AP Calculus AB SYllabus for APCENTRAL by b8REurq

VIEWS: 88 PAGES: 18

									                         AP Calculus AB Syllabus


This course is designed to teach the student to solve problems using the concepts of
calculus graphically, numerically, analytically, and verbally. The main objective of this
course is for the student to learn to use calculus to model and solve real life problems.
This course will give students a strong foundation to succeed in any future endeavors in
mathematics.




RESOURCE REQUIREMENTS (Resource Requirements #1 and #2)
Text:   Calculus of a Single Variable (Sixth Edition)
         By Larson, Hostetler, Edwards 1998

Supplementary Materials: College Board AP Central

                              AP Calculus Institute
                              University of Georgia
                              Summer 2006
                              Activities and Resource Manual by Dane Marshall
                              Instructor: Dane Marshall

                              TI Interactive!
                              Texas Instruments, 2001

                              Derive 5
                              Texas Instruments, 2000

.
Prerequisites: Students in this class are required to have completed Honors
Precalculus or must be taking Honors Precalculus.

                              Text: Precalculus (Fourth Edition)
                                    By Larson & Hostetler 1997

Graphing calculators: Each student is required to have a TI-83 or TI-84. I have a TI-
89 for use in the classroom. The calculator is used extensively in this class to explore,
discover, and reinforce concepts that are learned. Students are allowed to use
calculators on all assignments and on most assessments.

Grading Policies: Our school year is divided into four 9-week grading periods. Each
nine week grade is 42.5% of the semester grade and the semester exam is 15%. Each
nine-week grade will consist of assessments from tests, quizzes, and projects.
Homework is not graded but required.




                                        Page 1 of 18
Assessments: Tests are designed in the same format of the AP Exam – multiple-
choice and free-response. Questions from previous AP Exams influence the free-
response and text test generator questions are used for the multiple-choice. Teacher
designed problems are also used.

Time Line: The time spent on each chapter is an estimate and varies each year
depending on the caliber of students in this class. Each semester has 90 days. The
approximate times include time for teaching and assessment. The twelve missing days
are due to four scheduled exam days and to at least eight days of review for the AP
Calculus AB Exam. A day consists of 49 minutes of class instruction.




CURRICULAR REQUIREMENTS (Curricular Requirement #2, #3, #4, #5)
The Course Outline is a list of the topics from the text that are covered and the
sequence in which those topics are covered. Supplementary materials are used to
enhance the objectives learned in the text or to fulfill AP Course Audit requirements.
The Standards required by the State of Tennessee are also included.

The Student Syllabus by Nine Weeks is a detailed outline of problems and notes that
have been assigned during the 2006-2007 school year. This syllabus will vary slightly
from year to year as the course continues to become more rigorous.

The Class Activities Section is a sampling of activities used in this course.




Course Outline (Curricular Requirement #2)
Course description: Calculus is an advanced mathematics course that uses
meaningful problems and appropriate technology to develop concepts and applications
related to continuity and discontinuity of functions and differentiation, and integration.

Prerequisite

Text:   Calculus of a Single Variable (Sixth Edition)
         By Larson, Hostetler, Edwards 1998

Chapter P Preparation for Calculus (Prerequisite and/or Summer Assignment and
1 day in class)

    P.1 Graphs and models
        The graph of an equation
        Intercepts of a graph
        Symmetry of a graph
        Points of intersection


                                         Page 2 of 18
                Mathematical models

     P.2 Linear Models and Rates of Change
         The slope of a line
         Equations of a line
         Ratios and Rates of change
         Graphing linear models
         Parallel and perpendicular lines


    P.3 Functions and Their Graph
        Functions and function notation
        Domain and range of a function
        The graph of a function
        Transformations of functions
        Classifications and combinations of functions

    P.4 Fitting Models to Data
        Linear Regressions
        Quadratic regressions
        Trigonometric regressions




Tennessee Standard 1.0: Functions

Students will expand the concept of functions to include the analysis and interpretation of both continuous
and discontinuous functions in problem situations and the development of the concept of limit.

