ADVANCED PLACEMENT CALCULUS AB
COURSE SYLLABUS
2013-2014
INSTRUCTOR: AMANDA SALT
ROOM NUMBER: / High School Room 369
PLANNING PERIOD: / 2nd HOUR (8:55 – 9:45)
SCHOOL PHONE: / 918-443-6257 or 918-443-6000 x 1
E-MAIL ADDRESS: /
PREREQUISITE(S): / Successful completion of Trigonometry
A. COURSE DESCRIPTION
In teaching AP Calculus I hope to enable students to succeed in further collegiate level mathematics courses. Everything listed on the AP Calculus Course Description for Calculus AB is covered in this course. Throughout this course there is on ongoing balance of understanding, comprehension, technology usage and skills.
B. METHOD OF INSTRUCTION
Students are held to a high expectation in our AP curriculum. A complete tentative schedule is given to the students on the first day of class. My classroom has tables instead of desks making group work more conducive. Throughout the course, students work together on a regular basis, formally and informally. In developing new concepts a whole class discourse is used. Students may make a contribution to the class discourse at any open opportunity, not having to raise their hands and be called upon. I allow for students to explain solutions or give further interpretation to their classmates. This allows me to see the comprehension of my students as well as those needing extra help.
C. COURSE OBJECTIVES
1. The course teaches all topics associated with Functions, Graphs, Limits, Derivatives, and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course.
2. The course provides students with the opportunity to work with functions represented in a variety of ways – graphically, numerically, analytically, and verbally – and emphasizes the connection among these representations.
3. The course teaches students how to communicate mathematics and explain solutions to problems both verbally and in written sentences.
4. The course teaches students how to use graphing calculators to help solve problems, experiment, interpret results, and support conclusions.
D. COURSE TOPICS/UNITS AND DATES
1st semester AP Calculus covers chapters 1 – 4 with chapters 5 – 7 covered in 2nd semester AP Calculus.
Chapter 1: Prerequisite for Calculus: Pre-Calculus Review (1 ½ weeks)
A. Lines
1. Slope of a line
2. Parallel and perpendicular lines
3. Equations of lines
B. Functions and Graphs
1. Functions
2. Domain and Ranges
3. Viewing and Interpreting Graphs
4. Even and Odd Functions and Symmetry
5. Piecewise, Absolute Value and Composite Functions
C. Exponential and Logarithmic Functions
1. Exponential Growth and Decay
2. One-to-One Functions
3. Inverses
4. Logarithmic Properties
5. Logarithmic Functions
D. Trigonometric Functions
1. Radian Measure
2. Graphs of Trigonometric Functions
3. Periodicity
4. Even and Odd Trigonometric Functions
5. Transformations and Inverse Trigonometric Functions
Chapter 2: Limits and Continuity (3 weeks)
A. Rates of Change and Limits
1. Average and Instantaneous Speed
2. Limit Definition and Properties
3. One-sided and Two-sided Limits
4. Sandwich Theorem
B. Equations of lines
1. Finite and Infinite Limits
2. End Behavior
3. Visualizing Limits
C. Continuity
1. Continuity at a Point
2. Continuous Functions
3. Discontinuous Functions
a. Removable Discontinuity
b. Jump Discontinuity
c. Infinite Discontinuity
4. Composites
5. Intermediate Value Theorem for Continuous Functions
D. Rates of Change and Tangent Lines
1. Average Rates of Change
2. Tangent to a Curve
3. Normal to a Curve
4. Instantaneous Rates of Change
Chapter 3 and 4: Derivatives (7 weeks)
A. Derivative of a Function
1. Definite of Derivative
2. Derivative Notation
3. Relationships between the Graphs of and
4. Graphing the Derivative from Data
B. Differentiability
1. Local Linearity
2. Derivatives on a Calculator
3. Differentiability Implies Continuity
4. Intermediate Value Theorem for Derivatives
C. Rules for Differentiation
1. Integer Powers of x, Multiples, Sums and Differences
2. Products and Quotients
3. Second and Higher Order Derivatives
D. Velocity and Other Rates of Change
1. Instantaneous Rates of Change
2. Motion along a Line
3. Derivatives in Economics
E. Derivatives of Trigonometric Functions
1. Derivative of the Six Basic Trigonometric Functions
2. Simple Harmonic Motion
3. Jerk
F. Chain Rule
1. Derivatives of Composite Functions
2. “Outside-Inside” Rule
3. Power Chain Rule
G. Implicit Differentiation
1. Implicitly Define Functions
2. Tangents and Normal Lines
3. Derivatives of Higher Order
4. Rational Powers of Differentiable Functions
