**Disclaimer**: The lessons and information provided on this page, along with the associated links, are intended to serve as a helpful guideline to support your understanding of the subject matter. However, they are not designed to replace the comprehensive content found in your textbook. The textbook remains the primary resource for in-depth explanations, detailed examples, and the full scope of the curriculum. While these supplementary materials can enhance your learning experience, they should be used in conjunction with the textbook to ensure a complete and thorough grasp of the topics covered. False Reality Publishing LLC is not affiliated with Pearson Publishing. Textbook used as reference for this crash course: College Algebra by Michael Sullivan and Pearson Publishing

### Review

**R.1 Real Numbers****R.2 Algebra Essentials****R.3 Geometry Essentials****R.4 Polynomials****R.5 Factoring Polynomials****R.6 Synthetic Division****R.7 Rational Expressions****R.8 nth Roots; Rational Exponents**

### Equations and Inequalities

**1.1 Linear Equations****1.2 Quadratic Equations****1.3 Complex Numbers; Quadratic Equations in the Complex Number System****1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations****1.5 Solving Inequalities****1.6 Equations and Inequalities Involving Absolute Value****1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications**

### Graphs

**2.1 The Distance and Midpoint Formulas****2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry****2.3 Lines****2.4 Circles****2.5 Variation**

### Functions and Their Graphs

**3.1 Functions****3.2 The Graph of a Function****3.3 Properties of Functions****3.4 Library of Functions; Piecewise-defined Functions****3.5 Graphing Techniques: Transformations****3.6 Mathematical Models: Building Functions**

### Linear and Quadratic Functions

**4.1 Properties of Linear Functions and Linear Models****4.2 Building Linear Models from Data****4.3 Quadratic Functions and Their Properties****4.4 Building Quadratic Models from Verbal Descriptions and from Data****4.5 Inequalities Involving Quadratic Functions**

### Polynomial and Rational Functions

**5.1 Polynomial Functions****5.2 Graphing Polynomial Functions; Models****5.3 Properties of Rational Functions****5.4 The Graph of a Rational Function****5.5 Polynomial and Rational Inequalities****5.6 The Real Zeros of a Polynomial Function****5.7 Complex Zeros; Fundamental Theorem of Algebra**

### Exponential and Logarithmic Functions

**6.1 Composite Functions****6.2 One-to-One Functions; Inverse Functions****6.3 Exponential Functions****6.4 Logarithmic Functions****6.5 Properties of Logarithms****6.6 Logarithmic and Exponential Equations****6.7 Financial Models****6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models****6.9 Building Exponential, Logarithmic, and Logistic Models from Data**

### Analytic Geometry

**7.1 Conics****7.2 The Parabola****7.3 The Ellipse****7.4 The Hyperbola**

### Systems of Equations and Inequalities

**8.1 Systems of Linear Equations: Substitution and Elimination****8.2 Systems of Linear Equations: Matrices****8.3 Systems of Linear Equations: Determinants****8.4 Matrix Algebra****8.5 Partial Fraction Decomposition****8.6 Systems of Nonlinear Equations****8.7 Systems of Inequalities****8.8 Linear Programming**

### Sequences; Induction; the Binomial Theorem

**9.1 Sequences****9.2 Arithmetic Sequences****9.3 Geometric Sequences; Geometric Series****9.4 Mathematical Induction****9.5 The Binomial Theorem**

### Counting and Probability

**10.1 Counting****10.2 Permutations and Combinations****10.3 Probability**