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

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

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