V. “Logarithmic, Exponential, and Other Transcendental Functions”.
Chapter 5. AB 17 days.
A. Topics.
1. Differential and Integration of Any Logarithmic Functions
2. The Number e
3. The Natural Logarithmic Function – Differentiation and Integration
4. Inverse Functions
5. Differentiation of Inverse Functions
6. Exponential Functions: Differentiation and Integration
7. Solving Exponential Equations
8. Solving Logarithmic Equations
9. Bases other than e and their Applications
10. Compound Interest Formulas
11. Logistic Growth
12. Slope Fields
13. Differential Equations
14. Inverse Trigonometric Functions – Differentiation and Integration
15. *Enrichment: Hyperbolic Functions. Done after the AP exam.
a. Definitions
b. Identities
c. Differentiation and Integration
d. Inverse Hyperbolic
e. Differentiation and Integration of Inverse Hyperbolic Functions
B. Teaching Methods and Evaluations.
1. Each topic presented through lecture, student and group interaction, graphing calculator usage, projects, supplements, Power Point presentations, and assignments where applicable.
2. Teacher led and student involvement in the proofs of the Differentiation and Integration of Exponential and Logarithmic Functions through handouts and group work.
3. Exponential, Logarithmic, and Polynomial Function comparison graphically to compare rate of change.
4. Student mastery of differentiation and integration of exponential and logarithmic functions of base e and base a.
5. Functions and their Inverses. Teacher and student led presentation of the proofs of the Inverse Trig functions.
a. Student mastery of Integration related to the inverse trig functions.
b. Students solve differential equations related to trig inverse functions and draw their solutions using slope fields.
6 Supplements of Chapter 5:
a. Proofs of Logarithmic and Exponential Functions.
b. au and logau integration and differentiation.
c. Proofs of the derivatives of Inverse Trig Functions.
7 Evaluations.
a. Teacher created individual and group tests, individual and group projects.
b. Multiple Choice and Free Response questions of the College Board and Fast Track to a 5 listed in XI of the syllabus.
C. Assignments.
Text: Larson, Ron., Edwards, Bruce and Robert P.Hostetler. Calculus. Boston: Houghton Mifflin, 2006.
1. 5.1: Natural Logarithm and Differentiation. 1-33o( algebra 2 and pre-calculus review), 37, 41, 47, 49, 51, 57, 65, 69-97o.
2. 5.2: Natural Logarithm Differentiation and Integration. 5-91o. Supplements.
3. 5.3: Inverse Functions. 5, 7, 9-13, 19, 25, 35, 39, 43, 49, 51-63o, 71-81o.
4. 5.4: Exponential Functions - Differentiation and Integration. 3, 7, 13, 15, 21-24, 25, 27, 33, 37, 45-73o, 77, 83-115o, 128. Supplements. 5. 5.5: Bases other than e and Applications. 9-35o (review), 41, 43, 47-71o, 81-88, 89, 93, 95. Supplements. *E: 111, 112.
6. 5.6: Inverse Trigonometric Functions - Differentiation. 1-39 (review), 41, 45, 49, 51, 55, 61-77o, 91. Supplements.
7. 5.7: Inverse Trigonometric Functions - Integration. 1-67o. Supplements. Thinkfive 33.
8. *5.8: Hyperbolic Functions. 1-5o, 7-13, 15-89o. Supplements. *E: 103, 104.
9. Selected problems of AP Test Preparation of section XI and the College Board.
10. Fast Track to 5.
11. Free Response AP.
Parents and Students: Grading.
Major grades: (70%)
Daily grades: (20%). Fast Track; Class Presentations; Supplements; in Class Activities; Quizes; Free Response; Group work.
Homework grades: (10%). Assignments. (view Calendar)
Parents and students are to be aware that the student receives use of a solution key to the homework exercises and receives solutions to all supplements in class.
Grade Sheets issued 2 times per 6 weeks. Gradespeed is updated within 48 hours of an assignment and or test.
Teacher Website updated per week. Calendar of pace on the website/Calendar.
Teacher Contact: Use email, NOT Voice Mail please.
Student Signature: ______
Parent Signature: ______