MAT 121

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COURSE SYLLABUS

1.

TITLE OF COURSE:

College Algebra

PREFIX/NUMBER:

MAT 121

CREDIT HOURS:

4

2.

PREREQUISITE:

Successful completion of MAT 106 with a C or better or math assessment

3.

RESOURCES NEEDED:

TEXT:

College Algebra, 10/e by Margaret L. Lile, John Hornsby, and David I. Schneider

SUPPLIES:

Pencil, paper, and scientific calculator

4.

COURSE DESCRIPTION:

Includes a brief review of intermediate algebra, equations and inequalities, functions and their graphs, exponential and logarithmic functions, linear and nonlinear systems, selection of topics from among graphing of the conic sections, introduction to sequences and series permutations and combinations, the binomial theorem, and theory of equations.

5.

STANDARD COMPETENCIES

A.

Be familiar with set notations, subsets of the real numbers and properties of real numbers.

B.

Perform algebraic manipulations including working with exponents, radicals, polynomial operations, factoring and algebraic fractions.

C.

Present methods for solving first and second degree equations and inequalities and related topics.

D.

Solve the following types of equations: linear, quadratic, equations involving radicals, equations in quadratic form and equations involving absolute value.

E.

Work with formulas including formula evaluation and solving formula for any of the variables.

F.

Read and analyze problems in the form of word problem applications and obtain solutions using equations.

G.

Solve first degree inequalities, higher degree inequalities and inequalities involving absolute value.

H.

Recognize and graph linear functions, absolute value functions, and graph inequalities in two variables.

I.

Work with function notation and demonstrate knowledge of the meaning "function."

J.

Demonstrate an understanding of function composition, one-to-one functions, and inverse functions.

K.

Examine, evaluate and graph exponential functions.

L.

Examine, evaluate and graph logarithmic functions.

M.

Work problems and solve equations containing exponential and logarithmic functions.

N.

Explore a variety of techniques use to solve linear and non-linear systems of equations.

O.

Use at least two of the following techniques to solve linear and non-linear systems of equations: substitution, addition, Gaussian elimination, Cramer's Rule.

P.

Have some familiarity with matrices and operations involving matrices.

Q.

Graph systems of inequalities.

R.

Graph conic sections including circles, parabolas, ellipses and hyperbolas.

S.

Identify the conic sections represented by a given second degree equation.

T.

Introduce various topics related to sequences and series.

U.

Work with series notation and sequence formulas, and counting principles.

V.

Apply the Binomial Theorem.

W.

Demonstrate an understanding of proof by mathematical induction.

X.

Present topics in theory of equations.

Y.

Perform synthetic division.

Z.

Use the Remainder Theorem and the Factor Theorem to factor and evaluate polynomials.

AA.

Solve polynomial equations using the Rational Root Theorem and/or approximation techniques.

AB.

Write and speak clearly and logically.

AC.

Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.

6.

COURSE OUTLINE

R.0

Review of Basic Concepts (This is review material that will NOT be covered in the course.)

R.1 Sets

R.2 Real Numbers and Their Properties

R.3 Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Rational Exponents

R.7 Radical Expressions

1.0

Equations and Inequalities

1.1 Linear Equations

1.2 Applications and Modeling with Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications and Modeling with Quadratic Equations

1.6 Other Types of Equations and Applications

1.7 Inequalities

1.8 Absolute Value Equations and Inequalities

2.0

Graphs and Functions

2.1 Rectangular Coordinates and Graphs

2.2 Circles

2.3 Functions

2.4 Linear Functions

2.5 Equations of Lines; Curve Fitting

2.6 Graphs of Basic Functions

2.7 Graphing Techniques

2.8 Function Operations and Composition

3.0

Polynomial and Rational Functions

3.1 Quadratic Functions and Models

3.2 Synthetic Division

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models

3.5 Rational Functions: Graphs, Applications, and Models

3.6 Variation

4.0

Invers, Exponential, and Logarithmic Functions

4.1 Invers Functions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

4.5 Exponential and Logarthmic Equations

4.6 Applications and Models of Exponential Growth

5.0

Systems and Matrices

5.1 Systems of Linear Eqautions

5.2 Matrix Solution of Linear Systems

5.3 Determinant Solution of Linear Systems

5.4 Partial Fractions

5.5 Nonlinear Systems of Equations

5.6 Systems of Inequalities and Linear Programming

5.7 Properties of Matrices

6.0

Analytic Geometry

6.1 Parabolas

6.2 Ellipses

6.3 Hyperbolas

6.4 Summary of Conic Sections

7.0

Further Topics in Algebra

7.1 Sequences and Series

7.4 The Binomial Theorem

7.

