Download - Deer Creek High School

AP Calculus (AB)
Course Syllabus
Shannon Phelps
Primary Text Used:
Larson, R.; Hostetler, R.; & Edwards, B. Calculus of a Single Variable (7th ed., $103.17)
Houghton Mifflin. 2002.
Course Description/Objectives:
The objective of this course is to prepare students for the College Board AP Calculus (AB) Exam
since students in this course are highly recommended to take the AP exam in the spring. This course
thoroughly covers all topics listed in the College Board’s Calculus AB topic outline. Methods of
instruction include, but are not necessarily limited to: lecture, group work, demonstration, discovery,
and practice. Throughout the course, students will be taught and tested on their ability to
communicate mathematically by explaining their results in sentences. This course is designed to
thoroughly introduce students to the foundational topics of calculus as outlined by the College Board.
Topics covered are listed below.
Topic Outline for Calculus AB (as outlined by College Board)
I.
Functions, Graphs, and Limits Analysis of graphs, limits of functions (including one-sided
limits), asymptotic and unbounded behavior, continuity as a property of functions
II.
Derivatives - Concept of the derivative, derivative at a point, derivative as a function,
second derivatives, applications of derivatives, computation of derivatives
III.
Integrals - Interpretations and properties of definite integrals, applications of integrals,
Fundamental Theorem of Calculus, techniques of antidifferentiation, applications of
antidifferentiation, and numerical approximations to definite integrals
Student Expectations/Conduct:
Because this is a higher level course, higher expectations are set. As the student, you are expected
to come to class prepared to engage in class discussions, defend your solutions to problems, and
possibly even lead discussions. This course is highly interactive, requiring you to be ready at all times
to contribute to class discussions and lab activities. This course is also designed to be investigative in
nature, often requiring you to make and test hypotheses. Often, the class will use a graphing
calculator to assist in the hypothesis, so you are expected to have adequate knowledge of the
functions and capabilities of a graphing calculator. You are expected to conduct yourself in a
respectful and appropriate manner. You are responsible for working diligently during the time given as
well as keeping track of due dates and exam days.
Some tips to keep in mind:
1. Do your daily work. You cannot expect to learn the material by watching someone else do it.
You must do it yourself.
2. Keep working until you can do the homework on your own.
3. Participate in class. The only person who can tell me if you don’t fully understand a concept is
you. Please communicate with me.
4. Take Notes! Your notes can refresh your memory as well as assist in comprehension of a
concept.
5. Prepare for exams! Make sure that you work a few problems of each type until you can work
them efficiently and accurately. Remember that our main goal is preparation for the AP exam,
so working problems that you are less familiar with is a great place to begin the review.
Graphing Calculators:
Students are expected to have access to a TI-83, TI-84, or TI-89 calculator for several activities.
These graphing calculators are used to enhance and compliment daily learning. Often the calculator
allows students to visualize abstract solutions and understand what they have really found. One of
the first topics that we discuss with a graphing calculator is how to properly utilize a calculator.
Another activity that students utilize their graphing calculators for is finding the equation of a tangent
line at a point so that they can then graph the line and the curve and “zoom in” at the point of
tangency to see the local linearity. Students also use a graphing calculator to verify their results when
finding where a function is increasing and decreasing, concave up and concave down, and its
extreme values. By the end of the course, students are capable of graphing equations, finding roots,
and finding numerical derivatives and integrals, as well as knowing when it is appropriate to use
technology.
AP Exam
Section I
Multiple Choice: ½ of the total points.
Part A: 55 minutes, 28 questions, no calculator (Students usually run out of time.)
Part B: 50 minutes, 17 questions, calculator required but not needed for all questions
Section II
Free Response: ½ the total points
Part A: 30 minutes, 2 questions with several parts, calculator required
Part B: 60 minutes, 4 questions, no calculator (Students may go back to the previous
two questions.)
