AP Calculus BC Syllabus Teacher: Mr. Bell Room: S601 Website: https://sites.google.com/site/mrbellscalculusphysics/ Tutoring: After School 2:20 PM to 2:45 PM or special appointment Telephone: 704-788-4111; Cell 704-657-5712 Email: robert.bell@cabarrus.k12.nc.us Text: Add l Resources: Calculus: Early Transcendentals, 6 th edition, James Stewart New York, NY; Thomsom Brooks/Cole, 2008. Change and Motion: Calculus Made Clear, 2 nd Edition, Starbird, University of Texas; Understanding Calculus,Edwards, University of Florida (Both by The Teaching Company), itunesu videos and Slader.com. Overview: This course is structured to satisfy the requirements for the College Board s AP Calculus AB course. It is essentially a college level course in calculus. (Passing the AP Calculus AB test normally provides college credit. Check with individual colleges to verify their policy.) Schedule: We will meet every day. Each class is about 1-1/2 hours long and can accommodate lectures, internet research, group projects, student presentations, video classes and portfolio work. Goal: Strategy: Our goal is to pass the AP Calculus AB examination with a 3 or higher. We will build problem solving skills by gaining knowledge of advanced mathematics, applying consistent methodologies, fostering creativity, and studying past AP questions and solutions. Students will use written, verbal, graphical and numerical methods to express their understanding of key concepts. Content: We are going to study the following content areas of the Calculus: Semester I Chapter 1 Functions, Graphs & Models, 1/2 week Functions expressed as equations, tables, graphs and verbal descriptions Properties of linear, polynomial, rational, power, exponential, logarithmic, and trigonometric functions; even and odd functions, inverse functions, etc. Functions as models Chapter 2 Limits & Their Properties, 1 week Using Graphs and tables of data to determine limits Properties of limits Evaluating limits Determining continuity and one-sided limits Applying the Intermediate Value Theorem Determining infinite limits Using limits to find the asymptotes of a function
Chapter 3 Differentiation, 3 weeks Developing verbal descriptions of the derivative Evaluating the graphical and numerical definitions of the derivative Analytical understanding of the derivative, rates of change from graphs and tables, instantaneous rate of change, the slope of a curve at a point Differentiation rules for basic functions, including power functions, exponential, logarithmic and trigonometric functions and for sums, differences, products, and quotients of functions Evaluating Higher order derivatives Applying the chain rule Applying Implicit differentiation Solving related rate problems Chapter 4 Applications of Differentiation, 2-1/2 weeks The Extreme Value Theorem Rolle s Theorem and the Mean Value Theorem, and their geometric consequences, Increasing and decreasing functions and the first derivative test Concavity and its relationship to the first and second derivatives Applying the Second derivative test Relating the graphs of f, f f Optimization including both relative and absolute extrema Finding the tangent line to a curve Application to position, velocity, acceleration, and rectilinear motion Applying Newton s Method Chapter 5 Integration, 4 weeks Antiderivatives and indefinite integration Basic properties of the definite integral, Understanding the meaning of area under a curve Riemann sums Meaning of the definite integral and the definite integral as a limit of Riemann sums Use of Riemann trapezoidal sums to approximate definite integrals of functions that are represented analytically, graphically, and by tables of data First Fundamental Theorem of Calculus and its use, Substitution of variables to evaluate definite integrals Integration by substitution, partial fractions Second Fundamental Theorem of Calculus The Mean Value Theorem for Integrals The average value of a function Trigonometric integrals Integration by parts Numerical Integration Improper integrals Chapter 6 Applications of Integration, 2 weeks The integral as an accumulator of rates of change Washer and shell methods Calculating area of a region between two curves Calculating volumes of a solids of revolution Calculating volumes of known cross section. Applications of integration in physical, biological, and economic contexts.
