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# MATHEMATICS

Basic Algebra (The Accelerated Learning System); Learned and Tested

Unit 1 - Integers and Rotational Numbers
Unit 5 - Dividing Integers
Unit 6 - Fractions with Negative Signs
Unit 7 - Positive and Negative Fractions
Unit 8 - The Language of Algebra
Unit 9 - Exponents
Unit 10 - Exponential Arithmetic
Unit 11 – Order of Operations
Unit 12 - Literal Expressions and Formulas
Unit 13 – Combining Like Terms
Unit 14 - Multiplying and Dividing Literal Numbers
Unit 15 – Removing Parentheses
Unit 16 – Introduction to Equations
Unit 17 - Solving Equations by Adding and Subtracting
Unit 18 – Solving Equations by Multiplying and Dividing
Unit 19 – Solving Equation by Combining Operations
Unit 20 – Solving Formulas
Unit 21 – Solving Inequalities
Unit 22 - Introduction to Word Problems
Unit 23 - Solving Mixture and Solution Problems
Unit 24 - Solving Rate, Time, and Distance Problems
Unit 25 - Solving Proportion and Variation Problems
Unit 26 - Introduction to Polynomials
Unit 27 – Adding and Subtracting Polynomials
Unit 28 - Multiplying Monomials by Polynomials
Unit 29 – Factoring a Monomial from a Polynomial
Unit 30 – Multiplying Two Binomials
Unit 31 – Factoring Trinomials I
Unit
32 – Factoring Trinomials II
Unit 33 – Special Products
Unit 35 – Multiplying Polynomials
Unit 36 – Dividing Polynomials
Unit 37 – Reducing Algebraic Fractions to Lowest Terms
Unit 38 – Multiplying and Dividing Algebraic Fractions
Unit 39 – Finding the Least Common Denominator
Unit 40 – Writing Equivalent Algebraic Fractions
Unit 41 – Adding and Subtracting Algebraic Fractions
Unit 42 – Simplifying Complex Algebraic Fractions
Unit 43 – Solving Equations with Algebraic Fractions
Unit 44 – Solving Word Problems with Algebraic Fractions
Unit 45 – Introduction to Graphing
Unit 46 – Graphing Linear Equations
Unit 47 – Finding the Shape of a Line
Unit 48 – Writing Equations in Slope-Intercept Form
Unit 49 – Graphing Inequalities
Unit 50 – Solving Systems of Equations by Graphing
Unit 51 – Solving Systems of Equations by Substitution
Unit 52 – Solving Systems of Equations by Addition
Unit 53 – Solving Word Problems with Systems of Equations
Unit 54 – Introduction to Radical Expressions
Unit 55 – Properties of Radical Expressions
Unit 57 – Multiplying and Dividing Radical Expressions
Unit 58 – Writing Radical Expressions in Simplest Form
Unit 59 – Solving Radical Equations
Unit 60 – Writing Quadratic Equations in Standard Form
Unit 62 – Quadratic Equations Factoring
Unit 63 – The Pythagorean Theorem
Unit 64 – Quadratic Equations Completing the Square

Basic College Math: Algebra Connections

Tape #1: Whole Numbers: Adding, Subtracting and Estimating
Tape #2: Whole Numbers: Multiplying and Dividing
Tape #3: Exponents
Tape #4: Multiplying and Dividing Fractions
Tape #5: Adding and Subtracting Fractions
Tape #6: Decimals
Tape #7: Ratio and Proportion
Tape #8: Percent
Tape #10: Geometry: Plane Figures
Tape #11: Geometry: Circles and Volumes
Tape #12: Algebra: Signed Numbers
Tape #13: Algebra: Solving Linear Equations
Tape #14: Descriptive Statistics
Tape #15: Consumer Mathematics
Tape #16: Basic Elementary of Geometry

Intermediate Algebra

Tape #1: Real Numbers
Tape #2: Powers and Roots ; Order of Operations
Tape #3: Linear Equations and Formulas
Tape #4: Applications of Linear Equations
Tape #5: Linear Inequalities; Absolute Value
Tape #6: Integer Exponents
Tape #9: Division of Factoring
Tape #10: Uses of Factoring
Tape #11: Algebraic Fractions
Tape #15: Complex Numbers

