Course Syllabus and Outline – AP Calculus AB
COURSE DESCRIPTION AND BACKGROUND INFORMATION
AP Calculus AB is a college level course covering material traditionally taught in the first semester of college calculus. The course is taught in one semester consisting of 90minute daily classes. Students need a strong foundation to be ready for the rigorous work required throughout the term. Completing the summer review packet before the beginning of the course will ensure a proper background.
This packet consists of review material studied during Algebra II and Analysis. Students should expect to work approximately 10 hours on the assignment. The packet will be collected on the first day of the semester and will be given a grade that will be based on completeness of solutions and accuracy. In preparation for the AP test, students need to show all work with logical steps. You must show your work for problems in the review packet. Do not list only an answer.
Students enrolled in AP Calculus AB will be using a graphing calculator throughout the course since a graphing calculator is required on the AP test. Students will be issued a TI 89 calculator to be used in class during the semester and, with parental permission, students may take the calculator home to use as well.
The success of each student in the AP Calculus program depends upon diligent effort and practice of newly learned skills. Although a suggested assignment is given for each lesson, completion of the assignment is optional and homework is not graded or checked for completion. The previous night’s assignment will be reviewed in class each day and there will be ample opportunity to ask questions.
Calculus is a challenging, stimulating, and dynamic field of mathematics and I look forward to sharing my enthusiasm for the material with you. .
TEXTBOOK
Stewart, James. Calculus: Concepts and Contexts (2nd edition). Pacific Grove, CA: Brooks/Cole 2001.
REQUIRED SUPPLIES
Notebook (spiral or looseleaf), paper, pencils
TI89 Graphing Calculator (calculators are available to students who do not own a TI89) Composition or Spiral Notebook
AP Calculus AB Course Outline
1. Limits and Continuity (Sections 2.22.5)• Evaluate the limit of a function graphically, numerically, and algebraically and investigate limits
both with and without the use of a calculator.• Calculate limits using Limit Laws• Determine limit existence and explore limits involving infinity• Investigate and determine continuity/discontinuity of a function and relate to limits• Identify the three conditions that must be satisfied in order for a function to be considered
continuous at a point• Classify discontinuities as “removable”, “jump”, or “infinite”• Understand and use the Intermediate Value, Extreme Value, and “Sandwich” Theorems• Find equations of vertical and horizontal asymptotes using limits• Compare and contrast relative rates of change
2. Introduction to Differential Calculus (Sections 2.1, 2.62.10)• Find slopes and equations of tangent lines and normal lines to a curve at a point• Investigate the relationship between the slope of the curve at a point and the slope of the
tangent line at that point using a graphing calculator• Explain the relationship between continuity and differentiability and identify situations for which
a function might be continuous, but not differentiable• Evaluate and apply tangents, velocities, and other rates of change• Explain the relationship between average velocity and instantaneous velocity and calculate
each appropriately• Define and find the derivative of a function using the difference quotient• Use Linear Approximation methods to estimate function values and rates of change• Compare functions and their derivatives
• Explore the derivative as a function both with and without using the calculator.
3. Differentiation Rules for Functions (constant, linear, polynomial, exponential, trigonometric, and logarithmic) (Chapter 3)
• Use Power Rule, Constant Multiple Rule, Sum Rule, Difference Rule, Product Rule, Quotient Rule, and Chain Rule
• Use Implicit and Logarithmic Differentiation
4. Applications of Differentiation (Chapter 4)• Solve related rate problems• Analyze graphs of functions comparing with first and second derivative graphs and apply the
First and Second Derivative Tests• Find relative and absolute extreme values, points of inflection, concavity, intervals where a
