Title: Module 2 Algebraic Essentials Learning Objectives
Course: Technical Math for Industry > Section: Module 2.0: Fundamental Concepts and Operations of Algebra

Overview and Introduction

This module contains interactive tutorials to help you practice or refresh your math skills on the following topics:

Fundamental Concepts and Operations of Algebra

Lesson 12 Learning Objectives-Introduction and Operations of Real Numbers

- Adding Integers
  - Add two or more integers with the same sign.
  - Add two or more integers with different signs.
- Adding Real Numbers
  - Add two or more real numbers with the same sign.
  - Add two or more real numbers with different signs.
  - Simplify by using the identity property of 0.
  - Solve application problems requiring the addition of real numbers.
- Subtracting Real Numbers
  - Subtract two or more real numbers.
  - Simplify combinations that require both addition and subtraction of real numbers.
  - Solve application problems requiring subtraction of real numbers.
- Multiplying and Dividing Real Numbers
  - Multiply two or more real numbers.
  - Simplify by using the identity property of 1.
  - Divide real numbers.
  - Solve application problems requiring multiplication or division of real numbers.

Lesson 13 Learning Objectives-Properties of Real Numbers

- Identify and use the commutative properties for addition and multiplication.
- Identify and use the associative properties for addition and multiplication.
- Identify and use the distributive property.

Lesson 14 Learning Objectives-Symplifying Expressions

- Use the order of operations to simplify expressions.
- Simplify expressions containing absolute values.

Algebraic Equations

Lesson 15 Learning Objectives-Solving Equations

- Solving Equations
  - Isolate variables using the Inverse Property or Inverse Operations.
  - Solve algebraic equations using the Properties of Equality.
- Solving Multi-Step Equations
  - Simplify algebraic equations using the Properties of Equality and the Distributive Property to clear parentheses and fractions.
- Writing Expressions and Equations
  - Translate word problems into algebraic expressions and equations.
- Solving for a Specific Variable
  - Rearrange formulas to isolate specific variables.

Lesson 16 Learning Objectives-Solving Inequalities

- Absolute Value
  - Find the absolute value of numbers and expressions.
  - Represent absolute values with numerical statements and on number lines.
- Solving Absolute Value Equations
  - Find all possible solutions for absolute value equations involving variables and variable terms.

Lesson 17 Learning Objectives-Compound Inequalities and Absolute Value

- Solving and Graphing Linear Inequalities in Two Variables
  - Represent linear inequalities as regions on the coordinate plane.
  - Determine if a given point is a solution of a linear inequality.

Lesson 18 Learning Objectives-Graphing Systems of Equations and Inequalities

- Graphing Systems of Linear Equations
  - Solve a system of linear equations by graphing.
  - Determine whether a system of linear equations is consistent or inconsistent.
  - Determine whether a system of linear equations is dependent or independent.
  - Determine whether an ordered pair is a solution of a system of equations.
  - Solve application problems by graphing a system of equations.
- Graphing Systems of Inequalities
  - Solve a system of linear inequalities by graphing.
  - Determine whether an ordered pair is a solution of a system of inequalities.
  - Solve application problems by graphing a system of inequalities.

Lesson 19 Learning Objectives-Algebraic Methods to Solve Systems of Equations

- The Substitution Method
  - Solve a system of equations using the substitution method.
  - Recognize systems of equations that have no solution or an infinite number of solutions.
  - Solve application problems using the substitution method.
- The Elimination Method
  - Solve a system of equations when no multiplication is necessary to eliminate a variable.
  - Solve a system of equations when multiplication is necessary to eliminate a variable.
  - Recognize systems that have no solution or an infinite number of solutions.
  - Solve application problems using the elimination method.

Lesson 20 Learning Objectives-Systems of Equations in 3 or More Variables

- Solving Systems of Three Variables
  - Solve a system of equations when no multiplication is necessary to eliminate a variable.
  - Solve a system of equations when multiplication is necessary to eliminate a variable.
  - Solve application problems that require the use of this method.
  - Recognize systems that have no solution or an infinite number of solutions.