Learning Expectations:

Students will:

        1.1 demonstrate an understanding of the concepts and applications related to a variety of
         continuous functions;
        1.2 calculate and estimate limits;
        1.3 represent a variety of functions graphically;
        1.4 use graphical representations to demonstrate an understanding of asymptotes;
        1.5 use a variety of methods to analyze and interpret functions;
        1.6 apply functions in problem situations

Student Performance Indicators:

        analyze the graphs of polynomial, rational, radical, and transcendental functions using appropriate
         technology;
        predict and explain the observed local and global behavior of a function;
        calculate limits using algebra;
        estimate limits from graphs or tables of data.
        demonstrate an understanding of asymptotes in terms of graphical behavior;
        describe asymptotic behavior in terms of infinite limits and limits at infinity;
        compare relative magnitudes of functions and their rates of change.



                                                 Page 3 of 18
        demonstrate an understanding continuity in terms of limits;
        demonstrate a geometric understanding of graphs of continuous functions.




Text:     Calculus of a Single Variable (Sixth Edition)
           By Larson, Hostetler, Edwards 1998

Chapter 1 Limits and Properties (approximately 20 days)

    1.1 Preview of Calculus

    1.2 Finding Limits Graphically and Analytically
        An introduction to limits
        Limits that fail to exist
        A formal definition of a limit

    1.3 Evaluating Limits Analytically
        Properties of limits
        Strategies for finding limits
        Cancellation and rationalization techniques
        The squeeze theorem

    1.4 Continuity and One-sided Limits
        Continuity at a point and on an open interval
        One-sided limits and continuity on a closed interval
        Properties of continuity
        The Intermediate Value Theorem

    1.5 Infinite Limits
        Infinite limits
        Vertical asymptotes




Tennessee Standard 2.0: Derivatives

Students will extend the concept of slope of a line to develop the concept of derivative.

Learning Expectations:

The student will:

        2.1 define, represent and interpret the concept of derivative;
        2.2 use the derivative of a function to characterize the function and vice versa;
        2.1 connect the relationships among a function and its first and second derivative;
        2.2 apply basic rules for differentiation;
        2.3 apply derivatives in problem situations.

Student Performance Indicators:



                                                  Page 4 of 18
       represent the concept of the derivative geometrically, numerically, and analytically;
       interpret the derivative as an instantaneous rate of change;
       define the derivative as the limit of the difference quotient;
       articulate the relationship between differentiability and continuity.
       articulate corresponding characteristics of graphs of f and f ´ ;
       communicate the relationship between the increasing and decreasing behavior f and the sign of f ´
        ;
       demonstrate an understanding of the Mean Value Theorem and its geometric consequence;
       translate verbal descriptions into equations involving derivatives and vice versa.
       articulate corresponding characteristics of the graphs of f , f ´ , and f ´´ ;
       communicate the relationship between the concavity of f and the sign of f ´´ ;
       identify points of inflection;
       analyze curves using the notions of monotonicity and concavity;
       optimization, both absolute (global) and relative (local) extrema;
       model rates of change, including related rates problems;
       use implicit differentiation to find the derivative of an inverse function;
         interpret the derivative as a rate of change in varied applied contexts;
       apply basic rules for the derivative of basic functions and their sum, product, and quotient;
       use the chain rule and implicit differentiation




Text:    Calculus of a Single Variable (Sixth Edition)
          By Larson, Hostetler, Edwards 1998

Chapter 2 Differentiation (approximately 30 days)

   2.1 The derivative and the Tangent Line Problem
       The tangent line problem
       The derivative of a function
       Differentiability and continuity

   2.2 Basic Differentiation Rules and Rates of Change
       The Constant Rule
       The Power Rule
       The Constant Multiple Rule
       The Sum and Difference Rules
       Derivatives of sine and cosine functions
       Rates of Change

   2.3 The Product and Quotient Rules and Higher-order Derivatives
       The Product Rule
       The Quotient Rule
       Derivatives of trigonometric functions
       Higher-order derivatives

   2.4 The Chain Rule
        The Chain Rule
        The General Power Rule
        Simplifying derivatives


                                              Page 5 of 18
               Trigonometric functions and the Chain Rule

    2.5 Implicit Differentiation
         Implicit and explicit functions
         Implicit differentiation

    2.6 Related Rates
         Finding related rates
         Problems with related rates




Chapter 3 Applications of Differentiation (approximately 27 days)

