Algebra I is "the" fundamental subject that is the stepping stone to all other math. It is a core subject required of all students in order to graduate from high school.
Mary Jane Sterling teaches mathematics at Bradley University in Peoria, Illinois. She has been teaching mathematics for over 30 years.
Introduction.Types of Numbers.
Notation.
Pretest.
Pretest Questions.
Key to Pretest Questions.
Chapter 1: The Basics.
Order of Operations.
Basic Order of Operations.
Grouping Symbols.
Basic Math Operations.
Addition and Subtraction.
Multiplication and Division.
Powers (Exponents).
Roots.
Absolute Value.
Combining “Like” Terms.
Properties of Algebraic Expressions.
Commutative Property of Addition and Multiplication.
Associative Property of Addition and Multiplication.
Distributive Property of Multiplication over Addition (or Subtraction).
Identities.
Inverses.
Multiplication Property of Zero.
Integer Powers (Exponents).
Laws for Using Exponents.
Square Roots and Cube Roots.
Approximating Square Roots.
Simplifying Square Roots.
Rationalizing Fractions.
Exponents for Roots.
Divisibility Rules.
Prime Numbers.
Prime Factorization.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 2: Numbers.
Signed Numbers.
Number Lines.
Addition of Signed Numbers.
Subtraction of Signed Numbers.
Multiplication and Division of Signed Numbers.
Exponents That Are Signed Numbers.
Fractions.
Lowest Terms and Equivalent Fractions.
Multiplying and Dividing Fractions.
Mixed Numbers and Complex Fractions.
Decimals.
Percents.
Scientific Notation.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 3: Linear Equations and Algebraic Fractions.
Solving Linear Equations.
Solving Linear Equations with More Than One Operation.
Solving Linear Formulas.
Ratios and Proportions.
Operations with Algebraic Fractions.
Multiplying and Dividing Algebraic Fractions.
Adding and Subtracting Algebraic Fractions.
Equations with Fractions.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 4: Polynomials and Factoring.
Multiplying Monomials.
Multiplying Polynomials.
The “FOIL” Method.
Other Products.
Special Products.
Dividing Polynomials.
Divisors with One Term.
Long Division.
Synthetic Division.
Factoring.
Greatest Common Factor.
Factoring Binomials.
Factoring Trinomials.
Factoring Other Polynomials.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 5: Inequalities, Absolute Value Inequalities, and Radicals.
Inequalities.
Rules for Operating on Inequalities.
Solving Inequalities by Graphing on a Number Line.
Absolute Value Equations.
Absolute Value Inequalities.
Simplifying Square Roots.
Simplifying Other Roots.
Radical Equations.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 6: Introducing Quadratic Equations—Testing Solutions.
Solving Quadratic Equations by Factoring.
Solving Quadratic Equations with the Quadratic Formula.
Solving Quadratic Equations by Completing the Square.
Solving Quadratic-Like Equations.
Quadratic and Other Inequalities.
Radical Equations with Quadratics.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 7: Graphing and Systems of Equations.
Coordinate System.
Graphing Points and Quadrants.
Graphing Lines.
Graphing Other Curves.
Finding the Equation of a Line.
Graphing Inequalities.
Systems of Equations—Linear and Quadratic.
Solving Systems of Equations by Graphing.
Solving Systems of Equations Using Addition.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 8:Functions.
Functions and Relations.
Domain and Range.
Domain.
Range.
Graphs of Functions—Vertical Line Test.
Inverse Functions and Function Notation.
Chapter Problems and Solutions.
Problems.
Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Chapter 9: Story Problems.
Number Problems.
Consecutive Integer Problems.
Age Problems.
Geometric Problems.
Distance Problems.
Mixture Problems.
Coin and Interest Problems.
Working Together Problems.
Chapter Problems and Solutions.
Problems.
Answers and Solutions.
Supplemental Chapter Problems.
Problems.
Answers.
Customized Full-Length Exam.
Index.