Syllabus. Course Description:

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1 AP Calculus BC Syllabus Course Description: Name: Period: Mr. Turkin / Mrs. Catalina Perricone rrturkin@cps.edu / cguerrero28@cps.edu Office Hours: Tuesdays & Thursdays Lunch Or by appointment Phone #: Website: AP Calculus BC is an Advanced Placement math offering for high school students equivalent to a college Calculus 1 course. The course culminates in a nationally delivered exam in the first two weeks of May. Students who score 3 or higher (out of 5) typically receive college credit (varies by college). To pass, students must be driven, motivated and willing to put forth more effort to study than for previous math classes. The course follows a rigorous and fast-paced schedule aligned with the AP college board curriculum to prepare students for success on the AP exam. Essentially, the course is delivered in two semesters. Semester I is Differentiation; Semester II is Integration. A focus on group work and problem-solving will be used in class to approach the challenging AP questions. Grading policy: Grades will be given on an ongoing basis and always updated by 9am each Friday. Students and parents are encouraged to check grades often on the CPS portal. Classwork 35 %: This includes homework and class participation. It is important that students not only actively participate in class but that they also practice concepts taught that day. Classwork: Some classroom activities will be collected and graded as part of the Classwork Grade. Students who have not completed, or partially completed, the classwork will not receive a grade. Homework: Any late/missing assignments will be accepted with a penalty until the day of the Unit Test, after the Unit Test they will not be accepted. Work not submitted at the beginning of the class period will automatically have a small penalty (1 pt) if turned in later on that day. Homework turned in the next day will have a 2 pt deduction and work turned in more than 1 day late will be accepted but at a 50% penalty of the assignment grade. Please see Attendance policy for excused and unexcused absences. Do Nows: Students will be expected to answer 2-3 questions at the beginning of every class. This will sometimes be collected as a part of the Classwork Grade. On a collection day, any student who is late (unexcused) will not be allowed to make that grade up, absent students will be excused for

2 that grade. Writing/AP Multiple Choice & Free Response Question 30%: This will consist of writing assignments, Math Talks and AP Free Response Questions. AP Multiple Choice Questions: These will consist of 5-15 AP Multiple Choice (Calculator or Non- Calculator) timed questions. During this section of class, students will answer the question as if they were taking the real AP. After the answers have been graded, students will be given their scores back and may re-try/correct their incorrect responses. Writing Assignments/AP Free Response Questions: These will consist of Free Response AP Style questions, vocabulary sheets, and end of year after school hours. Students will be given free response AP style questions where they must plan and strategize on how to solve the problem while using both mathematical and written forms of justification. The written component where students will explain and justify their mathematical procedure or rational using full sentences. Students will be graded on a rubric and will be evaluated on Mathematical reasoning and communication. These free response questions will be graded based on AP scoring rubrics. Weekly Quizzes/ Unit Tests/Calculus Hours 35%: Weekly Quizzes: Students will be given weekly quizzes based on learning targets for the unit. These quizzes are designed to assess student knowledge and conceptual understanding of these learning targets. Students may earn the right to re-take a specific learning target to demonstrate mastery through a remediation given to them by the teacher. Students will be given the re-take and the score received will be the score posted on gradebook. Learning Target re-takes can be taken until the day of the test of the following chapter. Unit tests: Will be given at the end of each unit and will assess student knowledge of all learning targets for that Unit. There may be some material from previous Units to help students review past targets. Practice Test will be given prior to the Unit Test and students will be allowed to do test corrections where they must correct their mistake AND explain why they got the incorrect answer. NOTE: Students must have a 70% in the Quiz category in order to be able to do Test Corrections AND must do them in front of a Mathematics Teacher. Calc Hours: During the two month period before the AP Tests students will be expected to complete at least 8 hours (an average of 1 hr per week) of after school math tutoring in order to prepare for the test. The percent completion of these hours will be reflected as a test grade in gradebook.

3 Devry s Grade Scale: Materials/Resources: 90% and above A Book: Students will be using the Calculus of the Single Variable: 80%-89% B 9 th ed. Houghton-Mifflin, On occasion, handouts for extra 70%-79% C practice will be given. 60%-69% D Calculator: Suggested calculators for this course are any TI 83, TI 59% and below F 84, or TI 89. (Please note that students will be able to borrow a Ti 84 calculator from DeVry-replacement cost is roughly $120 if lost/damaged) Other Materials: Binder, Notebook and pencils are required. Attendance: Students are expected to be in class, on time every student attendance throughout the year. However, I understand that life happens but we need to stay on task and work hard every day for this next year. Excused Absences- Students will be allowed to make up the work for full credit. Unexcused Absences- Students will be allowed to make up the work for a penalty. Tardies- Students who arrive after class starts must come in quietly, write their names on the Tardy Sign In Sheet and sit down ready to pick up where the class is and work. All tardy students will be expected to make up their time with me either after school or during lunch. Constantly being tardy and/or tardies not made up may result in extra time being served. Discipline/Expectations: At Devry Advantage Academy, students are held to high standards both academically and behaviorally. Students are expected to be respectful of others, show pride in their work, and follow all University and CPS policy outlined in the student handbook at all times. Failure to follow CPS and University policies will result in parent contact and disciplinary action. Please note that, following DAAHS and University policies, cell phone* use, food and drink are NOT allowed in class at any time. *Cell phones may only used when specifically instructed by teacher. Classroom Website: Students must join the classroom website. I will be posting announcements, HW assignments, quizzlets and other resources that will be useful to students throughout the year. Additionally, I may require students to take part in discussion groups throughout the year. NOTE: The discussion groups may be graded therefore netiquette should be strongly followed!

