# ELEMENTARY ALGEBRA

## I.THE REAL NUMBER SYSTEM & INTRODUCTION TO ALGEBRA:

(Suggested pacing guide 1 week or 3 sessions)

1.Introduction: The Sets of Integers, Rational, Irrational and Real Numbers.
2.The Real Number Line
3. Absolute Value
4.Comparing, Ordering (<; =; >) and Trichotomy.
5.Addition of Real Numbers and Its Properties .

6. Subtraction of Real Numbers.
7. Multiplication of Real Numbers and Its Properties.
8.Division of Real Numbers.
9.Powers of Real Numbers with Natural Number Exponents.
10.Order of Operations Including Grouping Symbols .

11.The Concept of Variable and Constant.
12.Definition of Algebraic Expressions.
a.Term
i. Numerical Coefficient
ii. Literal Part
b.Like terms.
13.The Substitution Principle.
14.Evaluating Formulas and Algebraic Expressions

## II.LINEAR EQUATIONS IN One Variable & APPLICATIONS:

(3 weeks or 9 sessions)

1.Simplifying Expressions
2.Definition and Solution of a Linear Equation in One Variable.
4.Equivalent Equations: Addition and Multiplication Principle.
5.Solving a Linear Equation by Using Equivalent Equations:
a.With Integral Coefficients
b.With Fractional and Decimal Coefficientes.
c.Literal Equations

6.Solving Word Problems (application problems) Using a Linear Equation or System of Linear Equations:
a.Translating from English to Algebra
b.Number Relation Problems
i.Number Problems
ii.Consecutive Integers
c.Rectangle Problems
d.Age Problems
7.Application or word problems that involve a linear equation with percents, proportions formulas etc.
a.Percent Problems
b.Proportion Problems
c.Rate Problems
d.Mixture or Solution problems
e.Average Problems

## III.EXPONENTS & OPERATIONS WITH POLYNOMIALS & SPECIAL PRODUCTS

(1 ½ weeks or 5 sessions)

1.Operations and Powers of Real Numbers with Integer Exponents.
2. Exponential Expressions
3.Negative Exponents and Scientific Notation
4.Introduction: Basic Concepts of Polynomials.

6.Multiplication of Polynomials.
a. A Monomial times a Monomial
b. A Polynomial times a Monomial
c. A Binomial times a Binomial
d. A Polynomial times a Polynomial
7.Division of Polynomial
a. A Monomial by Monomials
b. A Polynomial by a Monomial
c. A Polynomial by a Polynomial

## IV.FACTORING AND APPLICATIONS:

(3 weeks or 9 sessions)

1. Factor, Prime Factor and Greatest Common Factor
2. Factoring a Polynomial that has a Common Factor in each of its Terms
3. Factoring by Grouping Method
4. Factoring Trinomials of the Form x2+bx+c
5. Factoring Trinomials of the Form ax2+bx+c

6. Factoring Perfect Square Trinomials
7. Factoring the Difference of two Squares
8. Factoring Completely
9. Solving Quadratic Equations by Factoring
10. Applications of Factoring to Rational Expressions:
a. Reduction of Rational Expressions to Lowest Terms
b. Multiplication of Rational Expressions
c. Division of Rational Expressions
d. Addition and Subtraction of Rational Expressions (optional)

## V. MIDTERM (Certification for COMPASS)

1 week

1.The Cartesian - Coordinate System
2.Ordered Pairs of Real Numbers and Points in a Plane
3.Geometry in Coordinate Plane; Concepts of parallel, perpendicular
4.Slope, Square Root and Distance Formula, Pythagorean Theorem.
5.Review for Midterm

## VI. LINEAR EQUATIONS IN TWO VARIABLES: (2 week = 6 sessions)

(Continuation of graphing)

6.Definition and Solution of a Linear Equation in Two Variables
7. Graphing a Linear Equation:
a.by finding Two Points
b.by the Intercepts Method
5. Concept of Slope of a Straight Line
a. Finding the Slope of a Line When Two Points are given
b. Graphing a Straight Line Using the Slope y-Intercept Method
c. Vertical and Horizontal Lines
6. Graphing Systems of Two Linear Equations in Two Variables:
a. Intersecting Lines
b. Parallel Lines
c. Coincident Lines
7. Find the Equation of a line
a. by using the slope-intercept formula
b. given two points on the line
c. given a point on the line and the slope of a parallel/perpendicular line
8. Algebraic Solution of Systems of Two Linear Equations In Two Variables
b. Substitution Method

## VI. ROOTS & RADICALS (1 ½ week or 4 sessions)

2.Simplifying Radicals-(Distance Formula & Pythagorean Theorem)
4.Multiplication & Division of Radicals – Rationalizing the Denominator
5.Rational Exponents

REVIEW FOR FINAL EXAM (1 week or 3 sessions)
Total weeks = 13 with 1 week for review
Total sessions = 39 + 3 review

(*) Please be advised that while the instructor is responsible for covering each topic in this syllabus he/she may change the order and the pacing in which the topics are presented.

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