AP CALCULUS (MCN21X) COURSE SYLLABUS. Course Description: Course Objectives: Course Essential Questions: Instructor: Mr. Goncalves

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Gwendolyn Clementine Hampton
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AP CALCULUS (MCN21X) COURSE SYLLABUS Course Description: Our study of calculus, the mathematics of motion and change, is divided into two major topics: differential and integral calculus.

1 AP CALCULUS (MCN21X) COURSE SYLLABUS Course Description: Our study of calculus, the mathematics of motion and change, is divided into two major topics: differential and integral calculus. Differential calculus enables us to calculate rates of change, to find the slope of a curve, and to calculate velocities and accelerations of moving bodies. Integral calculus is used to find the area of an irregular region in a plane, to measure lengths of curves, and to calculate centers of mass of arbitrary solids. An AP Calculus course is equivalent to one semester of college calculus. Therefore, you should prepare for this class as if you were in college. This class will demand a lot of your time and commitment. Course Objectives: This course is intended to provide you with a sound understanding of the concepts of calculus. You will study limits, derivatives, and integrals, and applications of all of these ideas. Your study will be based on a balanced approach. You will be asked to solve graphically, support numerically, confirm analytically, and solve algebraically, all while applying calculus to problem situations. I want you to be able to precisely present the solutions both verbally and in writing. Course Essential Questions: 1. What is Calculus? 2. How do we measure the rate of change of any object at any particular time? 3. How do we find the area and/or volume of any irregular shape? Instructor: Mr. Goncalves Contact Information: Phone: Office (212) ggoncalves@erhsnyc.net Classroom: Room 401

Extra help hours: Monday through Thursday at 3:30 p.m. Tuesday through Friday at 8 a.m. Required Materials: Primary Textbook: Finney, Demana, Waits, Kennedy.

Calculus of a Single Variable AP Edition, Florence: Cengage Learning, 9 th edition, 2010. Calculator - TI-83 or TI-84 required Each student must have his/her own graphing calculator.

2 Extra help hours: Monday through Thursday at 3:30 p.m. Tuesday through Friday at 8 a.m. Required Materials: Primary Textbook: Finney, Demana, Waits, Kennedy. Calculus: Graphical, Numerical, Algebraic: AP Edition. Boston: Pearson Prentice Hall, 2st edition, Supplementary Textbook: Larson/Edwards. Calculus of a Single Variable AP Edition, Florence: Cengage Learning, 9 th edition, Calculator - TI-83 or TI-84 required Each student must have his/her own graphing calculator. Pencil and eraser Ink is not allowed on any assignment or test or classwork/homework. Folder or Binder It is suggested that students have a folder to keep assignments, handouts, and practice AP problems. Expectations: You can expect 100% from me because I am expecting 100% from you. Be on time and prepared for class everyday. Do not come late and always do your homework. In addition, I strongly encourage you to go beyond the assigned homework questions and do more. Your success in the class depends mostly about your commitment and dedication. Exams and Quizzes Exams and quizzes are an important part of our coursework. Exams allow you to assess yourself and allow me to evaluate how the class is progressing. Old exams and quizzes are also excellent study tools for future exams. Be prepared for exams and quizzes; there will be no opportunity for a retake or revision. Be aware of when exams/quizzes are scheduled; you will be expected to take them even if you are absent that week. If you are absent on a quiz/exam day, it is your responsibility to speak with me to set up a day after school to make up the quiz/exam. All exams and quizzes must be made up within 5 days upon return to school, otherwise the quiz/exam will be scored as a zero. To schedule a make up exam you must your teacher with possible dates and times you are available for the make up. Your teacher will you a confirmation of your exam make up date and time. Ideally, the make up exam should be scheduled before your return to school.