Rational Expressions

Lesson 21 Learning Objectives-Operations with Rational Expressions

- Introduction to Rational Expressions
  - Find values of a variable that make a rational expression undefined.
  - Simplify rational expressions.
- Multiplying and Dividing Rational Expressions
  - Multiply rational expressions and simplify.
  - Divide rational expressions and simplify.
- Adding and Subtracting Rational Expressions
  - Add rational expressions and simplify.
  - Subtract rational expressions and simplify.
  - Find the Least Common Multiple of several algebraic expressions.
  - Simplify problems that combine both adding and subtracting.
- Complex Rational Expressions
  - Simplify complex rational expressions.

Lesson 22 Learning Objectives-Rational Equations

- Solving Rational Equations and Applications
  - Solve rational equations.
  - Check for extraneous solutions.
  - Solve application problems involving rational equations

Lesson 23 Learning Objectives-Formulas and Variation

- Rational Formulas and Variation
  - Solve a formula for a specified letter.
  - Identify direct, inverse, and joint variation.
  - Find the unknown in a variation problem.
  - Solve application problems involving direct variation.
  - Solve application problems involving inverse variation.
  - Solve application problems involving joint variation.

Radical Expressions and Quadratic Equations

Lesson 24 Learning Objectives-Operations with Radicals

- Multiplying and Dividing Radical Expressions
  - Multiply and simplify radical expressions that contain a single term.
  - Divide and simplify radical expressions that contain a single term.
- Adding and Subtracting Radicals
  - Add radicals and simplify.
  - Subtract radicals and simplify.
- Multiplication of Multiple Term Radicals
  - Multiply and simplify radical expressions that contain more than one term.
- Rationalizing Denominators
  - Rationalize a denominator with a monomial containing a square root.
  - Rationalize a denominator that contains two terms.

Lesson 25 Learning Objectives-Radical Equations

- Solving Radical Equations
  - Solve equations containing radicals.
  - Recognize extraneous solutions.
  - Solve application problems that involve radical equations as part of the solution.

Lesson 26 Learning Objectives-Complex Numbers

- Complex Numbers
  - Express roots of negative numbers in terms of i.
  - Express imaginary numbers as bi and complex numbers as a + bi.
- Operations with Complex Numbers
  - Add complex numbers.
  - Subtract complex numbers.
  - Multiply complex numbers.
  - Find conjugates of complex numbers.
  - Divide complex numbers.

Lesson 27 Learning Objectives-Solving Quadratic Equations

- Square Roots and Completing the Square
  - Solve quadratic equations by using the Square Root Property.
  - Identify and complete perfect square trinomials.
  - Solve quadratic equations by Completing the Square.
- The Quadratic Formula
  - Write a quadratic equation in standard form and identify the values of a, b, and c in a standard form quadratic equation.
  - Use the quadratic formula to find all real solutions.
  - Use the quadratic formula to find all complex solutions.
  - Compute the discriminant and state the number and type of solutions.
  - Solve application problems requiring the use of the Quadratic Formula.

Functions

Lesson 28 Learning Objectives-Introduction to Functions

- Identifying Functions
  - Determine whether a relation is a function.
  - Determine the domain of a function and the range of a function.
  - Determine whether a graph is that of a function by using a vertical line test.

Lesson 29 Learning Objectives-Using Functions

- Evaluating Functions
  - Given a function, described by an equation, find function values (outputs) for specified inputs.
- Graphing Types of Functions
  - Graph linear functions.
  - Graph quadratic functions.
  - Graph radical functions.
- Finding Domain and Range
  - Find the domain of a square root function.
  - Find the domain and range of a function from the algebraic form.

Lesson 30 Learning Objectives-Operations with Functions

- Arithmetic Operations with Functions
  - Given two functions, f and g, find their sum, f + g.
  - Given two functions, f and g, find their difference, f – g.
  - Given two functions, f and g, find their product, f • g.
  - Given two functions, f and g, find their quotient, f/g.

The lessons are designed to be self-paced and accomplished at your own pace.

If you have taken the Math Readiness Quiz, you will understand where your math strengths and weakness are and can tailor your learning to just the topics and modules you need. You may review the material as many times as you need and take the quizzes as many times as needed to increase your proficiency in the math concept.