4 Topic Outline for Calculus BC I. Functions, Graphs, and Limits a. Analysis of graphs. b. Limits of functions-including one-sided limits b.i. An intuitive understanding of the limiting process. b.ii. Calculating limits using algebra and on the graphing calculator. b.iii. Estimating Limits from graphs and tables of data created by students manually and on the graphing calculator. b.iv. Determine given a table, an equation and/or a graph whether a limit is reasonable and be able to provide a written justification. b.v. Determine if the limit of a function exists and justify why or why not using a table, equation or with the use of a graphing calculator. c. Asymptotic and unbounded behavior c.i. Understanding asymptotes in terms of graphical behavior. (Exploration using the graphing calculators to create a table of values and then link these values to the graph.) c.ii. Describing asymptotic behavior in terms of limits involving infinity. c.iii. Comparing relative magnitudes of functions and their rates of change d. Continuity as a property of functions d.i. An intuitive understanding of continuity d.ii. Understanding continuity in terms of limits (Exploration comparing computing limits algebraically and graphically to come up with the definition of continuity in terms of limits.) d.iii. Geometric understanding of graphs of continuous functions d.iii.1. Intermediate Value Theorem d.iii.2. Extreme Value Theorem e. Parametric, polar and vector functions. II. Derivatives a. Concept of the derivative a.i. Derivative presented graphically, numerically, and analytically. a.ii. Derivative interpreted as an instantaneous rate of change. a.iii. Derivative defined as the limit of the difference quotient. a.iv. Relationship between differentiability and continuity. b. Derivative at a point b.i. Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are not tangents. b.ii. Tangent line to a curve at a point and local linear approximation. b.iii. Instantaneous rate of change as the limit average rate of change. b.iv. Approximate rate of change from graphs and tables of values. (Students will be able to compute algebraically and on their graphing calculator.) c. Derivative as a function c.i. Corresponding characteristics of graphs of and. c.ii. Relationship between the increasing and decreasing behavior of and the sign of. c.iii. The Mean Value Theorem and its geometric interpretation. c.iv. Equations involving derivatives. Verbal description as are translated into equations involving derivatives and vice versa. d. Computation of derivatives d.i. Knowledge of derivatives of basic functions, including power, exponential, logarithmic and trigonometric and inverse trigonometric functions.

5 d.ii. Derivative rules for sums, products, and quotients of functions. d.iii. Chain rule and implicit differentiation. III. IV. Derivative Applications a. Second Derivative a.i. Corresponding characteristics of the graphs of,, and. a.ii. Relationship between the concavity of and the sign of. a.iii. Points of inflection as places where concavity changes. b. Application of derivatives b.i. Analysis of curves, including the notions of monotonicity and concavity. b.ii. Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration. b.iii. Optimization, both absolute (global) and relative (local) extrema. b.iv. Modeling rates of change, including related rates problems and determine if answers are reasonable given a context. b.v. b.vi. Use of implicit differentiation to find the derivative of an inverse function. Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration. Also, determine if answers are reasonable given a context. b.vii. Geometric Interpretation of differential equation via slope fields and the relationship between slope fields and solution curves for differential equations. b.viii. Numerical solution of differential equations using Euler s method. b.ix. L Hopital s Rule, including its use in determining limits and convergence of improper integrals and series. Integrals a. Interpretation and properties of definite integrals a.i. Definite integral as a limit of Reimann sums. a.ii. Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: a.iii. Basic properties of definite integrals. (Students will be able to compute algebraically and on their graphing calculator.) b. Fundamental Theorem of Calculus b.i. Use of the Fundamental Theorem to evaluate definite integrals. b.ii. Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined. c. Techniques of antidifferentiation c.i. Antiderivatives following directly from derivatives of basic functions. c.ii. Antiderivatives by substitution of variables, parts and simple partial fractions. c.iii. Improper integrals V. Integration Techniques a. Applications of integrals b. Applications of antidifferentiation b.i. Finding specific antiderivatives using initial conditions, including applications to motion along a line. b.ii. Solving separable differential equations and using them in modeling-including exponential growth. c. Solving logistic differential equations and using them in modeling.

6 VI. d. Numerical Approximations to definite integrals Polynomial Approximations and Series a. Concepts of series b. Series of constants b.i. Examples b.ii. Geometric Series with applications b.iii. Harmonic Series b.iv. Alternating series with error bound. b.v. Terms of series as areas of rectangles and their relationship to improper integers, including the integral test and its use in testing the convergence of p-series. b.vi. The ratio test for convergance and divergence. b.vii. Comparing series to test for convergance and divergence. c. Taylor series c.i. Taylor polynomial approximation with graphical demonstration of convergence. c.ii. Maclaurin series and the general Taylor series centered around x=a. c.iii. Maclarin series for the functions. c.iv. Formal manipulation of Taylor series and shortcusts to computing Taylor series, including substitution, differentiation, antidifferentiation and the formation of new series from known series. c.v. Functions defined by power series. c.vi. Lagrange error bound for Taylor polynomials.

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