Linear Equations and Inequalities in One Variable | |
Linear Equations in One Variable | |
Problem Recognition Exercises: Equations versus Expressions | |
Applications of Linear Equations in One Variable | |
Applications to Geometry and Literal Equations | |
Linear Inequalities in One Variable | |
Compound Inequalities | |
Absolute Value Equations | |
Absolute Value Inequalities | |
Problem Recognition Exercises: Identifying Equations and Inequalities | |
Group Activity: Understanding the Symbolism of Mathematics | |
Summary | |
Review Exercises | |
Test | |
Linear Equations in Two Variables and Functions | |
Linear Equations in Two Variables | |
Slope of a Line and Rate of Change | |
Equations of a Line | |
Problem Recognition Exercises: Characteristics of Linear Equations | |
Applications of Linear Equations and Modeling | |
Introduction to Relations | |
Introduction to Functions | |
Graphs of Basic Functions | |
Problem Recognition Exercises: Characteristics of Relations | |
Group Activity: Deciphering a Coded Message | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Systems of Linear Equations and Inequalities | |
Solving Systems of Linear Equations by the Graphing Method | |
Solving Systems of Linear Equations by the Substitution Method | |
Solving Systems of Linear Equations by the Addition Method | |
Problem Recognition Exercises: Solving Systems of Linear Equations | |
Applications of Systems of Linear Equations in Two Variables | |
Linear Inequalities and Systems of Linear Inequalities in Two Variables | |
Systems of Linear Equations in Three Variables and Applications | |
Solving Systems of Linear Equations by Using Matrices | |
Group Activity: Creating a Quadratic Model of the Form y = at2 + bt + c | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Polynomials | |
Properties of Integer Exponents and Scientific Notation | |
Addition and Subtraction of Polynomials and Polynomial Functions | |
Multiplication of Polynomials | |
Division of Polynomials | |
Problem Recognition Exercises: Operations on Polynomials | |
Greatest Common Factor and Factoring by Grouping | |
Factoring Trinomials | |
Factoring Binomials | |
Problem Recognition Exercises: Factoring Summary | |
Solving Equations by Using the Zero Product Rule | |
Group Activity: Investigating Pascal’s Triangle | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Rational Expressions and Rational Equations | |
Rational Expressions and Rational Functions | |
Multiplication and Division of Rational Expressions | |
Addition and Subtraction of Rational Expressions | |
Complex Fractions | |
Problem Recognition Exercises: Operations on Rational Expressions | |
Solving Rational Equationsv | |
Problem Recognition Exercises: Rational Equations vs. Expressions | |
Applications of Rational Equations and Proportions | |
Variation | |
Group Activity: Computing the Future Value of an Investment | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Radicals and Complex Numbers | |
Definition of an nth Root | |
Rational Exponents | |
Simplifying Radical Expressions | |
Addition and Subtraction of Radicals | |
Multiplication of Radicals | |
Problem Recognition Exercises: Simplifying Radical Expressions | |
Division of Radicals and Rationalization | |
Solving Radical Equations | |
Complex Numbers | |
Group Activity: Margin of Error of Survey Results | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Quadratic Equations and Functions | |
Square Root Property and Completing the Square | |
Quadratic Formula | |
Equations in Quadratic Form | |
Problem Recognition Exercises: Quadratic and Quadratic Type Equations | |
Graphs of Quadratic Functions | |
Vertex of a Parabola: Applications and Modeling | |
Nonlinear Inequalities | |
Problem Recognition Exercises: Recognizing Equations and Inequalities | |
Group Activity: Creating a Quadratic Model of the Form y = a(x - h)2 + k | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Exponential and Logarithmic Functions and Applications | |
Algebra and Composition of Functions | |
Inverse Functions | |
Exponential Functions | |
Logarithmic Functions | |
Problem Recognition Exercises: Identifying Graphs of Functions | |
Properties of Logarithms | |
The Irrational Number and Change of Base | |
Problem Recognition Exercises: Logarithmic and Exponential Forms | |
Logarithmic and Exponential Equations and Applications | |
Group Activity: Creating a Population Model | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Conic Sections | |
Distance Formula, Midpoint Formula, and Circles | |
More on the Parabola | |
The Ellipse and Hyperbola | |
Problem Recognition Exercises: Formulas and Conic Sections | |
Nonlinear Systems of Equations in Two Variables | |
Nonlinear Inequalities and Systems of Inequalities | |
Group Activity: Investigating the Graphs of Conic Sections on a Calculator | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Binomial Expansions, Sequences, and Series | |
Binomial Expansions | |
Sequences and Series | |
Arithmetic Sequences and Series | |
Geometric Sequences and Series | |
Problem Recognition Exercises: Identifying Arithmetic and Geometric Sequences | |
Group Activity: Investigating Mean and Standard Deviation | |
Summary | |
Review Exercises | |
Test | |
Cumulative Review Exercises | |
Additional Topics Appendix | |
Determinants and Cramer’s Rule | |
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