of the two quarter grades. The assignment of grades will be based on the standard grading scale of the school system:90 to 100 = A 80 to 89.9 = B70 to 79.9 = C60 to 69.9 = D 0 to 59.9 = EThe student will be assigned homework daily, and he/she is expected to attempt each problem assigned. At the beginning of each class, questions from the homework will be answered. Homework will be checked on a random basis. Your homework will be graded on completion, rather than accuracy, unless otherwise stated.There will be a test at the end of each major topic unit. These major course topics are centered on the Big Ideas of the AP Calculus AB course. Some longer units may require a mid-unit test, in addition to the end of unit test. All tests will be announced several days in advance to provide you adequate time for study and preparation. Most tests will include several questions in which you will not be allowed to use the calculator. All tests will consist of both multiple choice and free-response questions, with a heavy emphasis on free-response questions. Students will be assessed on their ability to effectively communicate the justification for their answer/solution.Lesson quizzes will be given on a frequent basis to ensure mastery of key concepts and skills. Problems on these quizzes will resemble homework problems. The importance of attempting your homework every night cannot be overemphasized. Class assignments and labs will used throughout the semester to solidify difficult concepts and provide adequate opportunities for practice.Progress reports will be provided after each major test. Remember that you may also track your grade using STI Home, which can be accessed from the school website.PREREQUISITESBefore studying Calculus, all students will have completed courses in algebra, geometry, trigonometry, and elementary functions. Students should be familiar with linear, polynomial, rational, exponential, logarithmic, trigonometric, and piecewise defined functions. Specifically, students should have a thorough understanding of the properties of functions, the algebra of functions, the graphs of functions, and the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, etc.). Knowledge of the values of trigonometric functions at angles 0, , , , , and their multiples is also crucial.TEACHING STRATEGIESIn this course, significant time will be dedicated to providing students with opportunities to demonstrate their mastery of the material presented. Students will be asked to work homework problems on the board for the class, explaining the method they used to solve the problem using proper vocabulary. Further, students will frequently be assigned to groups to work on labs, class activities, and test reviews. Students will be expected to assist one another by explaining difficult concepts and tutoring one another as needed.As stated, technology will be used throughout the course to enhance both teaching and learning. Each student will have a graphing calculator to use. We will use the calculator’s graphing and table features to describe function behavior, limits, continuity, linearization, and other concepts. After using the calculator to represent functions graphically and numerically, students then can draw conclusions given the analytical representation of the function. Finally, students will be expected to verbally express these conclusions, citing evidence from the calculator and the function itself. In so doing, students will recognize the connections between the graphical, verbal, numerical, and analytical representations of functions.Finally, new material will be presented in such a way so as to involve the entire class in the “discovery” process. Rather than the instructor simply disseminating the information to the class, students will be encouraged to actively participate in the instruction. Emphasis will be given to asking higher-order thinking questions to move the students toward the new material. Students will be asked to draw on previously learned concepts to arrive at the desired conclusions. Students will be encouraged to share their thoughts, ideas, and questions. When students are sharing ideas and asking questions, a richer and more thorough understanding of the material will be attained.ATTENDANCE POLICYAttendance at school is a prerequisite to success in the classroom. Students are expected to be present and ready to learn on a daily basis. The attendance policy for this course follows the policy for this school system. Five or more unexcused absences may result in loss of credit for the course. Absences with a doctor’s note will be excused, and a total of four absences may be excused using a parent’s note. After four parent notes, any further parent notes will be considered unexcused absences. MAKE-UP POLICYWhen a student is absent, it is the responsibility of the student to submit assignments due on the date of the absence in a timely manner. Furthermore, it is the responsibility of the student to obtain any missed assignment. Missed tests or quizzes must be made up within one week from the day the student returns to school. Missed tests must be made up after school, and it is the student’s responsibility to schedule a time to make up the test. Missed homework assignments are to be submitted on or before the day that the student takes that unit test.This make-up policy will be strictly enforced so that students will be encouraged to make up missed assignments in a reasonable time period. COURSE FRAMEWORKThe framework for the course is designed around the Big Ideas of AP Calculus AB: Limits, Derivatives, and Integrals/Fundamental Theorem of Calculus. These big ideas are subdivided into smaller units that combine related material.UNIT 1: FUNCTIONAL ANALYSIS (1 WEEK)The student will be able to…Represent functions numerically, graphically, analytically, and verballyIdentify the graphs of the parent functions of linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, root, greatest integer, and absolute value functionsTransform each of the above functions by shifting, stretching, and reflectingDefine inverse functions and composition of functionsInvestigate components of functions using the graphing calculator, including extrema, roots, symmetry, asymptotes, and interceptsUse appropriate terminology with functions, including domain, range, roots, and interceptsIdentify the slope as the average rate of changeSample Student Activity: Students will complete the Parent Function Worksheet. This will require students to draw on past knowledge to graph 18 parent functions from previous courses. In small groups, students will then identify the domain, range, discontinuities, symmetry, roots, end behavior, and extreme values of each parent function. Students must use proper notation (i.e., set builder or interval notation) when discussing graphical characteristics.UNIT 2: LIMITS AND CONTINUITY (3 WEEKS)The student will be able to…Calculate limits of functions graphically and numerically (using a table of values) Calculate limits of functions algebraically using the Limit LawsDefine continuity and test functions for continuity over open and closed intervalsDistinguish between removable and nonremovable discontinuitiesUnderstand continuity in terms of limitsFind one-sided limitsDemonstrate an understanding of graphs of continuous functions, with specific emphasis on the Intermediate