AP Calculus AB Syllabus

Transcription

1 AP Calculus AB Syllabus Course Overview: All topics that are listed on the AP Central website for Calculus AB will be covered in this class and are listed below in the AP Calculus AB Course Outline. The pacing for AP Calculus AB is approximate and includes time for review and testing. The main objectives class are to prepare the students for college level mathematics. Time will be spent learning how to use technology appropriately. Problems will be presented analytically, numerically, graphically, and verbally. Students will use a graphing calculator to determine the value of a derivative at a point, to find the value of a definite integral, to graph a function in an appropriate window, and to solve equations. Assignments & Assessments: Students can expect homework on a daily basis. In addition to problems from the textbook, students can expect supplemental assignments that contain released free response questions for additional free response practice. Most tests will have a calculator part and a non-calculator part and will contain multiple choice questions as well as free response questions. Sometimes, two or three free-response questions similar to the AP exam questions will be included on the tests. Another emphasis in this course will be having students explain and justify their responses verbally and on their paper. The final exam for both semesters which all students are required to take will be similar in structure and grading to the AP Calculus AB Exam given in May. Teaching Strategies: I maintain a high level of student expectation as I feel students will rise to the level that I expect m. I stress communication and work ethic as a major goal and requirement of this course. Students are expected to explain problems using proper vocabulary and terms. Much of calculus depends on an understanding of a concept taught in a previous lesson. Students are encouraged to form study groups on their own time and tutor themselves. In discovering new concepts, the class works as a whole. Students are encouraged to contribute positively to the class and explain problems to their peers. This allows me to step back and listen to the interaction among my students as they explore a topic. It also will show me the level and depth of their understanding on that topic. Textbook: Larson, Edwards, and Hostetler. Calculus of a Single Variable (8 th edition). Boston: Houghton Mifflin. Textbook Price: $ Supplemental Resources: Crawford, Debra, Mary Ann Gore, Jill Gough, and Sam Gough. : Calculus Activities for the TI-82 and 83. Venture Publishing. Hockett, Shirley. Barron s How to Prepare for the Advanced Placement Examinations: Mathematics; 6 th edition. Hauppauge, N.Y.: Barron s Education Services, Cade, Sharon, Rhea Caldwell, and Jeff Lucia. Fast Track to a 5: Preparing for the AP Calculus AB and Calculus BC Examinations. McDougall Littell Foerster, Paul A. Calculus: Concepts and s. Emeryville, CA: Key Curriculum Press. Foerster, Paul A. Calculus Explorations. Emeryville, CA: Key Curriculum Press Released Free Response Questions provided by the College Board

2 Additional Materials Needed: A graphing calculator is required for this course as well as for the AP Calculus AB Exam. A TI-83 graphing calculator will be provided both semesters if a student does not have one and only if the calculator contract has been signed and returned to the teacher. Topic Time Subtopic Text Supplementary Resources (Released Free Response Questions) 2 weeks Throughout the year Solves problems including: Selecting appropriate approaches and tools. Using estimating strategies to predict computational results. Judging reasonableness of results P.1 - P Ch. 1-3 Throughout the year Solves problems that relate concepts to practical applications and to other concepts using appropriate tools. P.1 - P Ch. 1-3 Throughout the year Identifies the characteristics of functions and relations with respect to domain, range, intercepts, symmetries (including odd and even functions), asymptotes, and zeros. Graphs functions and relations with respect to these characteristics and identifies these characteristics from graphs. P.1 - P.3 Applies the algebra of functions by finding sum, product, quotient, composition, and inverse where they exist. P.3 Identifies and applies properties of algebraic, trigonometric, exponential, and logarithmic functions. Includes the following: polynomial (existence, number, and location of zeros), trigonometric (fundamental identities, addition formulas, graphs, amplitude, periodicity), exponential, logarithmic (properties, graphs, inverse, the number e as a limit), absolute value (f(lxl), lf(x)l ), and bounded/ unbounded behavior. P.3 A.3 Ch. 5 Calculus: Concepts & s Paul A. Foerster 6.6 for expressing the number e as a limit 3 weeks Evaluates limits of functions algebraically, numerically, and graphically. Applies properties of limits, including one-sided limits Calculator Activities for the TI-82 & TI -83

