# POTENTIAL SYLLABUS: AP CALCULUS AB Miss Hall's School

### PRIMARY TEXT:

AP Calculus AB, Kaplan, 2004 edition.
Understanding Calculus, Carol J.V. Fisher (handouts)

### OPTIONAL SUPPLEMENTAL TEXT:

One Mathematical Cat, Please! by Carol J.V. Fisher, copyright 1998.
This is available both as a spiral-bound softcover at the MHS bookstore, and on the web.
There are 121 class meetings in the 2004–2005 academic year: 62 in the Fall term, and 59 in the Spring term. Calculus meets four days per week, typically Monday, Tuesday, Wednesday, and Friday, with 50 minutes per class, and an extra 30 minutes on Wednesday.

This schedule offers an approximate syllabus that will complete the course objectives by year's end. The objectives in parentheses, e.g. (GOAL1), are more fully explained in the Course Objectives List: Calculus. Emphasis should be on these course objectives. Additional material in the text, that is not specified in the course objectives, may be covered at the discretion of the instructor, as time permits.

1. Review of Calculus Prerequisite test material
2. Review of Calculus Prerequisite test material
3. Review of Calculus Prerequisite test material
4. Prerequisite Test

CHAPTER 1: FUNCTIONS AND MODELS
5. 1.1 Four Ways to Represent a Function (GOAL1)
6. 1.1 Four Ways to Represent a Function (GOAL1)
7. 1.2 New Functions From Old Functions (GOAL1)
8. 1.2 New Functions From Old Functions (GOAL1)
9. 1.5 Exponential Functions (FGRL7)
10. 1.5 Exponential Functions (FGRL7)
11. 1.6 Inverse Functions and Logarithms (FGRL7)
12. 1.6 Inverse Functions and Logarithms (FGRL7)
13. 1.7 Models and Curve Fitting (GOAL7)

CHAPTER 2: LIMITS AND DERIVATIVES
14. 2.1 The Tangent and Velocity Problems
15. 2.2 The Limit of a Function (FGRL2, FGRL4)
16. 2.2 The Limit of a Function (FGRL2, FGRL4)
17. 2.3 Calculating Limits Using the Limit Laws (FGRL3)
18. 2.3 Calculating Limits Using the Limit Laws (FGRL3)
19. 2.4 Continuity (FGRL8)
20. 2.4 Continuity (FGRL9, FGRL10)
21. 2.4 Continuity (FGRL9, FGRL10)
22. 2.5 Limits Involving Infinity (FGRL5, FGRL6)
23. 2.5 Limits Involving Infinity (FGRL5, FGRL6)
24. 2.6 Tangent, Velocities, and Other Rates of Change (DER1, DER2, DER3)
25. 2.6 Tangent, Velocities, and Other Rates of Change (DER1, DER2, DER3)
26. 2.7 Derivatives (DER5, DER7, DER8)
27. 2.7 Derivatives (DER5, DER7, DER8)
28. 2.8 The Derivative as a Function (DER9, DER4)
29. 2.8 The Derivative as a Function (DER9, DER4)
30. 2.9 Linear Approximations (DER6, DER10)
31. 2.9 Linear Approximations (DER6, DER10)
32. 2.10 What does f' say about f? (DER12, DER13, DER14, DER15)
33. 2.10 What does f' say about f? (DER12, DER13, DER14, DER15)
34. 2.10 What does f' say about f? (DER15)

CHAPTER 3: DIFFERENTIATION RULES
35. 3.1 Derivatives of Polynomials and Exponential Functions (DER21, DER22)
36. 3.1 Derivatives of Polynomials and Exponential Functions (DER21, DER22)
37. 3.2 The Product and Quotient Rules (DER22)
38. 3.2 The Product and Quotient Rules (DER22)
39. 3.3 Rates of Change in the Natural and Social Sciences (DER20)
40. 3.3 Rates of Change in the Natural and Social Sciences (DER20)
41. 3.4 Derivatives of Trigonometric Functions (DER21)
42. 3.4 Derivatives of Trigonometric Functions (DER21)
43. 3.5 The Chain Rule (DER23)
44. 3.5 The Chain Rule (DER23)
45. 3.6 Implicit Differentiation (DER23)
46. 3.6 Implicit Differentiation (DER19; problem #47, p. 246)
47. 3.7 Derivatives of Logarithmic Functions (DER21)
48. 3.7 Derivatives of Logarithmic Functions (DER21)

