Download AP Calculus AB Course Syllabus 2016-2017

AP Calculus AB
BMHS 2016 - 2017
Teacher: Mr. C. Brommer
Classroom: 220
I. COURSE DESCRIPTION
Calculus is for advanced placement students. Since calculus is a certain kind of calculation,
students should do many problems. It is in the solving of problems with and without
graphing calculators that the student comes to understand the theory. While the student is
acquiring skill in calculus per se, he improves, at the same time, his grasp of Algebra,
Trigonometry, and Analytical Geometry.
II. COURSE ORGANIZATION
A.
Advanced placement calculus is an elective in the mathematics curriculum for students
in the college preparatory program.
B. It is a two semester course worth 1 credit for a passing grade of at least D-, credit weight
of 0.5, level R, and is computed for class rank and honor roll.
C. It meets five periods per week.
D. The prerequisite for the course is completion of Honors Pre-Calculus.
III. COURSE OBJECTIVES
A. To satisfy a demand, in engineering and scientific fields, for earlier introduction of
calculus.
B. To develop the students' mathematical intuition and computational power.
C. To break down the barriers of the traditional subject divisions of mathematics and make
use, in developing new concepts of all the mathematics the student has already learned.
D. To show that mathematics is a matter of logical development.
E. To illustrate a wide variety of applications of calculus.
F. To effectively communicate complex math concepts to others.
IV. COURSE CONTENT
FIRST NINE WEEKS
A. Introduction to the Calculus
1. Algebraic Skills
a. Real Numbers, Inequalities, Interval Notation, Absolute Value
b. Distance Formula, Lines, Slope
c. Functions and Ordered Pairs
d. Even and Odd Functions
e. Inverse Functions
2. Limits and Continuity
a. Basic Limits
(1) Estimating limits via graphing calculators and graphs to be
Followed by algebraic solutions.
b. Limits Involving Infinity
c. Continuity
(1) By Algebraic Definition
(2) By Graph, Asymptotes
3. Analytic Geometry – Conic Sections
a. Circles
b. Ellipses
c. Hyperbolas
d. Parabolas
B. Differentiation
1. Computation of the differential by
a. Definition
b. Basic Formula
c. Multiplication Rule
d. Division Rule
e. Chain Rule and Power of Function Rule
2. Differentiation and Continuity
3. Geometric Interpretation of the Derivative - Introduced by graphic and numeric
analysis – computation of slope about tangent point.
a. Derivative and Slope
b. Equation of Tangent and Normal Lines
4. Intermediate Value Theorem
5. Rolle's Theorem
6. Theorem of the Mean
SECOND NINE WEEKS
C. Application of the Derivatives
1. Graph Sketching
a. Higher Order Derivatives
b. Preliminary, Informal Ideas
c. Graph Sketching
(1) Quadratics, Cubics, and Biquadratics
(2) Discontinuous Graphs
(3) Restricted Domain and/or Range
(4) Newton’s Method
(a) introduced by numeric and graphic analysis
2. Maxima and Minima-Reading Problems - each area introduced by numerical
experimentation (use of graphing calculator and tables) evolving into use of
derivatives.
a. Perimeter and Area
b. Number and Algebra Problems
c. Volume and Borders
d. Triangular and Circular Area and Volume
e. Distance, Rate and Time
f. Velocity and Acceleration
g. Implicit Differentiation
h. Related Rates
(1) numerical experimentation(via graphing calculator and
tables )evolving into application of derivatives.
D. Antidifferentiation
1. Differentials
2. Indefinite Integral – Fundamental Theorem of Calculus
a. Basic Rules of Integration
b. Change of Variable Method
c. Differential Equations
d. Separable Equations
3. Definite Integral
a. Computation of the definite integral
b. Symmetric and Constant Properties
4. Slope Fields (manual and graphing calculator derived)
E. Area Beneath Curve
1. Trapezoid, Simpson Method, and Riemann Sums -numerical experimentation(use
of graphing calculator and tables) evolving into application of definite integral.
2. Area to x-axis
a. Regions in First Quadrant
b. Signed Area
3. Area to y-axis
a. Regions in First Quadrant
b. Signed Area
4. Area Between Curves
a. By x and y-axis
b. By y-axis
c. Infinite and Restricted Area
THIRD NINE WEEKS
F. Solids of Revolution - numerical experimentation(use of graphing calculator and tables)
evolving into use of definite integral.