    3.1    Extrema on an Interval
           Extrema of a function
           Relative extrema and critical numbers
           Finding the extrema on a closed interval

    3.2       Rolle’s Theorem and the Mean Value Theorem

    3.3       Increasing and Decreasing Functions and the First Derivative Test

    3.4 Concavity and the Second Derivative Test

    3.5 Limits at Infinity

    3.6 A Summary of Curve Sketching

    3.8       Newton’s Method

    3.7       Optimization Problems

    3.10 Business and Economic Applications

   3.9        Differentials
              Slope fields (supplementary material)
              Rectilinear motion (supplementary material)


Tennessee Standard 3.0: Integrals

Students will develop the concepts of integrals and their applications.

Learning Expectations:

The student will:

         3.1    define and apply basic properties of definite integrals;
         3.2    evaluate or approximate define integrals;



                                                   Page 6 of 18
       3.3    apply techniques of antidifferentiation.

Student Performance Indicators:

       communicate the relationship between a Riemann sum and a definite integral;
       apply basic properties of definite integrals;
       evaluate definite integrals using the Fundamental Theorem;
       apply techniques of antidifferentiation;
       find specific antiderivatives using initial conditions, including applications to motion along a line;
       use separable differential equations in modeling;
       use Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions
        represented algebraically, geometrically, and by tables of values




Text:    Calculus of a Single Variable (Sixth Edition)
          By Larson, Hostetler, Edwards 1998

Chapter 4 Integration (approximately 30 days)

    4.1 Antiderivatives and the Indefinite Integration

             Antiderivatives
             Notation for antiderivatives
             Basic integration rules
             Initial conditions and particular solution

   4.2 Area
       Sigma notation
       Area
       The area of a plane region
       Upper and lower sums

   4.3 Riemann Sums and Definite Integrals
       Riemann sums
       Definite integrals
       Properties of definite integrals

   4.4 The Fundamental Theorem of Calculus
       The Fundamental Theorem of Calculus
       The Mean Value Theorem of Integrals
       Average value of a function
       The Second Fundamental Theorem of Calculus
       The distance traveled by a particle (Supplementary material)

   4.5 Integration by Substitution
       Pattern recognition
       Change of variables
       The general Power Rule for integration
       Change of variables for definite integral


                                                  Page 7 of 18
         Integration of even and odd functions

   4.6 Numerical Integration
       The Trapezoidal Rule
       Simpson’s Rule
       Error analysis



Chapter 5 Logarithmic, Exponential, and other Transcendental Functions
(approximately 30 days)

   5.1 The Natural Logarithmic Function and Differentiation
       The natural logarithmic function
       The number e
       The derivative of the natural logarithmic function

   5.2 The natural logarithmic function and integration
       Log Rule for integration
       Integrals of trigonometric functions

   5.3 Inverse Functions
       Inverse functions
       Existence of an inverse function
       Derivative of an inverse function

   5.4 Exponential Functions: Differentiation and Integration
       The natural exponential function
       Derivatives of exponential functions
       Integrals of exponential functions

   5.5 Bases of than e and Applications
       Bases other than e
       Differentiation and integration
       Applications of exponential functions

   5.6 Differentiation Equations: Growth and Decay
       Differential equations
       Growth and decay models

   5.7 Differential Equations: Separation of Variable
       General and particular solutions
       Separation of variables
       Homogeneous differential equations
       Applications

    5.8 Inverse Trigonometric Functions and Differentiation
        Inverse trigonometric functions
        Derivatives of inverse trigonometric functions
        Review of basic differentiation rules



                                      Page 8 of 18
    5.9 Inverse Trigonometric Functions and Integration
        Integrals involving inverse trigonometric functions
        Completing the square
        Review of basic integration rules

    5.10 Hyperbolic Functions
        Hyperbolic Functions
        Differentiation and integration of hyperbolic functions
        Differentiation and integration of inverse hyperbolic functions

Chapter 6 Applications of Integration (approximately 18 days)

   6.1 Area of a Region between Two Curves
       Area of a region between two curves
       Area of a region between intersecting curves

