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Algebra 1

Algebra 1, Part 1
Basic Numbers Ideas
Odd & Even Numbers
Exponents: Exponential Form
Exponents: Expanded Form
Exponents: Product Rule
Exponents: Power Rule
Subtracting Integers
Multiplying Integers
Dividing Integers
Multiplying & Dividing Mixed Numbers
Using Basic Number Ideas
Mental Math with Whole Numbers &
Decimals
Mental Math with Fractions & Percents

Math Sentences
Order of Operations
Expressions in 1 Variable
Expressions in 2 or More Variables
Determining the Truth Value of a
Statement
Subtracting Monomials
Multiplying Monomials
Dividing Monomials
Subtracting Binomials & Monomials
Multiplying Binomials & Monomials
Dividing Binomials by Monomials
Linear Equations in 1 Variable:
Solving by Inspection
Linear Equations in1 Variable:
Isolating the Variable
Linear Inequalities in 1 Variable, Part 1
Linear Inequalities in 1 Variable, Part 2
More Difficult Linear Inequalities in 1
Variable
Using Linear Equations to Solve Problems
Problems

Graphing Basics
Coordinate Plane
Identifying Points on a Coordinate
Plane
Ordered Pairs as Solutions of Linear
Equations
Graphing Linear Equations in 2
Variables
Solving & Graphing Systems of
Equations
Solving Problems with Systems of
Linear
Equations

Equations & Formulas
Literal Equations

Special Topics
Visualizing Percents Less than 1%
Converting Percents Less than 1% to
Decimals
Finding the Amount with Percents
Less than 1%
Visualizing Percents Greater than
100%
Visualizing Percents Greater than
100% to Decimals
Converting a Number Greater than 1
to a Percent
Mean, Median, Mode
Probability & Possible Outcomes
Probability of an Event
Solving Problems with Percents
Solving Problems with Mean, Median,
& Mode
Solving Problems with Probability
Estimation Basics
Estimation by Clustering
Scaling & Proportion, Part 1
Scaling & Proportion, Part 2

Introduction to Functions
Patterns & Sequences
Functions
Describing Functions with Equations,
Tables, & Graphs
Linear Patterns
Graphs, Slopes, & y-Intercepts
Interpreting Graphs to Solve Problems

Algebra 1, Part 2

Sets & Numbers
Integer Sum
Integer Difference
Integer Quotient
Subtracting Fractions
Multiplicative Inverse of Fraction
Product of Fractions
Quotient of Fractions
Basic Set Concepts: Elements in a Set
Basic Set Concepts: Finite or Infinite
Basic Set Concepts: Subsets
Basic Set Concepts: Roster & Setbuilder
Forms
Union Sets
Intersection of Sets
Positive & Negative Exponents
Integer Exponents & the Product Rule
Integer Exponents & the Quotient Rule
Integer Exponents & the Power Rule,
Part 1
Integer Exponents & the Power Rule,
Part 2
Square Roots of Integers
Review: Fractions & Sets

Polynomials & Factoring
Classifying Polynomials
Monomial Sum
Monomial Difference
Monomial Product
Monomial Quotient
Binomial Sum
Binomial Difference
Value of Polynomial
Polynomial Sum
Polynomial Difference
Product of a Monomial & Polynomial
Simplifying Polynomial Expressions
Product of Polynomials
Quotient of a Monomial & Polynomial
Quotient of a Binomial & Polynomial
Greatest Common Factors of Monomials
Monomial Factors of Polynomials
Binomial Factors of Polynomials, Part1
Binomial Factors of Polynomials, Part
2
Factoring the Difference of 2 Squares
Factoring Perfect Square Trinomials
Factoring Trinomials, Part 1
Factoring Trinomials, Part 2
Review: Polynomials & Factoring

