## 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

(3 weeks or 9 sessions)

1.Simplifying Expressions

2.Definition and Solution of a Linear Equation in One Variable.

3.Conditional, Identities and Contradictions.

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.

5.Addition and Subtraction of Polynomial

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 x^{2}+bx+c

5. Factoring Trinomials of the Form ax^{2}+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

a. Addition Method

b. Substitution Method

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

1. Introduction to Radicals

2.Simplifying Radicals-(Distance Formula & Pythagorean Theorem)

3.Addition and Subtraction of Radicals

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.