PowerMath - Algebra
- Powered by Excellence -
| - Subject - |
| - Preface - |
PowerMath Algebra® is a complete course of study, the equivalent of an entire academic year. The curriculum includes 14 chapters with 79 lessons, totaling 1231 minutes or 20 hours & 31 minutes, of continuous animated mathematical instruction (in virtual-reality). Topics span from Pre-Algebra to more advanced subjects in 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 the field of Algebra later on.
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PowerMath Algebra® assumes very little prior mathematical knowledge and experience, other than basic skills in Arithmetic. 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.
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PowerMath Algebra® 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.
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PowerMath Algebra® 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 can be skipped to the end of this course.
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PowerMath Algebra® suggests that you 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 (in the blue text).
| - Contents - |
In PDF Format
| - Lessons - |
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SHOW 2100 |
The Number-Sets and Real Number Axioms
(Runtime 23 minutes / Prerequisite None ) Natural, Whole, Integer, Rational, Irrational & Real Numbers, and Computational Laws of Real-Numbers |
(24 Hours Viewing-Window) |
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SHOW 2101 |
Set Theory
(Runtime 20 minutes / Prerequisite SHOW 2100 ) Definition of Sets, Unions, Intersections and Complements |
(24 Hours Viewing-Window) |
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SHOW 2105 |
The Prime-Numbers
(Runtime 15 minutes / Prerequisite SHOW 2100 ) Prime & Composite Numbers, Prime Factorization, and the Divisibility of Primes |
(24 Hours Viewing-Window) |
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SHOW 2110 |
Order of Operations
(Runtime 10 minutes / Prerequisite SHOW 2105 ) Equal & Opposite Signs, Directional, Precedence & Notational Conventions |
(24 Hours Viewing-Window) |
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SHOW 2115 |
Prime Factorization
(Runtime 9 minutes / Prerequisite SHOW 2110 ) Prime & Composite Numbers, and Prime Factorization Technique |
(24 Hours Viewing-Window) |
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SHOW 2120 |
Greatest Common Divisor & Least Common Multiple
(Runtime 18 minutes / Prerequisite SHOW 2115 ) Prime-Factoring Technique to Find the G. C.D. & L.C.M. |
(24 Hours Viewing-Window) |
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SHOW 2150 |
The Laws of Exponents & Properties of Exponents
(Runtime 17 minutes / Prerequisite SHOW 2120 ) Parts of Exponential Numbers, The Four Laws of Exponents, and the Algebra of Exponents |
(24 Hours Viewing-Window) |
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SHOW 2155 |
Operations with Exponential Numbers
(Runtime 14 minutes / Prerequisite SHOW 2150 ) Addition, Subtraction, Multiplication & Division of Exponential Numbers, and Patterns of Exponentials |
(24 Hours Viewing-Window) |
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SHOW 2180 |
Roots of Real Numbers
(Runtime 19 minutes / Prerequisite SHOW 2155 ) Square, Cubic & Nth Roots, the Principal & Alternative Roots |
(24 Hours Viewing-Window) |
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SHOW 2185 |
The Algebra of Radicals
(Runtime 21 minutes / Prerequisite SHOW 2180 ) Radical Algebraic Rules, Reducing Radical Expressions, and Eliminating Radicals from Denominators |
(24 Hours Viewing-Window) |
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SHOW 2190 |
Operations with Radicals
(Runtime 20 minutes / Prerequisite SHOW 2185 ) Addition, Subtraction, Multiplication and Division of Radical Numbers, and Common Squares & Roots |
(24 Hours Viewing-Window) |
