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PowerMath - Algebra
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- Subject -
Algebra Topic
- Preface -

PURPOSE :


PowerMath Algebra®   is a complete course of study.   Suitable from Grade-8 up to College-Algebra level.   The curriculum includes 13 chapters, 94 lessons, totaling 24.05 hours (or 1443 minutes) of continuous animated mathematical instruction (in virtual-reality).


Topics range from Pre-Algebra to Advanced-Algebra.   Its content is not a terminal course in Algebra but rather, the basis to develop skills enabling any person to effectively study more advanced topics in this field later on.


APPLICATION :


Assuming very little prior mathematical knowledge and experience other than basic skills in Arithmetic, the first four chapters cover Pre-Algebra for those needing a refresher.   This course combines theory proved by logical reasoning with plenty of examples and illustrations, stressing both the theoretical and computational aspects, in a rigorous representation of traditional topics in Algebra.


For Students, lessons are self-paced and self-learning requiring no instructional intervention.


For Teachers, lessons are content specific and optimal to augment their own classroom lectures.


RECOMMENDATION :


Lesson-Shows were designed to be watched sequentially, Chapter-1 on up . . . with the exception of Chapter-5 (Logarithms), Chapter-6 (Complex Numbers) and Chapter-7 (Factorial Numbers), which may be skipped to the very end of this course.


We suggest that students start with the very first lesson of the subject (Chapter One - Lesson One), while working your way up.   Your starting-point (depending on your abilities), is when you find a specific lesson content challenging.   Alternatively, match your instructor most recent lecture topic or corresponding part of your textbook, with any lesson Title & Description below.


- Contents -

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Arithmetic LIB
In PDF Format

- Lessons -

CHAPTER 1 - The Real Numbers
       
Lesson Icon SHOW 2100 The Number Sets
Natural, Whole, Integer, Rational, Irrational & the Real Numbers
runtime 20 minutes
requires None
       
Lesson Icon SHOW 2101 Set Theory
Definition of Sets, Unions, Intersections and Complements
runtime 20 minutes
requires SHOW 2100
       
Lesson Icon SHOW 2102 The Axioms of Real Numbers
Commutative, Associative, Distributive & Other Computational Rules
runtime 23 minutes
requires SHOW 2101
       
Lesson Icon SHOW 2105 Basic Arithmetical Rules
Signed Numbers, Operational Notation, and Divisibility of Numbers
runtime 16 minutes
requires SHOW 2102
       
Lesson Icon SHOW 2110 Order of Operations
Directional & Precedence (PEMDAS)
runtime 10 minutes
requires SHOW 2105
       
Lesson Icon SHOW 2112 The Prime Numbers
Prime versus Composite Numbers
runtime 12 minutes
requires SHOW 2110
       
Lesson Icon SHOW 2115 Prime Factorization
Factorization Technique
runtime 10 minutes
requires SHOW 2112
       
Lesson Icon SHOW 2120 The Greatest Common Divisor
Method to Find the G. C.D.
runtime 16 minutes
requires SHOW 2115
       
Lesson Icon SHOW 2125 The Least Common Multiple
Technique to Compute the L.C.M.
runtime 17 minutes
requires SHOW 2120

CHAPTER 2 - Exponents and Radicals
       
Lesson Icon SHOW 2140 The Concept of Exponents
Graphic Simulation of Exponents
runtime 11 minutes
requires SHOW 2125
       
Lesson Icon SHOW 2145 Properties of Exponents
A Detailed Look at the Base and the Power
runtime 16 minutes
requires SHOW 2140
       
Lesson Icon SHOW 2150 The Laws of Exponents
Basic Rules of Exponentiation
runtime 24 minutes
requires SHOW 2145
       
Lesson Icon SHOW 2155 Operations with Exponential Numbers
Adding, Subtracting, Multiplying & Dividing Exponential Numbers
runtime 19 minutes
requires SHOW 2150
       
Lesson Icon SHOW 2160 The Concept of Roots
A Look at the Notion of Roots, the Principal & Alternate Roots
runtime 13 minutes
requires SHOW 2155
       
Lesson Icon SHOW 2165 Roots of Real Numbers
Square, Cubic and Higher Roots
runtime 26 minutes
requires SHOW 2160
       
Lesson Icon SHOW 2170 Properties of Radicals
The Behavior of Roots & Radicals
runtime 12 minutes
requires SHOW 2165
       
Lesson Icon SHOW 2175 Working with Roots & Radicals
Numeric Guidelines for Roots & Radicals
runtime 18 minutes
requires SHOW 2170
       
Lesson Icon SHOW 2180 Operations with Radicals 1
Addition & Subtraction of Radicals
runtime 13 minutes
requires SHOW 2175
       