CHAPTER 4: APPLICATIONS OF DIFFERENTIATION
49. 4.1 Related Rates (DER18)
50. 4.1 Related Rates (DER18)
51. 4.2 Maximum and Minimum Values (DER17)
52. 4.2 Maximum and Minimum Values (DER17)
53. 4.3 Derivatives and the Shapes of Curves (DER11, DER17)
54. 4.3 Derivatives and the Shapes of Curves (DER11, DER17)
55. 4.4 Graphing with Calculus and Calculators
56. 4.6 Optimization problems (DER17)
57. 4.6 Optimization problems (DER17)
58. 4.7 Applications to Economics
59. 4.9 Antiderivatives (INT13, INT15)
60. 4.9 Antiderivatives (INT13, INT15)
61. extra day
62. EXAM #1
63. EXAM #2
64. EXAM #3
65. EXAM #4

END OF FALL TERM

CHAPTER 5: INTEGRALS
66. 5.1 Areas and Distances (INT1)
67. 5.1 Areas and Distances (INT1)
68. 5.2 The Definite Integral (INT2)
69. 5.2 The Definite Integral (INT4)
70. 5.3 Evaluating Definite Integrals (INT7, INT11)
71. 5.3 Evaluating Definite Integrals (INT10, INT3)
72. 5.3 Evaluating Definite Integrals (INT10, INT3)
73. 5.4 The Fundamental Theorem of Calculus (INT11)
74. 5.4 The Fundamental Theorem of Calculus (INT12)
75. 5.4 The Fundamental Theorem of Calculus (INT12)
76. 5.5 The Substitution Rule (INT14)
77. 5.5 The Substitution Rule (INT14)
78. 5.8 Approximate Integration (INT1)
79. 5.8 Approximate Integration (INT1)

CHAPTER 6: APPLICATIONS OF INTEGRATION
80. 6.1 More about Areas (INT7)
81. 6.1 More about Areas (INT7)
82. 6.2 Volumes (INT8, INT6)
83. 6.2 Volumes (INT8, INT6)
84. 6.4 Average Value of a Function (INT9)
85. 6.4 Average Value of a Function (INT9)
86. 6.5 Applications to Physics and Engineering (INT5, INT6, INT17)
87. 6.5 Applications to Economics and Biology (INT5, INT6, INT17)

CHAPTER 7: DIFFERENTIAL EQUATIONS
88. 7.1 Modeling with Differential Equations (INT16)
89. 7.1 Modeling with Differential Equations (INT16)
90. 7.2 Direction Fields (INT18)
91. 7.2 Direction Fields (INT18)
92. 7.4 Separable Equations (INT16)
93. 7.4 Separable Equations (INT16)
94. practice AP problems
95. practice AP problems
96. practice AP problems
97. practice AP problems
98. practice AP problems (timed, part of grade, no calculator)
99. practice AP problems (timed, part of grade, no calculator)
100. practice AP problems (timed, part of grade, no calculator)
101. practice AP problems (timed, part of grade, no calculator)
102. practice AP problems (timed, part of grade, no calculator)
103. practice AP problems (timed, part of grade, with calculator)
104. practice AP problems (timed, part of grade, with calculator)
105. practice AP problems (timed, part of grade, with calculator)
106. practice AP problems (timed, part of grade, with calculator)
107. practice AP problems (timed, part of grade, with calculator)
108. EXAM #1
109. EXAM #2
110. EXAM #3
111. Talk about the AP Exam!!!

Wednesday, May 5, 2004, AP CALCULUS AB EXAM

112. 5.6 Integration by Parts
113. 5.6 Integration by Parts
114. 5.7 Integration Using Tables and Computer Algebra Systems
115. 5.7 Integration Using Tables and Computer Algebra Systems
116. 5.9 Improper Integrals
117. 5.9 Improper Integrals
118. 5.9 Improper Integrals
119. 6.3 Arc Length
120. 6.3 Arc Length
121. 8.1 Sequences
122. 8.1 Sequences
123. 8.2 Series
124. 8.2 Series
125. EXAM #4

END OF SPRING TERM