   6.2 Volume: The Disc Method
       The Disc Method
       The Washer Method
       Solids with known cross-sections

   6.3 Volume: The Shell Method
       The Shell Method
       Comparison of Disc and Shell Method

   6.4 Arc Lengths and Surfaces of Revolution
       Arc length
       Area of a surface of revolution




                                      Page 9 of 18
Student Syllabus by Nine Weeks (Curricular Requirement #2)
     First Nine Weeks                                                      AP Calculus AB




Optional Summer Assignment         Section P1 (Page 3 - 7)
Optional Summer Assignment         Page 9 (1 - 4,7,13,15,17,23,25,27,29)
Optional Summer Assignment         Section P1 (Page 3 - 7)
Optional Summer Assignment         Page 9 (31 - 51 odd, 55 )
Optional Summer Assignment         Section P2 ( Page 11 - 16)
Optional Summer Assignment         Page17 ( 1 - 9 odd, 15,17,21-25 odd, 32,36,37)
Optional Summer Assignment         Section P3
Optional Summer Assignment         Page 28 (3 - 7, 11 - 21, 35,41,47,49)
Optional Summer Assignment         Section P4 (Page9 #55)
Optional Summer Assignment         Page34 ( 1 - 5,7,9,13,15)
Optional Summer Assignment         Review Page 37 ( 1- 7 odd,21,25,29-33,42)
                                   NO TEST over Chapter P
          8/7/06              1.   Section 1.1
          8/7/06              2.   Page 46 ( 1,3,5,7,11)
          8/8/06              3.   Section 1.2
          8/8/06              4.   Page 53 ( 1 - 19 odd)
          8/9/06              5.   Section 1.2
          8/9/06              6.   Page 53 ( 21 - 37 odd)
         8/10/06              7.   Section 1.3
         8/10/06              8.   Page 64 ( 1 - 27 odd)
         8/11/06              9.   Section 1.3
         8/11/06             10.   Page 64 ( 29 - 43 odd)
    8/14/2006 - 8/16/06      11.   Section 1.3
    8/14/2006 - 8/16/06      12.   Page 64 ( 45 - 67 odd 87 89 90 91 92) and Limits of Trigonometric Functions WS
                             13.   Review for Test (Page 87 #3 - 20 all)
         8/17/06                   TEST 1.1 - 1.3
         8/18/06             14.   Section 1.4
         8/18/06             15.   Page 75 ( 1 - 25 odd)
         8/21/06             16.   Section 1.4 cont'd
         8/21/06             17.   Page 75 ( 27 -51 odd)
         8/22/06             18.   Section 1.4 cont'd
         8/22/06             19.   Page 75 ( 57 - 81 odd omit 71,77)
     8/23/06 - 8/24/06             Free-response Problem: Continuity
         8/25/06                   TEST 1.1 - 1.4
         8/28/06             20.   Section 1.5
         8/28/06             21.   Page 84 ( 1 - 43 odd)
         8/29/06             22.   Section 1.5
         8/29/06             23.   Page 84 (16,24,38,47 - 52 all)
         8/29/06             24.   Page 84 (48 - 52 all)
         8/30/06             24.   Section 2.1
         8/30/06             25.   Page 99 (1,3,5 - 15 odd)




