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AP Calculus AB

AP Calculus AB

Course Overview

This course will cover all topics included in the Calculus AB topic outline as it appears in the AP Calculus Course Description. The student will be able to work the problems from a graphical, numerical, and analytical point of view and will then be able to communicate their solutions both verbally and in written form. Students will use a graphing calculator to help them solve problems, experiment, interpret results, and support their conclusions. The purpose of this multiple approach is to foster a deeper understanding of calculus and prepare students to take and perform well on the AP exam this spring and in subsequent courses. The AP Exam in May is a requirement for this course.

AB Course Outline

This is a preliminary schedule for the course and may change based on student performance.

Topic I ~ Pre Calculus Review                                             (3 days)       

  • Logarithmic functions
  • Trigonometry, including
    • The Unit Circle
    • Trigonometric Identities
    • Graphs of Trigonometric Functions
  • The family of functions graphs

Topic II ~ Limits & Continuity                                            (7 days)

  • Average Velocity, Instantaneous Velocity
  • Find limits graphically and numerically
  • Evaluate limits analytically
  • Continuity and one-sided limits
  • Intermediate Value Theorem
  • Infinite limits and vertical asymptotes

Topic III ~ Analytical Development of the Derivative       (7 days)

  • The derivative and the tangent line problem
  • Basic differentiation rules and rates of change (average and instantaneous)
  • Derivative rules for basic functions
  • Product and Quotient Rules and other Higher Order derivatives
  • Exponential derivatives
  • Trigonometric derivatives
  • Chain Rule
  • Implicit differentiation
  • The second derivative

Topic IV ~ Application of the Derivative                            (12 days)

  • Tangent and normal lines and linear approximations
  • The Mean Value Theorem and Rolle’s Theorem
  • Analysis of function graphs
    • Increasing & decreasing functions
    • Local and global extrema
    • Extreme Value Theorem
    • Concavity and points of inflection
    • Using graphs of f, f’, and f’’
  • Modeling and optimization
  • L’Hospital’s Rule
  • Related Rates
  • Position, velocity, and acceleration
  • Antiderivatives
  • Differentials

Topic V ~ Integration                                                                       (10 days)

  • Development of the integral
  • Riemann Sums
  • The definite integral
  • The Fundamental Theorem of Calculus
  • Properties of the definite integral
  • Calculating definite integrals using geometry
  • Integration by substitution

Topic VI ~ Application on Integrals                                                (12 days)

  • Area/accumulation
  • Net and total distance with definite integrals
  • Average value of a function
  • Net change of a function
  • Motion
  • Inverse trigonometric functions (derivative and antiderivative)
  • Volumes
    • Disk method
    • Washer method
    • Shell method
    • Cross sections

Topic VII ~ Differential Equations                                     (5 days)

  • Differential equations with initial conditions
  • Slope fields
  • Separation of variables
  • Modeling with differential equations

Topic VIII ~ Review                                                             (up to 10 weeks)

  • All previous topics included in preparation form the AP Exam.

Teaching Strategies

I will utilize a variety of activities with each class period. A typical class will consist of a combination of lecture, to introduce topics, and classroom/group work. We will have daily classroom work that will be collected, graded, and returned the next class period. Students will work together on a regular basis, both formally and informally. Collaboration with classmates will be an invaluable tool.

I will encourage different approaches to solving a problem and believe that we will learn through our mistakes. Emphasis is placed on students communicating their method of solution and a justification of their answer. Groups will also present work to the class.

Technology

Each student is required to have a graphing calculator. All classroom work requiring the use of a calculator will be completed on a Ti-84 Plus for this is the type of calculator utilized on our Smart Board immolator. Calculators are used to assist in the understanding of topics, as well as for experimentation. There will be numerous assignments, quizzes and portions of exams in which a calculator will not be used.

All classroom presentations will be done with the Smart Board.

Notes and Worksheets

Notes will be given in class as part of the educational practice. Students are expected to take notes in class and follow along with the lecture. Students who miss class are expected to get the notes from another student in class. If a student after copying down the notes is still struggling with the topic, then the student may come in for additional help regarding the topic. Worksheets are available to print off my website. Students may choose to do the work on additional paper, but it is the student’s responsibility to clearly label what worksheet is being completed.

Student Evaluation

Evaluations are based on assignments, quizzes, and exams.

Daily Quizzes (5%): Daily quizzes will be given every class and range from 1 – 20 points. If a student misses a daily quizzes it is their responsibility to come and make up the quiz. Daily quizzes are used to help review topics as well as introduce new topics based upon previous knowledge.

 

Assignments (10%): Homework and Classwork will be assigned daily for students to complete. Students will be given one week to complete homework and should come into for additional help if they are struggling with concepts found on the homework. Helpful resources can be found on my website to help assist students with homework. Homework is graded for completion on a 0 – 5 scale. Students who have a 90% or higher in the homework category will receive an additional curve at the end of each semester.

Quizzes (45%): quizzes will be given on a regular basis (every 2 – 3 weeks). Quizzes will range in difficulty including multiple choice and free response questions. Quizzes will always include current and past material. Second semester students will be receiving former AP Free Response questions which will be scored as a quiz grade out of 9 points.

Exams (40%): First semester will consist of two tests, one take home test and one final at the end of the semester. Second semester will have one test in late April. All tests will be composed of former AP Test Questions as well as sample AP questions provided by College Board.

Make Up Policy

The Jefferson County Public School policy for make-up work will be strictly enforced. Check the district website for information pertaining to this.

Grade Breakdown

A         90% or higher                         Exceptionally strong knowledge of content

B          80% - 89.9%                           Strong knowledge of content

C          70% - 79.9%                           A good knowledge of content

D         60% - 69.9%                           Some knowledge of content

F          Below 60%                              No evidence of knowledge of the content

Grade Breakdown with Additional Curve

A         70% or higher                         Exceptionally strong knowledge of content

B          55% - 69.9%                           Strong knowledge of content

C          40% - 54.9%                           A good knowledge of content

D         20% - 39.9%                           Some knowledge of content

F          Below 20%                              No evidence of knowledge of the content

Primary Textbooks

Larson, Hostetler and Edwards (2006). Calculus of a Single Variable (8th Ed.) Boston: Houghton Miffin Company

* This textbook will be used in class assignments and not checked out to students.

The Princeton Review, Inc. (2017) Cracking the AP Calculus AB & BC Exams (2017Ed.) New York: Random House Incorporated.

 

*The workbook needs to be purchased. Lakewood has purchased a classroom set and are available for $20.00 through Ms. Boonstra

Supplementary Materials

AP Calculus Multiple Choice Questions, 1969 – 1997

AP Calculus AB Multiple Choice Questions, 1998, 2003, and 2008, 2013, and 2014, 2015, 2016, 2017

AP Calculus Free Response Questions, 1969 – 1997

AP Calculus AB Free Response Questions, 1999 – 2017

Cell Phones

Cell phones may only be used in class if permitted by the teacher.

            I reserve the right to alter or change this syllabus without notice.


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