Math 0901 Basic Algebra
Self-Guided Review of Algebra
This is the website containing the materials I used when I taught Math 901 at UMM fall 2009. If you wish to review algebra over the summer with the intent of retaking the math placement exam and starting in precalculus in the fall, you can use the materials on this website to structure your review.
You can buy the text to have additional problems to work on and additional explanations--but that is NOT absolutely necessary: you can use the purplemath website and Notes and Examples below as your text. You can do the homework problems, the practice tests, and read purple math and my course handouts for more information.
My advice would be to look over the Notes and Examples for each topic, practice with some of the Homework Examples, then try the Practice Test. If you feel you need more practice, work through some more problems from the Homework Examples (the Homework Examples show the steps of the solution, whereas the Practice Tests just have the final answer). Your goal is to be able to answer all the question on the Practice Test correctly without using any notes or aids other than a calculator (and ideally you would rarely use the calculator).
Most people learn math best in a cyclical manner--we learn something, forget it, relearn it, and continue that process. With each relearning the concepts should come back to you quicker, and ultimately you will master the concepts (meaning you can use the concepts at will, when needed, to solve problems). Do not be afraid to look back at previous units for a refresher if you need to!
One final note: you may have learned alternate ways to solve some of these problems. Feel free to use the techniques you are comfortable with even if they are not the techniques I suggest here.
| Topic |
PurpleMath Lectures |
Examples |
Resources |
| 1: Prealgebra Review
|
 factoring numbers
fractions
decimals, fractions, and percents
|
0.1 Simplifying Fractions
0.2 Adding, Subtracting Fractions
0.3 Multiplying, Dividing Fractions
0.5 Percents
|
Notes and Examples
Practice Test
|
| 2: Real Numbers and Variables
|
order of operations
absolute value
negative numbers
exponents
simplifying with exponents
simplifying parentheses
|
1.1 Adding Real Numbers
1.2 Subtracting Real Numbers
1.3 Multiplying, Dividing Real Numbers
1.4 Exponents
1.5 The Order of Operations
1.6 The Distributive Property
1.7 Combining Like Terms
1.8 Substitution to Evaluate Formulas
1.9 Simplifying Parentheses
|
Notes and Examples
Practice Test
|
| 3: Equations and Inequalities
|
solving linear equations
word problems
solving linear inequalities
|
2.1 The Addition Principle
2.2 The Multiplication Principle
2.3 Addition, Multiplication Principles Together
2.4 Solving Equations with Fractions
2.5 English to Algebraic Expressions
2.6 Word Problems
2.7 Word Problems: Geometric Formulas
2.8: Solving Linear Inequalities
|
Notes and Examples
Practice Test
Solving Literal Equations
|
| 4: Graphing Linear Equations and Inequalities
|
slope and graphing
straight lines equations
graphing linear inequalities
|
3.1 Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 The Slope of a Line
3.4 Writing Equation of Line
3.5 Graphing Linear Inequalities
|
Notes and Examples
Practice Test
Interactive Practice for Graphing Line
Interactive Practice with Linear Inequalities
Calories | Sols
|
| 5: Systems of Linear Equations and Inequalities
|
systems of linear equations
systems of linear inequalities
|
4.1 Systems Linear Equations in Two Variables
4.3 Applications of Systems
4.4 Systems of Linear Inequalities
|
Notes and Examples
Practice Test
Linear Systems in Chemistry
|
| 6: Exponents and Polynomials
|
rules of exponents
polynomials
polynomials: adding
polynomials: multiplying
polynomials: dividing
|
5.1 Rules of Exponents
5.2 Negative Exponents
5.3 Fundamental Polynomial Operations
5.4 Multiplying Polynomials
5.5 Multiplying Special Cases
5.6 Dividing Polynomials
|
Notes and Examples
Practice Test
Exponents in Chemistry
FYI: Pascal`s Triangle
|
| 7: Factoring Part I
|
simple polynomial factoring
factoring quadratics
|
6.1 Removing a Common Factor
6.2 Factoring by Grouping
6.3 Factoring x2 + bx + c
6.4 Factoring ax2 + bx + c
|
Notes and Examples
Practice Test
|
| 8: Factoring Part II
|
special factoring formulas
solving quadratics
(first page by factoring only at this point)
|
6.5 Special Cases of Factoring
6.6 Factoring Review
6.7 Solving Quadratic Equations by Factoring
|
Notes and Examples
Practice Test
|
| 9: Rational Expressions
|
simplifying rational expressions
multiplying rational expressions
adding rational expressions
|
7.1 Simplifying Rational Expressions
7.2 Multiplying, Dividing Rational Expressions
7.3 Adding, Subtracting Rational Expressions
|
Notes and Examples
Practice Test
|
| 10: Rational Equations
|
complex fractions
solving rational equations
ratios and proportion
|
7.4 Complex Rational Expressions
7.5 Solving Equations Involving Rational Expressions
7.6 Ratios and Proportion
|
Notes and Examples
Practice Test
Ratio and Proportion in Chemistry
|
| 11: Rational Exponents and Radicals
|
rational exponents
introduction to function notation
domain and range
radicals
(including rationalizing denominator)
|
8.1 Rational Exponents
8.2 Radical Expressions and Functions
8.3 Adding, Subtracting Radicals
8.4 Multiplying, Dividing Radicals
|
Notes and Examples
Practice Test
Functional Notation
Radicals in Geology
|
| 12: Radical Equations
|
solving radical equations
complex numbers
variation
solving absolute value equations
solving absolute value inequalities
|
8.5 Radical Equations
8.6 Complex Numbers
8.7 Variation
9.7 Absolute Value Equations and Inequalities
|
Notes and Examples
Practice Test
|
| 13: Quadratics
|
completing the square
the quadratic formula
the vertex form
|
9.1 Quadratic Equation
9.2 Quadratic Formula
9.3 Transforming into Quadratic
9.4 Applications of Quadratics
9.5 Sketching Quadratics
|
Notes and Examples
Practice Test
Quadratic Formula in Chemistry
|
| 14: Logarithms
|
logarithms
solving exponential equations
solving logarithmic equations
|
|
Notes and Examples
|
