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HOSTOS COMMUNITY COLLEGE
DEPARTMENT OF MATHEMATICS
MAT 020
ELEMENTARY ALGEBRA
CREDIT HOURS:
2.0
EQUATED HOURS:
4.5
CLASS HOURS:
4.5
PREREQUISITE:
MAT 010 or placement on the COMPASS/CMAT
REQUIRED TEXTS:
Martin-Gay Introductory Algebra, 3nd Edition,
Prentice Hall, 2003
Baker/Brenner/Dias Practice for ACT/COMPASS and you
Introductory Algebra Course, Pearson Custom Publishing,
2007
Mathxl Software & Video Lecture C.D.
DESCRIPTION:
This course develops basic skills in algebra, as well as algebraic
and critical thinking of students. During the semester,
students develop understanding of algebraic relationships and
strategies of problem solving. Topics to be discussed include:
Operations with real numbers; algebraic expressions; solving
linear equations; solving applications or word problems;
exponential expressions; operations with and factoring of
polynomials; solving quadratic equations; graphing linear
equations; solutions of systems of linear equations; roots and
radicals.
EXAMINATIONS:
A minimum of three partial tests, a departmental midterm and
a comprehensive departmental final examination.
Students who do not receive an acceptable grade on the
departmental midterm exam will not be certified to take the
COMPASS exam.
GRADES:
A, A-, B+, B, B-, R, I, F.
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MAT 020
COURSE OUTLINE
I.
THE REAL NUMBER SYSTEM & INTRODUCTION TO ALGEBRA:
(Suggested pacing guide 1 week or 3 sessions)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
II.
Introduction: The Sets of Integers, Rational, Irrational and Real
Numbers.
The Real Number Line
Absolute Value
Comparing, Ordering (<; =; >) and Trichotomy.
Addition of Real Numbers and Its Properties.
Subtraction of Real Numbers.
Multiplication of Real Numbers and Its Properties.
Division of Real Numbers.
Powers of Real Numbers with Natural Number Exponents.
Order of Operations Including Grouping Symbols.
The Concept of Variable and Constant.
Definition of Algebraic Expressions.
a. Term
i. Numerical Coefficient
ii. Literal Part
b. Like terms.
The Substitution Principle.
Evaluating Formulas and Algebraic Expressions
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
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7.
III.
ii.
Consecutive Integers
c. Rectangle Problems
d. Age Problems
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
EXPONENTS & OPERATIONS WITH POLYNOMIALS & SPECIAL
PRODUCTS
(1 ½ weeks or 5 sessions)
1.
2.
3.
4.
5.
6.
Operations and Powers of Real Numbers with Integer Exponents.
Exponential Expressions
Negative Exponents and Scientific Notation
Introduction: Basic Concepts of Polynomials.
Addition and Subtraction of Polynomial
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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Factor, Prime Factor and Greatest Common Factor
Factoring a Polynomial that has a Common Factor in each of its Terms
Factoring by Grouping Method
Factoring Trinomials of the Form x2+bx+c
Factoring Trinomials of the Form ax2+bx+c
Factoring Perfect Square Trinomials
Factoring the Difference of two Squares
Factoring Completely
Solving Quadratic Equations by Factoring
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)
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V.
MIDTERM (Certification for COMPASS)
1.
2.
3.
4.
5.
VI.
1 week
The Cartesian -Coordinate System
Ordered Pairs of Real Numbers and Points in a Plane
Geometry in Coordinate Plane; Concepts of parallel, perpendicular
Slope, Square Root and Distance Formula, Pythagorean Theorem.
Review for Midterm
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.
2.
3.
4.
5.
Introduction to Radicals
Simplifying Radicals-(Distance Formula & Pythagorean Theorem)
Addition and Subtraction of Radicals
Multiplication & Division of Radicals – Rationalizing the Denominator
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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