Lesson Icon SHOW 2185 Operations with Radicals 2
Multiplication of Radical Numbers and the Index
runtime 21 minutes
requires SHOW 2180
       
Lesson Icon SHOW 2190 Operations with Radicals 3
Division of Radicals & Rationalizing Denominators
runtime 25 minutes
requires SHOW 2185
       
Lesson Icon SHOW 2195 Square-Roots by Hand
Computing Square Roots Manually
runtime 22 minutes
requires SHOW 2190

CHAPTER 3 - Fractional Numbers
       
Lesson Icon SHOW 2230 The Concept of Fraction
Defining Mathematical Fractions
runtime 13 minutes
requires SHOW 2190
       
Lesson Icon SHOW 2235 An Introduction to Fractions
Similar Fractions, Reducing Fractions, Ratio of Fractions and Types of Fractions
runtime 13 minutes
requires SHOW 2230
       
Lesson Icon SHOW 2240 The Multiplication of Fractions
Standard & Mixed Forms, and Fraction Multiplication
runtime 9 minutes
requires SHOW 2235
       
Lesson Icon SHOW 2245 The Division of Fractions
Standard & Mixed Forms, and Fraction Division
runtime 10 minutes
requires SHOW 2240
       
Lesson Icon SHOW 2250 The Denominator
Rationalizing the Denominator & No Zero Denominator
runtime 13 minutes
requires SHOW 2245
       
Lesson Icon SHOW 2255 Least Common Denominator
Adding & Subtracting Fractions
runtime 19 minutes
requires SHOW 2250
       
Lesson Icon SHOW 2260 Mixed Fractions
Adding & Subtracting
runtime 12 minutes
requires SHOW 2255
       
Lesson Icon SHOW 2265 Advanced Fractions 1
Including Composite, Exponential, and Radical Numbers
runtime 14 minutes
requires SHOW 2260
       
Lesson Icon SHOW 2270 Advanced Fractions 2
Involving Polynomial Expressions
runtime 14 minutes
requires SHOW 2265 & SHOW 2680

CHAPTER 4 - Equivalent Numeric Forms
       
Lesson Icon SHOW 2275 Rounding Off Decimal Numbers
When to Round-Off Numbers UP or DOWN
runtime 16 minutes
requires SHHOW 2270
       
Lesson Icon SHOW 2280 Numeric Forms: Fractional Numbers
Form of Representing Numbers
runtime 17 minutes
requires SHOW 2275
       
Lesson Icon SHOW 2285 Numeric Forms: Scientific Notation
Form of Representing Numbers
runtime 11 minutes
requires SHOW 2280
       
Lesson Icon SHOW 2290 Numeric Forms: Percent
Form of Representing Numbers
runtime 13 minutes
requires SHOW 2285
       
Lesson Icon SHOW 2295 Conversion of Equivalent Numerical Forms
Converting Decimal, Fraction, Scientific & Percent
runtime 16 minutes
requires SHOW 2290

CHAPTER 5 - Logarithms
       
Lesson Icon SHOW 2300 Introduction to Logarithms
Definition & Components of Logarithms: The Exponent, the Base and the Output
runtime 14 minutes
requires SHOW 2290
       
Lesson Icon SHOW 2305 Logarithm Properties
The Basic, Reciprocal, Inverse, Product, Quotient and Power Properties of Logs
runtime 13 minutes
requires SHOW 2300
       
Lesson Icon SHOW 2310 Introduction to Common Logarithms
Rational & Irrational Exponents, Standard Notation & Characteristics
runtime 17 minutes
requires SHOW 2305
       
Lesson Icon SHOW 2315 Working with Common Logarithms
Logarithm of Large Numbers, Charecteristics of Logarithms and Logarithm Tables
runtime 16 minutes
requires SHOW 2310 & SHOW 2285
       
Lesson Icon SHOW 2320 Natural Logarithms
The Mathematical Constant "e," Properties of Natural Logs and the Log Table
runtime 13 minutes
requires SHOW 2315
       
Lesson Icon SHOW 2325 Logarithm Base Conversion
Logarithm Conversion Mechanism and Applications
runtime 16 minutes
requires SHOW 2320
       
Lesson Icon SHOW 2330 Common & Natural Logarithm Conversion
The Conversion Factor from Base-10 to Base-e and vice-versa, and to other Bases
runtime 14 minutes
requires SHOW 2325
       
Lesson Icon SHOW 2335 Anti-Logarithms
Parts of the Logarithm, Definition of Anti-Logs, Side-by-Side LOG & ALOG Examples
runtime 23 minutes
requires SHOW 2330

