AB Calculus Syllabus 2010-2011
Instructor:
Room:
Debbi Carson
235
Office:
Email:
203
mailto:[email protected]
Attendance: You are expected to attend class every day that the class meets. Please be on time for each class. If
you know you will be missing a class, please notify me before the class. If you miss a class, contact me before the
next class to find out what you missed. The best way to avoid problems is to communicate with me as much as
possible.
Homework: Practice is the key to success. It is imperative that you reinforce new concepts outside the classroom.
Assignments should be completed by the next class. Many days class will begin with a homework quiz. If you have
difficulty completing assignments, see me during AcLab or after school in Room 203. I expect you to attempt all parts
of the homework. Each of you can succeed as long as you are willing to learn from your mistakes and reinforce your
success. Homework is an important part of the learning process in math courses. You should expect to spend two
hours outside of class for every hour spent in class. You will receive a homework assignment for each section we
cover in this class. These assignments will be only a minimum of what you should complete in order to be successful.
It is important to develop good work habits now in order to be successful in all of your mathematics coursework.
Homework will not be collected, but quizzes will be based on the homework problems.
Quizzes: Eleven or more short quizzes will be given during each semester. Each quiz will consist of one or
more problems similar to recent homework problems. Quizzes will be unannounced, closed book, and
open notes. Quizzes will be given at the beginning of class; make-ups will not be allowed for late or absent
students. Only your ten best quiz grades per semester will be counted as part of your final grade.
Problem Sets: Problem sets will be given periodically throughout the year. They will be graded for
accuracy, not completion. These questions will not be discussed in class, so if you have questions, you
may come see me during AC Lab, before or after school. You may work on these problem sets with your
classmates, but you may not ask another Math teacher or a tutor for help.
COURSE DESCRIPTION: This course is designed to follow the AP Calculus AB course guidelines as set by the
College Board for AP Calculus. The primary focus of the course is to develop a thorough understanding of the
concepts covered in Calculus AB and master the skills necessary to solve problems related to those concepts.
Students will learn through a variety of methods. Classroom activities will emphasize graphical representations of
calculus concepts with and without graphing calculators. Students may work in groups to discuss homework problems
as well as solve more open-ended applications problems requiring discussion and written explanations.
EVALUATION: Student work will be assessed on a regular basis. Assessments will include daily homework problems,
quizzes, tests and AP problem sets assigned with each chapter from the text. The problem sets are intended to help
students grasp the foundations of the topics and their applications and answer in precise mathematical language, both
verbally and in written sentences. They also serve to help familiarize the students with the style of the AP questions.
Quizzes and tests will include, but not be limited to, problems like those in the homework and problem sets. Quizzes
and tests may include both calculator and non-calculator sections.
FINAL EXAM: Each semester a cumulative exam will be given during the period designated on the semester final
exam schedule.
REFERENCE MATERIALS:
Primary Textbook
Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy, Calculus: Graphical, Numerical, Algebraic,
Boston, Massachusetts, 2007; David Lederman, Multiple-choice & Free-Response Questions in Preparation for the AP
Calculus (BC) Examination (Sixth Edition), Brooklyn, New York, D & S Marketing Systems, Inc., 1999.
Web Resources
AP Central, Visual Calculus Website, www.ies.co.jp/math/java/calc/index.html (various calculus applets)
Calculator
Students are required to have and to use a graphing calculator. Demonstrations will be done in class using TI-83, TI83+ and TI-84 calculators. If you need to check one out, see me in the math office.
TOPIC OUTLINE:
Chapter 1: Prerequisites for Calculus
• Lines
• Functions and Graphs
Analysis of graphs, with and without graphing calculator
• Exponential Functions
Students will discuss and identify situations that may result in and exponential growth or decay situation.
• Functions and Logarithms
• Trigonometric Functions
Asymptotic and unbounded behavior; Comparing relative magnitudes of functions and their rates of change
including discussion of the various types of functions.
