Class Description

Advanced Math is an intensive review of the topics from algebra, trigonometry and analytic geometry that are necessary for success in calculus. We cover in depth all the topics normally taught in the first two semesters of a three-semester college calculus sequence.

The course is designed for students who are interested in mathematics, life sciences, physics, business or engineering. It can be very useful for those who do not have plans on pursuing college majors in science or business.

Class Expectations

Daily Assignments:

1. Assignments will be given daily.
2. Assignments will be corrected the following day by the student so they can receive immediate feedback on how they are doing.
3. Assignments are always passed in and scored by the teacher and not returned to the student.
4. Credit for the daily work is primarily given for the effort and amount of work shown.
5. Most students average 40 minutes a day on the daily work.

Tests:

1. Tests are given after every fourth or fifth lesson.
2. Grades will be determined by the accuracy of answers and the work shown.

Final Grade:

1. The nine weeks grade is determined by having daily work counting 15% and test grades counting 85%..
2. The semester grade is calculated as follows: first nine weeks 40%, second nine weeks 40%, and the semester exam 20%.

Class Outline

1. Quadratic Relations
   • Parabolas
   • Circles
   • Ellipses
   • Hyperbolas
   • Translations
2. Sequences and Series
   • Mathematical Patterns
   • Arithmetic
   • Geometric
   • Area Under a Curve
3. Periodic Functions and Trigonometry
   • Radian Measure
   • Sine, Cosine, and Tangent Functions
   • Trigonometric Identities
4. Limits
   • Constants
   • Infinity
   • Zero
   • Undefined
   • Sums, Differences, Products, & Quotients
5. Derivatives
   • Development by definition
   • Constant Multiple Rule
   • Sums, Diff., Products, & Quotients
   • Implicit Differentiation
   • Applications of 1st Derivative
     • Maximizing & Minimizing
     • Graphing
     • Related rate Problems
   • Chain Rule
   • Trig Functions
   • Differentials
   • 1st vs 2nd Derivatives
   • Applications of 2nd Derivatives
     • Graphing
     • Change in Rate - Distance vs Velocity vs Acceleration
6. Anti-derivatives
   • Integration
   • Sums, Differences, Products, and Quotients
   • Riemann Sum
   • The Definite Integral
   • Fundamental Principles of Calculus
   • Integration by Parts
   • Volume of Solids
   • Work Applications