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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.
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 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
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.

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