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Lecture Notes and Sample Exams - Algebra


Lecture Notes and Worksheets

About Mathematics
The Words And and Or    
The Basic Operations
The Order of Operations Agreement    
Factors of a Number    
Perimeter and Area of Rectangles
Perimeter and Area of Right Triangles
Perimeter and Area of General Triangles
Perimeter and Area of Parallelograms
Area of Trapezoids
Circmference and Area of a Circle
Division with Remainder
Divisibility Tests
New! Is this Number a Prime?    
Prime Factorization    
The GCF and LCM
Algebraic Expressions
Equations and Inequalities
One- and Two-Step Equations (N)
Introduction to Signed Numbers
Subtracting Signed Numbers
Multiplying and Dividing Signed Numbers
The Set of All Integers

Division by Zero
Order of Operations on Integers
More Practice
    Part 1 - the definition
  Practice Quiz and Quiz
    Part 2 - Equivalent Fractions
    Part 3 - Improper Fractions and Mixed Numbers
    Part 4 - Adding and Subtracting Fractions
    Part 5 - Multiplying and Dividing Fractions
Introduction to Ratios
Basic Percent Problems   -  
Solving Two-Step Linear Equations
New! Introduction to Decimals
Fractions, Decimals, Percents - Conversions
Conversions between units of measurement
Standard labeling in triangles
Angles in a Triangle
New! Volumes
Decimals and Fractions

Beginning Algebra

Lecture Notes and Worksheets

The Set of All Natural Numbers
Introduction to Set Theory
The Set of All Integers
Order of Operations on Integers
Angles in a Triangle
New! Angles in a Polygon
Set Operations
Square Root of an Integer
Algebraic Expressions and Statements
Graphs of Equations     Examples - Answers
Combining Like Terms
Simplifying Algebraic Expressions over Z
One- and Two-Step Equations
Multiplying Algebraic Expressions over Z
Linear Equations - Part 2 (Z)
Equations with the Unknown on Both Sides
Solving Linear Equations - Part 2
Solving Linear Equations - Part 3
Weighted Average
Angles In a Triangle:   Theory - Problem Solving -
Solving Linear Inequalities
Linear Inequalities (practice)
Graphing Straight Lines
        Practice     Examples - Answers
Basic Percent Problems
Word Problems 1 (Linear)
Solving Linear Systems by Elimination
Solving Linear Systems by Substitution
Slope of a Line
More on Linear Systems
The Zero Product Rule
Factoring out the GCF
Factoring via the difference of squares theorem
Factoring by Trial and Error
Factoring by Grouping
Factoring by the AC-method - Practice
Rational Expressions
Factoring the Sum and Difference of Cubes
Factoring the difference of cubes (Practice)
Factoring the sum of cubes (Practice)
The Pythagorean Theorem
Quadratic Word Problems (Algebra 1)
Rules of exponents (formulas only)
Natural Exponents
Integer Exponents
Sample Exams

Exam 1 Review
Exam 2 Review
Exam 3 Review
Exam 4 Review - Version A
Exam 4 Review - Version B

Intermediate Algebra

Lecture Notes and Worksheets

Introduction to Intermediate Algebra
Introduction to Sets
Set Operations
More on Sets
Introduction to Combinatorics
Introduction to Number Theory
The nth Root of a Number
Simplifying Algebraic Expressions over Z (no FOIL)
One- and Two-Step Equations
Review of Linear Equations over (Z)
Summation 1     Part 1,   Part 2,   Part 3
Simplifying Algebraic Expressions (with FOIL)
More Linear Equations
Factoring by completing the square   Part 1   Part 2   Part 3   Part 4
Review of Factoring (GCF, difference of squares theorem)
Review of Factoring 1 (GCF, difference of squares, completing the square)
Review of Factoring 2 (grouping, AC-method, sum and difference of cubes)
Quadratic Word Problems (Algebra 2)
Solving Linear Systems by Elimination
Linear Word Problems
Mixture Problems
Motion Problems
The Triangle Inequality
The Pythagorean Theorem
Similar Triangles
Writing Equations of Straight Lines
Compound Inequalities
Smallest Value of a Quadratic Expression
Graphing a Parabola - Part 1 - Practice (Z) or Practice (R)
Graphing a Parabola - Part 2
Rational Expressions
Complex Fractions
Radical Expressions - Part 1
Radical Expressions - Part 2
Radical Expressions (1 and 2)
Radical Equations
Absolute Value Equations
Rational Expressions - Part 1
Rational Expressions - Part 2
Rational Equations
Systems of Equations in Three Variables
The Real Number System (N to Z to Q to R)
The Real Number System (axioms)
The Quadratic Formula
The proof that square root of 2 is irrational
Rules of Exponents
Rational Exponents
Work Word Problems
Digit Word Problems
Complex Numbers
New! Tangents to Circles

Fun, Challenging Problems:
Algebraic Transformations

Sample Exams Updated!

Exam 1 Review
Exam 2 Review
Exam 3 Review
Final Review - Version A
Final Review - Version B

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This page was last updated on October 14, 2023. Questions, comments: please e-mail to