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SHOW 2195 |
Square-Roots by Hand
(Runtime 15 minutes / Prerequisite SHOW 2190 ) Computing Square-Roots of Real Numbers Manually |
(24 Hours Viewing-Window) |
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SHOW 2250 |
Introduction to Fractions
(Runtime 10 minutes / Prerequisite SHOW 2190 ) Proper & Improper, Visual Concept of Fractions, No Zero Denominators, and Denominator Standards |
(24 Hours Viewing-Window) |
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SHOW 2255 |
Least Common Denominator
(Runtime 17 minutes / Prerequisite SHOW 2120 ) Prime-Factorization Technique to Find the Least Common Denominator |
(24 Hours Viewing-Window) |
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SHOW 2260 |
Operations with Basic Fractions
(Runtime 20 minutes / Prerequisite SHOW 2255 ) Step-by-Step Multiplication, Division, Addition & Subtraction of Fractions |
(24 Hours Viewing-Window) |
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SHOW 2265 |
Operations with Intermediate Fractions
(Runtime 20 minutes / Prerequisite SHOW 2260 ) Including Composite, Exponential, and with Radical Numbers |
(24 Hours Viewing-Window) |
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SHOW 2270 |
Operations with Advanced Fractions
(Runtime 22 minutes / Prerequisite SHOW 2265 & SHOW 2665 ) Including Polynomials, Exponential, and with Radical Numbers |
(24 Hours Viewing-Window) |
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SHOW 2280 |
Numerical Forms: Decimal & Fractional
(Runtime 17 minutes / Prerequisite SHOW 2270 ) Rounding-Off Decimals, Proportionality of Fractionals, and Trailing Zeroes |
(24 Hours Viewing-Window) |
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SHOW 2285 |
Numerical Forms: Scientifc & Percentage
(Runtime 17 minutes / Prerequisite SHOW 2280 ) Representation of Very Large & Very Small Numbers, and Percent of any Number |
(24 Hours Viewing-Window) |
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SHOW 2290 |
Conversion of Equivalent Numerical Forms
(Runtime 17 minutes / Prerequisite SHOW 2285 ) Conversion Among Decimal, Fraction, Scientific and Percent Numbers |
(24 Hours Viewing-Window) |
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SHOW 2300 |
Introduction to Logarithms
(Runtime 14 minutes / Prerequisite SHOW 2290 ) Definition & Components of Logarithms: The Exponent, the Base and the Output |
(24 Hours Viewing-Window) |
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SHOW 2305 |
Logarithm Properties
(Runtime 13 minutes / Prerequisite SHOW 2300 ) The Basic, The Reciprocal and The Inverse Properties, and Product, Quotient & Power Properties |
(24 Hours Viewing-Window) |
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SHOW 2310 |
Introduction to Common Logarithms
(Runtime 17 minutes / Prerequisite SHOW 2305 ) Rational & Irrational Exponents, Standard Notation & Charecteristics |
(24 Hours Viewing-Window) |
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SHOW 2315 |
Working with Common Logarithms
(Runtime 16 minutes / Prerequisite SHOW 2310 & SHOW 2285 ) Logarithm of Large Numbers, the Charecteristics of Logarithms, and Logarithm Tables |
(24 Hours Viewing-Window) |
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SHOW 2320 |
Natural Logarithms
(Runtime 13 minutes / Prerequisite SHOW 2315 ) The Mathematical Constant "e", Properties of Natural Logs, and the Log Table |
(24 Hours Viewing-Window) |
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SHOW 2325 |
Logarithm Base Conversion
(Runtime 16 minutes / Prerequisite SHOW 2320 ) The Logarithm Conversion Mechanism and Applications |
(24 Hours Viewing-Window) |
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SHOW 2330 |
Common & Natural Logarithm Conversion
(Runtime 14 minutes / Prerequisite SHOW 2325 ) The Conversion Factor, Base-10 to Base-e, Base-e to Base 10, and Conversion to other Bases |
(24 Hours Viewing-Window) |
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SHOW 2335 |
