Course Syllabus: AP Calculus I (AB)
Text: Calculus Of A Single Variable, seventh edition; Larson, Hostetler & Edwards;
Houghton Mifflin Company, 2002.
Technology:
A graphing calculator is required for this course and for the AP exam. TI-84 calculators
will be available for students to borrow for the entire school year. I will regularly use a
TI-84 calculator &/or emulator to demonstrate and explore functions and applications of
calculus. Students are expected to follow along and then to do further exploration on their
own. Students may use the calculators on some but not all assessments.
Motion Detectors and other CBL (Calculator-Based Laboratory) instruments will
sometimes be used in conjunction with the graphing calculators, in order to provide
students with hands-on learning activities. These activities will focus both on using
technology and on relating mathematical concepts to real life situations.
Course Plan:
The following is an outline of the topics that will be covered, in their expected order,
during the course of the school year. Time limits are not set, because many of the
activities planned may lead to extra time spent on the discussion and exploration of
topics. Lessons are designed to first introduce students to the material, usually with a
discovery-based activity or proof, and then to lead into exploration of topics graphically,
analytically, numerically and verbally. As time goes on, students should feel confident
about providing their own verbal explanations for problems, both in writing and orally.
Unit/Chapter
Themes/Objectives/Skills
Assessments
Chapter 1
Limits and their Properties, Estimating
Limits from Graphs and Tables,
Asymptotes and
Local Linearity
Problem Sets, “Is There No
Limit to These Labs?”
Activity, Quizzes and a
Chapter Test
Chapter 2
Differentiation Graphical, Analytical
and Verbal Approaches, Including
Basic Rules of Differentiation (Chain
Rule, Product Rule, Quotient Rule),
Continuity & Differentiability, The
Derivative at a Point, Rates of Change
and Other Interpretations of the
Derivative, the Extreme Value
Theorem and an Introduction to
Implicit Differentiation
**Distance vs. Time
Activities, Problem Sets,
“What Goes Down, Must
Come Up . . .” Lab, Problems
Involving Rates and Realworld Applications, Quizzes
and a Chapter Test
(This unit takes about 4
weeks)
Chapter 3
Chapter 4
Chapter 5
Chapter 6.1 –
6.5
Chapter 7.17.3
Applications of Differentiation;
Extrema, Rolle’s Theorem, the Mean
Value Theorem, the First and Second
Derivative Tests, Relative and
Absolute Extrema, Maximizing or
Minimizing Functions (Critical
Values), Concavity, Inflection Points
and Related Rates.
Accumulation Functions, Riemann
Sums, The Trapezoidal Method, Area,
Integration, The Average Value of a
Function, The Fundamental Theorem
of Calculus, u-Substitution and Slope
Fields
Problem Sets,
Maximizing/Minimizing Areas
Project, Curve Sketching
Packet, “Mystery Curve”
Activity, and a Chapter Test
Integration Techniques, Focusing on
Integration By Parts
Problem Sets, and a Quiz
Problem Sets, Group Work for
Riemann Sums and the
Trapezoidal Method, Drawing
Slope Fields Activity, Quizzes
and a Chapter Test
(This unit also takes about 4
weeks.)
Logarithmic, Exponential and Inverse
Problem Sets, Trigonometric
Functions, Including Inverse
Functions Review Worksheet,
Trigonometric Functions and
“A Watched Cup Never
Exponential Growth and Decay Models Cools” Lab, M&M
Growth/Decay Activity,
Quizzes and a Chapter Test
Applications of Integration; Area, Arc
Problem Sets, Activities to
Length and Surfaces of Revolution,
Help Visualize Solids,
Volume (focusing on the Disk and
Mapping Islands activity,
Washer methods as well as Solids with “H2O in the S-K-Y” Activity,
Regular Cross-sections), and Work
Volume of an Object Projects,
(Center of Mass will be covered after
Quizzes and a Unit Test
the AP Exam.) The Shell Method is
studied, but not in great depth.
* Most labs and activities are adapted from the book, A Watched Cup Never Cools, by
Ellen Kamischke, 1999.
Teaching Strategies:
On the first day of school, I hand out TI-84 calculators and assign a library of curves for
memorization. The remainder of the first day as well as the second class is spent
reviewing important algebra and trigonometry concepts. This is the only time that will be
dedicated to reviewing past concepts. This will be a fast-paced course, and students are
urged to utilize the after school tutoring sessions in order to keep up with all materials.
Throughout the course, and especially during labs and activities, student exploration and
discovery is encouraged and fostered. Students work together on a regular basis. Using
the technology available to us, the “rule of four” is easily followed; topics are presented
graphically, numerically, algebraically, and verbally. This provides students with a real
understanding of the material and its many applications. Students often fit data that they
collect to various functions using their graphing calculators. Topics such as local
linearity, maximums, minimums, concavity, area under a curve and slope fields are also
investigated graphically. Computer programs as well as wooden models, clay models and
food items are used to help students visualize three-dimensional objects and to better
understand arc length, surface area and volume. Fold-out party decorations are used to
relate the area found with Riemann Sums to volume with the disk method. This allows
students to actually see the object that is formed from revolution about an axis.
I begin to integrate AP multiple-choice questions into quizzes and review sessions as
soon as possible. By October, students are tackling some free-response questions,
including learning how to provide justification for steps and answers. Students may spend
most of a class period working alone or together in small groups on previous freeresponse questions, and the rest of the period is dedicated to discussion and explanation
as a class. Many of the labs and activities require student-generated reports, in which they
are asked AP-type questions in order to foster a higher level of thinking. In the middle of
April (as long as the class is on track with all material), I begin to concentrate on AP
questions, both multiple choice and free-response. I also try to fit in a couple extra
activities to reinforce limits, local linearity and related rates.
There will be a comprehensive final exam given at the end of the course.
Daily Expectations For Students:
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Have respect for the teacher and for your fellow students.
Be on time and be prepared for class.
Pay attention during class and participate when appropriate.
Complete homework/assignments by their due date.
Ask questions when you do not understand.
Be curious.
Discover something new.
The main objectives of this course are 1) to prepare students for the Calculus AB exam
and 2) to cover all of the material students would encounter in a typical first-semester,
college calculus course and 3) to help students really understand Calculus and how it
relates to everyday life. This course ends at the close of the school year, not after the AP
exam.