                                                 Page 10 of 18
      8/31/06           26.   Section 2.1
      8/31/06           27.   Page 99 (17,19,23,25, 51 - 60 odd)
       9/1/06           28.   Review Page87 ( 23 - 31 35 - 43) Page99 even
       9/8/06                 TEST 1.1 - 2.1
       9/7/06           29.   Section 2.2
       9/7/06           30.   Page 110 ( 1 - 12)
      9/11/06           31.   Section 2.2
      9/11/06           32.   Page 110 ( 13 - 42 odd)
      9/12/06           33.   Section 2.2
      9/12/06           34.   Page 111 ( 43 - 51 59 65 71 72 73 74 79 81)
      9/13/06           35.   Section 2.3
      9/13/06           36.   Page 121 ( 1 - 21 odd)
      9/14/06           37.   Section 2.3
      9/14/06           38.   Page 121 (23 - 41 odd)
      9/20/06           39.   SECTION 2.3
      9/20/06           40.   Page 122 (47 - 61, 65 73 - 81ODD)
      9/21/06           41.   Section 2.4
      9/21/06           42.   Page 130 ( 1 - 25 odd)
      9/25/06           43.   Section 2.4
      9/25/06           44.   Page 130 (27, 29, 43 - 51, ODD)
      9/26/06           45.   Section 2.4
      9/26/06           46.   Page 130 ( 53 - 77 odd)
      9/27/06           47.   Review for test 2.2 2.3 2.4 Page 150 ( 7 - 73)
      9/28/06           48.   Section 2.4
      9/28/06           49.   Page 130 ( 53 - 77 even)
      9/29/06                 TEST 1.1 - 2.4
      10/2/06           50.   Section 2.5
      10/2/06           51.    Page 139 ( 9 - 25 odd)
                        52.   Section 2.5
                        53.   Page 139 ( 9 - 25 even)
      10/3/06           52.   Section 2.5
      10/3/06           53.   Page 139 ( 9 - 25 even)
      10/3/06           54.   Section 2.5
      10/3/06           55.   Page 139 (27, 31, 35, 41, 45)
      10/4/06           56.   Section 2.5
      10/4/06           57.   Page 150 ( 7 - 57 pick and choose)
      10/5/06                 TEST 2.5
      10/6/06           58.   Section 2.6
      10/6/06           59.   Page 146 ( 1 - 7 all, 9)




Second Nine Weeks                                                  AP Calculus AB




      10/16/06          1     Worksheet on related rates
10/17/2006 - 10/24/06   2     Worksheet #2 on related rates
10/17/2006 - 10/24/06   3     Section 2.6 (OMIT)



                                            Page 11 of 18
10/17/2006 - 10/24/06   4    Page 146 (11,12,13,14,16) (OMIT)
10/17/2006 - 10/24/06   5    Section 2.6 (OMIT)
10/17/2006 - 10/24/06   6    Page146 (17 - 21 all) (OMIT)
10/17/2006 - 10/24/06   7    Section 2.6 (OMIT)
10/17/2006 - 10/24/06   8    Page 146 ( 22,24,25,29,30,31) (OMIT)
      10/27/06               TEST 2.6
      10/25/06          9    Section 3.1
      10/25/06          10   Page 160 ( 1 - 21)
      10/26/06          11   Section 3.1
      10/25/06          12   Page 160 ( 23 - 40)
        omit            13   Section 3.1
        omit            14   Page160 (4)
      10/31/06          15   Section 3.2
      10/31/06          16   Page 167 (1 - 21 odd 27 29 )
      11/1/06           17   Section 3.3
      11/3/06           18   Page 176 ( 1 - 19 odd)
      11/6/006          19   Section 3.3 and even problems Page176
      11/1/06           19   Page 176 (21 -47 odd)
        omit            20   Review for test 3.1 3.2 3.3
      11/7/06           21   Section 3.4
      11/7/06           22   Page 184 (7 - 19 odd)
      11/8/06           23   Section 3.4
      11/8/06           24   Page 184 ( 21 - 35 odd)
      11/9/06           25   Section 3.4
      11/9/06           26   Page 184 (21 - 36 even)
      11/10/06               Test 3.1 3.2 3.3 3.4
      11/13/06          27   Section 3.5
      11/13/06          28   Page 193 ( 1 - 23 odd)
      11/14/06          29   Section 3.5
      11/14/06          30   Page 193 ( 35 - 51 odd)
      11/15/06          31   Section 3.6
      11/15/06          32   Page 202 ( 7, 9, 29, 33, 37)
        omit            33   Section 3.6
        omit            34   Page 202 (11 13 31 35 39)
        omit            35   Review for Test 3.5 3.6
        omit            36   Page 202 ( 17 21 29 31) OPTIONAL
      11/17/06               TEST 3.1 3.2 3.3 3.4 3.5 3.6
      11/20/06          37   Section 3.7
      11/20/06          38   Page 210 ( 1- 10)
      11/20/06          39   Section 3.7
      11/20/06          40   WS 3.7
11/21/2006 - 11/28/06   41   Optimization WS (44 - 58)
                        42   Review for Test 3.7 (Quiz 3.7 B)
      11/30/06               TEST 3.7
      11/29/06          43   Section 3.8
      11/29/06          44   Page 219 ( 1- 12 all)
      11/29/06          45   Section 3.8




