David's Math Tutoring

Greeting

Numbers on a Number Line 1

Numbers on a Number Line 2

Numbers on a Number Line 3

Numbers on a Number Line 4

Numbers on a Number Line 5

Numbers on a Number Line 6

Numbers on a Number Line 7

Numbers on a Number Line 8

Numbers on a Number Line 9

Numbers on a Number Line 10

Numbers on a Number Line 11

Numbers on a Number Line 12

Numbers on a Number Line 13

Numbers on a Number Line 14

The Opposite of A Number

Subtraction Redefined

Positive and Negative Numbers: Motivation

Counter Model for Numbers: First Iteration

Counter Model for Numbers: Addition Rules, First Iteration

Introduction of the Abax Model - A model based on the Greek Abacus

How to add numbers with the Abax

Observations made using the Abax regarding adding two numbers with the same sign

Observations made using the Abax regarding adding two numbers with the opposite sign

Absolute Value of a Number in Terms of the Abax Model

Translation of the Observations regarding adding numbers with the same sign into standard terminology

Translation of the Observations regarding adding numbers with opposite signs into standard terminology

The Opposite of a Number

Subtraction Redefinition

Introducing the Greek Abacus

A beautiful Greek Abacus

How to represent Numbers on the Greek Abacus

Adding 243 to 487 with the Greek Abacus

Subtracting 189 from 435 with the Greek Abacus

Subtracting 189 from 435 using the Greek Abacus while simultaneously exploiting the observations we made before

Where Variables Enter into Algebra Example 1

Where Variables Enter into Algebra Example 2

Where Do Variables Come From Example 3

Where Do Variables Come From Example 4

Introduction: Why is it necessary to Simplify Expressions?

Like Terms

Adding and Subtracting Like Terms

Adding And Subtracting Like Terms More Examples

Multiplying Expressions

Dividing Expressions

How To Simplify Expressions: Homework Set 1

How to Simplify Expressions Problem 1

How to Simplify Expressions Problem 2

How to Simplify Expressions Problem 3

How to Simplify Expressions Problem 4

How to Simplify Expressions Problem 5

How to Simplify Expressions Problem 8

How to Simplify Expressions Problem 9

How to Simplify Expressions Problem 10

Distributive Law Introductory Statement

Distributive Law: The Idea

Distributive Law Example 1

Distributive Law Example 2

Distributive Law Example 3

Distributive Law Example 4

Distributive Law Example 5

Distributive Law Example 6 (Optional on a first viewing): How using the Distributive Law can aid in hand calculation

Distributive Law Example 6 (Optional on a first viewing): How using the Distributive Law can aid in hand calculation (Backstory and Variation)

Distributive Law: Homework Set 1

Distributive Law Homework Problem 1

Distributive Law Homework Problem 2

Distributive Law Homework Problem 3

Distributive Law Homework Problem 4

Distributive Law Homework Problem 5

Distributive Law Homework Problem 6

Distributive Law Homework Problem 7

Distributive Law Homework Problem 9

Distributive Law Homework Problem 10

Exponentiation Introductory Lecture

Exponentiation Property 1

Exponentiation Property 2

Exponentiation Property 3

Exponentiation Property 4

Exponentiation Property 5

Exponentiation Property 6

Exponentiation Property 7

Linear Equations Lecture 1: What is an equation?

Linear Equations Lecture 2: What is a linear equation?

Linear Equations Lecture 3: Taxi Cab Company A Motivating Example

LinEqLec5

LinEqLec6

LinEqEx8

Algebraic Vistas: Homework Set 1 for Linear Equations

Homework Set 1 for Linear Equations: Problem 1

Homework Set 1 for Linear Equations: Problem 2

Homework Set 1 for Linear Equations: Problem 3

Homework Set 1 for Linear Equations: Problem 4

Homework Set 1 for Linear Equations: Problem 5

Homework Set 1 For Linear Equations Problem 6

Homework Set 1 For Linear Equations Problem 7

Homework Set 1 For Linear Equations Problem 8

Homework Set 1 For Linear Equations Problem 9

Polygon Internal Angles Example 2

Absolute Value Equations Lecture 1

Absolute Value Equations Lecture 3

Absolute Value Equations Lecture 4

Absolute Value Equations Lecture 5

Absolute Value Equations Lecture 6

Absolute Value Equations Lecture 7

Introduction To Percentage Problems

Percentage Example 1: Jill

Percentage Example 2: Failed Tortilla

Percentage Example 3: Kat's Mercantile

Percentage Example 4: Jessica's Secret Lab

Karla Katia Problem (Again)

Karla Katia Problem (Again) Solution

Henry Isabella Ship Problem(Worked Example)

Henry Isabella Ship Problem (Give it a Try)