function increases or decreases using the graphs of f, f ‘, and f ” as well as numerical methods• Use L’Hopital’s Rule, Newton’s Method, Rolle’s Theorem, and Mean Value Theorem• Solve optimization and minimal path problems and investigate the use of calculus in economic
applications• Solve particle motion problems involving position, velocity, and acceleration and explore the
relationships between these measurements and derivatives
5. Introduction to Integral Calculus (Sections 5.15.9)• Find antiderivatives graphically, numerically, and algebraically both with and without the use of
a calculator• Explore the relationships between area under a curve, distance and other accumulation
functions, and the definite integral• Explore the definition of an antiderivative using the limit of a sum• Use Riemann Sums with left, right, and midpoint evaluation points• Evaluate and use properties of definite integrals• State, interpret, and use the Fundamental Theorem of Calculus• Integrate functions using substitution• Estimate definite integrals using approximation methods that involve graphs, charts of values,
and algebraic representations• Use the Trapezoidal Rule to approximate the area under the curve• Solve particle motion problems involving position, velocity, and acceleration and explore the
relationships between these measurements and derivatives
6. Applications of Integration (Sections 6.16.4)• Find the area under a curve or between two curves. Use the calculator to determine points of
intersection and for graphing • Find the volume of a solid of revolution using the “disk” and “washer” methods and finding
volumes of solids with known cross sections• Find the average value of a function• Find the distance traveled by a particle along a line
7. Differential Equations (Sections 7.17.4)• Solve firstorder separable differential equations, finding both general solutions and solutions
to initial value problems• Use differential equations to model growth and decay • Explore solutions to differential equations through slope fields and discuss the relationship
between the slope field solution and the algebraic solution to differential equations. Construct slope fields manually as well as with the calculator
2006 2007 Daily Schedule
Bold and italicized assignments are due for a grade
Day Date Topic Assignment
1 8/14 Introduction to Calculus; issue textbooks and calculators Mon
2 8/15 Lesson 2.2 The Limit of a FunctionTues
3 8/16 Lesson 2.2 (cont’d) p. 108 #2, 4, 6, 8, 9, 10, 17, 22aWed Lesson 2.3 – Calculating Limits Using Limit Laws p. 117 #2, 1018 (even)
4 8/17 Lesson 2.3 (cont’d) – Squeeze Theorem p. 118 #22, 23, 25Thurs Lesson 2.4 – Continuity p. 128 #4, 6, 10, 14, 18, 26
5 8/18 Lesson 2.4 (cont’d) p. 129 #33, 36, 38, 40, 45, 47Fri Worksheet 2.22.3
6 8/21 Lesson 2.5 – Limits Involving Infinity p. 135 #4, 6, 12, 18, 31, 3536Mon Group Work: Worksheet
7 8/22 Review p. 182 #117, 21, 2324Tues
8 8/23 Quiz 2.22.5Wed
9 8/24 Lesson 2.6 (cont’d) – Tangents, Velocities, and p. 148 #5, 7, 10, 13, 16,18 Thurs Other Rates of Change
Lesson 2.7 – Derivatives p. 156 #3, 5, 9, 13, 17, 20, 23, 25,
26
10 8/25 Lesson 2.8 – The Derivative as a Function p.167 #1, 3, 10, 13, 2124, 31, 32, Fri 36, 37, 39
11 8/28 Lesson 2.10 – Comparing f ‘ with f p. 179 #23, 6, 8, 1218 (even), 24, Mon 28
12 8/29 Lesson 3.1 – Derivatives of Polynomials and p. 196 #224 (even), 31, 34, 38 Tues Exponential Functions 4142, 4652 (even)
Lesson 3.2 – Product and Quotient Rules Worksheet 3.2
13 8/30 Lesson 3.3 – Rates of Change p. 215 #3, 4, 7, 10, 13, 20, 23Wed Rates of Change Worksheet
14 8/31 Lesson 3.3 (cont’d)Thurs
15 9/1 Lesson 3.4 – Derivatives of Trig Functions p. 223 #115 (odd), 18, 19a, 23, 26Fri Trig Derivative Proofs
16 9/5 Lesson 3.5 – Chain Rule p. 233 #7, 9, 1417, 19, 22, 27, 29Tues
17 9/6 Review 2.62.8, 2.10, 3.13.5 Wed
18 9/7 Test 2.62.8, 2.10, 3.13.5 – includes both a noncalculator and calculator portion – be prepared Thurs to work derivatives without the aid of a calculator!
19 9/8 Lesson 3.6 – Implicit Differentiation p. 243 # 616 (even)Fri
20 9/11 Lesson 3.6 (cont’d) p. 244 #2733Mon Inverse Trig Proofs
21 9/12 Lesson 3.7– Derivatives of Logarithmic Functions p. 250 #519 (odd), 27, 30, 33, 38 Tues
22 9/13 Lessons 2.9 and 3.8 – Linear Approximations Group Work 2.9 and 3.8 Wed and Differentials
23 9/14 Lessons 2.9 and 3.8 (cont’d)Thurs
