Skip to content
M-Power Sitedocs
Derivation of Completing the Square
Initializing search
M-Power Sitedocs
M-Power Mathmatics Sitedocs
Art of Problem Solving
Art of Problem Solving
Critical Thinking
Critical Thinking Framework
Critical Thinking Framework
Mental Model
Individualized Toolset
Make Learning Fun
Pillars of Cognition
Pillars of Cognition
Foundation of Thinking
Developing Abstraction
Finding Patterns in Things
I ❤️ Puzzles
I ❤️ Puzzles
Puzzle 1 - What is my number?
Puzzle 2 - Magic Square, 3x3
Puzzle 3 - Magic Square, 4x4
Puzzle 4 - Frog and the Stairs
Logic Puzzles
Logic Puzzles
Turtle and the Hare
Fruit Basket
Three Weighty Coins
River Crossing
Jeaulous Husband
Counterfeit Coins
Math Competitions
Math Competitions
AMC-8
AMC-8
Problem Set 1
Problem Set 2
AMC 10
AMC 10
Problem Set 1
AMC 12
AMC 12
Problem Set 1
AIME
AIME
Problem Set 1
Olympiad
Olympiad
Problem Set 1
Math Excursions
Math Excursions
Did You Know?
Patterns in Numbers
Patterns in Numbers
Patterns in Nature
Hidden Patterns
Number Shapes
Mental Excercise
Mental Excercise
Variable Assignment
Number Assignment
Infinity
Sort by Colors
Tools & Resources
Language of Math
Language of Math
Semantics
Semantics
Constants vs Variables
Convention Used
Objects
Labels & Properties
Symbols and Notations
Symbols and Notations
Mathematic Notation & Syntax
Arithmetic Operators
Logic Notation
Set Notation
Sigma Notation
Quantifiers
Quantifiers
Logic Quantifiers
Set Quantifiers
What's the Difference
Algebraic Equations
Algebraic Equations
Terms and Expressions
Structure of Equalities
Structure of Inequalities
Structure of Polynomials
Objects & Labels
Objects & Labels
Attributes & Properties
Mathematical Objects
Elementary Mathematics
Elementary Mathematics
Definition & Properties
Definition & Properties
Notion of Units
Number Line
Constructs Used in Proofs
Sets, Lists, Tuples
Properties of Numbers
Properties of Numbers
General Properties of Numbers
Properties of Zero
Properties of One
Properties of Natural Numbers
Properties of Negative Number
Properties of Infinity
Properties of Real
Properties of Complex Numbers
Properties of Composites
Properties of Primes & Coprimes
Properties of Parity
Properties of Structures
Properties of Structures
Properties of Sets
Properties of Set-like Structures
Number Sets
Number Sets
Number Class
Natural Numbers
Integers
Real Numbers
Complex Numbers
Complex Numbers
Introduction
A Brief History
Complex Plane
Complex Magnitude
Polar Notation
Number System
Number System
Decimal - Base 10
Binary - Base 2
Binary - Base 2
Introduction
Exercises
Hexadecimal - Base 16
Number Patterns
Number Patterns
Why Find Patterns?
Patterns with Integers
Generalization Through Patterns
Generalization Through Patterns
Generalization Process Using Patterns
Sum of First n Natural Numbers
Derived Formulas & Theorems through Pattern Observation
Derived Formulas & Theorems through Pattern Observation
Basic Formulas
Fundamental Theorems
Montessori Bionmial Squares and Cubes
Montessori Bionmial Squares and Cubes
Bionomial Squares
Bionomial Cubes
Bionomial Cubes & Pathagorean
Number Operations
Number Operations
Aggregation
Aggregation
Aggregation in Mathematics
Segmentation
Segmentation
Segmentation in Mathematics
Divisibility & Grouping
Factors & Multiples
Factors & Multiples
Introduction
Properties of Factors
Properties of Multiples
Prime Factorization
Relationship of Factors & Multiples
Relationship of Factors, Multiples to GCF & LCM
GCF & LCM
GCF & LCM
Properties of GCF
Properties of LCM
Relationship of GCF & LCM
Quotients and Remainders
Rates, Ratios, Percents, & Proportions
Rates, Ratios, Percents, & Proportions
Rates, Ratios & Proportions
Percent
Direct vs. Inverse Proportion
Coordinate Systems
Coordinate Systems
Introduction
Functions & Graphs
Functions & Graphs
Introduction
Sequences, Series & Summations
Sequences, Series & Summations
Sequences
Summations
Arithmetic Series
Geometric Series
Appendix - Resources
Appendix - Resources
Applied Math
Applied Math
Physics
Physics
Newton's 1st Law of Motion: Law of Inertia
Newton's 2nd Law of Motion: Law of Acceleration
Cheatsheets
Cheatsheets
Core Ideas
Arithmetic Formulas
Factors Properties
Multiples Properties
Problem Solving
Algebra 1
Algebra 1
Class, Forms & Structures of Equations
Class, Forms & Structures of Equations
Equations, Functions, Curves & Graphs
Curves & Graphs
Types of Equations
X-intercept
Y-intercept
Slope
Resources
Resources
Differences between Equations and Functions
Differences between Curves and Graphs
Algebraic Techniques
Algebraic Techniques
Simplification
Rationalizing the Denominator
Exponentiation
Methods of Solving for Variables
Methods of Solving for Variables
Single Variable Equations
Two Variable Equations
Multi-Variable Equations
Linear Equations
Linear Equations
Introduction
Introduction
Structures of Linear Equations
What is a x-intercept?
