AP Calculus AB
Mr. Macaluso
IPFW MA 16500
Analytic Geometry & Calculus I
Course Overview
One objective of this course is to provide students with a foundation of
calculus that will allow them to be successful in mathematics courses in
college. Hopefully, we can build enough skills for them to score well on the AP exam
to receive college credit and begin with the second course of calculus in college. If
this doesn’t happen, at least they will have some of the necessary tools to be more
successful in the beginning level of calculus in college. We will work together to
develop an appreciation for calculus and its application.
Textbook
Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable. Ninth
Edition. Cengage Learning, 2010.
Course Planner
Chapter P: Preparation for Calculus—approximately 2 weeks
P.1:
Graphs and Models—pages 2-7
Pages 8-9 #1,2,3,4,21,27,28,31,37,45,53,54,59,63,67,71,73,
83,84,85,86,88,
P.2:
Linear Models and Rates of Change—pages 10-15
Pages 16-18 #9,14,17,25,27,30,33,37,43,57,63,71,72,99,100
P.3:
Functions and Their Graphs—pages 19-26
Pages 27-30 #1,4,7,9,13,16,27,30,35,57,61,64,69,71,99-102
P.4:
Fitting Models to Data—pages 31-33
Worksheet
Review—Worksheet
Test
Chapter 1: Limits and Their Properties—approximately 2½ weeks
1.1:
A Preview of Calculus—pages 42-46
Page 47 #8,9,11
1.2:
Finding Limits Graphically and Numerically—pages 48-54
State standards: C.1.1, C.1.2
Pages 54-58 #2,5,17,18,19,21,24,26,28,30,32,
1.2a: Using a Graphing Calculator to Find Limits
Worksheet
1.3:
Evaluating Limits Analytically—pages 59-66
State standards: C.1.3, C.1.4, C.1.5, C.1.8
Pages 67-69 #6-64 even, 65,73,117-122
1.4:
Continuity and One-Sided Limits—pages 70-78
State standards: C.1.9, C.1.10, C.1.11, C.1.12, C.2.10
Pages 78-82 #1-6 all, 10,14,17,19,27,29,35,37,41,43,46,49,59,
65,92,93,99-102
1.5:
Infinite Limits—pages 83-87
State standards: C.1.7
Pages 88-90 #1-9 all,19,23,27,29,35,40,43,45,50,55,68,
73-76 all
Review—Two Worksheets
Test
Chapter 2: Differentiation—approximately 3½ weeks
2.1:
The Derivative and the Tangent Line Problem—pages 96-103
State standards: C.2.1, C.2.2, C.2.10, C.3.1, C.3.2
Pages 103-106 #5,9,11,13,17,21,23,26,27,36,39,40,41,42,64,75,
79,83,84,87,93,95,97
2.2:
Basic Differentiation Rules and Rates of Change—pages 107-114
State standards: C.1.8, C.2.3, C.2.4, C.3.10, C.3.11
Pages 115-118 #1,3,7,10,17,19,23,25,27,29,32,35,41,45,47,49,
53,55,59,63,77,87-92 all
2.3:
The Product and Quotient Rules and Higher Order Derivatives—pages 119-125
State standards: C.2.3, C.2.4 , C.2.8
Pages 126-129 #2,3,6,8,11,18,19,21,23,26,30,31,34,38,40,42,44,
48,52,54,66,67,74,7594-102 even, 103,131-136 all, 139
2.4:
The Chain Rule—pages 130-136
State standards: C.2.5
Pages 137-140 #1-6 all, 8-36 even, 48,51,56,59,64,65,69,71,76,
78,80,82,91,93,95125,126,130,131,132
2.4a:
Evaluate Limits Using a Graphing Calculator
Worksheet
Review—Worksheet
2.5:
Implicit Differentiation—pages 141-145
State standards: C.2.6
Pages 146-148 #2-16 even,22-28 even,46,47,50,55,59,65
Review—Worksheet
2.6:
Related Rates—pages 149-153