Chapter 2: Limits and Continuity
• Rates of Change and Limits
Intuitive understanding of the limiting process; Demonstration of limits of functions at asymptotes and at
infinity using graphing calculator including discussion of these limits in verbal as written form; Calculating
limits using algebra; Estimating limits from graphs or tables of data
• Limits Involving Infinity
Limits of functions (including one-sided limits)
• Continuity
Continuity as a property of functions; Intuitive understanding of continuity; Continuity in terms of limits;
Intermediate Value Theorem
• Rates of Change and Tangent Lines
Estimating limits from graphs or tables of data, describing in groups what mathematics lead to these
conclusions; Demonstration of tangent lines on the graphing calculator; Group discussion of what these
tangent lines mean--setting up the discussion of the derivative in the next chapter.
Chapter 3: Derivatives
• Derivative of a Function
Concept of the derivative—graphically, numerically, and analytically; Definition of the derivative as a limit of
the difference quotient and as the limit of average rate of change; Derivative as an instantaneous rate of
change analytically, graphically, and numerically; Discussion as to what the rate of change represents.
• Differentiability
Differentiability implies continuity; Differentiability implies local linearity; Demonstration of local linear linearity
on the graphing calculator; Finding a numerical derivative on a graphing calculator
• Rules for Differentiation
Derivative at a point; Slope of a curve at a point; Power rule, product rule, quotient rule; Second derivatives
• Velocity and Other Rates of Change
Approximate average and instantaneous rate of change from tables and graphs; Equations involving
derivatives; Verbal descriptions are translated into equations involving derivatives and vice versa.
Approximate average and instantaneous rate of change from tables and graphs; Equations involving
derivatives; Verbal descriptions are translated into equations involving derivatives and vice versa.
• Derivatives of Trigonometric Functions
• Chain Rule
• Implicit Differentiation
• Derivatives of Inverse Trigonometric Functions
Using implicit differentiation to derive derivatives of inverse trigonometric functions
• Derivatives of Exponential and Logarithmic Functions
Computation of derivatives; During this chapter, students can start doing free response type questions
involving discussion about what one is actually doing when taking a derivative.
Chapter 4: Applications of Derivatives
• Extreme Values of Functions
Absolute and local extrema; Demonstration of extreme values of functions using graphing caculators
Extreme Value Theorem
• Mean Value Theorem
Increasing and decreasing functions, monotonicity
• Connecting f’, and f” with the Graph of f
Derivative as a function; Concavity, points of inflection; Using a graphing calculator to show the connection
between f’, and f” with the graph of f; Discussion of what type of behavior one would observe in f when f’ is
positive or negative; Discussion of what type of behavior one would expect in f when f” is positive or
negative.
• Modeling and Optimization
Interpretation of the derivative as a rate of change in varied applied contexts including velocity, speed, and
acceleration; Describe solutions both verbally and in written sentences; Solving verbal optimization problems
analytically and graphically with a graphing calculator. Describe solutions both verbally and in written
sentences.
• Linearization and Newton’s Method
Local linear approximation
• Related Rates
Simulation of sliding ladder using a graphing calculator; Solving verbal problems involving related rates.
Describe solutions both verbally and in written sentences
Chapter 5: The Definite Integral
• Estimating with Finite Sums
• Definite Integrals
Definite integral as a limit of Riemann sums
• Definite Integrals and Antiderivatives
Antiderivatives following directly from derivatives of basic functions; Mean Value Theorem for Integral
• Fundamental Theorem of Calculus
Using a graphing calculator to evaluate a definite integral
• Trapezoidal Rule
Chapter 6: Differential Equations and Mathematical Modeling
• Slope Fields and Euler’s Method
Demonstrating slope fields on the graphing calculator.
• Antidifferentiation by Substitution
• Antidifferentiation by Parts
• Exponential Growth and Decay
Solving separable differential equations with and without initial conditions; Demonstration of Newton’s Law of
Cooling. Students solve similar problems and describe solutions both verbally and in written sentences.;
Modeling exponential growth and decay verbal problems. Describe solutions both verbally and in written
sentences.
