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# Introductory Algebra

Prerequisite
Grade of “C” or better in MAT-010, or passing score on placement examination.

Catalog Course Description
Covers topics in elementary algebra: integral, rational and irrational numbers, techniques of
graphing and solving linear equations, polynomials and their operations , special products and
methods of solutions. Applications of linear and quadratic equations are included as well.

Objectives of Course

This is the first of a two-course sequence in algebra designed to introduce and develop the
elementary concepts embodied in the topics listed above. Students will be trained in critical
thinking, oral and written skills as they pertain to algebra and mathematics in general.

 Day Sections Topics ALEKS PIE & QUIZ 1 Introduction, R.4, 1.3 R.4 Introduction to Geometry Obj. 1-Perimeter Obj. 2-Area Obj. 4-Angles Obj. 5-Triangles 1.3 Addition of real Numbers Obj. 1-Addition of Real Numbers and the Number Line Obj. 2-Addition of Real Numbers Obj. 3-Translations Obj. 4-Applications Involving Addition of Real Numbers Work on Arithmetic Readiness, Practice Quiz # 1 and assign Mastery Quiz # 1 (Chapter R) 2 1.4, 1.5 1.4 Subtraction of Real Numbers Obj. 1-Subtraction of Real Numbers Obj. 2-Translations Obj. 3-Applications Involving Subtraction Obj. 4-Applying the Order of Operations 1.5 Multiplication and Division of Real Numbers Obj. 1-Multiplication of Real Numbers Obj. 2- Exponential Expressions Obj. 3-Division of Real Numbers Obj. 4-Applying the Order of Operations Work on Real numbers and variables, Practice Quiz # 2 and assign Mastery Quiz # 2 (Chapter 1) 3 1.6, 2.1 1.6 Properties of Real Numbers and Simplifying Expressions Obj. 1-Commutative properties of real Numbers Obj. 2-Associative properties of Real Numbers Obj. 3-Identity and Inverse Properties of Real Numbers Obj. 4-Distributive properly of Multiplication over Addition Obj. 5- Simplifying Algebraic Expressions 2.1 Addition, Subtraction, Multiplication, and Division properties of Equality Obj.1-Definition of a linear equation in One Variable Obj.2-Addition and Subtraction Properties of Equality Obj.3-Multiplication and Division Properties of Equality Obj.4-Translations Work on Linear Equations and Inequalities, Practice Quiz # 3 and assign Mastery Quiz # 3 (Chapter 2) 4 2.2, 2.3 2.2 Solving Linear Equations Obj.1-Solving Linear Equations Involving Multiple Steps Obj.2-Procedure for Solving a linear equation in One Variable Obj. 3-Conditional Equations, Identities, and Contradictions 2.3 Linear Equations: Clearing Fractions and Decimals Obj.1-Solving Linear equations with Fractions 5 2.4, 2.6 2.4 Applications of Linear Equations: Introduction to Problem Solving Obj. 1-Problem-Solving Strategies Obj. 2-Translations Involving Linear Equations Obj. 3-Consecutive Integer problems Obj. 4-Applications of Linear Equations 2.6 Formulas and Applications of Geometry Obj. 1-Formulas and Literal Equations Obj. 2-Geometry Applications 6 Review 7 TEST #1 Due Mastery Quizzes # 1,2, 3 8 3.1, 3.2 3.1 Rectangular Coordinate System Obj. 2-Plotting in a Rectangular Coordinate System Obj. 3-Applications of Plotting and Identifying Points 3.2 Linear Equations in Two Variables Obj. 1-Definition of a Linear equation in Two Variables Obj. 2-Graphing Linear equations in Two Variables by Plotting Points Obj. 3- x-and y- Intercepts Obj. 4-Horizontal and Vertical Line Work on Functions, lines, systems of equations, Practice Quiz # 4 and assign Mastery Quiz # 4 (Chapter 3) 9 3.3, 3.4 3.3 Slopes of a Line and Rates of Change Obj. 1-Introduction to Slope Obj. 2-Slope formula Obj. 3-Parellel and Perpendicular Lines Obj. 4-Applications of Slope: Rate of Change 3.4 Slope- Intercept Form of a Line Obj. 1-Slope-Intercept Form of a Line Obj. 2-Graphing a Line from Its Slope and y- Intercept Obj. 3-Determine Whether two Lines Are Parallel, Perpendicular, Or Neither Obj. 4-Writing an Equation of a line Using Slopeintercept Form 10 3.5, 4.1 3.5 Point-Slope Formula Obj. 1- Writing an equation of a Line using the Point- Slope Formula Obj. 2-Writing an Equation of a Line Given two Points Obj. 3-Writing an Equation of a Line Parallel or Perpendicular to Another Line Obj. 4- Different forms of Linear Equations: A Summary 4.1 Solving Systems of equations by the Graphing method Obj. 1-determine Solutions to a System of Linear Equations Obj. 2-Dependent and Inconsistent Systems of Linear Equations Obj. 3-Solving Systems of Linear Equations by