Jones College Prep AP Calculus AB Course Syllabus 2015 2016 School Year Ms. Kim Bowman Phone: 773-534-8600 ext. 26053 Email: KLBowman@cps.edu The world sees of us only what we show. Let s show them our best! Course Objectives The Advanced Placement Calculus AB course follows the Advanced Placement syllabus and prepares students to take the AP test in May. Course study will include properties of functions, limits, differential calculus, and integral calculus. Use of symbolic differentiation and integration utilities is also included. The main focus is a solid background in material needed to indicate good preparation for the Advanced Placement Calculus Test (AB) in the first week of May. The test will consist of 45 multiple-choice questions, most involving some computation, and 6 free-response questions, equally weighted. For 28 multiple-choice questions in 55 minutes, no calculator is allowed. For the other 17 multiple-choice questions in 50 minutes and the first half of the freeresponse section (45 minutes), a graphing calculator with certain features is assumed. For the second half of the free-response section (45 minutes), the calculator will no longer be permitted. Total test time is now three hours and fifteen minutes. The free-response questions are scored on content and presentation of the solution and the scores for both parts are combined to produce a raw score and then an index from 1 (no recommendation) to 5 (extremely well-prepared). Most colleges and universities will grant one semester's credit for a score of 3 or better. Required Materials 1. Text: Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic. Prentice Hall, New Jersey, 2012. 2. Graphing Calculator TI-83/89 3. Three Inch Binder with 5 Dividers 4. Loose Leaf College Ruled Paper and Pencils (colored and #2) 5. Graph Paper Supplemental Resources (for both teacher and students): 1. Themes for Advanced Placement Calculus: A Supplement to Accompany Calculus with Analytic Geometry; by Edwards, Houghton Mifflin Company, Boston, 2002. 2. Fast Track to a 5: Preparing for the AP* Calculus AB and Calculus BC Examinations; by Cade, Caldwell, and Lucia, Houghton Mifflin Company, Boston, 2006. 3. Holt Calculus with Analytic Geometry; by Ellis and Gulick; Holt, Rinehart and Winston, Inc, Austin, 1995, 5 th ed. 4. Holt Student Study Guide to accompany Calculus with Analytic Geometry, Ellis and Gulick, Holt, Rinehart and Winston, Inc, Austin, 1995, 5 th ed. 5. Calculus, by Larson, Hostetler, and Edwards, Houghton Mifflin Company, Boston, 2006, 8 th ed. 6. AP Test Prep Series: AP Calculus, by Barton,, et al, Pearson/Addison-Wesley, Boston, 2007 7. Calculus: Graphical, Numerical, Algebraic TestGen 7.2 CDROM, Pearson Education, Inc., Prentice Hall, 2007.
8. Texas Instruments Technology Resource Manual, Finney, Demana, Waits, Kennedy, Pearson Education, Prentice Hall, Boston, 2007, 3 rd ed. 9. Teacher s AP Correlations and Preparation Guide Finney, Demana, Waits, Kennedy, Pearson Education, Prentice Hall, Boston, 2007, 3 rd ed. Teaching Strategies and Methods: Various techniques will be used throughout the class to aid in student mastery of material. These strategies include, but are not limited to the following: Collaborative working environment Students are encouraged to work collaboratively in order to foster a classroom community that supports strengths and weaknesses of individual students. It will also aid in teaching students how to study mathematics and become more independent learners Each topic is presented numerically, geometrically, symbolically, and verbally as students learn to communicate the connections among these representations. This will include several discovery learning labs where students determine the conceptual information Justifications of responses and solutions are part of the routine when solving problems. Students are encouraged to express their ideas in carefully written sentences that validate their process and conclusions. Students make extensive use of the TI-83 plus and TI-84 calculator. Each student has his or her own calculator, and will be provided with one if finances are an issue. Students will receive specialty programs as part of the class. The multitude of functions on the calculator will be incorporated throughout the year. Some of these functions include: solving for the numerical values when asked for the derivative or integral, graphing functions, derivatives and integrals and analyzing the information, as well as experimenting with various