Unit 4: Division Facts
Unit 5: Naming Places and Groups
Unit 6: Numbers: Figures and Words
Unit 7: Rounding Numbers
Unit 8: Addition by Partial Sums
Unit 11: Subtraction by Expanded Notation
Unit 12: Subtraction by Borrowing
Unit 13: Using Subtraction
Unit 14: Multiplication: Counting Zeros
Unit 15: Multiplication by Partial Products
Unit 16: Multiplication by Carrying
Unit 21: Prime Numbers and Composite Numbers
Unit 22: Prime Factors
Unit 23: Least Common Multiples
Unit 24: Finding the LCM by Using Prime Factors
Unit 28: Improper Fractions and Mixed Numbers
Unit 31: Subtracting Fractions
Unit 32: Subtracting Mixed Numbers
Unit 33: Using Fractional Subtraction
Unit 34: Multiplying Fractions and Cancellation
Unit 35: Multiplying Mixed Numbers
Unit 36: Using Fractional Multiplication
Unit 37: Dividing Fractions
Unit 38: Dividing Mixed Numbers
Unit 39: Using Fractional Division
Unit 40: Decimal Place Value
Unit 41: Writing Decimals
Unit 42: Rounding Decimals
Unit 46: Subtracting Decimals
Unit 47: Using Decimal Subtraction
Unit 48: Multiplying Decimals
Unit 49: Multiplying Decimals by Powers of Ten
Unit 50: Using Decimal Multiplication
Unit 51: Dividing Decimals
Unit 52: Dividing Decimals by Powers of Ten
Unit 53: Using Decimal Division
Unit 54: Changing Fractions to Decimals and Decimals to Percents
Unit 56: Changing Percents to Decimals and Decimals to Percents
Unit 57: Changing Fractions to Percents
Unit 58: Using Percent I
Unit 59: Finding Percentage
Unit 60: Finding Percents
Unit 62: Using Percent II

BASIC COLLEGE MATHEMATICS: AN APPLIED APPROACH, 6e

Tape #4: Operations with Fractions
Tape #5: Decimals: Part I
Tape #6: Decimals: Part II
Tape #7: Ratio and Proportion
Tape #8: Problem Solving I
Tape #10: Solving Problems Involving Percents
Tape #11: Applications for Business and Consumers
Tape #12: Metric
Tape #14: Rational Numbers
Tape #15: Operations with Rational Numbers
Tape #16: Algebraic Expressions
Tape #17: Solving Linear Equations
Tape #18: Problem Solving II
Tape #19: Solving Word Problems that Involve Linear Equations
Tape #20: Geometry

BASIC COLLEGE MATHEMATICS: AN APPLIED APPROACH, 5e

Tape #1: Whole Numbers
Tape #3: Fractions
Tape #4: Operations with Fractions
Tape #5: Decimals: Part I
Tape #6: Decimals: Part II
Tape #8: Problem Solving I
Tape #9: Percent
Tape #10: Solving Problems Involving Percents
Tape #11: Applications for Business and Consumers: A Calculator
Tape #12: Metric and U.S. Systems of Measurement
Tape #13: Rational Numbers
Tape #14: Operations with Rational Numbers
Tape #15: Algebraic Expressions
Tape #17: Problem Solving II
Tape #18: Solving Word Problems that Involve Linear Equations
Tape #19: Geometry

Miller/Salzman/Hestwood
“Eye On Basic College Mathematics”[
4th ed. Basic College Mathematics
Tape #: 1-2; 4-12

Lial/Miller/Hornsby
Spotlight On Algebra
College Algebra – 6th ed.
Tape #: 1-2; 4-9

Lial/Miller/Hornsby
Spotlight On Algebra
Beginning Algebra – 6th ed
Tape #: 9-11; 14-15; 17; 28

Lial/Miller/Hornsby
Spotlight On Algebra
Intermediate Algebra – 6th ed
Tape #: 16; 19; 26; 33-37

Dana Mosely (Lectures for Larson, Hostetler: College Algebra, 2E)
Tape #: 1-10

# Math 095 Intermediate Algebra

Course Description: Number systems, fundamentals of algebra, graphs and equations of straight lines , exponents, polynomial expressions , factoring, rational expressions, roots, the quadratic formula ; applications. Credit for this course cannot be applied toward any degree program. Graded A, B, C, No record.

Prerequisite: Satisfactory placement exam score or grade of C or higher in MATH 090.

Schedule: Fall, Spring, Summer. 3 credit hours.

Required Text: Bittinger and Ellenbogen, Algebra Special Edition for Bowling Green State University, Addison-Wesley, 2002.