3 Classwork Classwork must be done in class, which includes staying on task, following directions, participation, completing a task, and attendance. Participation is the key element in making our classroom environment constructive and exciting. We will apply the skills we learn to group assignments, individual work and various tasks. To receive a 100% in this category students must complete assigned work in class, stay on task, follow directions, bring all necessary materials to class, and be an active learner. As our classroom is a place of inquiry, discussion and collaboration, we expect students to respect one another and all questions that arise. Absences and lateness with negatively affect your classwork grade. Homework You will be assigned homework daily. Homework is extremely important in the study of mathematics. You need to be able to complete problems on your own at home in order to master the topic. Late homework will not be accepted, as per school policy. If a student is absent, it is the responsibility of the student to show missed homework the same day he/she returns to school (If a student is absent Monday, returns to school on Tuesday, he/she is responsible for showing missed homework on Tuesday). This means that the student can show missed homework the day they return to school or the following day and receive full credit. Grading The median grade of each class will be an 80 at the end of each marking period. Typically, the median score of exams and quizzes will be an 80 as well. Median: In statistics and probability theory, the median is the number separating the higher half of a data sample, a population, or a probability distribution, from the lower half. 4 th Marking Period Pre-Exam April Madness!! AP CALCULUS EXAM Post-Exam 05/06/14 06/13/15 Date Assignments Weight 04/11/15 Friday exams 45% 80% 05/04/15 Daily Quizzes 20% Attendance 15% 05/05 at 8 am Group project and presentation Calculus BC topics Attendance Details Breakdown: Your last marking period (04/11 06/13) will be divided into two parts: Pre-exam and Post-exam. The first part counts for 80% of your 4 th Marking Period grade and the second part 20%. Pre-exam: Exams are worth 45% of your grade and will be given every Friday. Daily Quizzes are worth 20% of your grade and will be given every day. These quizzes will be 5 multiple choice questions in 5 minutes. I will drop your lowest score. Missed quizzes cannot be rescheduled. Attendance is worth 15% of your grade. You must come everyday to earn 15 points. Only absences due to illnesses, with a doctor s note, are excused. Afternoon sessions. I would like you to come in the afternoon from 3:00 pm to 4:30 pm Monday through Thursday for three weeks until the day prior to the exam. Although this 20%

4 is not mandatory, all students who came regularly to these sections in the past scored five on the AP Calculus exam. Post-exam: After the AP Calculus exam, your grade is composed of: (1) coming to class on time and (2) participating in all activities including projects. ERHS Academic Honesty Requirement: ERHS Academic Integrity Policy applies to all assigned material in this class. This includes homework, quizzes, tests, projects, extra credit work, and anything else assigned. Failure to do your own work, or providing work to others, will result in a zero for the assignment and a referral to the Principal. Grading Policy: Criteria for computing grades: Weight Exams 40% Quizzes 30% Free Response Questions 20% Participation/Attendance/Homework 10% AP Exam Cost: The AP Calculus exam is required of students. The cost for the AP Calculus exam is approximately $88. This may be a large amount for you to come up with at once in the spring, especially if you plan to take multiple AP exams. I suggest saving for it over the course of the year, and then when it is time to take the exam you already have the money set aside. Financial aid available for qualified students. Math Must-Dos: Come to class prepared. Bring your notebook, pencils, paper, and calculator every day. Do your homework!!!! Have fun!