Chapter 7 Log, Exponential & other Transcendental Functions, 1-1/2 weeks Differentiation and integration of the natural logarithmic function, inverse functions, exponential functions, other transcendental functions Bases other than e L Hospital s Rule and its use in determining limits and convergence of improper integrals and series Applications. Chapter 9 Geometric interpretation of differential equations via slope fields, 1 week Use of slope fields to interpret a differential equation geometrically Drawing slope fields and solution curves for differential equations Introduction to the use of Differential equations in the study of motion Separation of variables to solve differential equations Portfolio, 1 week Semester II Chapter 8 Additional Integration Techniques, ~1 Week Integration by Parts Integration by Trigonometric Substitution Trapezoidal and Simpson Rule approximations Review of the partial fraction method and Review of Improper Integrals. Chapter 9 Arc Length, surface area and applications, ~1 week Calculate the length of curves Calculate the surface areas of solids of revolution Using integration to solve physics and engineering problems. Chapter 10 Solving differential eqs and using them in modeling, ~1 week Solving separable differential equations Applications of differential equations in modeling, including exponential growth, limited growth, radioactive decay and electric circuits. Chapter 11 Parametric Equations, ~1 week Parametric equations Calculus involving vectors, including motion along a curve, position, velocity, acceleration, speed, distance traveled Analysis of curves given in parametric and vector form Chapter 11 Polar Coordinates, ~1 week Polar coordinates and polar graphs Analysis of curves given in polar form Calculating area of a region bounded by polar curves
Chapter 12 Series & Sequences, ~3 weeks Convergence and divergence of sequences, definition of a series as a sequence of partial sums, convergence of a series defined in terms of the limit of the sequence of partial sums of a series, geometric series and applications, the nth-term Test for Divergence, the Integral Test and its relationship to improper integrals and areas of rectangles, Taylor polynomials and approximations, using the graphing calculator, power series, and Taylor and Maclaurin series Portfolio, 1 week Exam Preparation, 3 weeks After the AP Exam, 4 weeks Various projects applying Calculus At the end of this course students will be able to: A. Limits and Continuity 1. evaluate limits algebraically, numerically, and graphically 2. find equations of vertical and horizontal asymptotes 3. determine whether a function is continuous at a point 4. classify discontinuities as: removable, jump, or infinite 5. understand the Intermediate Value Theorem B. The Derivative 1. find the derivative of a function using the definition of a derivative 2. find whether a function is differential at a point 3. find whether a function is locally linear at a point 4. use the theorems on differentiable on differentiation to find derivatives of polynomial and rational functions (Power Rule, Product Rule, Quotient Rule, and Chain Rule) 5. find the equation of the tangent line to a curve at a point 6. find the equation of the normal line to a curve at a point 7. understand average rate of change 8. understand instantaneous rate of change 9. use implicit differentiation 10. find higher order derivatives 11. graphing the derivative from data 12. understand the concept of Marginal Cost, Marginal Profit, Marginal Revenue 13. understand the definition of the derivative using the symmetric difference quotient 14. understand and apply the Extreme-Value-Theorem 15. understand and apply the Mean-Value-Theorem 16. use the First and Second Derivative Test 17. connect F (x) and F (x) with the graph F(x) 18. find derivatives of Polynomial, Rational, Exponential, and Trigonometric Functions 19. Solve Rectilinear Motion
C. Logarithmic Functions, Inverse Trigonometric Functions and Applications 1. evaluate limits algebraically, numerically, and graphically 2. find equations of vertical and horizontal asymptotes 3. determine whether a function is continuous at a point 4. classify discontinuities as: removable, jump, or infinite 5. understand the Intermediate Value Theorem D. Indefinite Integrals 1. evaluate indefinite integrals using the Power Rule and the Chain Rule for integration 2. use integration by u-substitution 3. evaluate definite integrals with and without a calculator 4. understand and apply the Fundamental Theorems of Calculus E. Applications of Integrals 1. find the net distance traveled 2. find the total distance traveled 3. understand the Riemann Sum definition 4. approximate areas using LRS, RRS, MRS, and Trapezoids 5. calculate areas under and between curves 6. calculate the average value of a function 7. find volumes of solids of revolution using the disk and washer method 8. find volumes of solids with known cross sections F. Differential Equations 1. solve differential equations of order 1 by the method of separation of variables 2. solve growth and decay problems, logistic problems, and other applications to differential equation 3. understand slope field 4. sketch a slope field given a differential equation G. Parametric Equations 1. find 1 st and 2 nd derivatives of parametric equations 2. solve for tangents to parametric curves 3. solve for areas of surfaces 4. solve for speed 5. find velocity and acceleration of particles following paths in two dimensional space H. Polar Equations 1. express curves in polar and rectangular coordinate systems 2. find 1 st derivatives of polar functions 3. solve for length of arcs of polar curves 4. solve for areas enclosed by polar curves
