Anne Arundel Community College

MAT 012: Intermediate Algebra


CATALOG DESCRIPTION:
Study intermediate algebra topics. Topics include the review of the algebra of polynomials; the binomial expansion; linear, rational, radical, quadratic, exponential and logarithmic equations and functions; systems of equations; problem solving; and graphing.

Prerequisite: Completion of MAT 011 with a grade of at least C or scoring at an appropriate level on the Mathematics Placement Test.

Note: Requires a grade of C or higher in order to enroll in MAT 100, MAT 121, MAT 131, MAT 133, MAT 135, MAT 221 or MAT 222. Requires a grade of B or better to enroll in MAT 151.

LEARNING OBJECTIVES:
Upon completion of this course, the student will be able to:
  1. Use the definitions and properties of exponents to evaluate, simplify, and transform expressions.
  2. Perform basic operations with polynomial, rational, radical and exponential expressions.
  3. Solve linear inequalities, linear, quadratic and rational equations.
  4. Use function notation and basic terminology associated with functions.
  5. Graph linear, quadratic, exponential and logarithmic functions.

COURSE OUTLINE:
Course Orientation and Brief Review of Fundamentals:

Rational Expressions and Equations:
  • Review: Rational Expressions and Their Simplification
  • Review: Multiplying and Dividing Rational Expressions
  • Adding and Subtracting Rational Expressions with the Same Denominator
  • Addition and Subtraction Rational Expressions with Different Denominators
  • Simplifying Complex Rational Expressions
  • Solving Rational Equations
  • Applications Using Rational Equations and Proportions
  • Modeling Using Variation - Direct and Inverse Variation
  • Modeling Using Variation - Joint and Combined Variation

Basics of Functions:
  • Introduction to Functions
  • Interpreting Graphs of Functions
  • Graphing Linear Functions and Basic Non-Linear Functions
  • Problem Solving and Applications of Linear Functions
  • The Algebra of Functions
  • Composition of Functions
  • Inverse Functions

Inequalities and Problem Solving:
  • Review: Linear Inequalities and Problem Solving
  • Compound Inequalities
  • Equations Involving Absolute Value
  • Inequalities Involving Absolute Values
  • Linear Inequalities in Two Variables

Radicals, Radical Functions and Rational Exponents:
  • Radical Expressions and Functions
  • Rational Exponents
  • Multiplying and Simplifying Radical Expressions
  • Adding, Subtracting, and Dividing Radical Expressions
  • Multiplying with More Than One Term and Rationalizing Denominators
  • Solving Radical Equations
  • Problem Solving with Radical Equations and Functions
  • Complex Numbers

Quadratic Equations and Functions:
  • The Square Root Property and Completing the Square
  • The Quadratic Formula
  • Quadratic Functions and Their Graphs
  • Problem Solving
  • Solving Equations in Quadratic Form [Note: Exclude problems with negative integer exponents and rational exponents.]
  • Polynomial Inequalities [Note: Exclude Rational Inequalities.]

Exponential and Logarithmic Functions:
  • Introduction to Exponential Functions
  • Introduction to Logarithmic Functions

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