AP Calculus AB Syllabus
Instructor:
Harley Revel
Room:
315
E-Mail:
hrevel@asd5.org
Phone:
537-4294
Introduction
In previous math classes everything has been static. The study of calculus is dynamic it
is the study of motion and change. Our main focus of study will be Differential and Integral
calculus. Differential calculus allows us to calculate rates of change, to find slope, velocities,
acceleration, and to graph a function easily. Integral calculus we will use to find area under a
curve, measure lengths of curves, and to calculate volumes of a solid.
In calculus students will need to be able to solve, analytically, numerically, graphically,
and verbally. Students will also need to be able to use graphing calculators to find a derivative,
at a point, find the value of a definite integral, to graph a function, and to solve an equation.
This class will cover the topics typically seen in the first semester of a college level
calculus class. When we finish, we will spend approximately four weeks studying for the AP
exam in May. After the exam we will cover a few topics not on the AP exam and review for
your High School final.
Teaching Strategies
Most topics will begin with one day of lecture using a power point. During the lecture
you will notice that we will approach functions using variety strategies know as the “Rule of
Four. I will consistently model the “Rule of Four” and students will also be asked to model the
“Rule of Four” which is stated below:
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Numerical Analysis (where data points are known, but not an equation)
Graphical Analysis (where a graph is known, but again, not an equation)
Analytic/algebraic analysis (traditional equation and variable manipulation)
Verbal/written methods of representing problems (classic story problems as well as
written justification of one’s thinking)
During non-lecture days, students are encouraged to work collaboratively in groups to
complete their assignments. Students will also be asked to present their results to the class.
Students will come to the whiteboards and solve problems in multiple ways. They will have to
explain their thinking. They will also be asked if there is another way they could solve the
problem. If they solved the analytically could they do it graphically.
One reason students come to the whiteboards is to stress communication which is a major
goal of this course. I expect students to explain problems and solutions using proper
vocabulary. Students are also expected to explain or justify their thinking with well-written
sentences.
Technology
In this class we will use technology often and in a variety of ways. You will have the
opportunity to use a smart board, geometer sketchpad, document camera, virtual TI, CBR to
explain, show work, or manipulate objects. The most important piece of technology we use in
this class is a graphing calculator. I will use a Texas Instrument 84 regularly. You do not need to
go and buy one. I got a grant to buy a classroom set of Texas Instrument 84’s that you will be
allowed to check out for the year.
We will use the graphing calculator to:
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Conduct explorations (ie Squeeze TH.)
Find roots
Justify and explain results
Estimate limits
Analyze and Interpret results
Approximate the derivative at a point
Approximate the Integral
Homework (20% of grade)
There will be an assignment each day and each assignment is worth 5 points. In order
to receive the entire 5 points the assignment must be complete, turned in on time, and have
work shown. As we grade our papers in class, a paper with only answers, and no work shown,
will not be accepted. Notes are part of the homework grade. Notes will be taken daily by
students and handed in at the time of the test. There will be a warm-up at the beginning of each
class. Warm-ups need to be done on a piece of note book paper and will be collected at the
end of every week.
Exams (70% of grade)
An exam will be given at the end of each chapter, as well as a final comprehensive exam
at the end of each semester.
Quizzes (10% of grade)
There will be a quiz every Friday except during test weeks.
Late work/Make-up work
All late work from a unit must be turned in, within a week after the unit test. Late work
will earn reduced credit. Missed work or tests from excused absences will be made up upon
your return to school. The normal time allowance for make-up work is one day per day of
excused absence.
Grading:
A:
100-93
A-:
92-90
B+:
89-88
B:
87-83
B-:
82-80
C+:
79-78
C:
77-73
C-:
72-70
D+:
69-68
D:
67-60
F:
59-0
Tests= 50% H.W. = 20% Quiz =10% Final=20%
Attendance
The student is responsible to attend all classes (unless excused for a school activity)
and actively engage in the day’s lesson. The student’s attendance in the class is crucial to the
student demonstrating proficiency in the subject. Excessive absences (more than 10 excused
or unexcused) may cause the student to be ineligible to earn credit in the class.
Unexcused absences may be regarded as truancy. For unexcused absences and
truancies, no make-up work is allowed per district policy.
ABSENCES: EXCUSED, UNEXCUSED, AND TRUANCY
Students are expected to attend all assigned classes each day. Teachers shall keep a
record of absences and tardiness. It is the student's responsibility to arrange for all make-up
work when they have an excused absence. Parents are encouraged to call the school if their
son/daughter will not be there for that day at 538-2060.
An absence is defined as any class session missed, or when a student is more than ten
(10) minutes late, with the exception of Advisory where a five (5) minute tardy would constitute
an absence.
Where to go for extra help
I am available in my room every day before school except for Tuesdays. If mornings are
not an option for you, please stop by after school or during advisory. If you cannot find me find
another teacher someone is around..
Course Outline
Unit Zero: Review of Pre-Calculus Topics (1 week)
Graphs and Models
Linear Models and Rates of Change
Functions and Their Graphs
Fitting Models to Data
Domain and Range
Unit One: Limits and Their Properties (2-3 weeks)
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Unit Two: Differentiation (4 weeks)
The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
Product and Quotient Rules
Higher-Order Derivatives
The Chain Rule
Implicit Differentiation
Related Rates
Unit Three: Applications of Differentiation (5 weeks)
Extrema on an Interval
Rolle’s Theorem
Mean Value Theorem
Increasing and Decreasing Functions and the First Derivative Test
Concavity and the Second Derivative Test
Limits at Infinity
A Summary of Curve Sketching
Optimization Problems
Differentials
Unit Four: Integration (5 weeks)
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Unit Five: Logarithmic, Exponential, and Other Transcendental Functions (6 weeks)
The Natural Logarithmic Functions: Differentiation
The Natural Logarithmic Functions: Integration
Inverse Functions
Exponential Functions: Differentiation and Integration
Bases Other Than e and Applications
Inverse Trigonometric Functions: Differentiation
Inverse Trigonometric Functions: Integration
Unit Six: Applications of Integration (2 week)
Area of a Region Between Two Curves
Volume: The Disk Method
Volume: The Washer Method
Unit Seven: Differential Equations (1 week)
Slope Fields and Euler’s Method
Differential Equations
Unit Eight: AP Review (3 weeks)
Multiple Choice Practice
Free response questions
AP Sample Test
Unit Nine:
Newton’s Method
Hyperbolic Functions
Review for final exam
Textbooks and Resources
Larson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus of a Single Variable. Boston:
Hougton Mifflin, 2006, 8th edition.
Lederman, David. Multiple-Choice and Free Response Questions in Preparation for AP Calculus
(AB) Examination. D & S Marketing, 1998, 6th edition.
Shaw, Michael J., and Taylor, Gary L. The Essentials Of Calculus. Copyright 2015