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The flow of this crash course is based on the outline from the Michael Sullivan College Algebra textbook and is for educational purposes. All work is original and intended for students to learn more efficiently.

**Review**

**How to Study**

**Real Numbers**

- Work with Sets
- Classify Numbers
- Evaluate Numerical Expressions
- Work with Properties of Real Numbers

**Algebra Essentials**

- Graph Inequalities
- Find Distance on the Real Number Line
- Evaluate Algebraic Expressions
- Determine the Domain of a Variable
- Use the Laws of Exponents
- Evaluate Square Roots
- Use a Calculator to Evaluate Exponents
- Use Scientific Notation

**Geometry Essentials**

- Use the Pythagorean Theorem and Its Converse
- Know Geometry Formulas
- Understand Congruent Triangles and Similar Triangles

**Polynomials**

- Recognize Monomials
- Recognize Polynomials
- Add and Subtract Polynomials
- Multiply Polynomials
- Know Formulas for Special Products
- Divide Polynomials Using Long Division
- Work with Polynomials in Two Variables

**Factoring Polynomials**

- Factor the Difference of Two Squares and the Sum and Difference of Two Cubes
- Factor Perfect Squares
- Factor a Second-Degree Polynomial ax2+bx+cax^2 + bx + cax2+bx+c
- Factor by Grouping
- Factor a Second-Degree Polynomial ax2+bx+cax^2 + bx + cax2+bx+c
- Complete the Square

**Synthetic Division**

- Divide Polynomials Using Synthetic Division

**Rational Expressions**

- Reduce a Rational Expression to Lowest Terms
- Multiply and Divide Rational Expressions
- Add and Subtract Rational Expressions
- Use the Least Common Multiple Method
- Simplify Complex Rational Expressions

**nth Roots; Rational Exponents**

- Work with nth Roots
- Simplify Radicals
- Rationalize Denominators and Numerators
- Simplify Expressions with Rational Exponents

**Equations and Inequalities**

**1.1 Linear Equations**

- Solve a Linear Equation
- Solve Equations that Lead to Linear Equations
- Solve Problems That Can Be Modeled by Linear Equations

**1.2 Quadratic Equations**

- Solve a Quadratic Equation by Factoring
- Solve a Quadratic Equation Using the Square Root Method
- Solve a Quadratic Equation by Completing the Square
- Solve a Quadratic Equation Using the Quadratic Formula
- Solve Problems That Can Be Modeled by Quadratic Equations

**1.3 Complex Numbers; Quadratic Equations in the Complex Number System**

- Add, Subtract, Multiply, and Divide Complex Numbers
- Solve Quadratic Equations in the Complex Number System

**1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations**

- Solve Radical Equations
- Solve Equations Quadratic in Form
- Solve Equations by Factoring

**1.5 Solving Inequalities**

- Use Interval Notation
- Use Properties of Inequalities
- Solve Inequalities
- Solve Combined Inequalities

**1.6 Equations and Inequalities Involving Absolute Value**

- Solve Equations Involving Absolute Value
- Solve Inequalities Involving Absolute Value

**1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications**

- Translate Verbal Descriptions into Mathematical Expressions
- Solve Interest Problems
- Solve Mixture Problems
- Solve Uniform Motion Problems
- Solve Constant Rate Job Problems
- Chapter Review
- Chapter Test
- Chapter Projects

**Graphs**

**2.1 The Distance and Midpoint Formulas**

- Use the Distance Formula
- Use the Midpoint Formula

**2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry**

- Graph Equations by Plotting Points
- Find Intercepts from a Graph
- Find Intercepts from an Equation
- Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin
- Know How to Graph Key Equations

**2.3 Lines**

- Calculate and Interpret the Slope of a Line
- Graph Lines Given a Point and the Slope
- Find the Equation of a Vertical Line
- Use the Point-Slope Form of a Line
- Identify Horizontal Lines
- Use the Slope-Intercept Form of a Line
- Find an Equation of a Line Given Two Points
- Graph Lines Written in General Form Using Intercepts
- Find Equations of Parallel Lines
- Find Equations of Perpendicular Lines

**2.4 Circles**

- Write the Standard Form of the Equation of a Circle
- Graph a Circle
- Work with the General Form of the Equation of a Circle

**2.5 Variation**

- Construct a Model Using Direct Variation
- Construct a Model Using Inverse Variation
- Construct a Model Using Joint Variation
- Chapter Review
- Chapter Test
- Cumulative Review
- Chapter Project