# Intermediate Algebra

Intermediate Algebra is a one-semester, three-credit course that covers the following topics:

**Real Numbers and Algebraic Expression**

Algebraic Expressions and Sets of Numbers

Properties of Real Numbers

Operations on Real Numbers

Order of Operations and Algebraic Expressions

Group Activity: Analyzing Newspaper Circulation

**Equations, Inequalities, and Problem Solving**

Linear Equations in One Variable

An Introduction to Problem Solving

Formulas and Problem Solving

Linear Inequalities and Problem Solving

Compound Inequalities

Absolute Value Equations

Absolute Value Inequalities

Group Activity: Investigating Compound Interest

**Graphs and Functions
**Graphing Equations

Introduction to Functions

Graphing Linear Functions

The Slope of a Line

Equations of Lines

Graphing Linear Inequalities

Group Activity: Modeling Japanese Automobile Imports

**Systems of Equations**

Solving Systems of Linear Equations in Two Variables

Solving Systems of Linear Equations in Three Variables

Systems of Linear Equations and Problem Solving

Solving Systems of Equations by Matrices

Solving Systems of Equations by Determinants

Group Activity: Locating Lightning Strikes

**Exponents, Polynomials, and Polynomial Functions**

Exponents and Scientific Notation

More Work with Exponents and Scientific Notation

Polynomials and Polynomial functions

Multiplying Polynomials

The Greatest Common Factor and factoring by Grouping

Factoring Trinomials

Factoring by Special Products and Factoring Strategies

Solving Equations by Factoring and Problem Solving

An Introduction to Graphing Polynomial Functions

Group Activity: Finding the Largest Area

**Rational Expressions**

Rational functions and Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Simplifying Complex Fractions

Dividing Polynomials

Synthetic Division and the Remainder Theorem

Solving Equations containing Rational Expressions

Rational Equations and Problem Solving

Variation and Problem Solving

Group Activity: Modeling Electricity Production

**Rational Exponents, Radicals, and Complex Numbers**

Radicals and Radical Functions

Rational Exponents

Simplifying Radical Expressions

Adding, Subtracting, and Multiplying Radical Expressions

Rationalizing Numerators and Denominators of Radical Expressions

Radical Equations and Problem Solving

Complex Numbers

Group Activity: Calculating the Length and Period of a Pendulum

**Quadratic Equations and Functions**

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by the Quadratic Formula

Solving Equations by Using Quadratic Methods

Nonlinear Inequalities in One Variable

Quadratic Functions and Their Graphs

Further Graphing of Quadratic Functions

Group Activity: Modeling the Position of a Freely Falling Object

**Conic Sections**

The parabola and the Circle

The Ellipse and the Hyperbola

Solving Nonlinear Systems of Equations

Nonlinear Inequalities and Systems of Inequalities

Group Activity: Modeling Conic Sections

**Exponential and Logarithmic Functions**

Composite and Inverse Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Common Logarithms, Natural Logarithms, and Change of Base

Exponential and Logarithmic Equations and Problem Solving

Group Activity: Modeling Temperature

**Sequences, Series, and the Binomial Theorem**

Sequences

Arithmetic and Geometric Sequences

Series

Partial Sums of Arithmetic and Geometric Sequences

The Binomial Theorem

Group Activity: Modeling College Tuition