Value Theorem and the Extreme Value TheoremDefine infinite limits and describe asymptotic behavior of functions in terms of limits involving infinitySample Student Activity: Important Limits Lab – students will use graphical means to discover the special limits involving trigonometric functions. In addition, students will use a numerical approach to identify the definition of “e”. Finally, students will connect these important limits to evaluate other limits algebraically. UNIT 3: DIFFERENTIATION (3 WEEKS)The student will be able to…Define the derivative as the limit of the difference quotientInterpret the derivative as the instantaneous rate of changeRelate the concepts of differentiability and continuityRelate the concepts of average rate of change and instantaneous rate of change, and interpret this relationship verballyApproximate the rate of change from graphs and tables of valuesFind the slope of a curve at a point and use it to write an equation of a tangent line if one existsCalculate the derivative using the basic differentiation rules, the chain rule, and implicit differentiationUse the tangent line to a curve as a linear approximationSample Student Activity: Door Activity – students will gather data points from a door closing (time versus door’s angle from closed position). Students will use these points to generate a best fit curve for the data. Then, students will use average rates of change over diminishing intervals to estimate the instantaneous rate at which the door is closing. Students will use proper notation in labeling the instantaneous rate of change as the derivative. Terms such as derivative, tangent line, local linearity, and linear approximation will all be introduced through this activity.UNIT 4: GRAPHING USING FIRST AND SECOND DERIVATIVES (1.5 WEEK)The student will be able to…Identify corresponding characteristics between the graphs of f, , and Use the sign of to find where the graph of f is increasing and decreasingUse the sign of to describe the concavity of fUse first derivatives to find extreme values and second derivatives to find inflection pointsUse the Mean Value Theorem and describe its geometric consequencesSample Student Activity: Curve Sketching Project – students will be provided 4 functions. The ultimate goal of the student is to sketch the graph of each function. However, they are to collect information used to sketch each curve. Students will use the process of differentiation to determine intervals of increase/decrease, extreme values, points of inflection, and intervals of concavity. Once all of those information has been gathered and communicated properly, the student will use this information to sketch the curve. Students may use technology to assess their sketch.UNIT 5: APPLICATIONS OF DIFFERENTIATION (1.5 WEEKS)The student will be able to…Use the derivative to optimize, finding both absolute and relative extremaUse the derivative to model rates of change, including related ratesUse the derivative in the study of motion (speed, velocity, and acceleration) and interpret verbally the derivative as the rate of change in that contextUse L’Hospital’s Rule of calculate the limit of functions of an indeterminate formSample Student Activity: Related Rates Box Activity – students will develop their own unique related rates question. Then students must design a model of their related rates question within a shoe box. The model must accurately portray the problem’s scenario. The question must be visible, and the solution of the problem must be provided. Students must take great care to communicate the problem to provide all required information to solve the problem.UNIT 6: INTEGRATION (3 WEEKS)The student will be able to…Interpret the definite integral as the limit of Riemann SumsCompute Riemann Sums using left, right, and midpoint evaluation points, and investigate upper and lower Riemann SumsInterpret the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the intervalEvaluate definite integrals using the basic properties of integralsUse the Fundamental Theorem of Calculus to evaluate definite integralsUse the Fundamental Theorem of Calculus to represent a particular antiderivative, and the analytical and graphical analysis of functions so definedFind antiderivatives from derivatives of basic functions and by substitution of variablesUse Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, geometrically, and by tables of valuesSample Student Activity: The graphing calculator activity Riemann Sums allows students to see different Riemann sums expressed graphically and to use the values of these sums to estimate the area of a region using left-hand endpoint, right-hand endpoint, and midpoint methods. They can then see the relationship between the exact area and the limit of the Riemann sum. Students will then draft an instruction sheet for calculating Riemann Sums and Trapezoidal Sums.UNIT 7: APPLICATIONS OF INTEGRATION (2 WEEKS)The student will be able to…Use integrals in a variety of applications, including the modeling of biological, social, and economic situationsCompute the area of a region, the volumes of solids of revolution, the volumes of solids with known cross sections, and the distance traveled by a particle along a lineDetermine the average value of a function over an interval and understand the geometric interpretation of average valueUse the integral of a rate of change to give accumulated changeSample Student Activity: Distance Velocity Project – students will gather data by driving for 13 minutes, recording the cars velocity every 30 seconds. Students will also record the total distance traveled. Then, using their data points, students will sketch a graph that goes through all data points. Students will use grids to estimate the area under their velocity curve and compare it to the total distance traveled. Students will recognize the connection between the area under a velocity curve and the distance traveled/displacement.UNIT 8: DIFFERENTIAL EQUATIONS (1 WEEK)The student will be able to…Write equations involving derivatives from verbal descriptionsFind specific antiderivatives using initial conditions, particularly with regards to motionSolve separable differentiable equations and use them in modelingInterpret differential equations geometrically via slope fieldsSample Student Activity: Sets of cards include 10 differential equations represented symbolically, as a slope field, and by a verbal description. Students match the cards to bring together all three representations.UNIT 9: AP EXAM REVIEW (2 WEEKS)Students will participate in reviews in preparation for the AP exam. Students will be required to provide justification for solutions (both orally and written). Students will work in small groups on free response questions to collaborate on solutions. Emphasis will be given to using proper terminology, discussing theorem requirements and conclusions, and demonstrating notational fluency.MATHEMATICS PRACTICESThese mathematical practices will be embedded into all instructional activities throughout the course:Reasoning with definitions and theoremsConnecting conceptsImplementing algebraic/computational processesUsing multiple representationsUtilizing notational fluencyCommunicating effectively using convention mathematical structures and terminology ................
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