Henry Isabella Ship Problem (Give it a Try) Solution

Katherine and John weight problem

Katherine John Weight Problem: Solution 1

Katherine John Weight Problem: Solution 2

Person X Works Out on Friday Saturday and Sunday Problem

Person X Works out on Friday Saturday and Sunday Problem: Solution 1

Person X Works out on Friday Saturday and Sunday Problem: Solution 2

Person X Works out on Friday Saturday and Sunday Problem: Solution 3

Rectangle Perimeter Example 1

A Rectangle Problem

Child and Adult Ticket Problem

A Taxicab Problem

A Triangle Similarity Type Problem

A Percent Problem

A Percent Problem Example 2

Simple Interest Introduction

Simple Interest Karla John

Definition

Function Definition and Introductory Example

Function Example 1

Function Example 2

Function Notation

Introduction to Lines

Introduction to the Slope

Slope Example 1

Slope Example 2

Slope Example 3

Slope Example 4

Different Kinds Of Line Equations

Finding Equation Of Line Example 1

Finding Equation of Line Example 2

Test Style Line Problem

Vertical Line Example1

Horizontal Line Example

Trick Question Line Example

Parallel and Perpendicular Lines Introduction and Characterization

Parallel Line Example

Perpendicular Line Example

Line Facts Homework Problem 1

Line Facts Homework Set 1

Line Facts Homework Problem 2

Line Facts Homework Problem 3

Line Facts Homework Problem 4

A catalog of the different forms of the Equations of Lines

Graphing A Line in Standard Form: Example 2

Graphing A Line in Standard Form: Example 1

Graphing A Line in Slope Intercept Form: Example 1

Graph A Line in Slope Intercept Form: Example 2

Jessica Janet Driving Line Problem

Introductory Example to Graph a Linear Inequality

Linear Inequality Example 1

Linear Inequality Example 2

Linear Inequality Example 3

Introduction And Overview Of Solving Quadratics

Quadratic Example Introduction

Quadratic Example 1

Quadratic Example 2

Quadratic Example 4

Factoring A Quadratic Example 5

Solving a Quadratic by Taking a Square Root Example 1

Solving a Quadratic by Taking a Square Root Example 2

Solving a Quadratic by Square Rooting Example 3

Solving a Quadratic by Square Rooting Example 4

Taking Square Roots: The square root of 48

Taking Square Roots: The square root of 72

Compute a Square Root

Answer to Computing the Square Root Assignment

Simplify a Square Root Problem 2

Answer to Simplifying Square Root Problem 2

Prelude to Completing the Square

Completing the Square Example 1

Completing the Square Example 2

Quadratic Formula Introduction

Some Implications Of The Quadratic Formula: The Discriminant

Solving a Quadratic With The Quadratic Formula: Example 1

Solving a Quadratic With The Quadratic Formula: Example 2

Solving Quadratics by Factoring: Homework Set 1

Solving Quadratics by Factoring Problem 2

Solving Quadratics by Factoring Problem 3

Solving Quadratics by Factoring Problem 4

Solving Quadratics by Factoring Problem 5

Solving Quadratics by Factoring Problem 6

Solving Quadratics by Factoring Problem 7

Solving Quadratics by Factoring Problem 8

Solving Quadratics by Factoring Problem 9

Solving Quadratics by Factoring Problem 10

Solving Quadratics by Completing The Square Problem 2

Solving Quadratics by Completing The Square Problem 3 Approach 1

Solving Quadratics by Completing The Square Problem 3 Approach 2

Solving Quadratics by Completing The Square Problem 3 Approach 3

Solving Quadratics by Completing The Square Problem 4

Graphing a Quadratic In Standard Form: Example 1

Graphing a Quadratic in Standard Form: Example 2

Graphing a Quadratic in Standard Form: Example 3

Graphing a Quadratic in Factored Form: Example 1

Graphing A Quadratic in Vertex Form: Example 1

Graphing A Quadratic in Vertex Form: Example 2

Graphing A Quadratic in Vertex Form: Example 4

Converting a Quadratic From Standard Form To Vertex Form: Example 1

Rectangle Example 1

Rectangle Problem Max Area

Business Mathematics Problem: Finding the Maximum Profit given the Revenue and Cost Functions

