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
&
shading)
· 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)
5-2: Adding 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 Equal addition
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
G. Radical expressions and equations
1. Roots and radical expressions
2. Multiplying and simplifying radical expressions
3. Dividing and simplifying radical expressions
4. Addition and subtraction of radical expressions
5. Rationalizing numerators and denominators
6. Rational numbers as exponents
7. Solving radical equations
H. More solving of quadratic equations
1. Basics of solving quadratic equations
2. The quadratic formula
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
1. Addition, subtraction
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
4. Solving quadratic equations
5. Applications of quadratic equations
F. Rational expressions
1. Fundamental property
2. Multiplication, division
3. LCD
4. Addition, subtraction
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
H. Roots and radicals
1. Finding roots
2. Products and quotients of radicals
3. Addition and subtraction of radicals
4. Rationalizing the denominator
5. Simplifying radicals
6. Equations with radicals
I. Quadratic equations