24 9/15 Lesson 4.1 – Related Rates Group Work: Problem Set #1Fri
25 9/18 Lesson 4.1 (cont’d)Mon
26 9/19 Lesson 4.1 (cont’d) Group Work: Problem Set #2Tues
27 9/20 Lesson 4.1 (cont’d)Wed
28 9/21 Review 2.9, 3.8, 4.1Thurs
29 9/22 Quiz: Lessons 2.9, 3.8, 4.1Fri
30 9/25 Related Rates Project PresentationsMon
31 9/26 Related Rates Project PresentationsTues
32 9/27 Lesson 4.2 – Minimum and Maximum Values p. 277 #311 (odd), 2335, (odd), 39, Wed 41, 43, 47, 53
33 9/28 Lesson 4.3 – Derivatives and Shapes of Curves p. 289 # 12, 20, 21, 27, 29, 32Thurs
34 9/29 Lesson 4.3 (cont’d) WS 4.3Fri Curve Sketching
35 10/2 Lesson 4.3 (cont’d) Laptop ActivityMon
36 10/3 Lesson 4.3 (cont’d) Group Work 4.3Tues Graphing f, f’, f’”
37 10/4 Lesson 4.3 (cont’d) AP Problems 1987 #4, 1989 #5,Wed 1991 #5, 1996 #1
38 10/5 Lesson 4.3 (cont’d)Thurs
39 10/6 Lesson 4.5 – L’Hopital’s Rule p. 305 # 512, 2125 Fri Quiz Review – Lessons 4.2 and 4.3 Review WS
40 10/9 Quiz – Lessons 4.2 and 4.3
Mon
39 10/6 Lesson 4.5 – L’Hopital’s Rule p. 305 # 512, 2125 Fri
40 10/9 Quiz – Lessons 4.2 and 4.3Mon
41 10/10 Lesson 4.6 – Optimization Problems p. 312313 # 7, 8, 10, 12, 13, 15, Tues 21, 22, 26, 36
42 10/11 Lesson 4.6 – Minimal Path Problems Exploration 68Wed
43 10/12 Lesson 4.7 – Applications to Economics p. 323 # 5 – 17 (odd)Thursday
10/13 No School – Teacher Workday
44 10/16 Lesson 4.8 – Newton’s Method p. 327 # 5, 7, 9, 13 Mon
45 10/17 Lesson 4.9 – Antiderivatives p. 334 # 521 (odd)), 37, 41Tues Explorations #19 & 26
46 10/18 Midterm ReviewWed
47 10/19 MidtermThurs
48 10/20 MidtermFri
49 10/23 Lessons 5.1 and 5.2 p. 355 # 5. 11. 13. 14 Mon Areas, Distances, and the Definite Integral p. 367 # 6, 29, 39, 42
50 10/24 Lesson 5.3 p. 377# 4, 6, 9, 13, 17, 21, 25, 52, 54, Tues Evaluating Definite Integrals 56, 57
51 10/25 Lesson 5.3 (cont’d) Group Work Sections 5.2 and 5.3Wed
52 10/26 Lesson 5.4 The Fundamental Theorem of CalculusThurs
53 10/27 Lesson 5.4 (cont’d) Group Work Section 5.4Fri p.. 386 # 3 – 7, 9, 17, 19
54 10/30 Lesson 5.5 – The Substitution Rule p. 395 # 9 29 (odd), 3747 (odd)Mon
55 10/31 Lesson 5.5 (cont’d) AP ProblemsTues
56 11/1 Lesson 5.6 – Integration by Parts p. 401 # 3, 5, 7, 11, 15, 17, 21, 23, 25, Wed 27
57 11/2 Review WorksheetThurs
59 11/3 Integration Quiz: Lessons 5.3, 5.55.6Fri
60 11/6 Lesson 5.9 – Trapezoidal Rule p. 426 # 7, 13, 23 a, b, 25 Mon Worksheet
61 11/7 STUDENT HOLIDAYTues
62 11/8 Review AP ProblemsWed
63 11/10 Chapter 5 TestFri
64 11/10 Lesson 6.1 – Area Between two Curves page 452 #5, 7, 11, 13, 18, 20, 22, 25, 37 Fri 65 11/13 Lesson 6.2 – Volume of Solids of Revolution page 463 #1, 3, 5, 7
Mon Disk and Washer Methods about x and y axis
66 11/14 Lesson 6.2 – Volume of Solids of Revolutions Worksheet 6.2 ATues Disk and Washer Methods about y = k or x = k
Solids with Known Cross Sections
67 11/15 Lesson 6.2 – Volume of Solids of Revolution Worksheet 6.2 B Wed Cylindrical Shells Method Worksheet 6.4
Lesson 6.4 – Average Value of a Function page 475 #3, 7a, b, 11 12, 16
68 11/16 AP Problems AP Problems – due at end of class Thurs Fri 11/17
69 11/17 AP Problems (cont’d)
70 11/20 Review Review Worksheet Mon
71 11/22 Quiz: Lessons 6.1, 6.2, 6.4 Tues
72 11/27 Practice: 1998 AB Multiple Choice Questions 1998 Multiple Choice Questions Mon
73 11/28 Lesson 7.1 – Modeling with Differential Equations p. 511512 #2, 5, 9–12Tues Lesson 7.3 – Separable Equations p. 527 # 2–18 (even), 34, 36
74 11/29 Lesson 7.4 – Exponential Growth and Decay p. 538 # 2 – 12 (even), 16, 18Wed Exploration #42
75 11/30 Differential Equations/Mathematical Modeling WorksheetThurs
76 12/1 Differential Equations/Mathematical Modeling WorksheetFri
77 12/4 Differential Equations/Mathematical Modeling AP ProblemsMon
78 12/5 Newton’s Law of Cooling Chill Out Lab with CBLTues Group Work 2&3, Section 7.3
p. 539 # 13 – 14
79 12/6 Lesson 7.2 – Slope Fields p. 519 # 1, 3 6 11, 13 Wed
80 12/7 Lesson 7.2 (cont’d) Slope Fields PacketThurs
81 12/8 Lesson 7.2 (cont’d)Fri
82 12/11 Differential Equations and Slope Fields ReviewMon
83 12/12 Quiz – Slope Fields and Differential EquationsTues
84 12/13 AP Problems – 2003 Multiple Choice Part 1Wed
85 12/14 AP Problems – 2003 Multiple Choice Part 2Thurs
86 12/15 AP Problems – 2003 Free Response Part 1Fri
87 12/18 AP Problems – 2003 Free Response Part 2Mon
88 12/19 FINAL EXAM – Free ResponseTues
89 12/20 or 12/21 FINAL EXAM Multiple Choice