COURSE TITLE: College Algebra
TEXTBOOK: Elementary and Intermediate Algebra. 3rd Edition. Tom Carson and Bill Jordan, 2011.
COURSE DESCRIPTION: Introduces basic concepts of algebra including real numbers, variables and algebraic expressions, equations, inequalities, ratios and proportions, Cartesian coordinate system and graphs of relations, rational expressions, complex numbers, and functions that are polynomial, rational, exponential or logarithmic. Emphasizes mathematical reasoning and problem solving utilizing multiple approaches (algebraic, geometric, and numeric techniques) with focus on mathematical definitions, theorems, symbols and notations
Prerequisite: Algebra II
COURSE REQUIREMENT/REQUIRED MATERIALS:
A. Text: Elementary and Intermediate Algebra; Carson, Jordan, Gillespie; 2011
B. A 3-ring binder for homework and class notes.
C. Pencils and red pens.
D. Graphing calculator (TI 83 or 84 Plus recommended).
COURSE OUTLINE:
I. Foundations of Algebra
A. Number Sets and the Structure of Algebra
B. Fractions
C. Adding and Subtracting Real Numbers; Properties of Real Numbers
D. Multiplying and Dividing Real Numbers
E. Exponents, Roots, and Order of Operations
F. Evaluating and Rewriting Expressions
II. Solving Linear Equations and Inequalities
A. Equations, Formulas, and the Problem-Solving Process
B. The Addition Principle of Equality
C. The Multiplication Principle of Equality
D. Applying the Principles to Formulas
E. Translating Word Sentences to Equations
III. Graphing Linear Equations and Inequalities
A. The Rectangular Coordinate System
B. Graphing Linear Equations
C. Graphing using Intercepts
D. Slope-Intercept Form
E. Point-Slope Form
F. Graphing Linear Inequalities
G. Introduction to Functions and Function Notation
IV. Polynomials
A. Exponents and Scientific Notation
B. Introduction to polynomials
C. Adding and Subtracting Polynomials
D. Exponent Rules and Multiplying Polynomials
E. Multiplying Polynomials; Special Products
F. Exponent Rules and Dividing Polynomials
V. Factoring
A. Greatest Common Factor and Factoring by Grouping
B. Factoring Trinomials of the Form
C. Factoring Trinomials of the Form
D. Factoring Special Products
E. Strategies for Factoring
F. Solving Quadratic Equations by Factoring
G. Graphs of Quadratic Equations and Functions
VI. Rational Expressions and Equations
A. Simplifying Rational Expressions
B. Multiplying and Dividing Rational Expressions
C. Adding and Subtracting Rational Expressions
D. Complex rational Expressions
E. Solving Equations Containing rational Expressions
F. Applications with Rational Expressions
VII. Inequalities, Absolute Value, and Functions
A. Compound Inequalities
B. Equations Involving Absolute Value
C. Inequities Involving Absolute Value
D. Functions and Graphing
E. Function Operation
VIII. Systems of Linear Equations
A. Solving Systems of Linear Equations Graphically
B. Solving Systems of Linear Equations by Substitution
C. Solving Systems of Linear Inequalities by Elimination
IX. Rational Exponents, radicals, and Complex Numbers
A. Radical Expressions and Functions
B. Rational Exponents
C. Multiplying, Dividing, and Simplifying Radicals
D. Adding, Subtracting, and Multiplying Radical Expressions
E. Rationalizing Denominators of Radical Expressions
F. Radical Equations and problem Solving
G. Complex Numbers
X. Quadratic Equations and Functions
A. The Square Root Principle and Completing the Square
B. Solving Quadratic Equations Using the Quadratic Formula
C. Solving Equations That Are Quadratic in Form
D. Graphing Quadratic Functions
XI. Exponential and Logarithmic Functions
A. Composite and Inverse Functions
B. Exponential Functions
C. Logarithmic Functions
D. Properties of Logarithms
E. Common and Natural Logarithms
F. Exponential and Logarithmic Equations with Applications
XII. Trigonometric Functions
A. Right Triangle Trigonometry
B. Angles and Angle Measure
C. Trigonometric Functions of General Angles
D. Law of Sines
E. Law of Cosines
F. Circular Functions
G. Inverse Trigonometric Functions
XIII. Trigonometric Graphs and Identities
A. Graphing Trigonometric Functions
B. Translations of Trigonometric Graphs
C. Trigonometric Identities
D. Verifying Trigonometric Identities
E. Sum and Difference of Angles Formulas
F. Double-Angle and half-Angle Formulas
G. Solving Trigonometric Equations
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