I. Sequences and Series 1. determine convergence or divergence of sequences 2. recognize and calculate convergence of a geometric series 3. determine the convergence or divergence of a series using a. the test for divergence b. p-series test c. integral test d. ratio test e. square root test f. alternating series test (AST) 4. determine the convergence of a power series 5. calculate Maclaurin and Taylor series formulas 6. recognize Maclaurin series formulas for sinx, cosx, e^x, lnx, 1/(1+x) and 1/(1-x) from memory Prerequisites: Satisfactory completion of algebra I, II and PreCalculus. Student Prep: Come to class having read the assignment, viewed assigned videos and completed the assigned homework. Bring your textbook and calculator to every class. Grades: This is a college level class and grades are assigned accordingly. The approximate weights given for each assessment are: Unit Tests Quizzes/Participation Nine Week Exam Final Exam Homework Portfolio 200 points 10 points 400 points 400 points 50 points 100 points Most test grades are assessed based upon the same methodology used in the AP Calculus AB examination. Grades are posted in class. Please do not bring these issues to me during class. Tests: Tests will be given at the end of each unit of material. They will cover the reading, homework and classroom activities. Exams will be problem solving oriented and will come from the mathematics objectives covered in our units. Exams are cumulative. Questions will mainly be taken from AP tests and therefore will not be exactly the same as the homework questions. However, they will incorporate the concepts learned in the homework exercises. All exams include multiple choice and free response non-calculator sections as well as some problems requiring the use of a calculator. (Important: Missed tests can be made upon a scheduled basis. You need an appointment. Don t show up unannounced and hope I ll have testing material ready for you. The make up will be different from the original test. )
Nine Week and Final Exams: These will be comprehensive exams covering all material covered. These will be problem solving oriented. Like most tests, these questions will be actual test questions from AP Tests, wherever possible. Class Participation/Quizzes: Engagement in class and performance on quizzes is an important part of mastering calculus. Much of the participation credit will be earned using clickers. Students will be assigned specific Clickers to be used in class. They will be responsible for returning the Clickers properly at the end of each class. If a Clicker is missing at the end of a class, the student responsible will be charged $45 to replace the Clicker. Portfolio: The portfolio is an individual project based on the course content. Each unit will be covered in the portfolio. The first section for each unit presents the topics in a manner that would allow another student to understand the concepts. The second section for each unit consists of the unit exam with the answers corrected by the student, including justifications. The completed portfolio will be hard bound. A three ring binder is not acceptable. Failure to bind the portfolio properly will result in a 15% deduction in the portfolio scoring. Two copies are required, one will be submitted to the instructor and the other will be kept by the student. The instructor s copy will not be returned to the student. Lab Experiments: Computers and calculators will be used in experiments to study physical phenomenon such as harmonic motion and capacitor charging.. You will be required to formulate a hypothesis, perform the experiments, analyze results and draw conclusions. Results will include graphical and numerical analyses that investigate how actual motion/physical change is consistent with the theoretical equations. Homework: We will be using Web Assign for homework. Your assigned homework problems will be placed on the internet and you will be responsible for completing the assignments on the website. You will usually have 10 opportunities to submit correct answers. The last submission will be the basis for your HW grade on that assignment. There is no penalty for answering correctly in the first 5 submissions. There is a penalty of 5% that is assessed after the 5th submission. For example, if you submit the correct answer on submission 7 on a 10 point question, you would receive 9 points. You must start the homework as soon as it is assigned. It is highly recommended that you print the assignment on the first day and use it to work on the problems, showing all of the steps you used to solve. Some of the problems will be assigned for completion before the full assignment is due. Deductions may be made to the final homework score based on the assigned completion dates. Web Assign ID enrollment: Your Institution is nwcabarrus.nc. You will be shown in class how to enroll. Please change your password when you first log on. If you do not have access to the internet, you will be allowed to print out your assignment(s) in the classroom. Flipping the Classroom : Students will be assigned videos to be watched on a routine basis. These videos, in concert with class lectures, are essential to student learning. Deductions to student grades will be assessed for not reviewing these videos. Notebooks: You must have one. Suggested index: Explanation of theorems, Homework problems, Free response write ups, Reading outlines, Class notes and Portfolio.
Calculators: A TI 83/84 calculator is the minimum acceptable calculator required for this course, but a TI 89 or higher is preferable. The TI-Nspire CX CAS is highly recommended. You must have a required calculator for each class session and test. Extra Credit: These are points will assigned based on a qualitative evaluation and clicker scores. They can be awarded based on outstanding attitudes in class, quality of class participation, or for just seeking help in understanding the material. Classroom management: Put assignments in the designated area for your period. I will return material to you using the in the same designated area. If you have any questions or believe there is a grading error regarding any grade in this class, you can communicate your concern in an email to robert.bell@cabarrus.k12.nc.us. Use this method to schedule make up tests, as well. You can also use the communication module of WebAssign, but this could delay response. Please do not bring these issues to me during class. Additional Note from Teacher AP Calculus is a very rigorous course designed to challenge each student. If a student fails to put forth effort, the teacher reserves the right to request the student be removed from the follow on AP Calculus BC course at the end of the first semester. I truly hope that I do not need to make such a request. Please understand that there will be bumps in the roads, but if each student is willing to work, he or she will improve his or her critical thinking and their mathematically ability. Any questions, please feel free to contact me.