1. About x and y-axis
2. Disk Method
3. Ring Method
4. Arc Length
5. Average Value
G. Logarithms and Exponential Functions
1. Basic Algebraic and Geometric Properties of Logarithm and Exponential
2. Properties of Logarithms
3. Derivatives of Logarithms
4. Derivative of Exponentials
5. Integration of Logarithms
6. Trick Derivatives
7. Integration of Exponentials
H. Trigonometry
1. Basic Review of
a. Radian Measure, Definition of Angle, Etc.
b. Trigonometric Functions
c. Special Angles
d. Trigonometric Identities
e. Addition Formulas
2. Calculus and Trigonometry
a. Trigonometric Limits
b. Derivative of Trigonometric Functions
(1) estimating limits via graphing calculators and graphs to be
followed by algebraic solutions.
c. L’Hopital’s Rule
d. Application of Trigonometric Derivative
FOURTH NINE WEEKS
3. Integration of Trigonometric Functions
a. Basic Integration
b. Substitution Method
c. Trigonometric Definite Integral
d. Area Beneath Curve
e. Applications of Trig Integration
4. Inverse Trigonometric Functions
a. Definition and Computation of
b. Derivatives of
c. Integration of
d. Newton and Simpson method revisited
I. Techniques of Integration
1. Involving Sin and Cos-odd Powers
2. Involving Sin and Cos-even Powers
3. Involving Sin and Cos Products
4. Integration of Trigonometry Involving Logarithms
5. Integration of Powers of other Trig Function
6. Integration of Parts
7. Partial Fractions
8. Improper Integrals
V. MAJOR MATERIALS AND EQUIPMENT LIST
A. Primary Textbooks:
Larson/Edwards. Calculus of Single Variable, AP Edition, 9th Edition, Holt 2012.
B. Resource Textbook:
Thomas and Finney. Calculus and Analytic Geometry. Addison Wesley.
Finney, Demana, Waits,& Kennedy. Calculus. Addison Wesley Longman, 2000.
C.
D.
E.
F.
Graphing and scientific calculators
Computers
Internet Resources
Notebooks
VI. EXPECTED LEVELS OF ACHIEVEMENT
All successful students, upon completion of the course, should be able to:
A. Perform advanced arithmetic and algebraic calculations.
B. Differentiate algebraic and transcendental functions.
C. Integrate algebraic and transcendental functions.
D. Graph algebraic and transcendental functions.
E. Apply calculus to real-life situations.
F. Appreciate and understand that calculus is a logical sequence of mathematical
interpretations.
G. Realize that mathematics is not only a science, but also an art.
VII. COURSE TECHNOLOGY
Students will use the TI-NSpire family of graphing handhelds to study topics in depth and
provide alternative analysis of concepts throughout the course. If you purchase your own,
any of the following are recommended: TI83+/TI84/TI84+/ or the TI-NSpire CX/CXCAS
family of graphing calculators. Some familiarity with the graphing calculator is expected,
but not required. I can and will teach you all that is needed for the course on any of the
previously listed calculators.
VIII. EVALUATION PROCEDURES
Students will be evaluated throughout the course using the following modes of assessment:
A.
Semester Exams
** Multiple Choice and Open Ended Problems requiring proper solution technique,
vocabulary, and explanations.**
B. Section Quizzes
C. Unit Tests
D. Homework
**Problems checked by teacher collection, checked at the classroom door, or oral
quizzing at the classroom door.**
E. Class Activities/Lab Projects/Oral Presentations
** These activities and projects will require students to use the NCTM Standard for
communicating mathematics through individual and group presentations to the class.
Grades will be based upon accuracy of results, presentation methods (charts, graphs,
graphing calculator, PowerPoint, etc.), and overall presentation style.**
F. Notebooks
G. Writing Assignments for Portfolios/Problem Solving Journal
** These assignments will require students to communicate in written format the
solution or solutions to traditional and more challenging problems. Each assignment will
require 2 or more pages of a completely worked out mathematical solution, supported with
graphs, etc., and a written explanation of how the solution was obtained. Grades are based
upon accuracy of results and detailed explanation of the solution process.**
H. Teacher Observation
**As part of the classroom lecture/instruction, students will be given the opportunity
to respond to teacher prompts about calculus concepts and problems that will require
verbal responses and explanations on the part of the student.**
For Your Information
1. Each student is required to have a notebook containing class notes, homework, and
writing assignments. This notebook, along with a pen/pencil will be brought to every
class.
2. If you are absent, it is your responsibility to check with the teacher and complete any
missed assignments.
3. Homework will be checked. Incomplete homework is no homework. An incomplete
homework will result in a loss of 5 points from your next test (for each occurrence),
parental notification, and an office disciplinary referral for subsequent occurrences
(second occurrence and onward).
4. If you find you need extra help, just ask. I am very willing and able to work out a
meeting time.
5. Although not required, having a scientific calculator or graphing calculator may be
helpful. Scientific calculators will NOT be provided. Graphing calculators will be
provided at student request.
6. My teacher webpage can be found at the following location:
http://teachersites.schoolworld.com/webpages/CBrommer/
You may find it useful to view information pertaining to class, review answers to class
work before major quizzes and tests, as well as listen to audio podcasts as a review tool
for vocabulary and major concepts prior to unit tests.
7. Cheating in any form will not be tolerated. Cheating includes using prohibited devices
on assignments or assessments, copying someone else’s work and claiming it as your
own, copying/sharing answers verbally or in writing on assessments, etc. Each
occurrence of cheating will result in no credit given (0 grade) for the specific item.
Additionally, a discipline referral will be made to the office for each occurrence.