The Advanced Placement Calculus AB course follows the Advanced Placement syllabus and students may take the AP test in May. Course study will include properties of functions, limits, differential calculus, and integral calculus. Use of symbolic differentiation and integration utilities is also included.

The main focus is a solid background in material needed to indicate good preparation for the Advanced Placement Calculus Test (AB) in the morning of Wednesday May 3, 2006. The test will consist of 45 multiple-choice questions, most involving some computation, and 6 free-response questions, equally weighted. For 28 multiple-choice questions in 55 minutes, no calculator is allowed. For the other 17 multiple-choice questions in 50 minutes and the first half of the free-response section (45 minutes), a graphing calculator with certain features is assumed. For the second half of the free-response section (45 minutes), the calculator will no longer be permitted. Total test time is now three hours and fifteen minutes. The free-response questions are scored on content and presentation of the solution and the scores for both parts are combined to produce a raw score and then an index from 1 (no recommendation) to 5 (extremely well-prepared). Most colleges and universities will grant one semester's credit for a score of 3 or better. All are expected to take the Advanced Placement Calculus Test, although a fee of $84 (including a $7 deposit about late Feb.) is required. Testing will occur again this school year at the Intermediate School District Offices beginning promptly at 8 am. Either the Calculus AB or Calculus BC can be taken—not both. (Note: The college Freshman Calculus, (Calc I & II or MATH141 & 142) for the well-prepared student may be an option but might also produce scheduling conflicts.)

Although our AP Calculus BC course is developing as a follow on to our AP Calculus AB course, many places offer it as a one year alternative to AP Calculus AB for well-prepared, motivated students. The major component of this course is a complete first year college Calculus. Students will review and extend their knowledge of algebra, geometry, trigonometry, calculus, and other areas as appropriate for contest preparation. Students study differentiation, integration, and other calculus topics. Proficiency using the TI-89 (TI-83+) Graphing Calculator is expected. The main focus is a solid background in material needed to indicate good preparation for the Advanced Placement Calculus Test (BC) in the morning of Wednesday, May 3, 2006. The test and fees will be composed as described above for the AB test. Most colleges and universities will grant two semester's credit for a score of 3 or better on the AP Calculus BC test. See above for testing date, location, restrictions, etc. About 40% of the BC test will be BC topics only. A separate AB subscore will now be provided.

Textbooks

Larson, Roland E.; Hostetler, Robert P.; Edwards, Bruce H. Calculus of a single variable. D.C. Heath and Company, Lexington, MA, 1994. This textbook is 10 chapters and we emphasize the first six. It actually is a subset of the 16 chapter version described below for AP Calculus BC.

Lederman, David. Multiple Choice Questions (and Solutions) in Preparation for the AP Calculus (AB) Examination, 7th edition. D & S Marketing Systems, Inc., New York, 1999.

Larson, Roland E.; Hostetler, Robert P.; Edwards, Bruce H. Calculus. D.C. Heath and Company, Lexington, MA, 1995.

Lederman, David. Multiple Choice Questions (and Solutions) in Preparation for the AP Calculus (BC) Examination, 6th edition. D & S Marketing Systems, Inc., New York, 1999.

Course Objectives

Review of Prerequisites, 2 weeks, Chapter 0

1. Real Numbers and the Real Line
2. The Cartesian Plane
3. Graphs of Equations
4. Lines in the Plane
5. Functions
6. Trigonometric Function Review

Limits and Their Properties, 3 weeks, Chapter 1

1. An Introduction to Limits
2. Properties of Limits
3. Techniques for Evaluating Limits
4. Continuity and One-Sided Limits
5. Infinite Limits

Differentiation and its application, 4 weeks, Chapter 2

1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rates of Change
3. The Product/Quotient Rules, Higher-Order Derivatives
4. The Chain Rule
5. Implicit Differentiation
6. Related Rates

Differentiation and its application, 5 weeks, Chapter 3

1. Extrema on an Interval
2. Rolle's Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test
4. Concavity and the Second Derivative Test
5. Limits at Infinity
6. A Summary of Curve Sketching
7. Optimization Problems
8. Newton's Method
9. Differentials
10. Business and Economic Applications—extra-credit

Integration, 5 weeks, Chapter 4

1. Antiderivatives and Indefinite Integration
2. Area
3. Riemann Sums and Definite Integrals
4. The Fundamental Theorem of Calculus
5. Integration by Substitution
6. Numerical Integration

Log, Exp, and Other Transcendentals, 6 weeks, Chapter 5

1. The Natural Logarithmic Function and Differentiation
2. The Natural Logarithmic Function and Integration
3. Inverse Functions
4. Exponential Functions: Differentiation and Integration
5. Bases Other than e and Applications
6. Differential Equations: Growth and Decay
7. Inverse Trigonometric Functions and Differentiation
8. Inverse Trigonometric Functions: Integration and Completing the Square
9. Hyperbolic Functions

Integration Applications, 3 weeks, Chapter 6

1. Area of a Region Between Two Curves
2. Volume: The Disc Method
3. Volume: The Shell Method
4. Arc Length and Surfaces of Revolution
5. Work—extra-credit
6. Fluid Pressure and Fluid Force—extra-credit
7. Moments, Centers of Mass, and Centroids—extra-credit

Integration Techniques, 3 weeks, Chapter 7

1. Basic Integration Rules
2. Integration by Parts—especially important
3. Trigonometric Integrals
4. Trigonometric Substitution
5. Partial Fractions—especially important
6. Tables and Other Techniques
7. L'Hôpital's Rule—especially important
8. Improper Integrals—especially important

Review for and take the AP test; Senior Grades Due