R. Prealgebra Review
R.1 Exponents and Order of Operations
R.2 Factors, Primes, and Least Common Multiples
R.3 Fractions
R.4 Decimals
R.5 Percent Conversions
1. Introduction to Real Numbers and Algebraic Expression
1.1 Real Numbers
1.2 Addition of Real Numbers
1.3 Subtraction of Real Numbers
1.4 Multiplication of Real Numbers
1.5 Division of Real Numbers
1.6 Algebraic Expressions, Translations, and Exponents
1.7 Evaluating Algebraic Expressions and Formulas
1. 8 Simplifying Algebraic Expressions
2. Solving Linear Equations and Inequalities
2.1 Solving Linear Equations: The Addition Property
2.2 Solving Linear Equations: The Multiplication Property
2.3 Solving Linear Equations by Combining Properties
2.4 Solving Literal Equations and Formulas
2.5 Solving Equations Involving Percent
2.6 Solving Linear Inequalities
3. Graphing Linear Equations and Inequalities in Two Variables
3.1 Introduction to Graphing
3.2 Slope
3.3 Linear Equations and Their Graphs
3.4 More on Linear Equations and Their Graphs
3.5 Linear Inequalities and Their Graphs
4. Solving Systems of Linear Equations
4.1 Introduction to Systems of Linear Equations: Solving by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination
4.4 Solving Systems of Linear Inequalities
5. Exponents and Polynomials
5.1 Laws of Exponents
5.2 More Laws of Exponents and Scientific Notation
5.3 Basic Concepts of Polynomials
5.4 Addition and Subtraction of Polynomials
5.5 Multiplication of Polynomials
5.6 Special Products
5.7 Division of Polynomials
6. Factoring Polynomials
6.1 Common Factoring and Factoring by Grouping
6.2 Factoring Trinomials Whose Leading Coefficient is 1
6.3 Factoring Trinomials Whose Leading Coefficient is Not 1
6.4 Factoring Perfect Square Trinomials, the Difference of Squares, and the Sum and Difference of Cubes
6.5 Solving Quadratic Equations by Factoring
7. Rational Expressions and Equations
7.1 Rational Expressions
7.2 Multiplication and Division of Rational Expressions
7.3 Addition and Subtraction of Rational Expressions
7.4 Complex Rational Expressions
7.5 Solving Rational Equations
7.6 Ratio and Proportion
7.7 Variation
8. Functions
8.1 Introduction to Functions
8.2 The Algebra of Functions and Inverse Functions
9. Radical Expressions, Functions, and Equations
9.1 Radical Expressions and Functions
9.2 Rational Exponents
9.3 Simplifying Radical Expressions
9.4 Addition and Subtraction of Radical Expressions
9.5 Multiplication and Division of Radical Expressions
9.6 Solving Radical Equations
9.7 Complex Numbers
10. Quadratic Equations, Functions, and Inequalities
10.1 Solving Quadratic Equations: The Square Root Property of Equality; Completing the Square
10.2 Solving Quadratic Equations: The Quadratic Formula
10.3 More on Quadratic Equations
10.4 Graphing Quadratic Functions
10.5 Solving Quadratic and Rational Inequalities
11. Exponential and Logarithmic Functions
11.1 Exponential Functions
11.2 Logarithmic Functions
11.3 Properties of Logarithms
11.4 Common Logarithms, Natural Logarithms, and Change of Base
11.5 Exponential and Logarithmic Equations
12. Conic Sections
12.1 Introduction to Conics; The Parabola
12.2 The Circle
12.3 The Ellipse and the Hyperbola
12.4 Solving Nonlinear Systems of Equations
12.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities
Appendixes
A. Table of Symbols
B. Introduction to Graphing Calculators
C. Review of Introductory Algebra
D. Basic Geometry (Online-only)
D.1 Introduction to Basic Geometry
D.2 Perimeter and Circumference
D.3 Area
D.4 Volume
D.5 SImilar Triangles
D.6 Square Roots and the Pythagorean Theorem
E. Solving Compound Inequalities
F. Solving Absolute Value Equations and Inequalities
G. Systems of Linear Equations in Three Variables
H. Solving Systems of Linear Equations by Using Matrices
I. Determinants and Cramer’s Rule
J. Synthetic Division
