marie.hanes@nacs.k12.in.us - Room 208
Course Description : AP Calculus BC is a demanding course for most students, requiring them to alter prior methods of learning mathematics. Previous courses often involve no more than learning a specific rule or concept and applying it to a multitude of similar problems or contrived applications. This calculus course requires students to investigate ideas and use a variety of skills and concepts to solve problems. Analytic, graphic and numeric techniques are explored and students learn, after some discomfort, to recognize which method or methods are viable and should be used to find the solution. Explaining results and methods of solution is vital to demonstrating understanding and an answer could require a diagram, an algebraic type proof or a written explanation. Recognizing answers in a variety of forms is also essential to success in AP calculus. The topic to be learned influences the way class is conducted. Graphing calculators provide a powerful tool with which we can explore relationships between equations quickly. We use the calculators to also work with real-world applications where equations and results do not turn out to be predictably “nice”.
Major Text : Larson, Ron and Bruce Edwards. Calculus: Early Transcendental Functions, 5 th edition. Brooks/Cole
Cengage Learning , 2011.
Graphing Calculator : A graphing calculator is required for this course. The preferred calculator is the TI 84+.
Student Evaluation : The 18-week grade for this course is determined by using 20% quiz scores and 80% test scores. A grade for the semester will be determined using 80% 18-week grade and 20% final exam (the grade submitted to IPFW for dual credit students will be determined using 75% 18-week grade and 25% final exam ). Quizzes and tests are presented in the AP style with some questions multiple choice and some questions free response, with and without calculator. A test is usually given at the completion of every chapter and quizzes are given periodically. Projects and activities are assigned when appropriate to the content.

Course Outline : The following course outline describes in general terms the variety of topics taught and their sequence.
This course is designed to meet the expectations as set forth by the CollegeBoard AP for Calculus AB. Students will be expected to apply learned concepts to different types of problems and use various methods to describe or explain solutions. Solutions will be given in a variety of forms including algebraically, graphically and/or verbally (in oral or written form).
Limits and Derivatives (Chapter 2)
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Differentiation Rules (Chapter 3)
Basic Differentiation Rules and Rates of Change
Product and Quotient Rules and Higher-Order Derivatives
Chain Rule
Implicit Differentiation
Derivatives of Inverse Functions
Related Rates
Integration (Chapter 5)
Antiderivaties and Indefinite Integration
Area Reimann Sums
Fundamental Theorem of Calculus
Integration by Substitution
Natural Logarithmic Function: Integration
Infinite Series (Chapter 9)
Sequences
Series and Convergence
Integral Test and p -Series
Comparisons of Series
Alternating Series
Ratio and Root Tests
Taylor Polynomials and Approximations
Power Series
Taylor and Maclaurin Series
Differential Equations (Chapter 6)
Slope Fields
Growth and Decay
Seperation of Variables
Techniques of Integration (Chapter 8)
Basic Integration Rules
Integration by Parts
Integration by Partial Fractions
-
Indeterminate Forms and L’Hopital’s Rule
Improper Integrals
(Approximate end of first semester)
Conics, Parametric Equations and Polar Coordinates (Chapter 10)
Conics
Plane curves and parametric equations
Polar coordinates
Area and arc length in polar coordinates

Vector-Valued Functions (Chapter 12)
Vectors
Differentiation and Integration of vector functions
Velocity and acceleration
Applications of Differentiation (Chapter 4)
Extrema on an Interval
Rolle’s Theorem and Mean Value
Increasing/Decreasing Functions
Concavity
Curve Sketching
Optimization
Applications of Integrals (Chapter 7)
Areas between curves
Volumes using disk, shell methods and with known cross sections Average value of a function
Arc Length
Student Evaluation:
Student grades will be figured with the following items weighted by the percentages indicated below. The grade is cumulative over the 18 week semester.
Tests: 80%
Quizzes 20%
Homework: 0%
Homework, when collected, must be turned in and complete.
An incomplete assignment will result in the student spending time
with me before and/or after school until the assignment is finished.
End of Semester Final Exam : 20% of semester
Dual credit students only: 25% of semester (for the grade submitted to IPFW)
C H S Grade
Scale
98-100 A+
94-97 A
91-93 A-
88-90 B+
84-87 B
81-83 B-
78-80 C+
74-77 C
71-73 C-
68-70 D+
64-67 D
60-63 D-
59
–Below F
Absent for a Test or Quiz: When a student is absent the day a test or quiz is given, the student is expected to take the test or quiz immediately upon their return. If many days were missed, discuss with me when the test will be taken. It is best if the test can be made up during study hall or before/after school.
Absent/Late Work Policy: Students are responsible for gathering missed work on their first day back to school whether they have class or not (block days). Any quiz or test taken on the day of absence should be made up immediately upon return. If multiple days were missed, discuss timing of make-up tests with me.
Class Expectations: 1. In the room when the bell rings.
2.
Actively take part in all discussions, examples and notes.
3.
Keep track of grades, check it on-line often.
4.
Have appropriate supplies daily
textbook, paper, pencil , Graphing Calculator
Online Resources: CalcChat.com (solutions to odd numbered book problems)