Anti-Logarithms
(Runtime 23 minutes / Prerequisite SHOW 2330 ) Parts of the Logarithm, Definition of Anti-Logs, Side-by-Side LOG & ALOG Examples |
(24 Hours Viewing-Window) |
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SHOW 2400 |
Introduction to Complex Numbers
(Runtime 14 minutes / Prerequisite SHOW 2190 ) Even & Odd Roots, The Definition and Axioms of Complex Numbers |
(24 Hours Viewing-Window) |
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SHOW 2405 |
The Set of Complex Numbers
(Runtime 25 minutes / Prerequisite SHOW 2400 & SHOW 2635 ) Real Numbers in Complex Form, the Addition, Subtraction, Multiplication & Division of Complex Numbers |
(24 Hours Viewing-Window) |
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SHOW 2410 |
The Conjugate of Complex Numbers
(Runtime 20 minutes / Prerequisite SHOW 2405 ) Standard & Ordered-Pair Forms, Conjugate & Graph of Complex Numbers, and Operations with Ordered-Pairs |
(24 Hours Viewing-Window) |
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SHOW 2430 |
Introduction to Factorials
(Runtime 11 minutes / Prerequisite SHOW 2525 ) The Definition of Factorial Numbers, and the Application of Factorials |
(24 Hours Viewing-Window) |
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SHOW 2435 |
The Algebra of Factorials
(Runtime 19 minutes / Prerequisite SHOW 2430 ) Factorial Properties, Patterns of Factorials, and Operations with Factorials |
(24 Hours Viewing-Window) |
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SHOW 2450 |
The Cartesian-Coordinate System
(Runtime 12 minutes / Prerequisite SHOW 2290 ) Quadrants, Positive & Negative Coordinates, Ordered Pairs, and X & Y Relationship |
(24 Hours Viewing-Window) |
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SHOW 2455 |
Introduction to Mathematical Functions
(Runtime 15 minutes / Prerequisite SHOW 2450 ) The X & Y Functionality, Plotting Lines & Curves on the Geometric Plane |
(24 Hours Viewing-Window) |
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SHOW 2470 |
The Midpoint Formula
(Runtime 11 minutes / Prerequisite SHOW 2455 ) The Characteristics of all 4 Quadrants, Finding the Mid-Point Coordinates |
(24 Hours Viewing-Window) |
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SHOW 2475 |
The Distance Formula
(Runtime 15 minutes / Prerequisite SHOW 2470 ) The Pythagorean Theorem, Finding the Distance Between Any 2 Points |
(24 Hours Viewing-Window) |
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SHOW 2480 |
The Slope of a Line
(Runtime 16 minutes / Prerequisite SHOW 2475 ) The Ordered Pairs, the Ratio of Rise over Run, Positive, Negative, Zero & Undefined Slopes |
(24 Hours Viewing-Window) |
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SHOW 2485 |
The Equation of the Line
(Runtime 20 minutes / Prerequisite SHOW 2480 ) Standard & Slope Intercept Forms, the X & Y Intercepts |
(24 Hours Viewing-Window) |
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SHOW 2490 |
Drawing the Line
(Runtime 15 minutes / Prerequisite SHOW 2485 ) How Many Points to Draw a Line, Computing the Coordinates for any Line of any Slope |
(24 Hours Viewing-Window) |
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SHOW 2495 |
Finding the Equation of the Line
(Runtime 17 minutes / Prerequisite SHOW 2490 ) Deriving the Equation of the Line from Known Points, Applying the Formula to any Line/Slope |
(24 Hours Viewing-Window) |
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SHOW 2500 |
Parallel Lines
(Runtime 11 minutes / Prerequisite SHOW 2495 ) The Definition of Algebraic Parallelism, Parallel Lines in Pratice for any Line & Slope |
(24 Hours Viewing-Window) |
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SHOW 2505 |
Perpendicular Lines
(Runtime 18 minutes / Prerequisite SHOW 2500 & SHOW 2250 ) Definition of Reciprocal Numbers, Perpendicular Lines in Pratice, Parallelism & Perpendicularity |
(24 Hours Viewing-Window) |