applications of the derivative and integral while interpreting the results and supporting the conclusions. Quizzes can be given at any time and can be unannounced. The best way to study for quizzes is to complete all homework in a timely fashion. Tests are given at the end of each chapter and are always cumulative like the AP Exam itself. Students are expected to be in class every day. All students are expected to regularly present and defend ideas, as well as question and suggest ideas to the presenter. Technology and Computer Software The course teaches students how to use graphing calculators to help solve problems, experiment, interpret, results, and support conclusions. The TI-83 and TI-89 graphing calculators will be used often for lecture presentations. All students in my classroom will use one of these two calculators. If students are unable to purchase a calculator, the school will loan the student a calculator for the duration of the school year. In conjunction with graphing calculators, the virtual TI program, and SMARTboard software to complete some experiments and make presentations. The SMARTboard will be used for most presentations of new material. Grade Breakdown 30% Tests 10% Homework/Classwork 20% Final Exam 25% Quizzes 15% Projects/POWs Grading Scale A 90-100 B 80-89 C 70-79 D 60-69 F 59 and below CHEATING POLICY: Academic dishonesty of any kind is detrimental to the educational progress of all students and will not be tolerated. The definition of academic dishonesty is specified in the student handbook. This includes, but not
limited to, cheating on tests and quizzes, copying homework, telling classmates about problems on tests, plagiarizing from another source, etc. Depending upon the seriousness of the offense, the student may earn zero points for the assignment up to failing the entire semester. HOMEWORK AND MAKE-UP WORK POLICY: Homework will be assigned every day, and it is a vital element of the curriculum. If a student cannot arrive at a solution to the homework problems, the student should come before school to work with the study group and/or teacher to complete the assignment. If a student fails to complete the assignment, then the student will receive zero homework points for that day. Students usually wait for a poor grade on a quiz or test before seeking the corrective action they need, which can result in several days of frustration, as well as unnecessary lost points towards the final grade. When out for a field trip, the homework for the missed day and the current day are due the day the student returns to class. When a student is out for an absence, homework will be due the following day. Late homework or class work will not be accepted unless it is verified as an excused absence (see student handbook book for definition). It is the student s responsibility to acquire all missed assignments and to make arrangements to make up missed quizzes and/or tests within one school day. SEMESTER FINAL EXAMINATIONS: Each semester final examination will cover all of the information covered in each respective semester. Each final examination will account for 20% of the final semester grade. The format of the examination will include both multiple choice questions, as well as open-response questions. Assessments: 1. Major Assessments will be given every five weeks which will include multiple choice and AP free response questions on the given topics. 2. Quizzes will be given every week. 3. Nightly readings & problem sets will be assigned from the text & supplemental materials by the teacher. 4. Two full length practice AP exams will be given. One will be given over Christmas break and the other during Spring break. 5. The final exam will consist of a full length AP exam. It will be given before the actual AP exam is to be administered. CPS ATTENDANCE POLICY Students must attend their classes in order to learn and retain course subject matter. Therefore, students success in earning credits towards promotion shall be determined by attendance in class as well as by performance on academic assignments. Students with excessive absences from their classes shall be penalized as follows. 1. Students who have unexcused absences in 10% of the classes shall earn no grade higher than a B in the course. 2. Students who have unexcused absences in 15% of the classes shall earn no grade higher than a C in the course. 3. Students who have unexcused absences in 20% of the classes shall not pass the course and shall receive no credit.
