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2011 – 2012 Porter High School AP Calculus AB Syllabus Prerequisite: Pre-Cal or Dual Credit College Algebra & Trig Cherish Reilly creilly@newcaneyisd.org 5th & 10th Period Conference Ext. 5770 Course Overview Upon successful completion, students should be able to: Work with functions represented graphically, numerically, analytically, or verbally and understand the connections between these representations. Understand the concept of limits and continuity. Use the derivative to solve a variety of problems. Recognize the uses of the definite integral as a limit of Reimann sums, as a net accumulation of a rate of change, and as Trapezoid approximations. Use technology to help solve problems, experiment, interpret results, and verify conclusions. Find the derivative and integral of trigonometric, logarithmic and exponential functions. Calculate the area between two curves. Model problem situations using limits, derivatives, indefinite integrals, and definite integrals. Communicate solutions to mathematical problems both verbally and in written sentences. Primary Textbook Finley, Demana, Waits, Kennedy. Calculus ~ Graphical, Numerical, Algebraic.Third Edition. Pearson/Prantice Hall Technology The TI-84 Plus graphing calculator will be used in class regularly to help maximize the learning process. It is strongly suggested that you have your own graphing calculator to be used at home as well as in future math classes. A class set will be provided and there will be a few available for extended checkout. Graphing calculators help students conduct explorations, graph functions, solve equations numerically, analyze and interpret results, and justify and explain results of graphs and equations. Supplies Notebook Paper Pencils TI-83 or TI-84 Calculator (classroom set provided) Grading Scale 10% Homework 30% Daily Work: class work & quizzes 60% Tests: 4 Major Grades per 9 weeks 2011 – 2012 Porter High School Tutorials & AP Lounge My Classroom (J113): Mornings: Tuesday & Friday 6:50 – 7:20 Afternoon tutoring can be scheduled AP Lounge: Dates to be announced (LMC3 in library) Re-Testing Policy Any student who makes below 70 on a major grade, may take a retest if the following requirements are met: 1. The student must attend at least 2 tutoring sessions provided by the teacher. 2. The retest must be taken no more than 2 weeks from the original date of the test AND must be completed within the grading period. Topic Outline Units will consist of daily note taking, frequent assignments, various quizzes, and end of unit tests. Fall and spring semester finals are also given. Unit 1: Relations, Functions, Graphs, & Geometric Transformations (August/September) Slope of a line as rate of change Parallel and Perpendicular Lines Domain and range of a function Piecewise functions Composition of functions Inverse functions Exponential and Logarithmic functions Domain and range of trig functions Graphs and transformations of trig functions Unit 2: Limits & Continuity (September) Describe, define, calculate, and apply properties of limits Asymptotic behavior of limits involving infinity Calculate limits at infinity and identify the vertical and horizontal asymptotes Sandwich Theorem Removable, jump and infinite discontinuity Calculate the average and instantaneous speed Unit 3: Limits & Concepts of the Derivative (September/October) Definition of a derivative as a limit of the difference quotient Interpret a derivative as an instantaneous rate of change Relationship between differentiability and continuity Unit 4: Differentiation (October/November) Rules for derivatives – constant, power, sum, difference, product, & quotient rules 2011 – 2012 Porter High School Slope of a curve at a point Tangent line to a curve at a point Evaluate the derivative of a trig function Implicit differentiation Understanding and applying the Chain Rule Compare characteristics of f and f’ Mean Value Theorem (MVT) Unit 5: Applications of Derivatives (December) Extreme values and local extrema Points of inflections as places where concavity changes First derivative test Second derivative test Characteristics of f, f’, f’’ and the relationship between them Optimization Implicit differentiation to find the derivative of an inverse function Derivative of an Inverse, Exponential, Logarithmic, and Trig function Unit 6: Integration (January/February) Basic antiderivative rules Area under a curve using Riemann sums (left, right, midpoint) Average Value Theorem Antiderivatives by substitution How and when to use integration by parts Integrate Exponential and Logarithmic functions Trapezoidal rule to approximate a definite integral Unit 7: Volumes of solids (February/March) Area between two curves Volumes of solids using the disc method Volumes of solids using the washer method Volumes of solids using the cross section method Unit 8: Differential Equations & Slope Fields (March) Solve separable differential equations Differential equations to solve growth and decay problems Draw slope field of a given derivative Recognize the function given its slope field Unit 9: AP Test Review (April/May) Multiple-choice practice Free-response practice 2011 – 2012 Porter High School Unit 10: After the Exam (May) Develop and present a Calculus Project Look at college math requirements Cooperative Learning I encourage cooperative learning during class. It is beneficial for students to work together as well as independently to solve complex problems. I believe that classroom situations should help prepare students for the working environment and students should be able to read and write mathematics and be able to determine if an answer is reasonable. Cooperative learning helps to foster student exploration and discovery. Teaching Strategies There are four types of problem solving approaches that are emphasized in mathematics: numerical analysis, graphical analysis, analytic/algebraic analysis, and verbal/written analysis. Developing all four skills will help students master important calculus concepts. Activities Average and instantaneous rates of change: A golf ball is dropped from a balcony of a two story building. What is the average speed during the first second of fall? Find the speed of the ball at the instant t = 1. Note: a dense solid object dropped from rest to fall freely near the surface of the earth will fall y x 2 . Sandwich Theorem: Students graph y1 x 2 , y2 x 2 , y3 sin( 1 ) in radian mode on the graphing calculator. The limit as x x approaches 0 of each function is explored in an attempt to “see” the limit as x approaches 0 of x 2 sin( 1 ) . x Expectations AP Calculus AB is an advanced mathematics class and I expect my students to put forth more than the necessary effort to excel in this course. A solid grasp of the main concepts will greatly benefit students in their future mathematics courses. One of the main goals of this class is passing the AP Exam. This will help position students for acceptance into a multitude of universities as well as gain valuable college credit which helps to save students money. In order to reach this goal I expect a great deal from my students. Here is a plan to excel: Attend class regularly. Be prepared to work hard each day. Ask questions. Take good notes. Do your homework. Use all resources available to you. Review your notes, don’t wait till the last minute. Form a study group that meets regularly to do the homework and study for tests

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posted: | 11/23/2011 |

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