Table of Contents
The Whole Numbers
1.1 Study Skill Tips for Success in Mathematics
1.2 Place Value, Names for Numbers, and Reading Tables
1.3 Adding and Subtracting Whole Numbers, and Perimeter
1.4 Rounding and Estimating
1.5 Multiplying Whole Numbers and Area
1.6 Dividing Whole Numbers
Integrated Review-Operations on Whole Numbers
1.7 Exponents and Order of Operations
1.8 Introduction to Variables, Algebraic Expressions, and Equations
Integers and Introduction to Solving Equations
2.1 Introduction to Integers
2.2 Adding Integers
2.3 Subtracting Integers
2.4 Multiplying and Dividing Integers
Integrated Review-Integers
2.5 Order of Operations
2.6 Solving Equations: The Addition and Multiplication Properties
Solving Equations and Problem Solving
3.1 Simplifying Algebraic Expressions
3.2 Solving Equations: Review of the Addition and Multiplication Properties
Integrated Review-Expressions and Equations
3.3 Solving Linear Equations in One Variable
3.4 Linear Equations in One Variable and Problem Solving
Fractions and Mixed Numbers
4.1 Introduction to Fractions and Mixed Numbers
4.2 Factors and Simplest Form
4.3 Multiplying and Dividing Fractions
4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions
4.5 Adding and Subtracting Unlike Fractions
Integrated Review-Summary on Fractions and Operations on Fractions
4.6 Complex Fractions and Review of Order of Operations
4.7 Operations on Mixed Numbers
4.8 Solving Equations Containing Fractions
Decimals
5.1 Introduction to Decimals
5.2 Adding and Subtracting Decimals
5.3 Multiplying Decimals and Circumference of a Circle
5.4 Dividing Decimals
Integrated Review-Operations on Decimals
5.5 Fractions, Decimals, and Order of Operations
5.6 Solving Equations Containing Decimals
5.7 Decimal Applications: Mean, Median, and Mode
Ratio, Proportion, and Percent
6.1 Ratio and Proportion
6.2 Percents, Decimals, and Fractions
6.3 Solving Percent Problems with Equations
6.4 Solving Percent Problems with Proportions
Integrated Review-Ratio, Proportion, and Percent
6.5 Applications of Percent
6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount
6.7 Percent and Problem Solving: Interest
Graphs, Triangle Applications, and Introduction to Statistics and Probability
7.1 Pictographs, Bar Graphs, Histograms, Line Graphs, and Introduction to Statistics
7.2 Circle Graphs
Integrated Review-Reading Graphs
7.3 Square Roots and the Pythagorean Theorem
7.4 Congruent and Similar Triangles
7.5 Counting and Introduction to Probability
Geometry and Measurement
8.1 Lines and Angles
8.2 Perimeter
8.3 Area, Volume, and Surface Area
Integrated Review-Geometry Concepts
8.4 Linear Measurement
8.5 Weight and Mass
8.6 Capacity
8.7 Temperature and Conversions Between the U.S. and Metric Systems
Equations, Inequalities, and Problem Solving
9.1 Symbols and Sets of Numbers
9.2 Properties of Real Numbers
9.3 Further Solving Linear Equations
Integrated Review-Real Numbers and Solving Linear Equations
9.4 Further Problem Solving
9.5 Formulas and Problem Solving
9.6 Linear Inequalities and Problem Solving
Graphing
10.1 The Rectangular Coordinate System
10.2 Graphing Linear Equations
10.3 Intercepts
10.4 Slope and Rate of Change
Integrated Review-Summary on Slope and Graphing Linear Equations
10.5 Equation of Lines
10.6 Functions
Solving Systems of Linear Equations
11.1 Solving Systems of Linear Equations by Graphing
11.2 Solving Systems of Linear Equations by Substitution
11.3 Solving Systems of Linear Equations by Addition
Integrated Review-Solving Systems of Equations
11.4 Solving Systems of Linear Equations in Three Variables
11.5 Systems of Linear Equations and Problem Solving
Exponents and Polynomials
12.1 Exponents
12.2 Polynomial Functions and Adding and Subtracting Polynomials
12.3 Multiplying Polynomials
12.4 Special Products
Integrated Review-Exponents and Operations on Polynomials
12.5 Negative Exponents and Scientific Notation