Semester One: Unit 1: Precalculus Review and Graphing Calculator Review (8 Days) (MAY BE CUT DUE TO TIME) This unit is designed to review Pre Calculus concepts. This will allow students to be refreshed on material before jumping into new material. A. Lines 1. Slope as rate of change 2. Parallel and perpendicular lines 3. Equations of lines B. Functions and graphs 1. Functions 2. Domain and range 3. Families of function 4. Piecewise functions 5. Composition of functions C. Exponential and logarithmic functions 1. Exponential growth and decay 2. Inverse functions 3 Logarithmic functions D. Trigonometric functions 1. Graphs of basic trigonometric functions a. Domain and range b. Transformations c. Inverse trigonometric functions 2. Applications E. Graphing Calculator Review 1. Graphing Functions a. Window Adjustment b. Zoom Functions 2. Finding points of intersection 3. Root tests 4. Using Tables Unit 2: Limits and Continuity (10 Days) In this unit, students will learn the definition of limits and continuity as well as applications. Students will learn graphic, numeric and algebraic methods of these topics. A. Rates of change B. Limits at a point 1. Properties of limits 2. Two-sided 3. One-sided C. Limits involving infinity 1. Asymptotic behavior 2. End behavior 3. Properties of limits 4. Visualizing limits D. Continuity AP Calculus AB Course Outline 1. Continuous functions 2. Discontinuous functions a. Removable discontinuity b. Jump discontinuity c. Infinite discontinuity E. Instantaneous rates of change Unit 3 and 4: The Derivative (24 Days) In this unit, students will learn the formal definition of the derivative and how to recognize the derivative as a limit. Students will learn the general derivative rules and deduce derivatives algebraically. A. Definition of the derivative B. Differentiability 1. Local linearity 2. Numeric derivatives using the calculator 3. Differentiability and continuity C. Derivatives of algebraic functions D. Derivative rules when combining functions E. Applications to velocity and acceleration F. Derivatives of trigonometric functions G. The chain rule H. Implicit derivatives I. Derivatives of inverse trigonometric functions J. Derivatives of logarithmic and exponential functions Unit 5: Applications of the Derivative (18 Days) In this unit, students will apply the definition of a derivative to real life scenarios. They will also determine how to interpret information from the derivative to the parent function both algebraically and graphically. A. Extreme values 1. Local (relative) extrema 2. Global (absolute) extrema B. Using the derivative 1. Mean value theorem 2. Increasing and decreasing functions C. Analysis of graphs using the first and second derivatives 1. Critical values 2. First derivative test for extrema 3. Concavity and points of inflection 4. Second derivative test for extrema D. Optimization problems E. Linearization models F. Related rates
Semester Two: Unit 6: The Definite Integral (18 Days) In this unit, students will derive the definition of an integral. Students will interpret the graphical meaning of the integral on a function as well as the rules for finding integrals algebraically. Students will also define and use the Fundamental Theorem of Calculus in this unit. A. Approximating areas 1. Riemann sums 2. Trapezoidal rule 3. Definite integrals B. The Fundamental Theorem of Calculus (part 1) C. Definite integrals and antiderivatives 1. The Average Value Theorem D. The Fundamental Theorem of Calculus (part 2) Unit 7: Differential Equations and Mathematical Modeling (22 days) In this unit, students will apply knowledge of integration to more complex functions algebraically. They will also learn how to solve differential equations and apply this to real life scenarios. A. Antiderivatives B. Integration using u-substitution C. Separable differential equations 1. Growth and decay 2. Slope fields 3. General differential equations Jones College Prep AP Calculus AB Course Syllabus 2015 2016 School Year Unit 8: Applications of Definite Integrals (20 Days) In this unit, students will apply knowledge of the integral to real life concepts. Students will use applications of the integrals on graphs of functions to find the volume of curves rotated around an axis. A. Summing rates of change B. Particle motion C. Areas in the plane D. Volumes 1. Volumes of solids with known cross sections. 2. Volumes of solids of revolution a. Disk method b. Shell method Review for AP Exam 17 days (including practice exams) After the AP Exam Unit 9: (introductions to BC topics): Sequences, L'Hôpital's Rule, and Improper Integrals (15 Days) In this unit, solve more complex integral problems. They will also be introduced to sequence/series and convergence theorems. A. Relative Rates of Growth B. Improper Integrals C. Partial Fractions & Integral Tables D. Power Series E. Taylor Series TIPS FOR SUCCESS 1. Take notes every day, and keep them in a neat and orderly fashion. 2. Read the textbook. 3. Come see me as soon as you begin having trouble. The material that we are covering will build upon itself as the year progresses, so if you are confused in the beginning and you do not clear it up, your confusion will only grow. 4. Make friends with other students in the class, and form study groups. Student Agreement Student s Name Phone Email: I have read the AP Calculus Syllabus and understand what is expected and required of me. Student Signature Date