GORE AP Calculus AB Syllabus 2011-2012 by changcheng2


									  Advanced Placement Calculus AB
       ’11 – ’12 School Year
           Mrs. Jami Gore
  jgore@nthurston.k12.wa.us                                    The Hawk Way
                                                            Hawks are:
              House A                                       Respectful
             Room 113                                       Responsible
           (360) 412-4820                                   Successful

This course introduces students to the four major concepts found within a typical first semester
of calculus: limits, derivatives, and definite and indefinite integrals. We will use a variety of
ways to approach and solve problems: numerical analysis (using known data points), graphical
analysis (using a known graph), algebraic analysis (using an equation and variables), and
verbal/written methods of representing problems (including justification of one’s thinking). A
detailed list of topics can be found in the AP Calculus Course Description, which is available at
the school or online at http://apcentral.collegeboard.com. This class is designed to prepare
you for the AP Calculus Test! The test date is Wednesday, May 9th at 8:00 a.m..
Foerster, Paul. Calculus: Concepts and Applications. Berkeley, CA: Key Curriculum
Press, 1998.
  Good attendance is critical for success in Mathematics. The school’s Attendance and Tardy
   Policy is strictly enforced. When absent, it is the student’s responsibility to obtain and
   complete the missed assignments and notes.
  NO electronic devices will be allowed in class. This includes cell phones, ipods, etc.
  Academic dishonesty will NOT be tolerated. Any student who is caught cheating on any
   individual test, quiz, or assignment will receive an automatic zero for that assignment with no
   chance to retake.
The AP Calculus curriculum demands the use of a graphing calculator. Because of this
requirement, each student should have their own TI-83 or TI-84 graphing calculator. Other
graphing calculators could be used, but support of those calculators will not be offered in this
course. Calculators for student use may be checked out in the library for the school year. We
will use graphing calculators to help solve a variety of problems, including: estimate limits,
determine asymptotic behavior, estimate roots, find points of intersection, calculate numerical
differentiation and perform numeric integration. We will also use graphing calculators to
experiment with and investigate. This includes investigating different functions, exploring the
numerical approach to limits, derivatives and integrals, and exploring the continuity of a
function. Finally we will use graphing calculators to interpret results, support conclusions, and
check solutions. Half of the AP Calculus exam requires the use of a graphing calculator so you
must be comfortable and confident in using one.
The overall grade will be determined (approximately) as follows:
                                                                          Grading scale:
     Free-Response Quizzes:                         20%                  85% -         A
                                                                          70 - 84%       B
     Homework/Class Participation:                  30%                  55 - 69%       C
                                                                          50 – 54%       D
     Tests/Projects:                                50%                  Below 50%      F

*I will follow the River Ridge grade incentive program. This states that if you pass the official
AP exam with a 3 you can move one semester grade up by one letter grade. If you earn a 4 or 5
on the AP exam you can change one semester grade to an A. To take advantage of this you must
bring proof to the main office (score reports usually arrive in July.)*

We will have one major project each quarter of both semesters. All projects will include
numeric, graphic, and algebraic analysis as well as written justification or explanation. They will
each be weighted the same as one unit test.

Late/Make-Up Work:
    One school day will be allowed for each day missed upon return to school. Make-up work is
     accepted for excused absences only.
    No late assignments or projects will be accepted for credit.

                                      Course Outline
By successfully completing this course, you will be able to:
  Work with functions represented in a variety of ways: graphically, numerically, analytically,
     or verbally, and understand the connections among these four representations.
  Understand the meaning of the derivative in terms of a rate of change and local linear
     approximation and be able to use derivatives to solve problems.
  Understand the meaning of the definite integral as a limit of Riemann sums and as the net
     accumulation of change and should be able to use integrals to solve problems.
  Understand the relationship between the derivative and the definite integral as expressed in
     the Fundamental Theorem of Calculus.
  Communicate mathematics and explain solution to problems verbally and in written
  Work effectively as part of a group or team of students to solve problems and present their
  Model a written description of physical situation with a function, differential equation, or an
  Use technology to help solve problems, experiment, interpret results, and support
  Determine the reasonableness of solutions.
  Develop an appreciation of calculus as a coherent body of knowledge and as a human
Units and Pacing: (Sections with an * indicate that they are BC topics only.)
All other sections are covered on both the AB and BC exam.