12.6 Dividing Polynomials
12.7 Synthetic Division and the Remainder Theorem
Factoring Polynomials
13.1 The Greatest Common Factor and Factoring by Grouping
13.2 Factoring Trinomials of the Form x2 + bx + c
13.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials
13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping
13.5 Factoring Binomials
Integrated Review-Choosing a Factoring Strategy
13.6 Solving Quadratic Equations by Factoring
13.7 Quadratic Equations and Problem Solving
Rational Expressions
14.1 Rational Functions and Simplifying Rational Expressions
14.2 Multiplying and Dividing Rational Expressions
14.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator
14.4 Adding and Subtracting Rational Expressions with Unlike Denominators
14.5 Solving Equations Containing Rational Expressions
Integrated Review-Summary on Rational Expressions
14.6 Problem Solving with Proportions and Rational Equations
14.7 Simplifying Complex Fractions
More on Functions and Graphs
15.1 Graphing and Writing Linear Functions
15.2 Reviewing Function Notation and Graphing Nonlinear Functions
Integrated Review-Summary on Functions and Equations of Lines
15.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions
15.4 Variation and Problem Solving
Inequalities and Absolute Value
16.1 Compound Inequalities
16.2 Absolute Value Equations
16.3 Absolute Value Inequalities
Integrated Review-Solving Compound Inequalities and Absolute Value Equations and Inequalities
16.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities
Rational Exponents, Radicals, and Complex Numbers
17.1 Radicals and Radical Functions
17.2 Rational Exponents
17.3 Simplifying Radical Expressions
17.4 Adding, Subtracting, and Multiplying Radical Expressions
17.5 Rationalizing Denominators and Numerators of Radical Expressions
Integrated Review-Radicals and Rational Exponents
17.6 Radical Equations and Problem Solving
17.7 Complex Numbers
Quadratic Equations and Functions
18.1 Solving Quadratic Equations by Completing the Square
18.2 Solving Quadratic Equations by the Quadratic Formula
18.3 Solving Equations by Using Quadratic Methods
Integrated Review-Summary on Solving Quadratic Equations
18.4 Nonlinear Inequalities in One Variable
18.5 Quadratic Functions and Their Graphs
18.6 Further Graphing of Quadratic Functions
Exponential and Logarithmic Functions
19.1 The Algebra of Functions: Composite Functions
19.2 Inverse Functions
19.3 Exponential Functions
19.4 Exponential Growth and Decay Functions
19.5 Logarithmic Functions
19.6 Properties of Logarithms
Integrated Review-Functions and Properties of Logarithms
19.7 Common Logarithms, Natural Logarithms, and Change of Base
19.8 Exponential and Logarithmic Equations and Problem Solving
Conic Sections
20.1 The Parabola and the Circle
20.2 The Ellipse and the Hyperbola
Integrated Review-Graphing Conic Sections
20.3 Solving Nonlinear Systems of Equations
20.4 Nonlinear Inequalities and Systems of Inequalities
Sequences, Series, and the Binomial Theorem
21.1 Sequences
21.2 Arithmetic and Geometric Sequences
21.3 Series
Integrated Review-Sequences and Series
21.4 Partial Sums of Arithmetic and Geometric Sequences
21.5 The Binomial Theorem
APPENDICES
Appendix A. Tables
A.1 Table of Geometric Figures
A.2 Table of Percents, Decimals, and Fraction Equivalents
A.3 Table on Finding Common Percents of a Number
A.4 Table of Squares and Square Roots
A.5 Geometric Formulas
Appendix B. Review of Algebra Topics
B.1 Equations (Linear and Quadratic Solved by Factoring)
B.2 Mixture and Uniform Motion Problem Solving
B.3 Graphing
B.4 Polynomials and Factoring
B.5 Rational Expressions
Appendix C. Stretching and Compressing Graphs of Absolute Value Functions
Appendix D. An Introduction to Using a Graphing Utility
Appendix E. Solving Systems of Equations by Matrices
Appendix F. Solving Systems of Equations by Determinants