                                           Page 12 of 18
       11/29/06            46   Page 219 (13 - 16, 21 - 24, 27, 29)
       12/1/06             47   Section 3.9 & Rectilinear Measurement
       12/1/06             48   Page 226 ( 7 - 19 odd)
       12/1/06             49   Section 3.9
       12/1/06             50   Page 226 (21 23 25 27 39 41)
         omit              51   Worksheet 3.8 3.9
       12/4/06             52   Section 3.10
       12/4/06             53   Page 232 ( 3 - 15 odd, 31 33)
         omit              54   Review for test
Take-home due 12/08/06          TEST 3.8 3.9 3.10
 12/6/2006 - 12/14/06           PROJECT PRESENTATIONS (Free-response AP Problems)
                                Semester Exam



  Third Nine Weeks                                                        AP Calculus AB




       1/3/2007            1    Section 4.1
       1/3/2007            2    Page 249 ( 1 - 36 odd)
       1/4/2007            3    Section 4.1
       1/4/2007            4    Page 249 ( 1 - 36 even)
       1/5/2007            5    Section 4.1 & Introduction to Slope Fields
       1/5/2007            6    WS on antiderivatives
       1/8/2007            7    Section 4.1
       1/8/2007            8    Page 249 (37 - 65 odd)
       1/9/2007            9    Review for TEST 4.1
       1/9/2007            10   Review sheet
      1/11/2007                 TEST 4.1
      1/10/2007            11   Section 4.2
      1/10/2007            12   Page 261 ( 1 - 9 & 15 - 21 odd)
 1/12/2007 – 01/16/07      13   Section 4.2
      1/16/2007            14   Page 261 ( 23 - 33 all)
       01/17/07            15   Section 4.2
       01/17/07            16   Page 261 (35-38)
       01/18/07            17   Section 4.2
  01/18/07 /01/19/27       18   Page 262 ( 41 - 44 all)
       01/22/07            19   Review for Test
       01/22/07            20   Page 262 ( 45 - 48)
       01/23/07                 TEST 4.2
       01/24/07            21   Section 4.3
       01/24/07            22   Page 271 ( 1 - 19 odd)
       01/25/07            23   Section 4.3
       01/25/07            24   Page 272 (21,23,25,29,43)
       01/26/07            25   Review for Test 4.3
       01/26/07            26   Page 211 ( 2 -30 EVEN 43)
 01/29/07 /     01/30/07        TEST 4.3      /     TI-Interactive Activity: Area Under the Curve
      01/31/047            27   Section 4.4
       01/31/07            28   Page 283 ( 1 - 21 odd)



                                                  Page 13 of 18
    02/01/07        29   Section 4.4
    02/01/07        30   Page283 ( 23 - 41, 47, 49 67 69 73 79)
    02/02/07        31   Review for Test
    02/05/07             TEST 4.4
                    32   Section 4.5
                    33   Page 291 ( 1 - 20 all)
                    34   Section 4.5
                    35   Page 297 ( 21 -51 odd)
                    36   Section 4.5
                    37   Page 297 ( 65 - 75 odd)
                    38   Review for test 4.5
                         TEST 4.5
                    39   Section 4.6
                    40   Page 304 ( 1 - 19 odd Trapezoidal Rule)
                    41   Section 4.6 Simpson’s Rule
                    42   Page 304 ( 1 – 19 odd)
                    43   Review for test
                         Test 4.6
                    44   Section 5.1
                    45   Page 318 (21 27 29 37 - 65 odd)
                    46   Section 5.1
                    47   Page 318 ( 67 69 73 75 83 85)
                    48   Section 5-2
                    49   Page 327 ( 1 - 9, 13, 23, 27,29,33, 37,47)
                    50   Review for TEST 5.1 5.2
                    51   Handout
                         TEST 5.1 5.2
                    52   Section 5.3
                    53   Page 335 ( 3 7 9-12 13 19 23 51 53 57 61 73 79 89)
                    54   Section 5.4
                    55   Page 344 ( 1-7 29 - 47 odd 49 57)
                    56   Review for test 5.3 5.4
                         Test 5.3 5.4