3 Estimates limits from graphs or tables of data. 1.2 Describes asymptotic behavior in terms of limits involving infinity Lab 2 Applies L'Hopital's Rule when appropriate. 8.7 Applies the definition of continuity to a function at a point. Determines if a function is continuous over an interval. 1.4 Lab AB 6a Demonstrates a geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem) 1.4, 3.1 s 4 weeks s Interprets the derivative when represented graphically, numerically, and analytically Ch. 2-3 s Defines the derivative of a function in various ways: a) the limit difference quotient b) the slope tangent line at a point. c) the instantaneous rate of change. d) the limit average rate of change s Relates differentiability and continuity (that differentiability implies continuity). 2.1 s Evaluates the slope of a curve at a point. 2.1 s Determines if a function is differentiable over an interval. Determine points where the derivative of a function fails to exist AB 6c s s Calculates the instantaneous rate of change as the limit average rate of change. Applies the rules of differentiation to algebraic and transcendental functions Ch. 3, Ch. 5 s Differentiates the sum, product, and quotient (including tan x and cot x) of functions. Ch. 2-3 Ch. 5 s Applies the chain rule to composite Ch AB6

4 s functions and implicitly defined functions. Ch AB AB4 Approximates the rate of change at a point, given the graph of a function or a table of values Calculus: Concepts & s Paul A. Foerster AB3 a, b 2005 AB3 a, d s Differentiates the inverse of a function, including inverse trigonometric functions. Uses implicit differentiation to find the derivative of an inverse function s 5 weeks s Models rates of change, including related rate problems. Ch AB AB 5 s Determines successive derivatives of functions and applies them to problems, such as speed, velocity, and acceleration. 2.3 Calculus Explorations Exploration 15 by Paul Foerster 1991 AB1a,b,d 2003 AB2 a, b s Applies the derivative to determine: the slope of a curve at a point, the equation of the tangent line to a curve at a point, and the equation normal line to a curve at a point. Ch AB4 a,b s Applies Rolle's Theorem and the Mean Value Theorem including the geometric consequences. 3.2 Lab 9 s Uses the relationships between f(x), f'(x), f''(x) to: Determine the increasing/decreasing behavior of f(x). Determine critical point(s) of f(x) and locate relative extrema. Determine the concavity of f(x) over an interval. Determine the point(s) of inflection of f(x). Sketch the graphs of f'(x) and f''(x), given f(x). Sketch the graph of f(x), given f'(x). Ch. 3 Lab AB AB AB4 a, b, d s Uses a geometric interpretation of differential equations via slope fields. Supplem ent s Applies the Extreme Value Theorem to 3.1

5 problem situations. s Solves optimization problems. 3.7 s s 11 weeks Defines the antiderivative and applies its properties to problems such as distance and velocity from acceleration with initial conditions, growth, and decay AB AB AB AB AB4 a, b, c s s Calculates the value definite integral as a limit of Reimann Sums. Uses Reimann Sums (using the left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values. Calculates areas by evaluating sums using sigma notation Lab 10 Calculus Explorations by Paul Foerster Mary Ann Gore's Trip Lab 1999 AB AB AB AB4b s Relates the definite integral to the concept area under a curve. Defines and applies the properties definite integral. Identifies and uses the Fundamental Theorem of Calculus in evaluating definite integrals AB5 s s Identifies the definite integral as the rate of change of a quantity over an interval interpreted as the change quantity over the interval: z b a f '( x) dx = f ( b) f ( a) Identifies and uses the Fundamental Theorem of Calculus in evaluating definite integrals. 4.4 Ch. 4-7 Lab 13, 15 s Integrates by substitution, by using identities, by changing variables, and by parts. Ch. 4-7

