| (For Students) (November, 2001) |
Download entire document in Acrobat format.
Download entire document in Postscript .
Course Description. (3 semester hours) Absolute values. Cartesian coordinates. Graphs of equations. Concept of function. Function notation. Lines. Linear systems. Word problems with linear models. Algebra of Polynomials. Factoring of polynomials. Polynomial Division. Algebra of fractional expressions. Literal equations. Rational equations. Word problems with rational models. Integer and rational exponents. Algebra of radical expressions. Radical equations. Complex numbers. Introduction of quadratic functions. Quadratic equations.
Materials. Required Textbook: Understanding Intermediate Algebra (5th edition) by Hirsh and Goodman, Brooks/Cole, 2002.
Prerequisite. Satisfactory score on basic mathematics screening test and ``C'' or better in MA097.
Objectives. The students are expected to understand how to start algebra and why it is necessary to solve application problems which can be seen in our daily life. The topic to be studied: Basics of skills of algebra including ``handling absolute value'', ``factoring of quadratic functions'', ``calculation of rational and radical expressions'', ``concept of function'', ``solving linear, rational, radical and quadratic equations''.
Course Outline-Topics.
Chapter 2
2.4 Absolute-Value Equations and Inequalities
The fundamentals of the absolute value of x shall be taught so that the student can solve Exercises 2.4.1 ~ 52. The problems 2.4.53 ~ 66 are optional.
(Section 2.4 is the only section in the syllabus in Chapter 2.)
Chapter 3
3.1 The Rectangular Coordinate System and Graphing Straight Lines
To solve some application problems in this course, some knowledge of geometry is necessary, especially the formulas for the area of a rectangle, triangle etc. They will be added in this section.
3.2 Graphs and Equations
3.3 Relation and Functions: Basic Concepts
Here Important concepts are ``function'' and its ``domain''. Optional Exercises: 3.3 1 ~ 8, 25 ~ 44, 63 ~ 68.
3.4 Function Notation
3.5 Interpreting Graphs
Chapter 4
4.1 Straight Lines and Slope
4.2 Equations of a line and Linear Functions as Mathematical Models
4.3 Linear Systems in Two Variables
(Section 4.4 will be omitted.)
Chapter 5
5.1 Polynomial Functions as Mathematical Models
5.2 Polynomials: Sums, Differences, and Products
5.3 General Forms and Special Products
5.4 Factoring Out the Greatest Common Factor
5.5 Factoring Trinomials
5.6 Solving Polynomial Equations by Factoring
5.7 Polynomial Division
Chapter 6
6.1 Rational Function
6.2 Equivalent Fractions
6.3 Multiplication and Division of Rational Expression
6.4 Sums and Differences of Radical Expressions
6.5 Mixed Operations and Complex Fractions
6.6 Fractional Equations and Inequalities
Fractional inequalities will be optional. Accordingly all fractional inequality problems in Exercise 6.5 are optional.
6.7 Literal Equations
6.8 Rational Functions and Equations as Mathematical Models
Chapter 7
7.1 Natural Number and Integral Exponents
7.2 Scientific Notation
Section 7.2 is an optional section.
7.3 Rational Exponents and Radical Notation
7.4 Multiplying Radical Exponents
As for the rationalization of the denominator, the students are expected to have a good understanding of the case of square root. Exercises 7.4.61 ~ 68 are optional.
7.5 Adding and Subtracting Radical Exponents
Exercises 7.5.47, 48, 51, 52, 57, 58 are optional.
7.6 Multiplying and Dividing Radical Exponents
7.7 Radical Functions and Equations
The graph of a radical function will be optional.
7.8 Complex Numbers
Chapter 8
8.1 Quadratic Functions as mathematical Models
8.2 Solving Quadratic Equations: The Factoring and Square Root Method
8.3 Solving Quadratic Equations: Completing the Square
8.4 Solving Quadratic Equations: The Quadratic Formula
(Sections 8.4 is the last section of the syllabus.)
Final Exam. In the Final Exam, topics in optional sections or optional portion of the sections in the syllabus will be excluded.
(Revised by the precalculus committee (November 2001))