Chapter 1: Introduction to Limits, Derivatives, and Integrals (7 days)
Section 1: Instantaneous rate of change as the limit of average rate of change
Section 2: Approximate rates of change from equations, graphs, and tables
Section 3: Estimating definite integrals
Section 4: Using the Trapezoidal Rule to estimate definite integrals from equations and tables
Section 5: Derivative as an instantaneous rate of change

Chapter 2: Properties of Limits (14 days)
Section 1/2: Exploring the Definition of Limit by graphical, numerical, and algebraic techniques
Section 3: Using the Limit Theorems
Section 4: Using the Definition of Continuity to tell whether a function is or is not continuous
Section 4: Exploring piecewise functions and continuity
Section 5: Limits involving infinity
Section 6: The Intermediate Value and Extreme Value Theorems

            *Our first unit assessment will be after Chapter 2 and will cover Limits*

Chapter 3: Derivatives, Antiderivatives, and Indefinite Integrals (14 days)
Section 1: Using difference quotients to estimate the slope of a tangent line and understanding
          the graphical implications
Section 2: Using the Definition of Derivative (at a point) to find derivatives
Section 3: Comparing functions and their derivatives numerically and graphically
Section 4: Using the (general) Definition of Derivative to find derivatives of Power Functions
Section 5: Displacement, Velocity and Acceleration relationships.
Section 6/8: The derivative of sine and cosine.
Section 7: Chain Rule
Section 9: Exponential and Logarithmic derivatives.

     *Our second unit assessment will be after Chapter 3 and will cover Basic Derivatives*

Chapter 4: Products, Quotients, and Parametric Functions (20 days)
Section 1: Making conjectures to find the derivative of combinations of functions.
Section 2: Using the Product Rules to find derivatives
Section 3: Using the Quotient Rules to find derivatives
Section 4: Finding the derivatives of Trigonometric Functions
Section 5: Finding the derivatives of Inverse Trigonometric Functions
Section 6: Relationship between differentiability and continuity.
       *Section 7: Derivatives of a Parametric Function*
Section 8: Differentiating implicit relations
Section 9: Related rates.

       *Our third unit assessment will be after Chapter 4 and will cover Differentiation*
Chapter 5: Definite and Indefinite Integrals (20 days)
Section 1: Exploring the definite integral
Section 2: Linear Approximations and Differentials
Section 3: Formal Definition of the Indefinite Integral
Section 4: Riemann Sums and Definite integrals
Section 5: The Mean Value Theorem
Section 6: The Fundamental Theorem of Calculus
Section 7: Definite integral practice
Section 8: Applying definite integrals to area
Section 9: Volume of a Solid by Plane Slicing
Section 10: The integration feature of you graphing calculator

          *Our fourth unit assessment will be after Chapter 5 and will cover Integrals*
                     *This should be the LAST assessment for 1st semester*

Chapter 6: The Calculus of Exponential and Logarithmic Functions (12 days)
Section 1: Integral of the reciprocal function
Section 2: Antidifferentiating the Reciprocal Function
Section 3: Properties of Logarithmic Functions
Section 4: Exploring e and the change of base theorem.
Section 5: Limits of Indeterminate Forms: I’ Hospital’s Rule
Section 6: Derivative and integral practice.

                                       *Unit Assessment*

Chapter 7: The Calculus of Growth and Decay (10 days)
Section 1: Expressing exponential growth and decay as a direct proportion
Section 2: Separating and integrating differential equations
Section 3: Applications for Differential Equations
Section 4: Slope Fields
       *Section 5: Euler’s Method*
       *Section 6: Logistic differential equations and modeling*

                                       *Unit Assessment*

Chapter 8: The Calculus of Plane and Solid Figures and Other Topics (16 days)
Section 1: Exploring cubic functions and their derivatives.
Section 2: Finding critical points from derivatives.
Section 3: Using derivatives to solve Maximum & Minimum problems
Section 4: Finding the area of a plane region
Section 5: Finding volume by plane slicing
Section 6: Finding the volume of a solid of revolution by using cylindrical shells
       *Section 7: Lengths and Areas for Polar Coordinates*

                                       *Unit Assessment*
       *Chapter 9: Techniques of Antidifferentiation* (15 days)
       *Section 2: Integration by Parts*
       *Section 3: Rapid Repeated Integration by Parts*
       *Section 6: Integration by Trigonometric Substitution*
       *Section 7: Integration of Rational Functions by Partial Fractions*
       *Section 10: Improper Integrals*

Chapter 10: The Calculus of Motion (10 days)
Section 1: Distance and Displacement for Motion along a Line
Section 2: Distance, Displacement and Acceleration
Section 3: Average Value of a Function
Section 4: Related Rates
Section 5: Maximum and Minimum Problems in Motion
       *Section 6: Vector Functions for Motion in a Plane*

                                       *Unit Assessment*

       *Chapter 12: The Calculus of Functions Defined by the Power Series* (20 days)
       *Section 1: Introduction to Power Series*
       *Section 2: Geometric Sequences and Series as Mathematical Models*
       *Section 3: Power Series for an Exponential Function*
       *Section 4: Power Series for Other Elementary Functions*
       *Section 5: Taylor and Maclaurin Series*
       *Section 6: The Ratio Technique*
       *Section 7: Convergence of Series (including harmonic series and the integral test)*
       *Section 8: The Lagrange Error Bound*

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