1.	TITLE OF COURSE:	College Algebra
	PREFIX/NUMBER:	MAT 121	CREDIT HOURS:	4
2.	PREREQUISITE:	Successful completion of MAT 106 with a C or better or math assessment

3.	RESOURCES NEEDED:
	TEXT:	College Algebra, 10/e by Margaret L. Lile, John Hornsby, and David I. Schneider
	SUPPLIES:	Pencil, paper, and scientific calculator
4.	COURSE DESCRIPTION:	Includes a brief review of intermediate algebra, equations and inequalities, functions and their graphs, exponential and logarithmic functions, linear and nonlinear systems, selection of topics from among graphing of the conic sections, introduction to sequences and series permutations and combinations, the binomial theorem, and theory of equations.

5.	STANDARD COMPETENCIES
	A.	Be familiar with set notations, subsets of the real numbers and properties of real numbers.
	B.	Perform algebraic manipulations including working with exponents, radicals, polynomial operations, factoring and algebraic fractions.
	C.	Present methods for solving first and second degree equations and inequalities and related topics.
	D.	Solve the following types of equations: linear, quadratic, equations involving radicals, equations in quadratic form and equations involving absolute value.
	E.	Work with formulas including formula evaluation and solving formula for any of the variables.
	F.	Read and analyze problems in the form of word problem applications and obtain solutions using equations.
	G.	Solve first degree inequalities, higher degree inequalities and inequalities involving absolute value.
	H.	Recognize and graph linear functions, absolute value functions, and graph inequalities in two variables.
	I.	Work with function notation and demonstrate knowledge of the meaning "function."
	J.	Demonstrate an understanding of function composition, one-to-one functions, and inverse functions.
	K.	Examine, evaluate and graph exponential functions.
	L.	Examine, evaluate and graph logarithmic functions.
	M.	Work problems and solve equations containing exponential and logarithmic functions.
	N.	Explore a variety of techniques use to solve linear and non-linear systems of equations.
	O.	Use at least two of the following techniques to solve linear and non-linear systems of equations: substitution, addition, Gaussian elimination, Cramer's Rule.
	P.	Have some familiarity with matrices and operations involving matrices.
	Q.	Graph systems of inequalities.
	R.	Graph conic sections including circles, parabolas, ellipses and hyperbolas.
	S.	Identify the conic sections represented by a given second degree equation.
	T.	Introduce various topics related to sequences and series.
	U.	Work with series notation and sequence formulas, and counting principles.
	V.	Apply the Binomial Theorem.
	W.	Demonstrate an understanding of proof by mathematical induction.
	X.	Present topics in theory of equations.
	Y.	Perform synthetic division.
	Z.	Use the Remainder Theorem and the Factor Theorem to factor and evaluate polynomials.
	AA.	Solve polynomial equations using the Rational Root Theorem and/or approximation techniques.
	AB.	Write and speak clearly and logically.
	AC.	Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.
6.	COURSE OUTLINE
	R.0	Review of Basic Concepts (This is review material that will NOT be covered in the course.)
		R.1 Sets
		R.2 Real Numbers and Their Properties
		R.3 Polynomials
		R.4 Factoring Polynomials
		R.5 Rational Expressions
		R.6 Rational Exponents
		R.7 Radical Expressions

	1.0	Equations and Inequalities
		1.1 Linear Equations
		1.2 Applications and Modeling with Linear Equations
		1.3 Complex Numbers
		1.4 Quadratic Equations
		1.5 Applications and Modeling with Quadratic Equations 1.6 Other Types of Equations and Applications 1.7 Inequalities 1.8 Absolute Value Equations and Inequalities
	2.0	Graphs and Functions
		2.1 Rectangular Coordinates and Graphs
		2.2 Circles
		2.3 Functions
		2.4 Linear Functions
		2.5 Equations of Lines; Curve Fitting
		2.6 Graphs of Basic Functions 2.7 Graphing Techniques 2.8 Function Operations and Composition

	3.0	Polynomial and Rational Functions
		3.1 Quadratic Functions and Models
		3.2 Synthetic Division
		3.3 Zeros of Polynomial Functions
		3.4 Polynomial Functions: Graphs, Applications, and Models
		3.5 Rational Functions: Graphs, Applications, and Models
		3.6 Variation
	4.0	Invers, Exponential, and Logarithmic Functions
		4.1 Invers Functions
		4.2 Exponential Functions
		4.3 Logarithmic Functions
		4.4 Evaluating Logarithms and the Change-of-Base Theorem 4.5 Exponential and Logarthmic Equations 4.6 Applications and Models of Exponential Growth
	5.0	Systems and Matrices
		5.1 Systems of Linear Eqautions 5.2 Matrix Solution of Linear Systems
		5.3 Determinant Solution of Linear Systems 5.4 Partial Fractions
		5.5 Nonlinear Systems of Equations
		5.6 Systems of Inequalities and Linear Programming 5.7 Properties of Matrices

	6.0	Analytic Geometry
		6.1 Parabolas
		6.2 Ellipses
		6.3 Hyperbolas
		6.4 Summary of Conic Sections
	7.0	Further Topics in Algebra
		7.1 Sequences and Series
		7.4 The Binomial Theorem