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# Topics in class for TEST 3 MATH 156

Ch 4 – number theory

4-4: Prime numbers:
· Definition
· Decide whether a number is prime (*largest prime needed to test?
THM 4-6)

4-4: Composite numbers:
· Definition
· Factoring composite numbers (not prime factorization)
o Visually (rectangles)
o numerically
· Prime factorization – tree or box method
· Fundamental Theorem of Arithmetic (THM 4-3)
· THM 4-4

4-5: Greatest Common Factor (GCF = GCD: Greatest Common Divisor ):
· Intersection of sets method
· Prime factorization method
· Euclidean Algorithm method
· Be able to tell what it is used for

4-5: Least Common Multiple (LCM = LCD: Least Common Denominator ):
· Intersection of sets method
· Prime factorization method
· Euclidean Algorithm method
· Be able to tell what it is used for

Chapter 5 – fractions (underlined topics = online tutorial available )

5-1: Introduction to Fractions:
· Set of rational numbers
· Difference between rational numbers and set of “fractions”
· Numerator
· Denominator
· Represent a particular fraction (draw a picture using a circles or rectangles &
· Equivalent fractions
· Mixed numbers
· Improper fractions (be able to convert back and forth )
· Estimating the value of a fraction (and decide whether estimation is high or
low
)
· Fundamental Law of Fractions
· Simplifying fractions (using the Fundamental Law of Fractions)

· Adding fractions – like and unlike denominators (visual and/or arithmetic)

5-3: Subtracting Fractions :
· Subtracting fractions
o Visual (with borrowing)
o Regrouping (borrowing)
o Improper fractions
· Alternate methods:
o Up-the-hill
o Negative numbers (Expanded Algorithm)

5-3: Multiplying Fractions:
· Multiplying fractions
o First number whole = “repeated addition”
o Second number whole = “part of a set”
o Visual (circle pieces or rectangles = array)
(intro:1 fraction) (2 fractions)
o Multiplying Mixed numbers:
· Change to improper
· Expanded algorithm (vertical)
· Distributive property (horizontal = FOIL)

5-3: Dividing Fractions :
· Dividing fractions
o Count elements (“size” of set)
o Count sets (how many sets that size)

5-3: Exponents:
· Exponents
o Whole number exponents
o Negative exponents
o Simplifying expressions with exponents

Test questions can also be taken from the Homework problems in the textbook ,
projects and the BLUE papers (any cooperative learning activity or take-home
activity).

Be ready to explain WHY (the theory behind the math).

# Course Outline for Intermediate Algebra

Course Description: A study of basic algebra for the student who has not successfully
completed two years of high school algebra . MATH 050 is a non-degree credit course
and will not count toward meeting minimum total credit requirements for graduation. It
does provide the student with a foundation for success in college level mathematics.

Text: Intermediate Algebra by Biftinger and Keedy

Topics Covered:

A. Algebra and the real numbers
1 . Introduction to algebra and algebraic expressions
2. The real number system
3. Operations on real numbers
4. Properties of real numbers
5. Exponential notation and order of operations
6. Properties of exponents and scientific notation

B. Solving equations and inequalities
1 .Solving equations
2. Applications
3. Formulae
4. Inequalities and applications
5. Sets and compound inequalities
6. Absolute value equations and inequalities

C. Graphs of equations and inequalities
1. Graphs
2. Graphing linear equations using x and y intercepts
3. Graphing linear equations using slope and y intercept
4. Other forms of linear equations
5. Applications of linear equations
6. Graphing inequalities in two variables

D. Systems of equations and inequalities
1. Systems of equations in two variables
2. Solving by substitution or elimination
3. Applications

E. Polynomials
1. Addition and subtraction of polynomials
2. Multiplication of polynomials
3. Common factors
4. Factoring by grouping
5. Factoring trinomials
6. Factoring trinomials which are squares of binomials
7. Factoring differences of squares , differences of cubes , and sums of cubes
8. General factoring strategies
9. Solving quadratic equations by factoring
10. Applications
1 1. Division of polynomials

F. Rational expressions and equations
1. Multiplying, dividing, and simplifying rational expressions
2. Least Common Multiple , Least Common Denominator , adding and subtracting
rational expressions
3. Solving rational equations
4. Applications
5. Complex rational expressions

2. Multiplying and simplifying radical expressions
3. Dividing and simplifying radical expressions
5. Rationalizing numerators and denominators
6. Rational numbers as exponents

H. More solving of quadratic equations
1. Basics of solving quadratic equations

Method of Instruction: Determined by the instructor. Typically lecture with class
discussion.

Course Requirements: A "scientific" calculator

Evaluation Process: Determined by the instructor. Typically a combination of
semester exams and quizzes, homework, group projects, journals, and a final
exam.

Prepared by: Wayne Larson
October 1998

# MTH 098 Basic Algebra

Department: Mathematics
Credit Hours: 3
Prerequisite: Placement Test
General Education: N/A
College Learning Outcomes : Quantitative Competence
______________________________________________________________________________

I. Course Description: This course introduces algebraic concepts , linear equations , solution of variable expressions , the quadratic formula . Offered on a satisfactory/ unsatisfactory basis . Credit does not apply to graduation.

II. Purpose of the Course: Basic Algebra is offered to prepare students for the algebra used in Lourdes ’ basic college-level math courses .

III. College Learning Outcomes and Objectives: While this course does not address Learning Outcome 9, Quantitative Competence, at the college level, it does address mathematical skills needed to acquire such competence. (L.O. #9: Students can solve quantitative problems by using mathematical skills and current technology.)

IV. Course Objectives:
1. Students should be able to simplify and evaluate variable expressions.
2. Students should be able to solve equations in one variable .
3. Students should be able to solve word problems that can be expressed in one variable .
4. Students should be able to graph and solve linear equations.
5. Students should be able to factor and solve quadratic equations.

V. Topical Outline

A. Number Systems
1. Symbols
2. Exponents and order of operations

B. Operations with signed numbers
2. Multiplication, division
3. Properties

C. Solving equations and inequalities
1. Simplifying expressions
2. Addition, multiplication properties of equality
3. Solving linear equations
4. From word problems to equations
5. Formulas
6. Ratio and proportion
7. Addition, multiplication properties of inequality

D. Exponents and polynomials
1. Rules for exponents
2. Scientific notation
3. Polynomials
4. Multiplication of polynomials
5. Products of binomials
6. Dividing a polynomial by a monomial
7. The quotient of two polynomials]

E. Factoring
1. GCF
2. Factoring trinomials
3. Special factorizations

F. Rational expressions
1. Fundamental property
2. Multiplication, division
3. LCD
5. Equations involving rational expressions

G. Graphing linear equations
1. Two variables
2. Ordered pairs
3. Linear equations
4. Slope and equation of the line
5. Linear inequalities

1. Finding roots
2. Products and quotients of radicals
4. Rationalizing the denominator