Graphing An Absolute Value Equation: Example 1

Graphing An Absolute Value Equation: Example 2

Graphing An Absolute Value Equation: Example 3

Graphing An Absolute Value Equation: Example 4

Graphing An Absolute Value Equation: Example 7

Square Root Graph: Example 2

Square Root Graph: Example 3

Square Root Graph: Example 4

Factoring by Grouping: Example 1

Factoring by Grouping: Example 2

Factoring by Grouping: Example 3

Factoring Polynomials of the Quadratic Type 1

Factoring Polynomials of the Quadratic Type 2

Factoring Polynomials of the Quadratic Type 3

Factoring Polynomials of the Quadratic Type 4

Factoring Polynomials of the Quadratic Type 5

Factoring Polynomials of the Quadratic Type 9

Long Division of Polynomials Introduction

Long Division of Polynomials Example 1

Long Division of Polynomials Example 2

Long Division of Polynomials Example 3

Long Division of Polynomials Example 4

Long Division of Polynomials Example 5

Long Division of Polynomials Example 6

Synthetic Division of Polynomials Example 1

Synthetic Division of Polynomials Example 2

Synthetic Division of Polynomials Example 3

Synthetic Division of Polynomials Example 4

Synthetic Division of Polynomials Example 5

Synthetic Division of Polynomials Example 6

Synthetic Division Homework Set Problem 1

Synthetic Division Homework Set Problem 2

Synthetic Division Homework Set Problem 3

Synthetic Division Homework Set Problem 4

Synthetic Division Homework Set Problem 5

Synthetic Division Homework Set Problem 6

Synthetic Division Homework Set Problem 7

Synthetic Division Homework Set Problem 8

Synthetic Division Homework Set Problem 9

Synthetic Division Homework Set Problem 10

Synthetic Division Homework Set Problem 11

Synthetic Division Homework Set Problem 12

Rational Roots Theorem Introduction

Rational Roots Theorem Example 1

Rational Roots Theorem Example 2

Graphing Polynomials: Example 1

Motivational Example for Systems of Linear Equations

Solution To Motivational Linear System Problem

Systems Of Linear Equations Child Adult Ticket Problem

Cooler Problem

Karls Coins Problem

Systems Of Linear Equations: Homework Set 1

Systems Of Linear Equations: Homework Set 1: Jessica Plot

Systems Of Linear Equations: Homework Set 1: Typical Ticket Problem

Introduction To The Geometry of Linear Systems

Systems Of Linear Equations: The Geometry of Two Dimensional Systems: Example 1

Systems Of Linear Equations: The Geometry of Two Dimensional Systems: Example 2

Systems Of Linear Equations: The Geometry of Two Dimensional Systems: Example 3

Systems of Linear Equations: The Geometry of Two Dimensional Systems Example 4

Davids Three By Three System Solved By Gauss Elimination

A 3x3 Linear System Solved by Gauss Elimination

Nut Problem and Solution by Substitution

Nut Problem System Solution by Gauss Elimination

The Zero Function

The Identity Function

The Square Function

The Cube Function

The Square Root Function

Composition of Functions: Definition and Motivational Example

Horizontal Shift Left Lesson and Example

Horizontal Shift Right Lesson and Example

Vertical Shift Lesson and Example

Reflection Across The X Axis

Vertical Stretch and Shrink

Horizontal Stretch and Shrink

Example 1 Graphed Naively

Example 1 Graphed Intelligently

Exponential Motivating Example 1

Exponential Motivating Example 2

Exponential Equations: What are they?

Exponential Equations: An Important preliminary Exercise

Exponential Equations: Solving our first Exponential Equation

Exponential Equations: Solving our Second Exponential Equation

Exponential Equations: Solving our Third Exponential Equation

Exponential Equations: A Couple Of Important Properties

Introduction to Graphing Exponentials

Graphing Exponentials: Basic Example 1

Graphing Exponentials: Basic Example 2

Graphing Exponentials: Basic Example 3

Graphing Exponentials: Basic Example 4

Graphing Exponentials: Gaining Some Insights

Karla Money Example

Logarithms and Logarithmic Expressions: Basic Definition

Logarithms and Logarithmic Expressions: A Special Property 1

Logarithms and Logarithmic Expressions: A Special Property 2

Logarithms and Logarithmic Expressions: Inverse Property 1

Logarithms and Logarithmic Expressions: Inverse Property 2

Logarithms and Logarithmic Expressions: Log of a Product Property

Logarithms and Logarithmic Expressions: Log of a Power Property

Logarithms and Logarithmic Expressions: Log of a Quotient Property

Logarithms and Logarithmic Expressions: Summary of Important Log Properties

Homework Sheet For this Homework

A reminder of the basic property that we will use repeatedly throughout this homework set

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Examples 8, 9, and 10

Exhibit 11

Example 12

Example 13

Example 14

Example 15

Example 16

Logarithm Example 1: Using log properties to condense a log expression

Logarithm Example 2: Using log properties to condense a log expression

Logarithm Example 3: Using log properties to condense a log expression

Logarithm Example 4: Using log properties to condense a log expression.

Logarithm Example 5: Solving an exponential equation using logarithms.

LogExample6

Logarithm Example 7: Solving an exponential Equation using Logarithms

Logarithm Example 8: Solving a word problem dealing with exponential decay using logarithms.

Distance Formula Introduction

Distance Formula Introductory Example

Beautiful Distance Formula Example

Circle Introduction

Find the Equation of a Circle

Find The Equation Of A Circle Solution

Beautiful Circle Example 2

Introduction to Sequences

Arithmetic Sequences Introduction

Arithmetic Sequence: Worked Example Number 1 with Observations

Geometric Sequences Introduction

Geometric Sequence: Worked Example Number 1 with Observations

Inverse Functions: Motivating Example

Rational Functions Definition

Rational Functions: What Is the Domain of a Rational Function?

Rational Functions: What happens near a point excluded from the Domain, or What are these Vertical Asymptotes and Holes?

Rational Functions: Horizontal Asymptotes