INTERMEDIATE ALGEBRA

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Course Prerequisite(s)

About Course

This course provides a preparation for more advanced study in mathematics and related fields. Topics include simplifying algebraic, rational, and radical expressions; solving quadratic, rational, radical, absolute value, exponential, and logarithmic equations; solving compound and absolute value inequalities, and graphing functions.

What Will You Learn?

  • Upon successful completion of this course, each student will be able to:
  • 1. Classify a real Number, Order of Operations, Properties of Real Numbers, Evaluate Algebraic
  • Expressions, Simplify Algebraic Expressions;
  • 2. Factor polynomials using the distributive property, reverse foil, grouping, the difference of squares, sum and difference of cubes;
  • 3. Perform operations on rational expressions, radical expressions, and complex numbers; solve rational and radical equations;
  • 4. Solve compound inequalities, absolute value equations and inequalities;
  • 5. Solve quadratic equations by using factoring, the quadratic formula, and completing the square and solve relevant applications;
  • 6. Use function notation, perform operations with functions including composition of functions, find the inverse of a one-to-one function, graph quadratic, exponential, and logarithmic functions, and identify the domain and range of a function; and
  • 7. Use properties of logarithms to solve logarithmic and exponential equations and relevant applications

Course Content

Algebra Essentials
The topic entails: Operations on Real Numbers Systems; Concept of Exponents and Scientific Notation and Introduction to Radicals and Rational Exponents

Polynomial and Rational Expressions
This course entails introduction to Polynomial Basics, Factoring Polynomials and Concept of Rational Expressions

The Rectangular Coordinate System and Equations of Lines
This topic consists of Introduction to Points and Lines in the Plane and Equations of Lines

Equations and Inequalities
Introduction to Equation-Solving Techniques Models and Applications Quadratic Equations Linear Inequalities and Absolute Value Inequalities

Function Basics and Algebraic Operations on Functions
Characteristics of Functions and Their Graphs Domain and Range of Functions Rates of Change and Behaviors of Graphs

Linear and Absolute Value Functions
Introduction to Linear Functions Graphs of Linear Functions Modeling With Linear Functions

Quadratic Functions
Introduction to Complex Numbers Graphs of Quadratic Functions Introduction to Analysis of Quadratic Functions

Power and Polynomial Functions
Characteristics of Power and Polynomial Functions Divide Polynomials Methods for Finding Zeros of Polynomials

Rational and Radical Functions
Introduction to Rational Functions, Radical Functions Introduction to Variation

Exponential and Logarithmic Functions
Exponential and Logarithmic Equations, Introduction to Logarithmic Functions Introduction to Graphs of Logarithmic Functions

Systems of Equations and Inequalities
Systems of Linear Equations: Two Variables Introduction to Solutions of Systems, Systems of Nonlinear Equations and Inequalities, Systems of Linear Equations: Three Variables Partial Fractions: an Application of Systems