CalculusAB
2008 - 2009
Brief Description of Course
We cover everything in the Calculus AB topic outline as it appears in the AP Calculus Course
Description. We also all cover topics required by the University of Southern Maine. Students
completing this course receive four collge credits from USM in CalculusAB. The primary textbook is
"Concepts and Calculators in Calculus" Second Edition, 2006 by George Best, Stephen Carter, and
Douglas Crabtree. The publisher is Venture Publishing. I also use, "Calculus with Analytic
Geometry",Eighth Edition, 2006 by Ron Larson, Robert P Hostetler, and Bruce H. Edwards as a
supplement. The objectives of this course are to prepare students for the AP Exam and to prepare
students for CalculusBC at any college, which means that the student needs to perform all operations
found in CalculusAB with and without a graphing calculator. In 95% of the classes, students are
expected, when applicable, to be able to solve problems without a calculator as well as with a
calculator using graphs, tables and the applicable special functions found on the TI-83 or the TI-84
Calculator. Students are expected to have their own graphing calculator; however, if a student cannot
provide his/her own calculator the school signs out to the student a TI-83 calculator for the year.
Classes meet twice a week for 80 minutes and once a week for 40 minutes.
Unit Information
Unit Name or Timeframe:
First Semester CalculusAB
Chapter/section numbers Topics Time
1.1-1.2 Basic Functions and Transformations 1 day
1.3 Linear Functions and Mathematical Modeling 1 day
1.4-1.5 Exponential Functins Compound Interest and the Number"e" 1day
1.6-1.7 Inverse Functions and Logarithms 1 day
1.8 Combining Functions: Polynomial and Rational Functions 1 day
1.9 Compostions of Functions 1 day
1.10 Trigonometric Functions 1 day
Review 1.1-1.10 Supplementary Problems 2 days
Evaluation Test, Homework, and Notes 1 day
2.1-2.2 Averag and Instantaneous Velocity, The Derivative of a Function at a Point 1 day
2.3 The Derivative Function 1 day
2.4 Calculating the Derivative Numberically 1 day
2.5 Critical Numbers: Relative Maximum and Relative Minimum 1 day
2.6 Inflection Points and the Second Dervivative 1 day
2.7 The Limit Function 2 days
2.8 Continuity 1 day
Review 2.1-2.8 Supplementary Problems 2 days
Evaluation Test, Homework and Notes 1 day
3.1 Calculating Distance Travelled 1 day
3.2 Calculating Riemann Sums 1 day
3.3 Definate Integrals 1 day
3.4 The Fundamental Theorem of Calculus 1 day
1
Review 3.1-3.4 Supplementary Problems 1 day
Evaluation Test, Homework and Notes 1 day
4.1 Derivative Rules for the Basic Functions 1 day
4.2 Differentiating Exponential Functions 2 days
4.3 The Product and Quotient Rules 2 days
4.4 Derivatives of Composite Functins; the Chain Rule 3 days
4.5 Functions Defined Implicitly 2 days
4.6 Related Rates 3 days
4.7 Approximations 2 days
Review 4.1-4.7 Supplementary Problems 2 days
Evaluation Test, Homework and Notes; Project if Elected 1 day
5.1 Increasing and Decreasing Functions 1 day
5.2-5.3 Applications of the Second Derivative, Limits Involving Infinity 1 day
5.4-5.5 Using Calculus to Solve Optimization Problems, the Mean Value Theorem 1 day
5.6 Antiderivatives 1 day
Review Supplementary Problems 2 days
Evaluation Test, Homework 1 day
Review 1.1-5.6 Selected Problems 1 day
Evaluation Mid-Year Exam 1 day
Second Semester
6.1 The Definite Integral Again 1 day
6.2 Functions Defined by Integrals; Accumulation Functions 1 day
6.3 The Fundamental Theorem Again 1 day
6.4 Area of Plane Regions 1 day
Review 6.1-6.4 Supplementary Problems 1 day
Evaluation Test, Homework 1 day
7.1 Antiderivatives 1 day
7.2 Integration Using the Chain Rule 1 day
7.3 The Method of Substitution 2 days
7.4 Integration by Parts 2 days
7.5 The Trigonometric Functions and Their Inverses 2days
7.6 Numberical Integration 2 days
Review 7.1-7.6 Supplementary Problems 2 days
Evaluation Test Homework 1 day
8.1 Net and Total Distance Travelled 1 day
8.2 Volumes by Slicing 2 days
8.3 the Shell Method 1 day
8.4 Average Value Function 1 day
8.5 More Applications of the Definite Integral 2 days
Review 81-8.5 Supplementary Problems 2 days
Evaluation Test, Homework 1 day
9.1-9.2 Solving Differential Equations Graphically; Slope Fields 1 day
9.3 Solving Differential Equations Numerically: Euler’s Method 1 day
9.4 Solving Differential Equations Symbolically: Seperation of Variables 2 days
Review 9.4-9.4 Supplementary Problems 1 day
Evaluation Test, Homework 1 day
Review 1.1-9.4 Selected Problems 2 days
Evaluation Exam 2 days
2
Major Assignments and/or Assessments:
Students are assigned homework from the chapter and section(s) covered each class. The homework
counts for 20% of the quarter grade.
Students are given quizzes each quarter. The quizzes are averaged and count as one test grade.
Students will keep a portfolio. A portfolio must contain the following: class notes, textbook
notes, tests and quizzes.
Class participation is graded.
At the end of the quarter the tests, quiz average, and portfolio average are calculated, averaged
together and accounts for 75% of the quarter grade. Homework accounts for 20% of the quarter grade
and class participation accounts for 5% of the quarter grade.
A mid-year exam is given and it counts for 20% of the first semester grade. The first and second
quarter grades each count for 40% of the semester grade
Second semester grades are calculated using the same process as the first semester grade. The two
semester grades are then averaged for the year grade.