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SHOW 2510 |
Intersecting Lines
(Runtime 17 minutes / Prerequisite SHOW 2505 ) Cross Multiplying, Finding the Coordinates of any Intersecting Point |
(24 Hours Viewing-Window) |
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SHOW 2600 |
An Introduction to Polynomials
(Runtime 11 minutes / Prerequisite SHOW 2290 ) Polynomials Explained, Graphical Repesentation of Polynomials, and Numerical Evaluation of Polynomials |
(24 Hours Viewing-Window) |
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SHOW 2605 |
Operations with Polynomials
(Runtime 14 minutes / Prerequisite SHOW 2600 ) Handling the Negative Signs, Polynomial Addition, Subtraction, Multiplication & Division |
(24 Hours Viewing-Window) |
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SHOW 2610 |
Complete Description of Polynomials
(Runtime 22 minutes / Prerequisite SHOW 2605 ) The Degree of Polynomials, Ascending & Descending Order, Polynomial Standard Form |
(24 Hours Viewing-Window) |
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SHOW 2615 |
Division of Polynomials
(Runtime 15 minutes / Prerequisite SHOW 2610 ) Long Division Method: Trynomial by Binomial |
(24 Hours Viewing-Window) |
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SHOW 2620 |
Visual Polynomial Division
(Runtime 14 minutes / Prerequisite SHOW 2615 ) Graphic Representation of Polynomials Division |
(24 Hours Viewing-Window) |
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SHOW 2625 |
Multiplication of Polynomials
(Runtime 14 minutes / Prerequisite SHOW 2620 ) The FOIL Method: Binomial x Binomial |
(24 Hours Viewing-Window) |
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SHOW 2630 |
Visual Polynomial Multiplication
(Runtime 12 minutes / Prerequisite SHOW 2625 ) Graphic Representation of Polynomials Multiplication |
(24 Hours Viewing-Window) |
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SHOW 2635 |
The Product of Polynomials
(Runtime 12 minutes / Prerequisite SHOW 2630 ) The Multiplication of Any Size Polynomials |
(24 Hours Viewing-Window) |
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SHOW 2650 |
Common Factors
(Runtime 12 minutes / Prerequisite SHOW 2120 ) Separating Prime Factors in Composite Expressions |
(24 Hours Viewing-Window) |
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SHOW 2655 |
An Introduction to Factoring
(Runtime 11 minutes / Prerequisite SHOW 2650 ) Polynomial Multiplication in Reverse, and Grouping Method |
(24 Hours Viewing-Window) |
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SHOW 2660 |
Visual Polynomial Factorization
(Runtime 15 minutes / Prerequisite SHOW 2655 ) Graphic Representation of Polynomial Factoring |
(24 Hours Viewing-Window) |
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SHOW 2665 |
Basic Factoring
(Runtime 19 minutes / Prerequisite SHOW 2660 ) The Elements of Factoring |
(24 Hours Viewing-Window) |
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SHOW 2670 |
Factoring Method
(Runtime 15 minutes / Prerequisite SHOW 2665 ) From Trinomial to Binomial Form |
(24 Hours Viewing-Window) |
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SHOW 2675 |
Special Case Factoring
(Runtime 17 minutes / Prerequisite SHOW 2670 ) Perfect-Square Trinomials & Difference of Two-Squares |
(24 Hours Viewing-Window) |
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SHOW 2680 |
Factoring Higher Order Polynomials
(Runtime 14 minutes / Prerequisite SHOW 2675 ) The Sum & Difference of Two-Cubes |
(24 Hours Viewing-Window) |
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SHOW 2700 |
Introduction to Quadratic Equations
(Runtime 16 minutes / Prerequisite SHOW 2680 ) Finding the Solution-Set |
(24 Hours Viewing-Window) |
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SHOW 2705 |
Factoring with Quadratic Equations
(Runtime 16 minutes / Prerequisite SHOW 2700 ) Advanced Factoring |
(24 Hours Viewing-Window) |
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SHOW 2710 |