6 5 weeks Interprets the integral of a rate of change to give accumulated change. Supplem ent 2000 AB AB AB AB AB AB2 Uses the Fundamental Theorem of Calculus to find specific antiderivatives using initial conditions. Ch 4-8 Uses the Fundamental Theorem of Calculus to solve problems involving motion along a line. Supplem ent 1999 AB AB2 Applies the integral to the average or mean value of a function on an interval. 7.1 Lab 12 Determines the area of a region bounded by two or more curves AB AB2 Determines the volume a) of a solid of revolution using various methods b) of a region with known cross sections AB AB AB AB AB AB AB1 Solve separable differential equations to solve problems involving exponential growth and decay Interprets ln x as the area under the curve of f(x) = 1/x. 5.1 Uses a geometric interpretation of differential equations via slope fields and identifies the relationship between slope fields and solution curves for differential equations. Ch 4 6 Supplem ent 2004 AB AB AB5

7 Course Expectations 1) Be Prepared (bring these items daily) 3-ring binder Pencil Textbook Classwork/Homework A College Board approved graphing calculator is required (I have only a limited number to issue, and a calculator contract must be on file with me). 2) Expect Excellence Follow all instructions. Challenge yourself (and meet course challenges). Do not distract yourself by using a cell phone for any reason (even as a clock). Respect class time: Take care of personal errands before class begins (restroom, attendance office, locker, etc.). Restroom passes are only for emergencies and will be limited. Lost class time = Lost learning opportunities Produce work of exceptional quality. Show all steps when solving a problem. This is non-negotiable. Show willingness to present work to the class. Do not cheat on assignments. Cheating will result in an office referral and you will be required to make up the assignment at the teacher s convenience and not your convenience. Failure to make up the assignment at the specified time will result in a zero. 3) Always Be on Time Be on time to class each day (see the school tardy policy for more details). Turn in work on time. Do not be late! Make up work on time (due dates will be posted or discussed for each assignment). 4) Respect Everyone Respect the opinions of others. Respect your teacher and her decisions. Do not make disrespectful comments about other students, teachers, or school staff. Be able to work both individually and cooperatively. 5) Show Bear Pride Do not bring outside food/drink into class (exception: bottled water). Keep the classroom clean and throw away trash. Do not demonstrate a lack of school pride. Always have a positive attitude in class! Pay attention to due dates (they will be posted on the board). Plan for your future. Take responsibility for your actions. Read and follow all rules in the Student Handbook. Textbooks: The student is responsible for their issued textbook the entire semester and should have it covered at all times. If the textbook is not covered, that will be an automatic detention. If the textbook is lost or damaged, the student is required to pay the textbook fee as soon as possible. Also, if the school barcode is removed from the assigned textbook, then the book is considered lost. Thus, the student must pay the full price for the assigned textbook.

8 Discipline Plan Teacher discretion can be used at any time on the discipline plan Step 1: Warning Step 2: 15 min. morning detention and parent contact Step 3: 30 min. after school detention and parent contact Step 4: Office referral Please Note: The discipline plan is progressive. For example, if a student has already received a 15 minute detention, he or she will automatically move to a 30 minute detention. Some offenses may automatically move a student to step 4 (for example: severe disrespect, fighting, cheating, etc.) Tutorial/Detention/Makeup Work (subject to change): Tutoring schedules will vary. Tutoring days will be posted each Friday in the classroom for the following week. Detentions are scheduled at my convenience and must be served by the assigned date or the student will receive an office referral. Grading System: Tests = 75%, Daily = 25% (homework and other assignments), Semester Exam = 15% of final grade Teacher Contact: If you have questions, please call me at ext or me at maggie.grange@hcbe.net.

9 Student Name (Please Print) Please sign this page stating that you and your child have read and understood the syllabus and have your child return this page by August 7 th. I have read and understood all requirements, expectations, and policies for Mrs. Grange s mathematics course. Student Signature Date Parent Signature Date Parent