5 Course Outline: Subject to change Unit I. Limits and Continuity (6 Days 1 Test) 1. From graphs 2. From tables 3. Symbolic evaluations 4. Limits at infinity 5. Infinite limits 6. Indeterminate forms: 0/0, /,, 0 * 7. Graphical look at removable discontinuities 8. Graphical look at nonremovable discontinuities 9. Symbolic consideration of removable discontinuities 10. Symbolic consideration of nonremovable discontinuities Unit II. Derivatives (21 Days 1 Test) 1. Average rate of change related to velocity 2. Average rate of change related to slope 3. Instantaneous velocity as the average velocity over a smaller time interval 4. Instantaneous velocity as the slope of a curve at a point 5. Local linearity 6. Definition of the derivative as a limit 7. Approximate the derivative at a point graphically 8. Approximate the derivative at a point numerically 9. Determine the graph of the derivative function from the graph of a function 10. Determine the derivative of a function by using the limit definition 11. Explore the relationship between differentiability and continuity 12. Practical meaning of the derivative in a variety of contexts 13. Techniques of differentiation: power rule, product rule, quotient rule 14. Chain rule (a) Using Leibniz notation (b) Using function notation (c) Using parametric equations 15. Implicit functions 16. Inverse functions using composition (e.g., use e lnx = x to obtain(d(ln x )/dx) 17. Graphical meaning of the second derivative 18. Key theorems relating to continuous functions (a) Mean Value Theorem (b) Intermediate Value Theorem (c) Extreme Value Theorem Unit III. Applications of the Derivative (21 days 1 Test) 1. Approximations using the tangent line 2. Related rates 3. Intervals of increase and decrease of a function 4. Intervals of increase and decrease of the derivative concave up and concave down 5. First derivative test

6 6. Second derivative test 7. Candidates test 8. Optimization 9. Geometric view of a solution to a differential equation using slope fields 10. Euler's Method to approximate the solution to a differential equation 11. L'Hopital's rule for cases of 0/0 and / 12. Motion on a line: moving left and right, speeding up and slowing down 13. Relationship of moving right and speeding up to a graph that is increasing and concave up, moving left and slowing down to decreasing and concave up, etc. Unit IV. Integration and Antidifferentiation (6 Days 1 Test) 1. Variety of examples of summing to approximate total change given tabular data 2. Concept of a Riemann sum 3. Definite Integral defined as the limit of a Riemann sum 4. Link between the definite integral and area advantages and pitfalls 5. Properties of the definite integral 6. Antidifferentiation motivated by finding a position function from a velocity function 7. Fundamental theorem of calculus motivated by finding distance traveled two different ways Unit V. Numerical Approximations of a Definite Integral (5 Days No Test) 1. Riemann sums left, right, midpoint 2. Trapezoid rule 3. Simpson s rule 4. Relationship between Trapezoid, Midpoint, and Simpson s rules 5. Investigation as to how each of these techniques improves if the number of subdivisions is doubled, tripled, or multiplied by a factor of k Unit VI. Techniques of Antidifferentiation (11 days 1 Test) 1. From known derivatives 2. From a graph of a derivative 3. Simple substitution form completion 4. Substitution actual substitution needs to be made, including trig substitution 5. Parts 6. Improper Integrals Unit VII. Applications of Definite Integral and Antidifferentiation (32 Days 2 Tests) 1. Determine specific antiderivatives using initial conditions 2. Solution to separable differential equations with and without initial conditions 3. Writing a differential equation to translate a verbal description 4. Partial fractions in the context of the logistic equation 5. Representation of a particular antiderivative by using the Fundamental Theorem of Calculus 6. Analysis of functions defined by a definite integral 7. Area, including regions bounded by polar curves 8. Average value of a function 9. Distance as the definite integral of speed 10. Length of a curve, including polar and parametric curves

7 11. Work 12. Variety of other problems using the integral of a rate of change to determine total or accumulated change 13. Variety of other problems where the emphasis is on setting up a Riemann Sum and taking its limit Unit VIII. Series (38 Days 3 Tests) 1. Infinite series defined as the limit of a sequence of partial sums 2. Series of constants (a) Geometric series (b) Harmonic series, P-series (c) Alternating series 3. Tests for convergence (a) Integral (b) Comparison (c) Limit comparison (d) Ratio test thought of as eventually geometric 4. Power series (a) Taylor polynomials as approximations for functions (b) Taylor series centered at x = a (c) Use of known Maclaurin series for e x, sin x, 1/(x+1), (1+x) p to form new series (d) Differentiation and antidifferentiation of series to determine new series (e) Functions defined by power series (f) Interval and radius of convergence (g) Error bounds i convergent geometric series ii using integral test iii convergent alternating series iv Lagrange

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a