Grade Breakdown: The grading scale will be the standard grading scale: 90-100 A; 80-89 B; 70-79 C; 60-69 D; below 60 F.

Chapters covered:
Chapter 1: Introduction to Algebraic Expressions
Chapter 2: Equations, Inequalities, and Problem Solving
Chapter 3: Introduction to Graphing
Chapter 4: Polynomials
Chapter 5: Polynomials and Factoring
Chapter 6: Rational Expressions and Equations
Chapter 8: Radical Expressions and Equations

## Detailed coverage:

Chapter 1 – Introduction to Algebraic Expressions

1.1 Introduction to Algebra
• We discuss algebraic expressions, translating algebraic expressions and translating to equations.

1.2 The Commutative, Associative, and Distributive Laws
• We discuss equivalent expressions , the commutative laws, associative laws, and distributive laws and factoring.

1.3 Fraction Notation
• We talk about what factors are and prime factorization, for the purpose of simplifying fractions.
• Multiplying/Dividing/Adding/Subtracting fractions with both like and unlike denominators.

1.4 Positive and Negative Real Numbers
• Definitions of integers, rational numbers, and real numbers. The students should be able to put real numbers in order on a number line.
• We discuss what absolute value is in terms of distance and how to find the absolute value.

• Adding real numbers (both positive and negative)
• Combining like terms (both positive and negative)
• Problem solving – Basic applications with temperature and bills

1.6 Subtraction of Real Numbers
• Opposites and Additive Inverses – we talk about these being the same
• Subtraction of positive and negative numbers
• Problem solving – Basic applications again
• Combining like terms

1.7 Multiplication and Division of Real Numbers
• Multiplication and division of positive and negative numbers

1.8 Exponential Notation and Order of Operations
• Exponential Notation – the basic idea that 2*2*2 = 2^3 along with simplifying these
• Order of Operations
• Simplifying and the distributive law – combining like terms with the distributive property
• The opposite of a sum – basically remembering to distribute the negative through a parenthesis

Chapter 2 – Equations, Inequalities, and Problem Solving

2.1 Solving Equations
• Solution of an equation
• Solving by adding or subtracting
• Solving by multiplying or dividing

2.2 Using the Principles Together
• Solving multi-step equations
• Solving by combining like terms
• Solving equation by clearing fractions and decimals first

2.3 Formulas
Evaluating formulas
• Solving for a letter

2.4 Applications with Percents
• Converting between percent notation and decimal notation
• Solving percent problems

2.5 Problem Solving
• 5 steps for problem solving
• Applying the 5 steps: being able to set up an equation and solve

2.6 Solving Inequalities
• Solutions of Inequalities
• Graphs of inequalities
• Solving inequalities

2.7 Solving Applications with Inequalities
• Translating to inequalities
• Solving problems

Chapter 3 – Introduction to Graphing

3.1 Reading Graphs, Plotting Points, and Estimating Values
• Problem solving with graphs
• Points and ordered pairs
• Estimations and predictions

3.2 Graphing Linear Equations
• Solutions of equations
• Graphing linear equations

3.3 Graphing and Intercepts
• Intercepts
• Using intercepts to graph
• Graphing horizontal and vertical lines

3.4 Rates
• Rates of Change
• Visualizing Rates

3.5 Slope
• Rate and slope
• Horizontal and vertical lines
• Applications – basic applications

3.6 Slope-Intercept Form
• Using the y-intercept and the slope to graph a line
• Equations in slope-intercept form
• Graphing and slope-intercept form

3.7 Point-Slope Form
• Writing equations in point-slope form
• Graphing and point-slope form

Chapter 4 – Polynomials

4.1 Exponents and Their Properties
• Multiplying powers with like bases
• Dividing powers with like bases
• Zero as an exponent
• Raising a power to a power
• Raising a product or a quotient to a power

4.2 Polynomials
• Terms
• Types of polynomials
• Degree and coefficients
• Combining like terms
• Evaluating polynomials and applications

4.3 Addition and Subtraction of Polynomials
• Opposites of polynomials
• Subtraction of polynomials
• Problem solving

4.4 Multiplication of Polynomials
• Multiplying monomials
• Multiplying a monomial and a polynomial
• Multiplying any two polynomials
• Checking by evaluating

4.5 Special Products
Product of two binomials
• Multiplying sums and differences of two terms
• Squaring binomials
• Multiplication of various types

4.6 Polynomials in Several Variables
• Evaluation of polynomials
• Like terms and degree
• Multiplication

4.7 Division of Polynomials
Dividing by a monomial
• Dividing by a binomial

4.8 Negative Exponents and Scientific Notation
• Negative integers as exponents
• The instructor has the option to cover scientific notation if time permits.