Grading
5: Extremely well qualified, 4: Well Qualified, 3: Qualified, 2: Possibly Qualified, 1: No
Recommendation
College Credit varies with different universities!
The AP Exam tests the ability of the students to apply the concepts of calculus as well as critical
thinking skills. Question include simple to very difficult questions. It is given on Wednesday morning
of the first full week of May. Application deadline @April 1
AP Calculus AB Course Outline:
Unit 1: Limits & Their Properties (2 weeks)
A. A Preview of Calculus
1. Tangent Line Problem (Investigation with Graphing Calculator)
2. The Area Problem (Approximation)
B. Finding Limits Graphically and Numerically
1. Finding a limit graphically
2. Estimating a limit numerically
3. Finding a limit analytically
4. Limits that fail to exist (unbounded behavior, oscillating behavior, behavior that differs from
the left and right) 5. Formal definition of a limit
C. Evaluating Limits Analytically
1. Properties of limits
2. Limits of composite functions
3. Limits of trigonometric functions
4. Squeeze Theorem
D. Continuity and One-Sided Limits
1. Definition of continuity
2. Discontinuous functions
Unit 2: Discontinuity (1 week)
A. Removable discontinuity
B. Non-removable discontinuity
3. One sided limits
4. Properties of Continuity
5. Intermediate Value Theorem
6 Infinite Limits
A. Definition of infinite limits
B. Graphically
C. Vertical asymptotes
D. Properties of infinite limits
Unit 3: Differentiation (4 weeks)
A. The derivative and the tangent line problem
1. The tangent line problem
2. Definition of tangent line with slope m
3. Definition of derivative using limits
4. Differentiability and continuity
5. Equation of the tangent line – derivative of a point
B. Basic Differentiation Rules and Rates of Change
1. The constant rule
2. The power rule
3. Finding the slope of a graph
4. The constant multiple rule
5. Sum and difference rules
6. Derivatives involving sine and cosine
7. Rates of change and the derivative
C. The Product and Quotient Rule
1. The product rule
2. The quotient rule
3. Derivatives of trigonometric functions
4. Higher order derivatives (second, third, etc.)
D. The Chain Rule
E. Implicit Differentiation
1. Guidelines for implicit differentiation
2. Finding the second derivative implicitly
3. The y method
F. Related Rates – Real-life Applications of the Derivative
Unit 4: Applications of Differentiation (5 weeks)
A. Extrema on an Interval
1. Definition of extrema (absolute)
2. Extreme Value Theorem
3. Definition of relative extrema (local)
4. Critical numbers and the derivative
B. Rolle’s Theorem and the Mean Value Theorem
1. Rolle’s Theorem
2. Illustrating Rolle’s Theorem
3. Mean Value Theorem
4. Instantaneous rate of change
C. Increasing and Decreasing Functions and the First DerivativeTest
D. Concavity and the Second Derivative Test
E. Limits at Infinity
1. Definition of limits at infinity
2. Definition of horizontal asymptote
3. Indeterminate form
4. Relation between horizontal asymptote and limit at infinity
F. A Summary of Curve Sketching
1. Analyzing the graph of a function using the first and second derivative
2. Sketching the graph of a function using the first and second derivative
G. Optimization Problems
1. Applied maximization problems
2. Applied minimization problems
H. Differentials
1. Tangent line approximation
2. Definition of differentials
3. Error propagation
4. Calculating differentials
Unit 5: Integration (5 weeks)
A. Antiderivatives and indefinite integration
1. Definition of an antiderivative
2. Basic integration rules
3. Initial conditions and particular solutions
4. Application – vertical motion problem
B. Area
1. Sigma notation
2. Summation formulas
3. Approximating the area of a plane region
4. Upper sums, lower sums, and midpoint sums
5. Definition of the area of a region in the plane using sums
C. Riemann Sums and Definite Integrals
1. Definition of Riemann sums
2. Definition of a definite integral
3. Evaluating a definite integral as a limit
4. Definite integral as the area of a region
5. Properties of definite integrals
D. The Fundamental Theorem of Calculus
