The textbook is no longer required for this class. All of the course content
comes from the lectures and the Student Workbook. This course was originally based on
Algebra, Structure and Method, Book 1 by Dolciani, Brown, Sorgenfrey, and Cole,
published by McDougal Littell, 2000 edition. The topics covered in this course will
correspond closely to the topics covered in this book, although the explanations in the
lectures are expanded over those in the book, at times significantly.
If needed, a copy of the textbook can be provided as a reference and as a source of
additional practice problems.
These topics comprise the material normally taught in a high school Algebra 1 course.
- Chapter 1: Introduction
Variables, Order of Operations, Equations, Translating Words into Symbols and Equations, An Approach to Problem Solving
- Chapter 2: Real Numbers
Basic Assumptions, The Number Line, Addition and Subtraction, The Distributive Property, Multiplication, Reciprocals, Division of Real Numbers
- Chapter 3: Solving Equations
Balancing Equations with Addition and Subtraction, Balancing Equations with Multiplication and Division, Solving Equations in Multiple Steps, Equations with Variables on Both Sides, Problem Solving using Charts
- Chapter 4: Polynomials
Exponents, Addition and Subtraction of Polynomials, Multiplying Monomials, Powers of Monomials, Multiplying Polynomials, Formulas, Distance-Rate-Time Problems, Area Problems, Problems with No Solutions
- Chapter 5: Factoring
Factoring Integers, Dividing Monomials, Monomial Factors, Multiplying Binomials, Difference of Two Squares, Squaring Binomials, Factoring Patterns, Factoring by Grouping, Factoring by Multiple Methods, Using Factoring to Solve Problems
- Chapter 6: Fractions
Simplifying Fractions, Multiplying and Dividing Fractions, Least Common Denominators, Adding and Subtracting Fractions, Mixed Expressions, Polynomial Long Division
- Chapter 7: Applying Fractions
Ratios, Proportions, Equations with Fractional Coefficients, Fractional Equations, Percents, Mixture Problems, Negative Exponents, Scientific Notation
- Chapter 8: Functions
Equations in Two Variables, Graphs of Points and Lines, The Slope of a Line, The Slope-Intercept Form of a Linear Equation, Determining the Equation of a Line, Linear and Quadratic Functions, Direct and Inverse Variation
- Chapter 9: Systems of Equations
Graphical Solutions to Systems of Equations, Solving Systems by Substitution, Solving Systems by Linear Combination, Applications of Systems of Equation
- Chapter 10: Inequalities
Order of Real Numbers, One Step Inequalities, Multiple Step Inequalities, Compound Inequalities, Absolute Value Inequalities, Graphing Linear Inequalities, Systems of Inequalities
- Chapter 11: Rational and Irrational Numbers
Properties of Rational Numbers, Decimal Forms of Rational Numbers, Rational Square Roots, Irrational Square Roots, The Pythagorean Theorem, Mathematical Operation of Radicals, Simple Radical Equations
- Chapter 12: Quadratic Functions
Quadratic Equations with Perfect Squares, Completing the Square, The Quadratic Formula, Graphs of Quadratic Equations, The Discriminant, Solving Problems Involving Quadratic Equations.