Roots of the Quadratic Equation Explained
(Runtime 19 minutes / Prerequisite SHOW 2705 ) The X-Intercept, Roots or Zeroes of the Quadratic |
(24 Hours Viewing-Window) |
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SHOW 2715 |
Complete Description of the Quadratic
(Runtime 16 minutes / Prerequisite SHOW 2710 ) The X & Y Intercepts, the Coefficients and the Vertex |
(24 Hours Viewing-Window) |
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SHOW 2720 |
Graphing the Quadratic Function
(Runtime 13 minutes / Prerequisite SHOW 2715 ) Mapping Intercepts & Vertex in the Cartesian Plane |
(24 Hours Viewing-Window) |
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SHOW 2725 |
Discriminant of the Quadratic Equation
(Runtime 9 minutes / Prerequisite SHOW 2720 ) Character of the Roots (Real & Complex) |
(24 Hours Viewing-Window) |
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SHOW 2730 |
Completing the Square
(Runtime 11 minutes / Prerequisite SHOW 2725 ) Convert Trinomials into Perfect Squares |
(24 Hours Viewing-Window) |
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SHOW 2800 |
Introduction to System of Equations
(Runtime 15 minutes / Prerequisite SHOW 2510 ) Intersecting Lines & the Common Solution-Set |
(24 Hours Viewing-Window) |
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SHOW 2805 |
Types of Solution Sets
(Runtime 12 minutes / Prerequisite SHOW 2800 ) Consistent & Independent, Consistent & Dependent, and Inconsistent Systems |
(24 Hours Viewing-Window) |
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SHOW 2810 |
2x2 System of Equations
(Runtime 15 minutes / Prerequisite SHOW 2805 ) Solving by Substitution Method |
(24 Hours Viewing-Window) |
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SHOW 2815 |
2x2 System of Equations II
(Runtime 16 minutes / Prerequisite SHOW 2810 ) Solving by Elimination Method |
(24 Hours Viewing-Window) |
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SHOW 2820 |
2x2 System of Equations III
(Runtime 13 minutes / Prerequisite SHOW 2815 ) Involving Quadratic Equations |
(24 Hours Viewing-Window) |
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SHOW 2825 |
Introduction to 3x3 System of Equations
(Runtime 9 minutes / Prerequisite SHOW 2820 ) Linking Tables, System of Equations, Matrices, and the Augmented Matrix |
(24 Hours Viewing-Window) |
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SHOW 2830 |
3x3 System of Equations
(Runtime 22 minutes / Prerequisite SHOW 2825 ) Solution-Set by the Matrix Row-Operations Method |
(24 Hours Viewing-Window) |
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SHOW 2850 |
Introduction to Mathematical Inequalities
(Runtime 15 minutes / Prerequisite SHOW 2830 ) Notational Inequality, Transitive Properties, Graphical Representation |
(24 Hours Viewing-Window) |
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SHOW 2855 |
Inequalities in One-Variable
(Runtime 9 minutes / Prerequisite SHOW 2850 ) Operations, Graphical Representation and Domain Intervals |
(24 Hours Viewing-Window) |
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SHOW 2860 |
Quadratic Inequalities
(Runtime 18 minutes / Prerequisite SHOW 2855 & SHOW 2101 ) Solution-Set Intervals |
(24 Hours Viewing-Window) |
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SHOW 2865 |
Inequalities in Two-Variables
(Runtime 12 minutes / Prerequisite SHOW 2860 ) Operations, Graphical Representation, and Domain & Range |
(24 Hours Viewing-Window) |
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SHOW 2870 |
System of Inequalities
(Runtime 16 minutes / Prerequisite SHOW 2865 & SHOW 2510 ) The Solution Region |
(24 Hours Viewing-Window) |
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SHOW 2875 |
Introduction to Linear Programming
(Runtime 19 minutes / Prerequisite SHOW 2870 ) Feasible Solution Optimization (Max & Min) |
(24 Hours Viewing-Window) |
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