Algebra: A Combined Course for Pace University

• Preface to Instructors
• Preface to Students
• XYZ Learning Strategies   New
  • Chapter Introduction
  • Learning Styles and Study Plans
  • Growth Mindset: Growth, Resilience, Hardiness, Grit
  • Reading and Cognitive Techniques
• 0 - Prealgebra Review
  • Chapter Introduction
  • 0.1 - Factors and Simplifying Fractions
  • 0.2 - Operations with Fractions
  • 0.3 - Decimal Notation
  • 0.4 - Operations with Decimals
  • 0.5 - Percents, Decimals, and Fractions
  • 0.6 - Exponents and Order of Operations
  • Chapter Test & Summary
• 1 - Real Numbers and Algebraic Expressions
  • Chapter Introduction
  • 1.1 - Real Numbers
  • 1.2 - Addition and Subtraction of Real Numbers
  • 1.3 - Multiplication of Real Numbers
  • 1.4 - Division of Real Numbers
  • 1.5 - Properties of Real Numbers
  • 1.6 - Simplifying Expressions
  • Chapter Test & Summary
• 2 - Linear Equations and Inequalities in One Variable
  • Chapter Introduction
  • 2.1 - Addition Property of Equality
  • 2.2 - Multiplication Property of Equality
  • 2.3 - Solving Linear Equations in One Variable
  • 2.4 - Formulas
  • 2.5 - Applications: Number, Age, Perimeter, Coin Problems
  • 2.6 - Applications: Integer, Interest, Triangle, Mixture Problems
  • 2.7 - Linear Inequalities in One Variable
  • Chapter Test & Summary
• 3 - Graphing Linear Equations and Inequalities in Two Variables
  • Chapter Introduction
  • 3.1 - The Rectangular Coordinate System
  • 3.2 - Solutions and Graphs of Linear Equations
  • 3.3 - Graphing Linear Equations Using Inercepts
  • 3.4 - Graphing Linear Equations Using Slope
  • 3.5 - Finding the Equation of a Line
  • 3.6 - Graphing Linear Inequalities in Two Variables
  • Chapter Test & Summary
• 4 - Systems of Equations
  • Chapter Introduction
  • 4.1 - Solving Linear Systems by Graphing
  • 4.2 - The Substitution Method
  • 4.3 - The Elimination Method
  • 4.4 - Applications of Systems of Equations
  • Chapter Test & Summary
• 5 - Exponents and Polynomials
  • Chapter Introduction
  • 5.1 - Multiplication with Exponents and Scientific Notation
  • 5.2 - Division with Exponents and Negative Exponents
  • 5.3 - Operations with Monomials
  • 5.4 - Addition and Subtraction of Polynomials
  • 5.5 - Multiplication of Polynomials
  • 5.6 - Special Products
  • 5.7 - Dividing a Polynomial by a Monomial
  • 5.8 - Dividing a Polynomial by a Polynomial
  • Chapter Test & Summary
• 6 - Factoring Polynomials
  • Chapter Introduction
  • 6.1 - The Greatest Common Factor and Factoring by Grouping
  • 6.2 - Factoring Trinomials of the Form x² + bx + c
  • 6.3 - Factoring Trinomials of the Form ax² + bx + c
  • 6.4 - The Difference of Two Squares and Perfect Square Trinomials
  • 6.5 - The Sum and Difference of Two Cubes
  • 6.6 - Factoring: A General Review
  • 6.7 - Solving Quadratic Equations by Factoring
  • 6.8 - Applications of Quadratic Equations
  • Chapter Test & Summary
• 7 - Rational Expressions and Equations
  • Chapter Introduction
  • 7.1 - Simplifying Rational Expressions
  • 7.2 - Multiplication and Division of Rational Expressions
  • 7.3 - Addition and Subtraction of Rational Expressions
  • 7.4 - Equations Involving Rational Expressions
  • 7.5 - Applications of Rational Equations
  • 7.6 - Complex Fractions
  • 7.7 - Proportions
  • 7.8 - Direct and Inverse Variation
  • Chapter Test & Summary
• 8 - Inequalities, Graphs and Functions
  • Chapter Introduction
  • 8.1 - Interval Notation and Linear Inequalities
  • 8.2 - Sets and Compound Inequalities
  • 8.3 - Absolute Value Equations
  • 8.4 - Absolute Value Inequalities
  • 8.5 - Graphs of Equations
  • 8.6 - Introduction to Functions
  • 8.7 - Function Notation
  • 8.8 - Algebra and Composition with Functions
  • Chapter Test & Summary
• 9 - Systems of Equations and Inequalities
  • Chapter Introduction
  • 9.1 - Systems of Linear Equations in Two Variables
  • 9.2 - Systems of Linear Equations in Three Variables
  • 9.3 - Matrix Solutions to Linear Systems
  • 9.4 - Determinants and Cramer’s Rule
  • 9.5 - Applications of Systems of Equations
  • 9.6 - System of Linear Inequalities and Applications
  • Chapter Test & Summary
• 10 - Rational Exponents and Radicals
  • Chapter Introduction
  • 10.1 - Rational Exponents
  • 10.2 - Simplifying Radicals
  • 10.3 - Addition and Subtraction of Radical Expressions
  • 10.4 - Multiplication and Division of Radical Expressions
  • 10.5 - Radical Equations and Functions
  • 10.6 - Complex Numbers
  • Chapter Test & Summary
• 11 - Quadratic Equations and Functions
  • Chapter Introduction
  • 11.1 - Completing the Square
  • 11.2 - The Quadratic Formula
  • 11.3 - The Discriminant and Multiplicity
  • 11.4 - Equations Quadratic in Form
  • 11.5 - Graphing Quadratic Functions
  • 11.6 - Polynomial and Rational Inequalities
  • Chapter Test & Summary
• 12 - Exponential and Logarithmic Functions
  • Chapter Introduction
  • 12.1 - Exponential Functions and Applications
  • 12.2 - Inverse Functions
  • 12.3 - Logarithmic Functions and Applications
  • 12.4 - Properties of Logarithms
  • 12.5 - Common and Natural Logarithms with Applications
  • 12.6 - Exponential Equations, Change of Base, and Applications
  • Chapter Test & Summary
• 13 - Conic Sections
  • Chapter Introduction
  • 13.1 - Circles
  • 13.2 - Parabolas
  • 13.3 - Ellipses
  • 13.4 - Hyperbolas
  • 13.5 - Nonlinear Systems of Equations and Inequalities
  • Chapter Test & Summary
• 14 - Sequences and Series
  • Chapter Introduction
  • 14.1 - Sequences and Recursion Formulas
  • 14.2 - Series
  • 14.3 - Arithmetic Sequences
  • 14.4 - Geometric Sequences
  • 14.5 - The Binomial Expansion
  • 14.6 - Permutations and Combinations
  • Chapter Test & Summary
• Answers
• Index