Algebra I

  
 


DESCRIPTION

Students learn fundamental concepts such as integers; linear equations; how to add, subtract, multiply and divide monomials and polynomials; factoring of polynomials and solving of quadratic equations.This course also includes radicals and exponents. This course is 1 unit of credit.

OBJECTIVES

After completing the course, students will be able to:

  • Perform basic operations with integers and rational numbers.
  • Solve equations and inequalities and word problems. Perform operations with monomials and polynomials.
  • Factor polynomials. Simplify rational expressions.
  • Graph linear equations and determine slope, x-intercept, and y-intercept.
  • Solve systems of linear equations, radical equations, and quadratic equations.
 
 

Course Outline, First Semester

  1. PROBLEM SOLVING
    1. Guess and Check
    2. Draw a Diagram
    3. Make a List or a Table
    4. Find a Pattern
    5. Work Backward
    6. Choose a Strategy

  2. THE LANGUAGE OF ALGEBRA
    1. Algebraic Expressions
    2. Terms, Factors, and Exponents
    3. The Number Line
    4. Using an Equation in an Algebraic Model
    5. Working With an Inequality

  3. REAL NUMBERS: PROPERTIES AND OPERATIONS
    1. Addition of Real Numbers
    2. Multiplication of Real Numbers
    3. Subtraction and Division of real numbers
    4. The Distributive Property; Summary of Properties

  4. EQUATIONS AND INEQUALITIES
    1. Solving an Equation by Applying Inverses
    2. Combining Like Terms in an Equation
    3. Working With a Formula
    4. Solving an Inequality
    5. Absolute Value in an Open Sentence

  5. APPLICATIONS OF EQUATIONS AND INEQUALITIES
    1. Consecutive-integer Problems
    2. Money-Value Problems
    3. Motion Problems
    4. Lever and Pulley Problems
    5. Angle Problems
    6. Triangle Problems
    7. Perimeter and Area Problems
    8. Surface Area and Volume Problems

Course Outline Second Semester

  1. POLYNOMIALS
    1. Adding and Subtracting Polynomials
    2. Properties of Exponents
    3. Scientific Notation
    4. Multiplying Polynomials
    5. Dividing Polynomials
    6. Factoring
    7. More about Factoring
    8. Solving a Quadratic Equation by Factoring

  2. RATIONAL EXPRESSIONS AND OPEN SENTENCES
    1. Simplifying a Rational Expression
    2. Multiplying and Dividing Rational Expressions
    3. Adding and Subtracting Rational Expressions
    4. Applying Open Sentences that Contain Fractional Coefficients
    5. Solving Equations that Contain Rational Expressions
  3. APPLYING RATIO AND PROPORTION
    1. Ratio
    2. Proportion
    3. Similarity

  4. RELATIONS, FUNCTIONS, AND GRAPHS
    1. Graphing in a Plane
    2. Relations and Their Graphs
    3. Functions and Their Graphs
    4. Lines and Linear Functions
    5. The Slope of a Line

  5. SYSTEMS OF EQUATIONS AND INEQUALITIES
    1. Solving a System of Linear Equations Graphically
    2. Solving a System of Linear Equations Algebraically
    3. Solving a System of Linear Inequalities Graphically

  6. IRRATIONAL NUMBERS
    1. Finding the Root of a Number
    2. Simplifying and Combining Radicals
    3. Multiplying and Dividing Radicals
    4. Solving a Radical Equation
 
 

TEXTBOOK:Algebra 1, Alan G. Foster, et al., 1995