State standards: C.3.8, C.3.12
Pages 154-157 #3,4,11,13,18,20,21,25
2.6a:
Translating Related Rates (Explaining what results mean in sentences)
Pages 154-157 #2,5,7,7,10
Review—Two Worksheets
Test
Chapter 3: Applications of Differentiation—approximately 4 weeks
3.1:
Extrema on an Interval—pages 164-168
State standards: C.1.13
Pages 169-171 #2,3,4,14,20,22,25,28,33,38,40,57-60 all,65-68 all
3.2:
Rolle’s Theorem and the Mean Value Theorem—pages 172-175
State standards: C.2.11
Pages 176-178 #2,3,12,15,17,20,23,26,40,43,77-80 all
3.3:
Increasing/Decreasing Functions and the First Derivative Test—pages 179-185
State standards: C.3.3, C.3.43
Pages 186-189 #6,7,18,22,24,27,32,34,36,38,44,47,60,64,72,74
3.4:
Concavity and the Second Derivative Test—pages 190-194
State standards: C.3.5, C.3.6, C.3.7
Pages 195-197 #19,21,24,27,34,37,41,48,54,66,74,91-94 all
3.5:
Limits at Infinity—pages 198-204
State standards: C.1.6
Pages 205-208 #1-6 all,16,22,28,38,46,60,62,68,70,76,107,108
3.6:
A Summary of Curve Sketching—pages 209-214
Pages 215-217 #1-4 all, 8,16,19,27,67,69,71,75,
3.6a:
Using Graphing Calculator to EXPERIMENT
*Plot functions to determine extrema on an interval
*Find Concavity
*Find Increasing/Decreasing
-WORKSHEET
Review—Worksheet
Test
3.7:
Optimization Problems—pages 218-222
State standards: C.3.9
Pages 223-228 #4,5,7,8,13,22,23,
3.9:
Differentials—pages 235-239
Pages 240-244 #3,4,8,9,15,43,44,45,46
Review—Worksheet
Test
Chapter 4: Integration—approximately 4½ weeks
4.1:
Antiderivatives and Indefinite Integration (include slopefields)—pages 248-255
State standards: C.4.2, C.5.1
Pages 255-258 #2,3,10-44 even,50,51-54 all,59,62,64,81,90-94 all
4.2:
Area—pages 259-267
State standards: C.4.1, C.4.2
Pages 267-270 #11,18,21,37,51,59
4.3:
Riemann Sums and Definite Integrals—pages 271—278
State standards: C.4.3
Pages 278-281 #23,25,27,34,36,38,40,41,43,57,60
4.4:
The Fundamental Theorem of Calculus—pages 282-292
State standards: C.4.4, C.4.5, C.5.5
Pages 293-296 #1,2,6-26 even, 29,32,34,35-38 all, 39,41,46,50,
52,76,78,80,84,113,114
4.5:
Integration by Substitution—pages 297-305
State standards: C.4.7
Pages 306-310 #1,3,5,12-38 even, 48-60 even, 68-84 even,129-134 all
4.6:
Numerical Integration (Trapezoidal & Simpson’s Rule)—pages 311-315
State standards: C.4.8
Pages 316-317 #5,10,13,14
4.6a:
Find Integrals by Use of Graphing Calculator
Worksheet
Review—Worksheet
Test
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions—approximately 5½ weeks
5.1:
The Natural Logarithmic Function: Differentiation—pages 324-330
State standards: C.2.9
Pages 331-333 #25,26,30,32,35,36,40,42,44,48-78 even,101,104
The Natural Logarithmic Function: Integration—pages 334-339
Pages 340-332 #2-44 even,54-60 even,77,78,93,95,98,99,105-108 all
Review—Worksheet
Test
5.3:
Inverse Functions—pages 343-348
Pages 349-351 #2-8 even, 9-12 all, 16,18,24-30 even,33,36,42,
45,59,61,64,65,73,76,80,82,101-104 all,110
5.4:
Exponential Functions: Differentiation and Integration—pages 352-357
Pages 358-361 #2,4,6,12,14,22,31,32,40-58 even,69,70,75,76,