1. Guidelines for using the Fundamental Theorem of Calculus
2. Mean Value Theorem for integrals
3. Average value of a function on an interval
4. The Second Fundamental Theorem of Calculus
E. Integration by Substitution
1. Antiderivation of a composite function
2. Recognizing the f(g(x))g’(x) pattern
3. Change of variables
4. General power rule for integration
5. Change of variables for definite integration
6. Integration of even and odd functions
F. Numerical Integration
1. The Trapezoidal Rule
2. Errors in the Trapezoidal Rule
Unit 6: Logarithmic, Exponential, and Other Transcendental Functions (4 weeks)
A. The Natural Logarithmic Function: Differentiation
1. Definition of the natural logarithmic function
2. Properties of the natural logarithmic function
3. Definition of e
4. Derivative of the natural logarithmic function
5. Derivative involving absolute value
B. The Natural Logarithmic Function: Differentiation
1. Log Rule for Integration
2. Using the log rule with a change of variables
3. Finding area with the log rule
4. Integrals of trigonometric functions
C. Inverse Functions
1. Definition of inverse functions
2. Reflective property of inverse functions
3. Derivative of an inverse function
4. Graphs of inverse functions have reciprocal slopes
D. Exponential Functions: Differentiation and Integration
1. Natural exponential function
2. Properties of the natural exponential function
3. Derivative of the natural exponential function
4. Integration rules for exponential functions
5. Finding areas bounded by exponential functions
E. Bases Other than e and Applications
1. Radioactive half life model
2. Derivatives for bases other than e
3. Integrating an exponential function to another base
4. Applications of exponential functions
a. Compound interest formulas
b. Bacterial culture growth
F. Differential Equations: Growth and Decay
1. Exponential growth and decay model
2. Radioactive decay
3. Population growth
G. Inverse Trigonometric Functions: Differentiation
H. Inverse Trigonometric Functions: Integration
Unit 7: Applications of Integrals (3 weeks)
A. Area of a Region between Two Curves
B. Volume:
1. The Disk Method (by slicing)
2. The Washer Method
3. Solids with Known Cross Sections
C. Volume: The Shell Method
D. Arc Length & Surfaces of Revolutions
The remaining time will be spent on review to prepare for the AP Exam. Please note weeks spent in
learning are estimates. I will modify as needed.
Grading Procedures:
Grades are comprised of homework, quizzes, take-home quizzes, and tests. I will drop your lowest
quiz score at the end of the semester. You may also retake one test at the end of the 1st semester.
Tests: 40%
Daily Work: 20%
Quizzes: 30%
Semester Exam: 10%
Chapter Tests: Chapter tests will be given at the conclusion of each chapter.
Daily Work: Students will receive a reasonable amount of independent practice problems. Time may
be given at the end of the class period to work on these problems. You are responsible for utilizing
the time given to minimize the amount of work taken home. All assignments are due before each quiz
or the chapter test. 10% deduction each day for late work.
Semester Exams: Semester exams are comprehensive. Students are only exempt if they meet the
criteria outlined in the student handbook.
Cheating Policy:
Cheating in any form is not tolerated and will result in a zero grade for that assignment in accordance
with school handbook.
Extra Help: I am available before school on Mondays and Fridays at 7:30 and after school Tuesday
through Thursday until 3:45. Please feel free to come in anytime, but a heads up would be nice.
That way I can make sure to be in my classroom. I also highly recommend study groups outside of
class.
I look forward to an amazing year! I am excited about teaching this course and hope you are
too! If I can help you in any way, please speak up. It never hurts to ask.
Shannon Phelps
[email protected]
Please fill out this form and return it to Mrs. Phelps by Friday, August 19th, 2015.
I have read the course syllabus for Mrs. Phelps’ class.
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