COLLEGE ALGEBRA
These brief notes are intended to guide you through the textbook and/or other course readings/materials. As you read the textbook pay particular attention to the "topics of importance" and be sure you know how to accomplish each. The "supplemental sites" may provide additional resources on the internet that supplement the topics. Note: this material is extensively elaborated upon in my optional e-book GOLDen Mathematics: College Algebra. This section of material only is downloadable for a nominal fee at www.lulu.com/content/432136. See "Tell me more about Keely's GM book".
Advanced Equations
Textbook correspondence: Chapter 1.6
GOLDen Mathematics - College Algebra: Section 1.1
Supplemental Sites:
MathOL Links - Calg 1.1
Topics of Importance
Polynomial equations by factoring, quadratic formula, etc.
Radical and fractional exponent equations
Absolute value equations
Solving equations using a substitution
Comments and Cautions
This chapter brings together a culmination of equation solving skills from
elementary/intermediate algebra then kicks it up a notch in preparation for
calculus. Be sure to practice all the types: polynomial, rational, radical,
fractional exponent, absolute value. Think about how to recognize when the
substitution method is useful. Concentrate on solving equations algebraically,
but you should also be able to solve graphically. "Checking" your algebraic
answers by graphing to solve is great practice! Reading my online
Graphing Calculator
Guide: x-Intercept Points and
Graphing
Calculator Guide: Intersection Points may be useful.
One caution regarding solving radical equations: You must ALWAYS CHECK your answers when you even-power both sides of a radical (or fractional exponent) equation due to the potential for extraneous solutions.
Text Notes (These notes refer to College Algebra 5th ed by Blitzer section 1.6.)
 | ch P and 1.1-1.5 should all be review from an elementary/intermediate algebra course. Skim and review as needed. |
| ch 1.6 ex 6 Try working without using substitution but instead by factoring directly. |
| ch 1.6 ex 7 Try working without using substitution but instead by factoring directly using fractional exponents in your factors. This is a good skill to practice before calculus. |
Compound and Absolute Value Inequalities
GOLDen Mathematics - College Algebra: Section 1.2
Supplemental Sites:
MathOL Links - Calg 1.2
Topics of Importance
Algebraically solving compound inequalities: “and”, “or”,
double
Solving compound inequalities graphically
Solving absolute value inequalities
Comments and Cautions
Before covering compound inequalities (the "and" intersection
kind, the "or" union
kind, the "double" inequality kind,
I strongly recommend that you review linear inequalities from an elementary algebra
course (see the supplemental sites for some resources). The reason being that
|x-2|=3 means x-2=3 OR x-2=-3. Similarly |x-2|<3 means -3<x-2<3 and |x-2|>3
means x-2<-3 OR x-2>3. See how absolute values inequalities reduce down to
"double" or "or" type compound inequalities?
Text Notes (These notes refer to College Algebra 5th ed by Blitzer section 1.7.)
| ch 1.7 is pretty straightforward. Be sure to practice solving graphically as well as algebraically. |
| ch 1.7 pg 174 has a good review of interval notation vs. inequality notation vs. graphing solutions on a number line. Interval notation is the notation most commonly used to express answers to inequalities in calculus. |
| ch 1.7 Concentrate on combining the compound inequalities, especially the "or" vs "and" kind, down into a single interval where possible. |
Polynomial and Rational Inequalities
GOLDen Mathematics - College Algebra: Section 1.3
Supplemental Sites:
MathOL Links - Calg 1.3
Topics of Importance
Solving polynomial and rational inequalities algebraically
by the sign chart method or test point method
Solving polynomial and rational inequalities graphically
Comments and Cautions
In Calculus I you are required to solve polynomial and
rational inequalities on f(x), f'(x) (the first derivative of f), and f"(x) (the
second derivative of f) all in one problem. So becoming proficient in the solving inequalities will be really be helpful!
The "sign chart" method of solving these inequalities is the most efficient and
reliable, but most texts use a "test point" method instead. Either
works and we can compare and contrast the methods in class. Be sure that you can
solve polynomial and rational inequalities both algebraically and graphically.
Be sure that you can write solutions in interval notation (the most common way
in Calculus), inequality or "set builder" notation, and graph solutions on a
number line.
Text Notes (These notes refer to College Algebra 5th ed by Blitzer section 3.6.)
| Yes we do jump up temporarily to chapter 3.6! |
| ch 3.6 example 4 includes the "position function" which you can skip this at this time. We'll pick it up after we cover graphs of quadratic functions (parabolas) in more detail. But the rest of this section is very important and takes some time to work through. Plan to practice solving a variety of polynomial and rational inequalities both algebraically and graphically! |
Originally written: 2006-09-04
Last revision:
2009-09-21 11:37 AM