What is a y-intercept?
What is a slope?
Semantic Structures
Semantic Structures
Introspection of Linear Forms
Art of Deconstruction
Forms of Linear Eq.
Linear Functions
Linear Curves & Graphs
Quadratic Equations
Quadratic Equations
Form & Structure
Form & Structure
Forms of Quadratics
Properties of Quadratics
Understanding Vieta's Formula
Curves and Graphs
Methods of Solving Quadratics
Methods of Solving Quadratics
Factoring
Factoring
Methods of Factoring
Factoring Techniques
Complete the Square
Complete the Square
Perfect Square Trinomials
Derivation of Completing the Square
Methods of Completing the Square
Resources
Resources
Quadratic Cheatsheet
Practice Problems
Practice Problems
Factoring of Quadratics
Completing the Square
Graphing Quadratics
Vieta Methods
Polynomials
Polynomials
Forms & Structures
Deconstruction of Polynomials
Identification of Polynomials
Excercises
Excercises
Problem Set 1
Appendix - Resources
Appendix - Resources
Definitions
Definitions
Equations, Functions, Curves & Graphs
Equations, Functions, Curves & Graphs
Laws & Properties
Laws & Properties
Fundamental Theorem of Arithmetic
Fundamental Theorem of Algebra
Laws of Equalities & Inequalities
Laws of Exponents
Peano Axioms
Theorems
Theorems
General
Quadratic Thorems
Pythagorean Theorem
Problem Solving
Problem Solving
Solve for x
Solve for x
Problem 1 - Radical
Problem 2 - Simultaneous Eq.
Problem 3 - Rational Powers
Problem 4 - Powers
Problem 5 - Linear Eq.
AoPS-A1
AoPS-A1
Lesson 1
Lesson 2
Cheatsheets
Cheatsheets
Algebraic Identities
Alegrba 1 Properties & Formulas
Algebra 2
Algebra 2
Coordinate Planes
Coordinate Planes
Plane Classifications
Cartesian Plane
Euclidean Plane
Complex Plane
Cubic Equations
Cubic Equations
Forms & Structures
Appendix - Resources
Appendix - Resources
Cartesian Plane vs Euclidean Plane
Cheatsheets
Cheatsheets
Algebraic Identities
Alegrba 2 Properties & Formulas
Trignometry Identities
Problem Solving
Problem Solving
AoPS-A2
AoPS-A2
Lesson 4 - Functions
Lesson 5 - Complex Numbers
Lesson 6 - Complex Planes
Lesson 7 - Quadratics
Geometry
Geometry
Circle
Circle
Form & Structures
Circle Math
Shapes
Shapes
Triangles
Appendix - Resources
Appendix - Resources
Cheatsheets
Cheatsheets
Geometry Properties & Formulas
Geometry Theorems
Logic
Logic
Foundation
Modular Arithmetic
Modular Arithmetic
Definition & Properties
Definition & Properties
Remainder Class
Remainder System
Modulo
Modulus
Clock Math
Appendix - Resources
Appendix - Resources
Cheatsheets
Cheatsheets
General
Exercises
Exercises
Problems Set 1
Number Theory
Number Theory
Definition & Properties
Definition & Properties
Segmentation
Factors & Multiples
Primality
Primality
What is a Prime?
Relative Primes
Prime Factorization
Class of Primes
Divisibility
Divisibility
General
Rules of Divisibility (1..25)
Rules of Divisibility (26..55)
Rules of 10s
Theorems
Theorems
Chicken McNugget Theorem
Fermat's Little Theorem
Euler's Theorem
Appendix - Resources
Appendix - Resources
Cheat-Sheets
Cheat-Sheets
Number Theory Theorems
Count Number of Factors
Exponentiation Method
Derivations of Completing the Squares
¶