H. Derivatives of Inverse Trigonometric Functions
1. Derivatives of Six Inverse Trigonometric Functions
I. Derivatives of Exponential and Logarithmic Functions
1. Derivative of and
2. Derivative of lnx and
3. Power Rule of Arbitrary Real Powers
Chapter 5: Applications of Derivatives (5 weeks)
A. Extreme Value Functions
1. Absolute (Global) and Local (Relative) Extreme Values
2. Finding Extreme Values
B. Mean Value Theorem
1. Mean Value Theorem (MVT)
2. Physical Interpretation of the MVT
3. Increasing and Decreasing Functions
C. Connecting and with the Graph of f
1. Critical Points
2. First Derivative Test for Local Extrema
3. Concavity
4. Points of Inflection
5. Second Derivative Test for Local Extema
6. Learning about Functions from Derivatives
D. Modeling and Optimization
1. Applications from Business and Industry
2. Applications from Mathematics and Economics
E. Linearization
1. Linear Approximation
2. Differentials
F. Related Rates
1. Related Rate Equations
2. Solution Strategy
3. Simulating Related Motion
Student Activities: Function/Derivative Match
Tootsie Roll Lab
Saving a Crewmate
Chapter 7: The Definite Integral (3 ½ weeks)
A. Estimating with Finite Sums
1. Distance Traveled
2. Rectangular Approximation Method (RAM)
a. Left-Endpoint (LRAM)
b. Right-Endpoint (RRAM)
c. Midpoint (MRAM)
B. Definite Integrals
1. Riemann Sums
2. Terminology and Notation of Integration
3. Definite Integral and Area
4. Constant Functions
5. Integrals on a Calculator
6. Discontinuous Integrable Functions
C. Definite Integrals and Antiderivatives
1. Properties of Definite Integrals
2. Average Value of a Function
3. Mean Value Theorem for Definite Integrals
4. Connecting Differential and Integral Calculus
D. Fundamental Theorem of Calculus
1. Fundamental Theorem of Calculus (part 1)
2. Fundamental Theorem of Calculus (part 2)
3. Area Connection
4. Applications
E. Trapezoidal Rule
1. Trapezoidal Approximations
Chapter 7: Differential Equations and Mathematical Modeling (3 ½ weeks)
A. Antiderivatives and Slope Fields
1. Solving Initial Value Problems
2. Slope Fields
3. Antiderivaties and Indefinite Integrals
4. Properties of Indefinite Integrals
5. Applications of Integration
B. Integration by Substitution
1. Power Rule in Integral Form
2. Trigonometric Integrands
3. Substitution in Indefinite and Definite Integrals
4. Separable Differential Equations
C. Exponential Growth and Decay
1. Law of Exponential Change
2. Continuously Compounded Interest
3. Radioactivity
4. Newton’s Law of Cooling
Student Activities: Creating a Slope Field
Chapter 7: Applications of Definite Integrals (2 ½ weeks)
A. Integral as Net Change
1. Linear Motion Revisited
2. Net Change from Data
B. Areas in a Plane
1. Area Between Curves
2. Area Enclosed by Intersecting Curves
3. Boundaries with Changing Functions
4. Integrating with Respect to y
5. Saving Time with Geometry Formulas
C. Volumes
1. Volume as an Integral
2. Square, Circular and Other Shaped Cross Sections
Student Activity: Cross-Section Model and Presentation
This schedule allows for 6 ½ weeks of flexibility/review for the AP Exam.
DESCRIPTION OF STUDENT ACTIVITIES
Function/Derivative Matching: This activity is used in connecting andf. Students are in groups of 4 to 6 students. Within each group the students split into a Function group and a Derivative group. Each Function group is given a set of cards displaying either a function description or a graph. Each description must be matched to the correct graph. The Derivative group is given a set of similar cards; however their cards display either a derivative description or a derivative graph. After the Functions and Derivatives have each matched the descriptions to the graph the two merge. The functions must now match to its derivative.
Tootsie Roll Lab: This lab is performed during the study or related rates. The students are asked to calculate the rate of change of the radius and volume of their lollipop. Each student is given a Tootsie Roll Pop, dental floss, ruler, stopwatch, and worksheet to record results. Students measure the initial radius of their lollipop with dental floss. After initial measurements are made the students suck on their lollipop for 30 seconds intervals. At the conclusion of each interval the radius is recorded. Students model the rate of change of the radius with a function of time and then use the rate of change to estimate the rate of change of the lollipop’s volume. This lab was obtained from the book, A Watched Cup Never Cools by Ellen Kamischke.
