Intermediate Algebra Syllabus

COURSE DESCRIPTION:

Reviews real numbers , polynomials, algebraic functions , first-degree equations
and inequalities. Studies quadratic equations , exponents, radicals and rational
expressions and equations , complex numbers, graphing equations and inequalities in
two variables , systems of equations in two and three variable, applications of first and
second degree equations and an introduction to functions.

Prerequisites: C or better in Math 25 or Math 26, or placement in Math 27.

COURSE OBJECTIVES:

To review the basic operations of sets, especially the set of real numbers .
To acquire proficiency in solving linear equations and linear inequalities,
including their applications.

To develop an understanding of (integer) exponents, their basic properties,
and the operations of polynomials, including solving polynomial equations
(up through the 3rd degree).

To develop an understanding of rational expressions , their basic operations,
and of solving (basic) rational equations.

To develop an understanding of rational exponents, radical expressions,
their basic operations, complex numbers, and solving radical equations.
To acquire proficiency in the graphing of linear equations (including an
understanding of their properties & applications) and linear inequalities.
To acquire proficiency in solving quadratic equations, and an initial
understanding of their applications.

To acquire proficiency in solving systems of linear equations.
To develop an understanding of functions, especially linear, quadratic, and
polynomial functions.

In addition, as in most mathematical courses, students will be presented
with the challenge of utilizing critical thinking along with development
of communicating their analyses in a neat and ordered fashion .

INSTRUCTIONAL MATERIALS:

Textbook:
INTERMEDIATE ALGEBRA for College Students
by Robert Blitzer ) Fourth Edition

Calculators:
A scientific calculator is required .

Recommended:
Graph paper or engineering pad;
A loose-leaf notebook for storing HomeWork, exams,
quizzes, and notes.

UNIT 1. Algebra, Mathematical Models & Problem Solving
Algebraic Expressions and Real Numbers; Operations with Real Numbers and
Simplifying Algebraic Expressions; Graphing Equations; Solving Linear
Equations; Problem Solving and Using Formulas; Properties of Integral
Exponents; Scientific Notation.

UNIT 2. Functions
Introduction to Functions; Algebra of Functions; Linear Functions & Slope;
Point-Slope Form of the Equation for a Line.

UNIT 3. Systems of Linear Equations
Systems of Linear Equations in Two Variables; Problem Solving and Business
Applications; Systems of Linear Equations in Three Variables.

UNIT 4. Inequalities & Problem Solving
Linear Equalities; Compound Inequalities; Equations with Absolute Value;
Linear Inequalities in Two Variables .

UNIT 5. Polynomial Expressions, Functions, & Factoring
Intro to Polynomials & Polynomial Functions; Multiplication of Polynomials;
Greatest Common Factors; Factoring Trinomials; Factoring Special Forms;
General Factoring Strategy; Polynomial Equations and Their Applications.

UNIT 6. Rational Expressions, Functions & Equations
Rational Expressions & Functions; Multiplying & Dividing; Compound Rational
Expressions; Division of Polynomials; Rational Equations; Formulas &
Applications with Rational Equations; Modeling Using Variation.

UNIT 7. Radical Expressions, Functions & Rational Exponents
Radical Expressions & Functions; Operations on Radicals; Rational Exponents;
Multiplying & Simplifying Radical Expressions; Adding, Subtracting & Dividing
Radical Expressions; Multiplying with More Than One Term & Rationalizing
Denominators ; Radical Equations; Complex Numbers.

UNIT 8. Quadratic Equations & Functions
Square Root Property; Quadratic Formula; Quadratic Functions; Equations in
Quadratic Form; Polynomial Inequalities.