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Syllabus for Intermediate Algebra
COURSE DESCRIPTION:
This course is designed for students with less than two years of high school
algebra. It
is not accepted for college transfer. Students must earn a grade of “C” or
higher in
order to progress to transferlevel mathematics courses. This course will cover
linear
equations and inequalities; graphs of equations —both linear and nonlinear
equations;
slope and equation of lines; systems of equations ; exponents; operations with
and
factoring of polynomials ; operations with rational expressions and solving
rational
equations; operations with radical expressions and solving radical equations;
complex
numbers; functions and graphs; quadratic equations and graphs; exponential and
logarithmic functions. The Texas Instrument TI83 or TI84 graphing calculator
or a
graphing calculator approved by the instructor is recommended for this course.
PREREQUISITES:
MAT 052 and MAT 061 both with a grade of “C” or higher or assessment
COURSE OBJECTIVES:
Upon completion of this course, the student will be able to:
1. Perform arithmetic operations with real numbers, complex numbers, algebraic
expressions, polynomials, rational expressions, and radical expressions.
2. Solve linear, rational, radical, absolute value, logarithmic and exponential
equations in one and two variables.
3. Solve linear inequalities and compound inequalities in one or two variables.
4. Factor polynomials, specifically binomials and trinomials, as well as be able
to
determine those polynomials that cannot be factored.
5. Use various methods to solve quadratic equations, including the quadratic
formula.
6. Use graphs to depict solutions to linear equations and inequalities in one
and two
variables, as well as systems of equations and inequalities in two unknowns .
7. Use slope, slope intercept form and/or pointslope form to find equations of
lines
and use slope and yintercept to determine if lines are parallel or
perpendicular.
8. Solve systems of equations in two and three variables by substitution or
elimination .
9. Use laws of logarithms to simplify logarithmic and exponential expressions.
10. Graph conic sections, exponential and logarithmic equations.
11. Apply problem solving strategies and algebraic solutions to problems
involving
linear expressions, equations and inequalities, rational equations, radical
equations, and systems of equations.
12. Determine the best method for solving systems of equations and then apply
that
method correctly.
13. Determine which law of exponents to apply, when to apply it, and how to
apply it
when simplifying exponential expressions.
14. Determine if a problem involves direct, inverse and joint variation and
solve
accordingly.
15. Apply problem solving strategies to real life problems and problem
situations.
16. Interpret graphs and charts as they apply to real life situations.
17. Graph simple functions, and given a graph, determine whether it is a graph
of a
function.
COURSE OUTLINE:
A. Chapter 1: SOLVING LINEAR EQUATIONS AND INEQUALITIES
1. Solving Equations
2. Formulas and Applications
3. Applications and Problem Solving
4. Sets, Interval Notation, and Inequalities
5. Intersections, Unions, and Compound Inequalities
6. Absolute Value Equations and Inequalities
B. Chapter 2: GRAPHS, MODELS, AND APPLICATIONS
1. Graphs of Equations
2. Functions and Graphs
3. Finding Domain and Range
4. Linear Functions: Graphs and Slope
5. More on Graphing Linear Equations
6. Finding Equations of Lines
C. Chapter 3: SYSTEMS OF EQUATIONS
1. Systems of Equations in Two Variables
2. Solving by Substitution
3. Solving by Elimination
4. Solving Applied Problems: Systems of Two Equations
5. Systems of Equations in Three Variables
6. Solving Applied Problems: Three Equations
7. Systems of Linear Inequalities in Two Variables
D. Chapter 4: POLYNOMIALS AND POLYNOMIAL FUNCTIONS
1. Introduction to Polynomials and Polynomial Equations
2. Multiplication of Polynomials
3. Introduction to Factoring
4. Factoring Trinomials x^{2} + bx + c
5. Factoring Trinomials ax^{2} + bx + c, a ≠ 1
6. Special Factoring
7. Factoring: A General Strategy
8. Applications of Polynomial Equations
E. Chapter 5: RATIONAL EXPRESSIONS AND EQUATIONS
1. Rational Expressions: Multiplying, Dividing, and Simplifying
2. LCMs, LCDs, Addition and Subtraction
3. Division of Polynomials
4. Complex Rational Expressions
5. Solving Rational Equations
6. Applications and Problem Solving
7. Formulas and Applications
8. Variations and Applications
F. Chapter 6: RADICAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS
1. Radical Expressions and Equations
2. Rational Numbers as Exponents
3. Simplifying Radical Expressions
4. Addition, Subtraction, and More Multiplication
5. More on Division of Radical Expressions
6. Solving Radical Equations
7. Applications Involving Powers and Roots
8. The Complex Numbers
G. Chapter 7: QUADRATIC EQUATIONS AND FUNCTIONS
1. The Basics of Solving Quadratic Equations
2. The Quadratic Formula
3. Applications Involving Quadratic Equations
4. More on Quadratic Equations
5. Graphs of Quadratic Equations of the Type f(x) = a(xh)^{2} + k
6. Graphs of Quadratic Equations of the Type f(x) = ax^{2} + bx + c
7. Polynomial and Rational Inequalities
H. Chapter 8: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
1. Exponential Functions
2. Logarithmic Functions
3. Properties of Logarithmic Functions
4. Natural Logarithmic Functions
5. Solving Exponential and Logarithmic Equations
COURSE REQUIREMENTS:
Required Materials. The textbook, along with the usual notebook, paper, pencils,
straightedge, etc. represents the required materials for the class. Your
homework
notebook should be loose leaf paper. Calculators will be allowed on all tests.
The TI83
or TI84 Graphing Calculator (or a graphing calculator approved by the
instructor) is
recommended for this course.
Homework. Homework will be assigned for each section of the text that is
covered. In
general, homework will not be collected nor graded, but the student should do
the
problems assigned as a minimum to attain the skill necessary to do well in the
course.
You are responsible for doing at least the selected odd numbered problems in
each
practice set. The student should expect to spend about two hours of study
outside of
class for each hour of class time.
Attendance. Attendance in this class is both expected and required. John A.
Logan
College’s attendance policy will be enforced:
1. Students are expected to attend all scheduled class periods for the courses
in
which they are enrolled unless they are participating in a scheduled, supervised
college trip or function. There are no excused absences or minimum number of
class “cuts.” All absences must be made up in a manner acceptable to the
instructor.
2. A student who is absent from a class for three consecutive meetings or who is
excessively absent as defined by the instructor (more than 5 absences), without
prior approval, may be required by the instructor to meet with the department
chair before being readmitted to the class. Students who claim illness as a
cause for excessive absences may be required to present a physician’s
statement before being readmitted to class.
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