Equations & Inequalities
Simple Equations in 1 Variable: Using
Inspection
Simple Equations in 1 Variable:
Isolating the Variable
More Difficult Linear Equations in 1
Variable
Absolute Value of a Number
Equations with Absolute Values
Graphing a solution Set of a Number Line
Solving & Graphing Equations in 1
Variable
Solving Problems with Linear
Equations in 1 Variable
Linear Inequalities in 1 Variable, Part
1
Linear Inequalities in 1 Variable, Part
2
Linear Inequalities in 1 Variable, Part
3
Factoring, Part 1
Factoring, Part 2
Factoring, Part 3
Equations
Review: Equations & Inequalities

SELECTED TOPICS IN ELEMENTARY ALGEBRA

College Algebra

Algebra I Video Tutor Instructional Series

VC 512 AL33 (Vol. 1 – 6)
*Combining Like Terms
*Simple Equations
* Solving Equations by Using Two or More Operations
*Combining Like Terms to Solve Equations
*Graphing Solution Sets/Number Lines
*Signed Numbers
*Evaluating Algebraic Expressions
*Subtracting Monomials
*Multiplying Monomials
*Dividing Monomials
*Dividing Polynomials by a Binomial (Polynomial)
*Equations Containing Parentheses
*Absolute Value Equations
*Solving Equations Containing More than One Variable
*Inequalities Containing One Variable
*Factoring Polynomials Whose Terms have a Common Factor
*Squaring a Monomial
*Multiplying the Sum & Difference of Two Numbers
*Factoring the Difference of Two Squares
*Finding the Product of Two Binomials
*Factoring Trinomials
*Factoring Completely
*Reducing Fractions
*Multiplying Fractions
*Dividing Fractions
*Adding Fractions Having the Same Denominator
*Subtracting Fraction having the Same Denominator
*Subtracting Fractions Having Different Denominators
*Mixed Expressions
*Solving Equations Containing Fractions
*Solving Decimal Equations
*Solving Inequalities Containing Fractional & Decimal Coefficients
*Solving for X when Many Variables re Involved
*Graphing/Plotting Points
*Graphing Solution Sets/Graphing Equations
*Graphing Lines Parallel to the X or Y Axis
*Slope
*Slope & Y-Intercept of an Equation
*Finding Equation when Slope & a Point are Given
*Finding Equation when Two Points are Given
*The Equation of a Line Y=mx + b
*Absolute Value Graphing
*Inequality Graphing
*Solving Equations Simultaneously
*Solving Equations by Substitution
*Graphing Solution Sets of Systems of Inequalities
*Repeating Decimals
*Square Roots

College Algebra (Beecher/Penna/Bittinger, 2nd ed.)
VC 512.9 C686ca 2005 (Pt. 1 – 11)
*Basic Concepts of Algebra
*Graphs, Function, and Models
*Functions, Equations, and Inequalities
*Polynomial and Rational Functions
*Exponential and Logarithmic Functions
* Systems of Equations and Matrices
*Conic Sections
*Sequences, Series, and Combinatorics

College Algebra (Brooks/Cole, 7th ed. 2001)
VC 512.9 C686G 2001 (Pt. 1 – 11)
*Basic Concepts
*Equations & Inequalities
*The Rectangular Coordinate System and Graphs of Equations
*Functions
*Exponential and Logarithmic Functions
*Solving Polynomial Equations
*Systems of Linear Equations
*Natural Number Functions and Probability
*The Mathematics of Finance

Video lectures on CD: to accompany College Algebra, 3rd ed. (Beecher/Bittinger/Penna)
CD-ROM 512.9 V668ca pt. 1-9
*Pt. 1 Chapter R – Basic Concepts of Algebra
R.1 The Real-Number System
R.2 Integer Exponents, Scientific Notation, & Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring
R.5 Rational Expressions
R.6 Radical Notation and Rational Exponents
R.7 The Basics of Equation Solving

*Pt. 2 Chapter 1 – Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 More on Functions
1.6 The Algebra of Functions
1.7 Symmetry and Transformations

*Pt. 3 Chapter 2 – Functions, Equations, and Inequalities
2.1 Linear Equations, Functions, and Models
2.2 The Complex Numbers
2.3 Quadratic Equations, Functions, and Models
2.4 Analyzing Graphs of Quadratic Functions
2.5 More Equation Solving
2.6 Solving Linear Inequalities