Fourth Nine Weeks                                              AP Calculus AB




                    1    Section 5.5
                    2    Page 354 (1 - 25 29 - 43 odd)
                    3    Section 5.5
                    4    Page 354 ( 47 51 - 75 odd)
                    5    Section 5.5
                    6    Page 354 ( 30 - 48 even, 45, 53 55 57 59)
                    7    Section 5.6
                    8    Page 363 ( 1- 25 odd)
                    9    Section 5.6
                    10   Page 363 ( 27 -    odd)



                                        Page 14 of 18
11   Review for Test
     TEST 5.5 5.6
12   Section 5.7
13   Page 374 ( 1 - 23 odd)
14   Section 5.7
15   Page 374 ( 25 - 59 odd)
16   Section 5.7
     TEST 5.7
17   Page 375 (61 - 85 odd)
18   Section 5.8
19   Page 383 ( 1 - 40 odd)
20   Section 5.8
21   Page 383 (41 - 61 odd)
     Test 5.8
22   Section 5.9
23   Page 390 ( 1 - 31 odd)
24   Section 5.9
25   Page 390 (33 - 41 odd)
26   Page 390 ( 34 - 40 even)
     TEST 5.9
27   Section 5.10
28   Page 400 ( 1 - 29 odd)
29   Section 5.10
30   Page 400 (31 - 51 odd)
31   Section 5.10
32   Page 400 ( 53 - 77 odd)
     TEST 5.10
33   Section 6.1
34   Page 413 (1- 20) odd
35   Section 6.1
36   Page 413 (21 - 31,65)odd
37   Section 6.2
38   Page 423 ( 1- 9 all)
39   Section 6.2
     Test 6.1 6.2
40   Page 423 ( 11- 19 odd)
41   Section 6.1 & 6.2
42   Page 413 (21 - 31,65) EVEN Page 423 12 - 20 even
43   Section 6.3
44   Page 432 (1 - 11 odd)
45   Section 6.3
46   Page 432 (13 - 23 odd)
47   Section 6.3
48   Page 432 (13 - 23 even)
     Test 6.3
     PROJECT PRESENTATIONS (Free-response AP Problems)
     Final Exam




                    Page 15 of 18
Class Activities Section (Curricular Requirement #3, #4, #5)

Calculators (Curricular Requirement #5)

              In my class, calculators are used daily to explore, discover, and
              reinforce concepts. Examples of use include finding a root;
              sketching a function in a specified window; approximating the
              derivative at a point; approximating the value of a definite integral


Project Presentations (Curricular Requirement #3, #4, #5)

                Each student is given a notebook of previous AP CALCULUS AB Exam
               Free-response problems. Each student is required to choose 3-4
               problems. At the end of each semester, each student is required to solve
               the problems and explain the solutions to the class.


Area and Pre-Riemann Sums (Curricular Requirement #3, #4, #5)

              As a introduction to area under a curve, we graph a simple function and
              use rectangles to estimate the area. We use 3 rectangles and find the
              area using both right- and left-endpoints; then 6 rectangles; then 12
              rectangles. Students come to the conclusion that the exact area is
              between the two and the more rectangles, the better estimate of area.

               We discuss and derive a summation formula needed to solve each of
               these problems. This is checked on the calculator. This leads to finding


                                          Page 16 of 18
               the summation formula for every function as the number of rectangles
               increase indefinitely.

               Students are then given a part of a piece of graph paper that has been
               randomly cut in half. Using skills learned in the above activity, they have
               to find the area under the curve and find the person that has the
               matching half.


Area under a Curve (Curricular Requirement #3, #4, #5)

               TI Interactive! Activity 10
               Texas Instruments, 2001

                Students first investigate the area under a curve by summing midpoint
                rectangles. The same method could be used with left-endpoint and
                right-endpoint. By the end of the activity, the students are able to find the
                numerical integral for any continuous function and the indefinite integral
                of the function.




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