ELEMENTARY & INTERMEDIATE 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: Elementary Algebra. This section of material only is downloadable for nominal fee at www.lulu.com/content/431016. See "Tell me more about Keely's GM book".
Introduction to Algebra
GOLDen Mathematics - Elementary Algebra: Section 1.1
Supplemental Sites: MathOL Links - Alg 1.1
Topics of Importance
Terminology: variable, constant, algebraic expression, term,
coefficient, equivalent expression, equation, solution
Evaluate algebraic expressions
Check if a given value is actually a solution to an equation
Translate words into an algebraic expression or equation
Model real-life data with an algebraic equation
Laws of Algebra: commutative, associative
Collecting "like terms"
Distributive law (forward and backward)
Applying order of operations to simplify an expression
Factoring via the dist law; "factors" vs. "terms"
Comments and Cautions
This lesson covers the basic processes of simplifying algebraic expressions.
The two most important of these is the "distributive law" and "collecting like
terms". Take your time with these and pay close attention to the signs. There is
lots of new terminology to learn. One caution to note is the difference between
an "algebraic expression" and an "algebraic equation". The former may be able to
be simplified but can never be solved. But an equation contains an equals sign
and can therefore be solved (and the answer checked by substitution). Another
caution is that when you
do check a solution in an equation (or evaluate an expression for a given value)
be sure to substitute the value in using parentheses or you may make sign
errors. E.g., evaluating x2y given that x=-3 and y=-2 would be (-3)2(-2)=-18
and not -3^2*-2 (which would give the incorrect answer of 18).
Text Notes (These notes refer to Introductory & Intermediate Algebra for College Students 2nd ed by Blitzer sections 1.4 + 1.8.)
 | ch 1.3 SKIP for now. This section will be covered later in the course. |
| ch 1.4 pg 40-41 includes definitions of the commutative and associative properties. Personally I care more that you know how these rules work than what there names are. For instance it is important to know that x*y = y*x but not as important that this is the "commutative law of multiplication" (IMO). |
| ch 1.4 pg 43-46 covers the distributive property (a.k.a. distributive law), combining like terms (a.k.a. collecting like terms), and simplifying expressions. These three processes are the guts of chapter 1. Learn them well! This material is needed to build a strong foundation of beginning algebra skills |
| ch 1.8 Focus on working with exponents and using order of operations to simplify an expression. |
| ch 1.8 pg 86-88 exs 12-13. This text introduces some pretty heavy-weight applications and "mathematical models" right from the get go primarily to provide motivation for the algebra that you are beginning to learn. Try to follow all the steps, but your main focus should be the step of evaluating a given formula by plugging-in a given value for a variable. We will cover evaluating formulas and solving word problems in more detail throughout the course. |
The Real Number System and the Calculator
GOLDen Mathematics - Elementary Algebra: Section 1.2
Supplemental Sites: MathOL Links - Alg 1.2
Topics of Importance
Real numbers: rational vs. irrational
Convert decimal
fraction, repeating
decimal
fraction (by hand and on
calc)
"Opposite", "Reciprocal", and "Absolute Value" (by hand and on calc)
Exponents and roots (mostly on calc)
Order of Operations (by hand and on calc)
Prime factorization (by hand)
Reducing algebraic fractions (by hand)
Calculator keys: ->FRAC, NEG, x-1, ABS, ^, SQRT, XthROOT
Comments and Cautions
The graphing calculator is going to be an invaluable tool in this class.
With this lesson we learn about the Real Number System as well as how to perform
real number operations on a calculator. BTW, "Real numbers" are just all the
numbers that you are used to dealing with -- decimals, fractions, the irrational
number pi, etc. as opposed to "imaginary numbers" which we will learn about in
intermediate algebra. Be sure to work through my online Calculator
Guide: Basics of Arithmetic with your calculator at hand.
Text Notes (These notes refer to Introductory & Intermediate Algebra for College Students 2nd ed by Blitzer sections 1.1-1.2 + 1.5-1.7.)
| ch 1.1 + 1.5-1.7 should all be review from a pre-algebra class. Skim and review as needed. This material is fair game for the first quiz! |
| ch 1.2 Pay particular attention to table 1.1 which describes the different types of Real numbers and provides examples of each. Particularly be able to identify rational vs. irrational numbers. We will discuss converting repeating decimals to fractions in class. |
Originally written: 2006-006-15
Last revision:
2008-01-04 09:49 PM