*Pt. 4 Chapter 3 – Polynomial and Rational Functions
3.1 Polynomial Functions and Models
3.2 Graphing Polynomial Functions
3.3 Polynomial Division; The Remainder and Factor Theorems
3.4 Theorems about Zeros of Polynomial Functions
3.5 Rational Functions
3.6 Polynomial and Rational Inequalities
3.7 Variation and Applications

*Pt. 5 Chapter 4 – Exponential and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions and Graphs
4.3 Logarithmic Functions and Graphs
4.4 Properties of Logarithmic Functions
4.5 Solving Exponential and Logarithmic Equations
4.6 Applications and Models: Growth and Decay; Compound Interest

*Pt. 6 Chapter 5 – Systems of Equations and Matrices
5.1 Systems of Equations in Two Variables
5.2 Systems of Equations in Three Variables
5.3 Matices and Systems of Equations
5.4 Matrix Operations
5.5 Inverses of Matices
5.6 Determinants and Cramer’s Rule
5.7 Systems of Inequalities and Linear Programming
5.8 Partial Fractions

*Pt. 7 Chapter 6 – Conic Sections
6.1 The Parabola
6.2 The Circle and the Ellipse
6.3 The Hyperbola
6.4 Nonlinear Systems of Equations and Inequalities

*Pt. 8 Chapter 7 (7.1 – 7.4) - Sequences, Series, and Combinatorics
7.1 Sequences and Series
7.2 Arithmetic Sequences and Series
7.3 Geometric Sequences and Series
7.4 Mathematical Induction

*Pt. 9 Chapter 7 (7.5 – 7.8) - Sequences, Series, and Combinatorics
7.5 Combinatorics: Permutations
7.6 Combinatorics: Combinations
7.7 The Binomial Theorem
7.8 Probability

Pre-calculus & Calculus

Pre-calculus

VC 512.1 P911 (Vol. 1 – 5)
*The Number System
*Inequalities & Intervals
*Absolute Value
*Graphs in the Coordinate
*The Distance Formula
*Graphs of Equations
*Circles in the Plane
*Introduction to Functions
*Domain, Range, & Graphs of Functions
*More Graphing Techniques
*Linear Functions & Their Graphs
*The Algebra of Functions & Inverses
*Polynomial Functions & Their Graphs
*Graphing Rational Functions

Pre-calculus, Mathematics Instructional DVD Series (Larson/Hostetler, 2007)
For use with:
Pre-calculus, 7th ed.
Pre-calculus with Limits
Pre-calculus: A Concise Course

DVD 515 L329 P pt. 1-11
*Pt. 1 Chapter 1 – Functions and Their Graphs
~1.1Rectangular Coordinates
~1.2 Graphs of Equations
~1.3 Linear Equations in Two Variables
~1.4 Functions
~1.5 Analyzing Graphs of Functions
~1.6 A Library of Functions
~1.7 Transformations of Functions
~1.8 Combinations of Functions: Composite Functions

*Pt. 2 Chapter 1 – Functions and Their Graphs
~1.9 Inverse Functions
~1.10 Mathematical Modeling and Variation

Chapter 2 – Polynomial and Rational Functions
~2.2 Polynomial Functions of Higher Degree
~2.3 Polynomial and Synthetic Division
~2.4 Complex Numbers
~2.5 Zeros of Polynomial Functions

*Pt. 3 Chapter 2 – Polynomial and Rational Functions
~2.6 Rational Functions
~2.7 Nonlinear Inequalities

Chapter 3 – Exponential and Logarithmic Functions
~3.1 Exponential Functions and Their Graphs
~3.2 Logarithmic Functions and Their Graphs
~3.3 Properties of Logarithms
~3.4 Exponential and Logarithmic Equations
~3.5 Exponential and Logarithmic Models

*Pt. 4 Chapter 4 – Trigonometry
~4. 2Trigonometric Functions : The Unit Circle
~4.3 Right Triangle Trigonometry
~4.4 Trigonometric Functions of Any Angle
~4.5 Graphs of Sine and Cosine Functions

