Precal Review/Preview, Session 2

Schedule: We will meet for two weeks, five days a week, 1.5 hours per day. (15 hours total.)

Format: An intro course to prep for a semester of precal, with lecture to cover concepts, and lots of class interaction and individual practice. We will learn concepts and practice them to attain the mastery we can in a short time, in preparation for a longer, graded course during a school year. No grading; homework is optional.

Cost: $250 per person for a group class of 4 or more students; $935 for one-on-one tutoring.

Payment options: Payments can be made via PayPal, Venmo, Zelle, cash, or check.

Materials: A graphing calculator like a TI-84, TI-89, HP Prime, or Casio is recommended. No text. We’ll use free worksheets on the Internet for homework and supplements.

For more details or to schedule a class, contact Michael by email at michaelgold@goldams.com or by phone at 281-770-2276.

Class Description.

We will learn some precal (analysis) and will work on developing a real understanding of mathematics.

We will have a mix of lecture, Q&A, and in-class work. We will have some interactive lecture in which students practice concepts and techniques as we go. Everyone will get a chance to ask and answer questions, get feedback, and check their understanding.

You will get some class notes posted everyday on Outschool (you will need to take some of your own notes!), some optional extra reading for understanding, and lots of optional practice work. All classes on Outschool are recorded, so you can watch ones you might have to miss and watch class over again to take notes or review.

Topics

1. Analyzing Graphs
2. Working with Functions
3. Exponential and Logarithms
4. Conic Sections
5. Parametric Equations
6. Polar Coordinates and Graphing
7. Analyzing Functions
8. Sequences and Series

Tentative schedule
Week 1
Day 1: polynomials; transformations of functions; increasing, decreasing, and constant; relative and absolute minima and maxima; roots
Day 2: composition of functions; inverse functions; even and odd functions; piecewise and greater integer functions
Day 3: polynomial and rational functions’ end behavior; complex zeroes; difference quotient
Day 4: exponential and logarithmic functions; growth and decay
Day 5: conic sections: circle, ellipse, parabola, hyperbola

Week 2
Day 6: parametric equations; polar coordinates
Day 7: polar coordinates; polar functions and graphing
Day 8: polar coordinates; polar functions and graphing
Day 9: vectors; partial fraction decomposition; binomial theorem
Day 10: sequences & series

Learning Goals.
To understand how to analyze graphs of functions.
To understand how to analyze functions.
To understand parametrics.
To know how polar coordinates work and to be able to graph in them.
To understand sequences and series.
To be prepared for a year-long course in precalculus.
To understand some foundations of calculus.
To understand how precal is useful to fields like physics, chemistry, and biology.
To learn some logic and thinking skills that will help all through life in all areas of life.