BOLSA GRANDE

Mr. Aviles Calculus AB

I.  COURSE DESCRIPTION: An introduction to Analytic Geometry and the differential and integral calculus of the elementary functions. Included is a study of limits, continuity, differentiation, applications of derivatives, anti-derivatives, integration, exponential, logarithmic and trigonometric functions.

II.  COURSE OBJECTIVES: To prepare students for the AP calculus AB form exam.

III.  STUDENT RESPONSIBILITIES: You will be expected to attend class every day. The intensive nature of the course makes attendance a must. You are expected to take notes on a daily basis (you will receive a grade for it). Homework will be assigned everyday (about two hours per day) and will be collected the next day.

IV.  CLASSROOM RULES:

a)  Respect others. This includes not talking while the teacher or someone else is talking, speaking kindly to others, and not putting people down.

b)  Raise hand to speak. While teacher is talking students are to remain silent until called upon to speak.

c)  Follow directions the first time given.

d)  Treat all materials in the classroom with care. If students damage calculators, computer or other materials, the parent or students will be financially responsible for the replacement of the item.

e)  Cheating on a test will result in an “F” on that particular test, “U” for citizenship, and possibly an “F” in the class. To avoid any problems, stay focused on your test; don’t look sideways; don’t have anything around you but your pencil, scratch paper and calculator when permitted.

V. TEST AND QUIZZES: Tests and quizzes will be given about once every 7 days. Grades will be determined in the following manner (Teacher reserves the right to make changes).

1st Semester

VI. GRADING SCALE:

2nd Semester

Course Overview

My main objective in teaching AP Calculus AB is to enable students to appreciate the beauty of calculus and receive a strong foundation that will give them the tools to succeed in future mathematics courses. Students know that they will be challenged, and their hard work will enable them to succeed in the course. We work together to discover the joys of calculus.

Instructional Materials

Calculus of a Single Variable, 6th edition, Larson, Hostetler, Edwards, 1998 by Houghton Mifflin Company

Slope Fields Supplementary Materials

Graphing Calculator TI-83,TI-84, TI-89 or equivalent.

Course Planner

First Quarter:

Sections / Topics
1.1 / What is calculus
1.2 / Finding limits graphically and numerically
1.3 / Evaluating limits analytically
1.4 / Continuity and one-sided limits
1.5 / Infinite limits
2.1 / Definition of derivative and tangent line problem
2.2 / Basic differentiation rules and rates of change
2.3 / Product rule, quotient rule, and higher-order derivatives
2.4 / Chain rule and composite functions
2.5 / Implicit differentiation
2.6 / Related rates

Second Quarter:

3.1 / Extrema on an interval
3.2 / Mean value theorem
3.4 / Increasing and decreasing functions
The First Derivative Test
3.5 / Concavity
The Second Derivative Test
3.6 / Limits at infinity (Horizontal Asymptotes)
3.7 / Summary of curve sketching
4.1 / Optimization
4.2 / Anti-derivative and indefinite integrals
Differential equations
Slope fields

Third Quarter

4.3 / Riemann Sums
Definite integrals
4.4 / Fundamental Theorem of Calculus
Mean Value Theorem for integrals
Second Fundamental Theorem of Calculus
4.5 / Integration by substitution
4.6 / Trapezoidal Rule
5.1 / Natural Log Function and differentiation
5.2 / Natural Log Function and integration
5.3 / Inverse functions and derivatives
5.4 / Natural Exponential Functions: differentiation and integration
5.5 / Bases other than e and applications
5.6 / Exponential growth and decay
5.7 / Integration by separation of variables
5.8 / Inverse trig functions and differentiation
5.9 / Inverse trig functions and integration
6.1 / Area between curves
6.2 / Volume – Disc and Washer Methods

After the AP Exam

Teachers’ choices include topics such as Shell method to find volume, L’Hopital’s Rule, integration by parts, sequences and series, projects that apply and reinforce earlier calculus concepts, and investigation of new ideas.

Students Evaluation and Activities

Students will be engaged in activities, experiences, and/ or projects that include:

∙ Investigating functions, graphs, limits, derivatives and integrals.

∙ Comparing functions represented graphically, numerically, analytically, and verbally and make the connections among these representations