80,84,100-116 even,122,124,126,134
5.5:
Bases Other Than e and Applications—pages 362-367
Pages 368-372 #1-4 all,6,8,10,12,22,23,26,27,42,52,59,63,66,68,
69,76,82,83,84,121-126 all
Review—Worksheet
Test
5.6:
Inverse Trigonometric Functions: Differentiation—pages 373-378
Pages 379-381 #6,8,9,14,16,18,21-30 all,44-50 even,54,58,91-96
all
5.7:
Inverse Trigonometric Functions: Integration—pages 382-386
Pages 387-389 #2-52 even83-86 all
5.2:
Review—Two Worksheets
Test
Chapter 6: Differential Equations—approximately 2 weeks
6.1:
Slope Fields and Euler’s Method—pages 406-410
Pages 411-414 #2,4,6,9,11,22,26,28,36,38,42-50 even,53,54,
68,70
6.2:
Differential Equations: Growth and Decay (include slopefields)—pages 415-419
State standards: C.5.3
Pages 420-422 #6,7,15,16,39,45,75-78 all
6.3:
Separation of Variables and the Logistic Equation—pages 423-430
State standards: C.5.2
Pages 431-433 #6,7,13,15,17,22
6.4
First Order Linear Differential Equations—pages 434-440
Pages 440-442
Review
Test
Chapter 7: Applications of Integration—approximately 4½ weeks
7.1:
Area of a Region Between Two Curves—pages 448-453
State standards: C.5.4
Pages 454-457 #2,3,6,8,11,20,23,25,30,33,49,52,99-102 all
7.2:
Volume: The Disk Method—pages 458-463
Pages 465-467 #2,5,8,12,13,21,25,27,58,59
7.3:
Volume: The Shell Method—pages 469-473
Pages 474-477 #4,7,9,11,16,21,25,30
Revisit 7.2: Volume of Solids with Known Cross Sectional Areas—
State standards: C.5.6
Pages 467-468 #71,72,74
Review—Worksheet
Test
pages 463-464
7.4:
Arc Length and Surfaces of Revolution—pages 478-484
State standards: C.5.7
Pages 485-488 #6,9,17,18,19,23,24
7.5:
Work—pages 489-494
State standards: C.5.7
Pages 495-497 #3,7,17,19
7.7:
Fluid Pressure and Fluid Force—pages 509-512
State standards: C.5.7
Pages 513-516 #9,10,21
Review—Worksheet
Test
Chapter 8: Integration Techniques, L´Hôpital’s Rule, and Improper Integrals—approximately 5½ weeks
8.1:
Basic Integration Rules—pages 520-523
Pages 524-526 #6-52 even,62,71
8.2:
Integration by Parts—pages 527-532
Pages 533-535 #2,4,6,7,9,12-38 even,51,53,55,57,91
Review—Page 591
Test
8.3:
Trigonometric Integrals—pages 536-541
Pages 542-544 #5,9,13,17,37,39,53,55,61,72
8.4:
Trigonometric Substitution—pages 545-550
Pages 551-553 #10,15,17,29,30,32.44.47
8.5:
Partial Fractions—pages 554-560
Pages 561-562 #8,13,18,22,27,28,47
8.6:
Integration by Tables and Other Integration Techniques—pages 563-566
Pages 567-568 #2,9,11,16,21,23,33,39
Review—Two Worksheets
Test
8.7:
Indeterminant Forms and L´Hôpital’s Rule—pages 569-575
Pages 576-579 #8,13,18,35
8.8:
Improper Integrals—pages 580-586
Pages 587-590 #9-14 all,19,23,24,25,27,31,32,34,39,47,
Test
Additional topics as time permits.
This schedule leaves some time for flexibility for student learning. It also leaves time for some
practice of test items from the AP exam.
Throughout the course, we do work with functions in all forms: graphically,
numerically, analytically, and verbally. Many of the sections we cover contain word problems
as well as true/false questions requiring justification for false answers.