Chapter 5 – Polynomials and Factoring

5.1 Introduction to Factoring
• Factoring monomials
• Factoring when terms have a common factor
• Factoring by grouping
• Checking by evaluating

5.2 Factoring Trinomials of the Type x^2+bx+c
• Constant term positive
• Constant term negative

5.3 Factoring Trinomials of the Type x^2+bx+c
• Factoring with FOIL
• Factor by grouping.

5.4 Factoring Perfect-Square Trinomials and Differences of Squares
• Recognizing perfect-square trinomials
• Factoring perfect-square trinomials
• Recognizing differences of squares
• Factoring difference of squares
• Factoring completely

5.5 Factoring: A General Strategy
• Choosing the right method

5.6 Solving Quadratic Equations by Factoring
• The principle of zero products
• Factoring to solve equations
• Graphing and quadratic equations – These are very basic. Being able to plot the zeros and determine if it opens up or down.

5.7 Solving Applications
• Applications
• The Pythagorean Theorem

Chapter 6 – Rational Expressions and Equations

6.1 Rational Expressions
• Simplifying rational expressions
• Factors that are opposites

6.2 Multiplication and Division

6.3 Addition, Subtraction, and Least Common Denominators
• Addition with denominators that are the same
• Subtraction when denominators are the same
• Least common multiples and denominators

6.4 Addition and Subtraction with Unlike Denominators
• Addition and subtracting with LCDs
• When factors are opposites

6.5 Complex Rational Expressions – SKIP

6.6 Solving Rational Equations
• Solving a new type of equation – basically what they are not used to seeing
• A visual representation – This is basically showing that you can solve by graphing.

6.7 Applications Using Rational Equations and Proportions
• Problem solving
• Problems involving work
• Problems involving motion
• Problems involving proportions

Chapter 8 – Radical Expressions and Equations

8.1 Introduction to Square Roots and Radical Expressions
• Square roots
• Irrational numbers
• Square roots and absolute value
• Problem solving

8.2 Multiplying and Simplifying Radical Expressions
• Multiplying
• Simplifying by factoring
• Simplifying square roots of powers
• Multiplying and simplifying

8.3 Quotients Involving Square Roots
• Rationalizing denominators

8.4 Higher Roots and Rational Exponents
• More with multiplication
• More with rationalizing the denominator

# FUNDAMENTALS OF MATHEMATICS

I. WHOLE NUMBERS

A. Place value and word names
B. Expanded notation and place value
C. Addition, subtraction, multiplication, and division
D. Order of operations

II. PRIMES AND MULTIPLES

A. Multiples
B. Divisors and factors
C. Divisibility tests: 2, 3, 5, 10
D. Primes and composites
E. Prime factorization
F. Least common multiple

III. FRACTIONS AND MIXED NUMBERS

A. Concept of a fraction
B. Improper fractions to mixed numbers
C. Mixed numbers to improper fractions
D. Equivalent fractions
E. Reducing fractions to lowest terms
F. Multiplication with fractions and mixed numbers
G. Division with fractions and mixed numbers
H. Least common denominator
I. Comparing fractions
J. Addition with fractions and mixed numbers
K. Subtraction with fractions and mixed numbers

IV. DECIMALS

A. Place value and word names
B. Expanded notation
C. Changing decimals to fractions
D. Changing fractions to decimals
E. Comparing decimals
F. Approximation by rounding
G. Addition, subtraction, multiplication and division with decimals

V. RATIO AND PROPORTION

A. Concept of ratio and proportion
B. Solving a proportion for the unknown

VI. PERCENT

A. Concept of percent
B. Changing decimals to percents
C. Changing percents to decimals
D. Changing fractions to percents
E. Changing percents to fractions
F. Finding percentage
G. Finding rate
H. Finding base
I. % increase/ decrease problems

VII. DENOMINATE NUMBERS AND MEASUREMENT

A. English units
B. Metric units
C. Conversion of units within each system
D. Perimeter and circumference
E. Areas of common geometric figures
F. Volumes of common geometric figures

VIII. PROBLEM SOLVING

A. Techniques for problem solving
B. Problems involving whole numbers, fractions, decimals, percents, ratio and proportion, and
measurement

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