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 purplemath icon factoring numbers
purplemath icon fractions
purplemath icon 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 purplemath icon order of operations
purplemath icon absolute value
purplemath icon negative numbers
purplemath icon exponents
purplemath icon simplifying with exponents
purplemath icon 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 purplemath icon solving linear equations
purplemath icon word problems
purplemath icon 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 purplemath icon slope and graphing
purplemath icon straight lines equations
purplemath icon 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 purplemath icon systems of linear equations
purplemath icon 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 purplemath icon rules of exponents
purplemath icon polynomials
purplemath icon polynomials: adding
purplemath icon polynomials: multiplying
purplemath icon 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 purplemath icon simple polynomial factoring
purplemath icon 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 purplemath icon special factoring formulas
purplemath icon 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 purplemath icon simplifying rational expressions
purplemath icon multiplying rational expressions
purplemath icon 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 purplemath icon complex fractions
purplemath icon solving rational equations
purplemath icon 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 purplemath icon rational exponents
purplemath icon introduction to function notation
purplemath icon domain and range
purplemath icon 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 purplemath icon solving radical equations
purplemath icon complex numbers
purplemath icon variation
purplemath icon solving absolute value equations
purplemath icon 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 purplemath icon completing the square
purplemath icon the quadratic formula
purplemath icon 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
purplemath icon logarithms
purplemath icon solving exponential equations
purplemath icon solving logarithmic equations
Notes and Examples

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The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.