Table of Contents
(Most Chapters begin with a Pretest section and end with Summary and Review, Test, and Cumulative Review sections.)
DIAGNOSTIC TEST.
R. Prealgebra Review.
Factoring and LCMs.
Fractional Notation.
Decimal Notation.
Percent Notation.
Exponential Notation and Order of Operations.
1. Introduction to Real Numbers and Algebraic Expressions.
Introduction to Algebra.
The Real Numbers.
Addition of Real Numbers.
Subtraction of Real Numbers.
Multiplication of Real Numbers.
Division of Real Numbers.
Properties of Real Numbers.
Simplifying Expressions; Order of Operations.
2. Solving Equations and Inequalities.
Solving Equations: The Addition Principles.
Solving Equations: The Multiplication Principle.
Using the Principles Together.
Applications and Problem Solving.
Applications with Percents.
Formulas.
Solving Inequalities.
Applications and Problem Solving with Inequalities.
3. Graphs of Equations; Data Analysis.
Graphs and Applications.
Graphing Linear Equations.
More on Graphing Linear Equations.
Applications and Data Analysis with Graphs.
4. Polynomials: Operations.
Integers as Exponents.
Exponents and Scientific Notation.
Introduction to Polynomials.
Addition and Subtraction of Polynomials.
Multiplication of Polynomials.
Special Products.
Operations with Polynomials in Several Variables.
Division of Polynomials.
5. Polynomials: Factoring.
Introduction to Factoring.
Factoring Trinomials of the Type x2 + bx + c.
Factoring ax2 + bx + c, a = 1, Using FOIL.
Factoring ax + bx+ c, a = 1 Using Grouping.
Factoring Trinomial Squares and Differences of Squares.
Factoring : A General Strategy.
Solving Quadratic Equations by Factoring.
Applications and Problem Solving.
6. Rational Expressions and Equations.
Multiplying and Simplifying Rational Expressions.
Division and Reciprocals.
Least Common Multiples and Denominators.
Adding Rational Expressions.
Subtracting Rational Expressions.
Solving Rational Equations.
Applications, Proportions, and Problem Solving.
Formulas and Applications.
Complex Rational Expressions.
7. Graphs, Slope, and Applications.
Slope and Slope-Intercept Form.
Equations of Lines.
Parallel and Perpendicular Lines.
Graphing Inequalities in Two Variables.
Direct and Inverse Variation.
8. Systems of Equations.
Systems of Equations in Two Variables.
The Substitution Method.
The Elimination Method.
Applications and Problem Solving.
Applications with Motion.
9. Radical Expressions and Equations.
Introduction to Square Roots and Radical Expressions.
Multiplying and Simplifying with Radical Expressions.
Quotients Involving Square Roots.
Addition, Subtraction, and More Multiplication.
Radical Equations.
Applications with Right Triangles.
10. Quadratic Equations.
Introduction to Quadratic Equations.
Solving Quadratic Equations by Completing the Square.
The Quadratic Formula.
Formulas.
Applications and Problem Solving.
Graphs of Quadratic Equations.
Functions.
Final Examination.
Appendixes.
A. Factoring Sums or Differences of Cubes.
B. Higher Roots.
C. Sets.
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