Graphing Practice Quiz # 5 and assign Mastery Quiz # 5 (Chapter 4) 11 4.2, 4.3 4.2 Solving Systems of Equations by the Substitution method Obj. 1-Solving Systems of Linear Equations by the Substitution Method Obj. 2-Solutions to Systems of Linear Equations: A Summary Obj. 3-Applications of the Substitution method 4.3 Solving Systems of Equations by the Addition Method Obj. 1-Solving a System of Linear equations by the Addition method Obj. 2-Summary of Methods for using Linear Equations in two Variables 12 4.4 and Review 4.4 Applications of Linear Equations in Two Variables Obj. 1-Applications Involving Cost 13 TEST # 2 Due Mastery Quizzes # 4,5 14 5.1, 5.2 5.1 Exponents: Multiplying and Dividing Common bases Obj. 1-Review of exponential Notation Obj. 2-Evaluating Expressions with exponents Obj. 3-Multiplying and Dividing Common Bases Obj. 4-Simplifying Expressions with Exponents 5.2 More properties of Exponents Obj. 1-Power Rule for Exponents Obj. 2-The Properties (ab)m and Work on Integer exponents and polynomials, Practice Quiz # 6 and assign Mastery Quiz # 6 (Chapter 5) 15 5.3, 5.4 5.3 Definitions of  b0 and  b-n Obj. 1-Definition of b0 Obj. 2-Definition of b-n Obj. 3-Properties of Integer Exponents: A Summary 5.4 Scientific Notation Obj. 1-Writing numbers in Scientific Notation Obj. 2-Writing Numbers in Standard Form Obj. 3-Multiplying and Dividing Numbers in Scientific Notation 16 5.5, 5.6 5.5 Addition and Subtraction of Polynomials Obj. 1-Introduction to Polynomials Obj. 2-Addition of polynomials Obj. 3-Subtraction of polynomials Obj. 4-Polynomials and applications to Geometry 5.6 Multiplication of Polynomials and Special products Obj. 1-Multiplication of Polynomials Obj. 2-Special case Products: Difference of Squares and perfect square Trinomials Obj. 3-Applications to Geometry 17 5.7, Review 5.7 Division of Polynomials Obj. 1- Division by a Monomial Obj. 2-Long Division (if time permits) 18 TEST # 3 Due Mastery Quiz # 6 19 6.1, 6.2, 6.3 6.1 Greatest Common Factor and Factoring by Grouping Obj. 1-Identifying the Greatest Common Factor Obj. 2-Factoring out the Greatest Common factor Obj. 3-Factoring out a Negative factor Obj. 4-Factoring out a Binomial factor Obj. 5-Factoring by Grouping 6.2 Factoring Trinomials of the Form x2 + bx + c 2 Obj. 1-Factoring Trinomials with a leading Coefficient of 1 6.3 Factoring Trinomials: trial-and-Error method Obj. 1- Factoring Trinomials by the Trial-and-Error method Work on Complex numbers and quadratic equations, Practice Quiz # 7 and assign Mastery Quiz # 7 (Chapter 6) 20 6.4,6.5 6.4 Factoring trinomials: AC-Method Obj. 1-Factoring Trinomials by the AC-Method 6.5 Difference of Squares and Perfect Square Trinomials Obj. 1-Factoring a Difference of Squares Obj. 2-Factoring Perfect Square Trinomials 21 6.7, 6.8 6.7 Solving Equations Using the Zero product Rule Obj. 1-Definition of a Quadratic Equation Obj. 2-Zero Product Rule Obj. 3-Solving Equations by Factoring 6.8 Applications of Quadratic Equations Obj. 1-Applications of Quadratic Equations 22 7.1, 7.2 7.1 Introduction to Rational Expressions Obj. 1-Definition of a Rational Expression Obj. 2-Evaluating rational Expressions Obj. 3-Domain of a rational Expression Obj. 4-Simplifying Rational Expressions to Lowest Terms Obj. 5-Simplifying a Ratio of -1 7.2 Multiplication and Division of rational Expressions Obj. 1-Multiplication of rational Expressions Obj. 2-Division of Rational Expressions Work on Rational expressions and proportions , Practice Quiz # 8 and assign Mastery Quiz # 8 (Chapter 7) 23 7.3, 7.4 7.3 Least Common Denominator Obj. 1-Least Common Denominator Obj. 2-Writing Rational Expressions with the Least Common Denominator 7.4 Addition and Subtraction of Rational Expressions Obj. 1-Addition and Subtraction of Rational Expressions with the Same Denominators Obj. 2-Addition and Subtraction of rational Expressions with Different Denominators Obj. 3-Using Rational Expressions in Translations 24 8.1, 8.2, 8.3 8.1 Introduction to Roots and radicals Obj. 1-Definition of a Square Root 8.2 Simplifying Radicals Obj. 1-Multiplication property of Radicals(Focus on square roots) Obj. 2-Simplifying Radicals Using the Multiplication Property of radicals 8.3 Addition and Subtraction of Radicals Obj. 1-Definition of Like Radicals Obj. 2-Addition and Subtraction of Radicals Work on Radicals and rational exponents, Practice Quiz # 9 and assign Mastery Quiz # 9 (Chapter 8) 25 Catch-up and Review 26 TEST # 4 Due Mastery Quizzes # 7,8,9 27 Final Review 28 FINAL