Saving A Crewmate: This activity is used during the study of optimization. Students are paired with another classmate for this activity. Students are given the scenario they are out at sea with their partner. One of them has a life-threatening accident while on board. An ambulance has been dispatched to meet their lifeboat somewhere along the shoreline. The distance from the shoreline initially is given. Students must find out appropriate meeting point along the shoreline in order to get their crewmate to the hospital on time.
Creating a Slope Field: This lab is used to introduce slope fields. Using my graphing calculator, I project a 5x5 grid on the front board. Each student is assigned coordinate points with in the region. For a given differential equation, each student computes the slope at his/her coordinate position. Each student will come to the board and draw a short line segment to indicate their calculated slope using their coordinate point as the midpoint of the segment. As an example, if and the student is given the coordinate point , he/she would draw a line segment of slope 1 at . This activity continues until the class has completed the slope field.
Gladys Woods presented this activity during a College Board AP Calculus AB workshop.
Cross-Section Creation: This project is completed after cross-sections are presented. Students create a solid whose bases are bounded by two curves. Students are given the opportunity to choose their materials, the two curves, and the cross sectional shapes they wish to use. Students must provide a written explanation of the two curves used in their project, what their cross-sectional shapes are supposed to represent and the area calculation of volume of their creation. A calculator answer is not accepted; physical handwritten explanation must be shown. Gladys Woods presented this activity during a College Board AP Calculus AB workshop.
E. TEXTBOOK(S) AND REQUIRED TOOLS OR SUPPLIES
1. Textbook: Calculus: Graphical, Numeric and Algebraic by Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy Pearson Education, Inc., publishing as Prentice Hall Copyright 2003
2. Textbook Price: $100.00
3. Supplies and/or tools:
a. writing utensil (NOT PURPLE)
b . paper
c. graphing calculator
d. 4 AAA batteries
e. Kleenex/box of tissues
Calculators will be used throughout the year. TI-84’s and TI-89’s are the most popular graphing calculators used. I have a few graphing calculators for student use in the classroom. The TI-89 and TI-84 calculators will be used during presentations. Students are encouraged to purchase a calculator of their own. If you have any calculator questions, please do not hesitate to communicate them to me.
F. GRADING PLAN
1. The overall grading scale will be as follows:
100% - 90% = A
89% - 80% = B
79% - 70% = C
69% - 60% = D
59% and ¯ = F
2. On the semester schedule grades are given at the conclusion of each 18-week semester. Semester grades are calculated using homework, projects, activities and exam scores.
3. There will be a Final Exam given at the conclusion of each semester. The Final Exam will be 20% of student’s final semester grade.
4. Semester grades are calculated by dividing the total points received from homework, portfolios, exams and quizzes by the total points possible.
G. COURSE COMPONENT SPECIFICS
1. HOMEWORK OPPORTUNITY: An opportunity to review, rehearse in class examples and solidify foundational conceptions will be given every day or couple days. Class time will be set aside to work on these lessons when possible. However, most students will find it necessary to complete the lesson at home. Students are expected to turn in their homework at the beginning of each class period as directed by their instructor. Homework opportunities will be graded and returned to the student.
Taking advantage of the homework opportunities are expected/encouraged in order to pass the class with a “C” or better.
2. NOTES: Students are allowed to take lecture notes for each lesson set. Notes will not be allowed on exams.
3. PROJECTS/LABS: Various projects/labs may be assigned corresponding to a certain topic. More information will be given at a later date.
4. LATE PAPERS: Late papers will NOT be accepted unless prior permission has been given by the instructor. Papers are considered “LATE” if they are not turned in when called for.
5. EXAMS AND QUIZZES: There will be one exam per chapter or major section and a comprehensive exam given at the conclusion of each semester. These exams are similar to AP exams having a calculator and non-calculator portion. AP multiple-choice questions are incorporated on these exams as early as possible. Quizzes using AP free response questions are given periodically following the rubric on AP Exam.
6. MAKE-UP POLICY:
a. A school activity: It is the student’s responsibility to get their missed work PRIOR to their absence.
b. It is the responsibility of the student to check for any homework assignments or tests that were missed during their absence.
c. It is the student’s responsibility to schedule any test missed during their absence.
d. Tests must be made-up before or after school.
e. Students will have three school days to schedule and make-up
exam(s).
f. Make sure you talk with me about your make-up test date, don’t
assume the test will be available. Students taking a make-up test may or may not be given a different exam than given on the actual test date.
7. INTER ACT MATH Tutorial Website: www.interactmath.com Get Practice and tutorial help online! This interactive tutorial website provides algorithmically generated practice exercises that correlate to the topics in our textbook. Every exercise is accompanied by an interactive guided solution with helpful feedback for incorrect answers.