• Logistic Growth
Partial Fractions; Solving verbal logistic differential equations and using them in modeling, Describe solutions
both verbally and in written sentences; Demonstration of logistic growth problems using a graphing calculator
Chapter 7: Applications of Definite Integrals
• Integral As Net Change
• Areas in the Plane
• Volumes
Volumes of with known cross sections including circular and square; Washer Method
1st Semester Schedule:
Section
2.1 Rates of Change and Limits
2.2 Limits Involving Infinity
Days
1
1
Assignment:
#1-4 all, 6-30 (Multiples of 3), 38, 39, 42, 50, 67
#1-25 odd, 55, 56, 61
2.3 Continuity
1
#1-23 odd, 31, 41, 49, 54, 56, 58
2.4 Rates of Change and Tangent Lines
3.1 Derivative of a Function
1
2
#1-33 odd
#1-23 odd, 24-26 all, 27-31 odd
3.2 Differentiability
1
#1-7 odd, 31, 40, 41, 44
3.3 Rules for Differentiation
3.4 Velocity and Other Rates of Change
2
1
#1-33 odd, 44, 53, 54, 57
#1, 5, 9, 10, 14, 15, 18, 19, 21, 24, 34, 47
3.5 Derivatives of Trigonometric Functions
1
#3-33 odd, 46
3.6 Chain Rule
3.7 Implicit Differentiation
2
2
#3-69 (Multiples of 3)
#3-48 (Multiples of 3), 54
3.8 Derivative Inverse Trigonometric Functions
1
#3-21 (Multiples of 3), 28, 29, 37
3.9 Derivatives Exponential and Logarithmic Functions
4.1 Extreme Values of Functions
2
2
#3-39 (Multiples of 3), 43, 47, 57
#3-30 (Multiples of 3)
4.2 Mean Value Theorem
1
#15-33 odd
4.3 Connecting f’ and f” with the Graph of f
4.4 Modeling and Optimization
2
2
4.5 Linearization and Newton’s Method
1
#1-11, odd, 15-30 (Multiples of 3), 47, 48
Day 1: #1-10, 12, 17, 20;
Day 2: Worksheet, #1-10, 12, 17, 18, 20, 27, 40, 43, 53
#1, 3, 11-14, 19, 23, 25, 27, 30, 60
4.6 Related Rates
2
#3, 6, 9, 12, 13, 15, 18, 21, 22, 24-45 (Multiples of 3)
Section
5.1 Estimating with Finite Sums
5.5 Trapezoidal Rule
5.2 Definite Integrals
5.3 Definite Integrals and Antiderivatives
5.4 Fundamental Theorem of Calculus
6.2 Antidifferentiation by Substitution
7.1 Integral as Net Change
7.2 Areas in the Plane
7.3 Volumes
Days
2
1
1
2
2
2
1
2
3
Assignment:
#1-25 odd, 29
#1, 5, 7, 9, 10, 27
#1-7 odd, 11, 13, 14, 15, 23, 27, 29, 31
#1-19 odd (make a complete graph)
#3-63 (Multiples of 3)
#1-11 odd, 15-66 (Multiples of 3)
#1-11 odd, 12-17, 20, 21, 25, 37
#3-42 (Multiples of 3)
#1-11 odd, 39-43 odd, 16, 19, 22, 23, 27, 34, 35, 38, 49, 51, 55
6.1 Slope Fields
2
#1-19 odd, 21-24 all, 25-40 all
2nd Semester Schedule:
Notes:
•
•
•
•
My assumption is that you will check all odd answers in the back of the book BEFORE getting to
class. ONLY even answers will be provided either in class or on my web-site.
Other assignments might be given in class for reinforcement. The assumption is that you will try as
much of the assignments as you need to in order to understand the topic.
Always check my web-site for the assignments.
Email me with any questions: [email protected]