Table of Contents
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Chapter 0 Preparing for Advanced Algebra
- 0-1 Representing Functions
- 0-2 FOIL
- 0-3 Factoring Polynomials
- 0-4 Counting Techniques
- 0-5 Adding Probabilities
- 0-6 Multiplying Probabilities
- 0-7 Congruent and Similar Figures
- 0-8 The Pythagorean Theorem
- 0-9 Measures of Center, Spread, and Position
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Unit 1 Linear Relations and Functions
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Chapter 1 Equations and Inequalities
- 1-1 Expressions and Formulas
- 1-2 Properties of Real Numbers
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1-3 Solving Equations
- Properties of Equality
- One-step Equations: Multiplication and Division
- One-step Equations: Addition and Subtraction
- Multistep Equations
- Reforming Equations for a Specific Variable
- Linear Equations with Variables on Both Sides
- Solving Equations with Rational Numbers
- Introduction to Equations
- Writing Algebraic Expressions
- 1-4 Solving Absolute Value Equations
- 1-5 Solving Inequalities
- 1-6 Solving Compound and Absolute Value Inequalities
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Chapter 2 Linear Relations and Functions
- 2-1 Relations and Functions
- 2-2 Linear Relations and Functions
- 2-3 Rate of Change and Slope
- 2-4 Writing Linear Equations
- 2-5 Scatter Plots and Lines of Regression
- 2-6 Special Functions
- 2-7 Parent Functions and Transformations
- 2-8 Graphing Linear and Absolute Value Inequalities
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Chapter 3 Systems of Equations and Inequalities
- 3-1 Solving Systems of Equations
- 3-2 Solving Systems of Inequalities by Graphing
- 3-3 Optimization with Linear Programming
- 3-4 Systems of Equations in Three Variables
- 3-5 Operations with Matrices
- 3-6 Multiplying Matrices
- 3-7 Solving Systems of Equations Using Cramer’s Rule
- 3-8 Solving Systems of Equations Using Inverse Matrices
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Chapter 1 Equations and Inequalities
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Unit 2 Quadratic, Polynomial, and Radical Functions and Relations
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Chapter 4 Quadratic Functions and Relations
- 4-1 Graphing Quadratic Functions
- 4-2 Solving Quadratic Equations by Graphing
- 4-3 Solving Quadratic Equations by Factoring
- 4-4 Complex Numbers
- 4-5 Completing the Square
- 4-6 The Quadratic Formula and the Discriminant
- 4-7 Transformations of Quadratic Graphs
- 4-8 Quadratic Inequalities
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Chapter 5 Polynomials and Polynomial Functions
- 5-1 Operations with Polynomials
- 5-2 Dividing Polynomials
- 5-3 Polynomial Functions
- 5-4 Analyzing Graphs of Polynomial Functions
- 5-5 Solving Polynomial Equations
- 5-6 The Remainder and Factor Theorems
- 5-7 Roots and Zeros
- 5-8 Rational Zero Theorem
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Chapter 6 Inverses and Radical Functions and Relations
- 6-1 Operations on Functions
- 6-2 Inverse Functions and Relations
- 6-3 Square Root Functions and Inequalities
- 6-4 𝑛th Roots
- 6-5 Operations with Radical Expressions
- 6-6 Rational Exponents
- 6-7 Solving Radical Equations and Inequalities
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Chapter 4 Quadratic Functions and Relations
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Unit 3 Advanced Functions and Relations
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Chapter 7 Exponential and Logarithmic Functions and Relations
- 7-1 Graphing Exponential Functions
- 7-2 Solving Exponential Equations and Inequalities
- 7-3 Logarithms and Logarithmic Functions
- 7-4 Solving Logarithmic Equations and Inequalities
- 7-5 Properties of Logarithms
- 7-6 Common Logarithms
- 7-7 Base 𝑒 and Natural Logarithms
- 7-8 Using Exponential and Logarithmic Functions
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Chapter 8 Rational Functions and Relations
- 8-1 Multiplying and Dividing Rational Expressions
- 8-2 Adding and Subtracting Rational Expressions
- 8-3 Graphing Reciprocal Functions
- 8-4 Graphing Rational Functions
- 8-5 Variation Functions
- 8-6 Solving Rational Equations and Inequalities
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Chapter 9 Conic Sections
- 9-1 Midpoint and Distance Formulas
- 9-2 Parabolas
- 9-3 Circles
- 9-4 Ellipses
- 9-5 Hyperbolas
- 9-6 Identifying Conic Sections
- 9-7 Solving Linear-Nonlinear Systems
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Chapter 7 Exponential and Logarithmic Functions and Relations
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Unit 4 Discrete Mathematics
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Chapter 10 Sequences and Series
- 10-1 Sequences as Functions
- 10-2 Arithmetic Sequences and Series
- 10-3 Geometric Sequences and Series
- 10-4 Infinite Geometric Series
- 10-5 Recursion and Iteration
- 10-6 The Binomial Theorem
- 10-7 Proof by Mathematical Induction
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Chapter 11 Statistics and Probability
- 11-1 Designing a Study
- 11-2 Distributions of Data
- 11-3 Probability Distributions
- 11-4 The Binomial Distribution
- 11-5 The Normal Distribution
- 11-6 Confidence Intervals and Hypothesis Testing
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Chapter 10 Sequences and Series
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Unit 5 Trigonometry
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Chapter 12 Trigonometric Functions
- 12-1 Trigonometric Functions in Right Triangles
- 12-2 Angles and Angle Measure
- 12-3 Trigonometric Functions of General Angles
- 12-4 Law of Sines
- 12-5 Law of Cosines
- 12-6 Circular and Periodic Functions
- 12-7 Graphing Trigonometric Functions
- 12-8 Translations of Trigonometric Graphs
- 12-9 Inverse Trigonometric Functions
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Chapter 13 Trigonometric Identities and Equations
- 13-1 Trigonometric Identities
- 13-2 Verifying Trigonometric Identities
- 13-3 Sum and Difference of Angles Identities
- 13-4 Double-Angle and Half-Angle Identities
- 13-5 Solving Trigonometric Equations
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Chapter 12 Trigonometric Functions