CHAPTER 6 - The Complex Numbers
       
Lesson Icon SHOW 2400 Introduction to Complex Numbers
Even & Odd Roots, Definition and Axioms of Complex Numbers
runtime 14 minutes
requires SHOW 2190
       
Lesson Icon SHOW 2405 The Set of Complex Numbers
Real Numbers in Complex Form, and the Addition, Subtraction, Multiplication & Division of Complex Numbers
runtime 25 minutes
requires SHOW 2400 & SHOW 2635
       
Lesson Icon SHOW 2410 The Conjugate of Complex Numbers
Standard & Ordered-Pair Forms, Conjugate & Graph of Complex Numbers, and Operations with Ordered-Pairs
runtime 20 minutes
requires SHOW 2405

CHAPTER 7 - Factorial Numbers
       
Lesson Icon SHOW 2430 Introduction to Factorials
The Definition of Factorial Numbers and Applications
runtime 11 minutes
requires SHOW 2525
       
Lesson Icon SHOW 2435 The Algebra of Factorials
Factorial Properties, Patterns of Factorials and Operations with Factorials
runtime 19 minutes
requires SHOW 2430

CHAPTER 8 - All About Lines
       
Lesson Icon SHOW 2450 The Cartesian-Coordinate System
Quadrants, Positive & Negative Coordinates, Ordered Pairs, and X & Y Relationship
runtime 12 minutes
requires SHOW 2290
       
Lesson Icon SHOW 2455 Introduction to Mathematical Functions
The X & Y Functionality, Plotting Lines & Curves on the Geometric Plane
runtime 15 minutes
requires SHOW 2450
       
Lesson Icon SHOW 2470 The Midpoint Formula
The Characteristics of all 4 Quadrants, Finding the Mid-Point Coordinates
runtime 11 minutes
requires SHOW 2455
       
Lesson Icon SHOW 2475 The Distance Formula
The Pythagorean Theorem and Finding the Distance Between Any 2 Points
runtime 15 minutes
requires SHOW 2470
       
Lesson Icon SHOW 2480 The Slope of a Line
The Ordered Pairs, Ratio of Rise over Run, Positive, Negative, Zero & Undefined Slopes
runtime 16 minutes
requires SHOW 2475
       
Lesson Icon SHOW 2485 The Equation of the Line
Standard & Slope Intercept Forms, the X & Y Intercepts
runtime 20 minutes
requires SHOW 2480
       
Lesson Icon SHOW 2490 Drawing the Line
Finding Coordinates for any Known Line with any Slope
runtime 15 minutes
requires SHOW 2485
       
Lesson Icon SHOW 2495 Finding the Equation of the Line
Deriving the Equation of the Line from Known Points
runtime 17 minutes
requires SHOW 2490
       
Lesson Icon SHOW 2500 Parallel Lines
The Definition of Parallel Lines for any Line of any Slope
runtime 11 minutes
requires SHOW 2495
       
Lesson Icon SHOW 2505 Perpendicular Lines
Definition of Reciprocal Numbers and Perpendicular Lines in Pratice
runtime 18 minutes
requires SHOW 2500 & SHOW 2250
       
Lesson Icon SHOW 2510 Intersecting Lines
Finding the Coordinates of any Line Intersecting Point
runtime 17 minutes
requires SHOW 2505

CHAPTER 9 - Algebraic Expressions
       
Lesson Icon SHOW 2600 An Introduction to Polynomials
Polynomials Explained, Graphical Repesentation and Numerical Evaluation
runtime 11 minutes
requires SHOW 2290
       
Lesson Icon SHOW 2605 Operations with Polynomials
Polynomial Addition, Subtraction, Multiplication & Division
runtime 14 minutes
requires SHOW 2600
       
Lesson Icon SHOW 2610 Complete Description of Polynomials
The Degree of Polynomials, Ascending & Descending Order, Polynomial Standard Form
runtime 22 minutes
requires SHOW 2605
       
Lesson Icon SHOW 2615 Division of Polynomials
Long Division Method
runtime 15 minutes
requires SHOW 2610
       
Lesson Icon SHOW 2620 Visual Polynomial Division
Graphic Representation of Polynomials Division
runtime 14 minutes
requires SHOW 2615
       
Lesson Icon SHOW 2625 Multiplication of Polynomials
The FOIL Method (Binomial x Binomial)
runtime 14 minutes
requires SHOW 2620
       
Lesson Icon SHOW 2630 Visual Polynomial Multiplication
Graphic Representation of Polynomials Multiplication
runtime 12 minutes
requires SHOW 2625
       
Lesson Icon SHOW 2635 The Product of Polynomials
The Multiplication of Any Size Polynomials
runtime 12 minutes
requires SHOW 2630