Teaching Strategies
I spend time modeling concepts and skills to be taught. When discovering new
concepts, we all work together. At times, the students lead the discussion. I encourage them to
work together. Many times they can discuss concepts amongst themselves and help others in
the class by doing so. I stress communication as one of the goals of this class. I expect students
to explain how they arrived at the solutions both verbally and on their paper as well as finding
what the solution is.
Technology
We use TI-83or TI-84 Graphing Calculators on a routine basis in class to discover and
explore Calculus concepts. Students use graphing calculators on most (but not all) of their
assignments. We routinely use graphing calculators to visually see the functions on graphs on
their homework. Use of these calculators also shows support for the results we have obtained
when solving problems.
We have a classroom set of the TI-92 Graphing Calculators that I taught my students to
use to easily find derivatives and integrals as well as to find extrema during curve sketching
but only after they have already learned the process.
Student Evaluation
Nine-weeks grades are computed using homework and tests. All homework
assignments collected will count as twenty percent of your grade and each test/quiz as eighty
percent of your grade. There are three to four of these tested units each nine weeks. Semester
grades are based on 40% from each nine weeks and 20% from the semester exam.
Grading Scale
100-97…….. A+
96-93……….A
92-90……….A-
89-87……….B+
79-77……….C+
86-83……….B
76-73……….C
82-80……….B72-70……….C59 and below………F
69-67……….D+
66-63……….D
62-60……….D-
Classroom Expectations
All students are expected to obey the following expectations regarding classroom
behavior.
 All school policies as stated in the Wabash High School student handbook will be
exercised and enforced in the classroom.
 Students are to be in their seat, quiet, and ready to start class before the bell rings.
Students will be counted tardy for not meeting this expectation.
 No candy, food, or drink is allowed in class.
 Bookbags are not allowed at any time in the classroom.
 Students must have their agenda with them at all times to be issued a pass from class
for any reason. Students who abuse pass priviledges will lose pass priviledges.
 Make appropriate use of any study time given in class. Remember that the bell is not
your dismissal from class but I am.
 Disturbance of others during the class will not be tollerated.
Students and Parents,
I am attaching a syllabus to this letter. Please take the time to look over the syllabus and let me know if you have
any questions or concerns. We will be using a graphing calculator for this course. You will be expected to learn
how to use one. You will not be expected to purchase a graphing calculator; however, you may if you wish.
This course is approved for dual credit through IPFW. If you are interested in this option, you need to speak with
Mr. Kaufman by Friday, August. This year the cost for this dual credit through IPFW is $25.00 per credit hour
and calculus is a 3 credit hour course. Since this course is an AP credit course, you will be expected to take the AP
exam in May 2015 to receive credit for this course through Wabash High School. The cost of this exam is
currently $87.00 but this fee is paid for you so you will not be charged this amount. You will, however, be
expected to take this exam and do your best on it. I will do my best to prepare you for this exam so that you can
be successful. If you score a 3 or higher on this exam, you can earn college credit.
The expectation is that you have prepared yourself through the Mathematics courses you have already taken at
WHS. With this said, I need for you to seriously consider your participation in Calculus. The course will be run
much like a college course. Homework assignments will be given to help you practice the material you will learn
in class. These assignments will not always be collected or graded. You will be expected to do them on a regular
basis and be prepared to move on to new material that will build on this material. Tests will be given but not as
often as in your previous Mathematics courses. About 80% of your grade will be based on tests and quizzes.
You chose to accept this challenge in May and I am assuming that you are still willing to accept this challenge.
Please sign and date this form below and have your parents sign, date, and provide the information requested.
Thank you.
Student Name (Printed)__________________________________________
Student Signature _________________________________________Date________________
Parent/Guardian Name (Printed)__________________________________________
Parent/Guardian Signature _____________________________________Date____________
Parent/Guardian Contact Information:
Phone Number(s))_________________________________________________________
Email Address(es)_________________________________________________________