*Pt. 5 Chapter 4 – Trigonometry
~4.6 Graphs of Other Trigonometric Functions
~4.7 Inverse Trigonometric Functions
~4.8 Applications and Models

Chapter 5 – Analytic Trigonometry
~5.1 Using Fundamental Identities
~5.2 Verifying Trigonometric Identities
*Pt. 6 Chapter 5 – Analytic Trigonometry
~5.3 Solving Trigonometric Equations
~5.4 Sum and Difference Formulas
~5.5 Multiple-Angle and Product-to-Sum Formulas
~5.6 Law of Sines (Precalculus: A Concise Course)
~5.7 Law of Cosines (Precalculus: A Concise Course)
Chapter 6 – Additional Topics in Trigonometry (Precalculus and Precalculus with
Limits)
* Chapter 6 Precalculus: A Concise Course is located on discs 9 and 10 of
the DVD set.
~6.1 Law of Sines (Precalculus and Precalculus with Limits)
~6.2 Law of Cosines (Precalculus and Precalculus with Limits)
~6.3 Vectors in the Plane (Precalculus and Precalculus with Limits)

*Pt. 7 Chapter 6 – Additional Topics in Trigonometry (Precalculus and Precalculus with
Limits)
~6.4 Vectors and Dot Products
~6.5 Trigonometric Form of a Complex Number
Chapter 7 - Systems of Equations and Inequalities (Precalculus and Precalculus
with Limits)
~7.1 Linear and Nonlinear Systems of Equations
~7.2 Two-Variable Linear Systems
~7.3 Multivariable Linear Systems
~7.4 Partial Fractions
~7.5 Systems of Inequalities
~7.6 Linear Programming

*Pt. 8 Chapter 8 – Matrices and Determinants (Precalculus and Precalculus with Limits)
~8.1 Matrices and Systems of Equations
~8.2 Operations with Matrices
~8.3 The Inverse of a Square Matrix
~8.4 The Determinant of a Square Matrix
~8.5 Applications of Matrices and Determinants
Chapter 9 – Sequences, Series, and Probability (Precalculus and Precalculus with
Limits)
~9.1 Sequences and Series
~9.2 Arithmetic Sequences and Partial Sums
~9.3 Geometric Sequences and Series

*Pt. 9 Chapter 9 – Sequences, Series, and Probability (Precalculus and Precalculus with
Limits)
~9.4 Mathematical Induction
~9.5 The Binomial Theorem
~9.6 Counting Principles
~9.7 Probability
Chapter 10 – Topics in Analytic Geometry (Precalculus and Precalculus with
Limits)
Chapter 6 – Topics in Analytic Geometry (Precalculus: A Concise
Course)
~10.1/6.1 Lines
~10.2/6.2 Introduction to Conics: Parabolas
~10.3/6.3 Ellipses

*Pt. 10 Chapter 10 – Topics in Analytic Geometry (Precalculus and Precalculus with
Limits)
Chapter 6 – Topics in Analytic Geometry (Precalculus: A Concise
Course)
~10.4/6.4 Hyperbolas
~10.5 Rotation of Conics (Precalculus and Precalculus with Limits)
~10.6/6.5 Parametric Equations
~10.7/6.6 Polar Coordinates
~10.8/6.7 Graphs of Polar Coordinates
~10.9/6.8 Polar Equations of Conics
Chapter 11 – Analytic Geometry in Three Dimensions (Precalculus with Limits)
~11.1 The Three- Dimensional Coordinate System

*Pt. 11 Chapter 11 – Analytic Geometry in Three Dimensions (Precalculus with Limits)
~11.2 Vectors in Space
~11.3 The Cross Products of Two Vectors
~11.4 Lines and Planes in Space
Chapter 12 – Limits and an Introduction to Calculus (Precalculus with Limits)
~12.1 Introduction to Limits
~12.2 Techniques for Evaluating Limits
~12.3 The Tangent Line Problem
~12.4 Limits at Infinity and Limits of Sequences
~12.5 The Area Problem

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