CHAPTER 10 - Factoring
       
Lesson Icon SHOW 2650 Common Factors
Separating Prime Factors in Composite Expressions
runtime 12 minutes
requires SHOW 2120
       
Lesson Icon SHOW 2655 An Introduction to Factoring
Polynomial Multiplication in Reverse and the Grouping Method
runtime 11 minutes
requires SHOW 2650
       
Lesson Icon SHOW 2660 Visual Polynomial Factorization
Graphic Representation of Polynomial Factoring
runtime 15 minutes
requires SHOW 2655
       
Lesson Icon SHOW 2665 Basic Factoring
The Elements of Factoring
runtime 19 minutes
requires SHOW 2660
       
Lesson Icon SHOW 2670 Factoring Method
From Trinomial to Binomial Form
runtime 15 minutes
requires SHOW 2665
       
Lesson Icon SHOW 2675 Special Case Factoring
Perfect-Square Trinomials & Difference of Two-Squares
runtime 17 minutes
requires SHOW 2670
       
Lesson Icon SHOW 2680 Factoring Higher Order Polynomials
The Sum & Difference of Two-Cubes
runtime 14 minutes
requires SHOW 2675

CHAPTER 11 - Quadratic Equations
       
Lesson Icon SHOW 2700 Introduction to Quadratic Equations
Finding the Solution-Set
runtime 16 minutes
requires SHOW 2680
       
Lesson Icon SHOW 2705 Factoring with Quadratic Equations
Advanced Factoring
runtime 16 minutes
requires SHOW 2700
       
Lesson Icon SHOW 2710 Roots of the Quadratic Equation Explained
The X-Intercept, Roots or Zeroes of the Quadratic
runtime 19 minutes
requires SHOW 2705
       
Lesson Icon SHOW 2715 Complete Description of the Quadratic
The X & Y Intercepts, the Coefficients and the Vertex
runtime 16 minutes
requires SHOW 2710
       
Lesson Icon SHOW 2720 Graphing the Quadratic Function
Mapping Intercepts & Vertex in the Cartesian Plane
runtime 13 minutes
requires SHOW 2715
       
Lesson Icon SHOW 2725 Discriminant of the Quadratic Equation
Character of the Roots (Real & Complex)
runtime 9 minutes
requires SHOW 2720
       
Lesson Icon SHOW 2730 Completing the Square
Convert Trinomials into Perfect Squares
runtime 11 minutes
requires SHOW 2725

CHAPTER 12 - System of Equations
       
Lesson Icon SHOW 2800 Introduction to System of Equations
Intersecting Lines & the Common Solution-Set
runtime 15 minutes
requires SHOW 2510
       
Lesson Icon SHOW 2805 Types of Solution Sets
Consistent & Independent, Consistent & Dependent, and Inconsistent Systems
runtime 12 minutes
requires SHOW 2800
       
Lesson Icon SHOW 2810 2x2 System of Equations
Solving by Substitution Method
runtime 15 minutes
requires SHOW 2805
       
Lesson Icon SHOW 2815 2x2 System of Equations II
Solving by Elimination Method
runtime 16 minutes
requires SHOW 2810
       
Lesson Icon SHOW 2820 2x2 System of Equations III
Involving Quadratic Equations
runtime 13 minutes
requires SHOW 2815
       
Lesson Icon SHOW 2825 Introduction to 3x3 System of Equations
Linking Tables, System of Equations, Matrices, and the Augmented Matrix
runtime 9 minutes
requires SHOW 2820
       
Lesson Icon SHOW 2830 3x3 System of Equations
Solution-Set by the Matrix Row-Operations Method
runtime 22 minutes
requires SHOW 2825

CHAPTER 13 - Inequalities
       
Lesson Icon SHOW 2850 Introduction to Mathematical Inequalities
Notational Inequality, Transitive Properties, Graphical Representation
runtime 15 minutes
requires SHOW 2830
       
Lesson Icon SHOW 2855 Inequalities in One-Variable
Operations, Graphical Representation and Domain Intervals
runtime 9 minutes
requires SHOW 2850
       
Lesson Icon SHOW 2860 Quadratic Inequalities
Solution-Set Intervals
runtime 18 minutes
requires SHOW 2855 & SHOW 2101
       
Lesson Icon SHOW 2865 Inequalities in Two-Variables
Operations, Graphical Representation, and Domain & Range
runtime 12 minutes
requires SHOW 2860
       
Lesson Icon SHOW 2870 System of Inequalities
The Solution Region
runtime 16 minutes
requires SHOW 2865 & SHOW 2510
       
Lesson Icon SHOW 2875 Introduction to Linear Programming
Feasible Solution Optimization (Max & Min)
runtime 19 minutes
requires SHOW 2870


 
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