NovoMathTM
educational technology

Visual-Dynamic School Mathematics
Using Technology for Implementing the 21st Century Pedagogy

  

mathematiX TM - Visual-dynamic Algebra, Trigonometry and Calculus

 

 

 

Lessons

 
 
   
 
Points Linear Function Quadratic Function More Functions Exploring Functions

 

 

 

 

 

 

 

 

LIST OF ALGEBRA LESSONS

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POINTS ON THE COORDINATE PLANE

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The Concept of Point Coordinates

Points on a Number Line. The Concept of a Signed Distance

A Coordinate Line and a Coordinate System

Points on the x-Axis

 

Points on the y-Axis

 

The Coordinates of Points in the First Quadrant

 

The Coordinates of Points in Any Quadrant

 

A Distance between Two Points and a Midpoint

 

The Distance of a Point from the Origin

 

The Distance Between Two Points

 

The Midpoint of a Segment

 

The Distance Between Two Points in Different Axes Systems

 

Transormations of Points and their Coordinates

Reflection of Points

Translation of Points

The Proportion in Points Coordinates

 

Different Dependencies Between the Points' Coordinates

 

                               

 

LINEAR FUNCTION

General

Points on the Horizontal Line. Points on the Vertical Line

 

The Equation of the Vertical Axis

 

The Equation of the Horizontal Axis

 

The Properties of a Point on a Line

 

The Distortion of the Scales

The Concept of a Slope

 

The Slope of a Segment between Two Points in the First Quadrant

 

The Slope of any Segment between Two Points

 

The Slope of a Linear Function Graph  y = mx

 

A Linear Function Passing through the Origin  y = mx  as a Graphic Representation of a Linear Proportion

The Slope-Intercept Form of Linear Equation  y = mx + b

 

The Slope of a Linear Function Graph  y = mx + b

 

The Meaning of the Free Term  b  in the Linear Function  y = mx + b   (Part I)

 

The Meaning of the Free Term  b  in the Linear Function  y = mx + b   (Part II)

 

Proportion Properties of a Linear Function Not Passing through the Origin  y = mx + b

 

The Representation of the  x-Intercept Point in a Linear Function in the Form  y = mx + b

 

The Graphical Representation of the Moving Problems

Parallel and Perpendicular Lines

 

The Equations of Parallel Lines

 

The Equations of Perpendicular Lines

 

A Perpendicular to a Line Passing through the Given External Point

 

The Distance from a Point to a Line

Standard Linear Equation Ax + By = C

 

Standard Linear Equation  Ax + By + C = 0 - General

 

Standard Linear Equation  Ax + By = C  when  A = 0

 

Standard Linear Equation  Ax + By = C when  B = 0

 

Standard Linear Equation  Ax + By = C - Exploring the Slope

 

Standard Linear Equation  Ax + By = C - Exploring the y-Intercept

 

The Standard Equations of Parallel Lines

 

The Standard Equations of Perpendicular Lines

 

The Equivalent Standard Equations

Other Forms of Linear Equation

 

The Equation of a Line of a Given Slope Passing through a Given Point.  Part I - General

 

The Equation of a Line of a Given Slope Passing through a Given Point.  Part II - The Pencil of Lines

 

A Family of Linear Functions Passing through a Given Point

 

The Linear Function Passing through Two Given Points

 

The Equation of a Segment

The Intersection of Two Straight Lines

 

The Intersection Point of Two Lines

 

The Intersection Point of Many Lines. The Pencil of Lines

 

The Graphical Solution of Two Standard Linear Equations

 

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QUADRATIC FUNCTION

General

 

The Quadratic Function's Graph and Its Properties

 

The Vertex (Completed Square) Form of a Quadratic Function

 

The corresponding values of  x  for a given value of  y . Part I: The Family of Functions  y = x2 + c  

 

The corresponding values of  x  for a given value of  y . Part II: The Family of Functions  y = x2 + Bx + C

 

Solving Quadratic Equations

Transformations of the Quadratic Function Graph

 

Horizontal Translation

 

Vertical Translation

 

Combined Translation

 

Shrinking and Stretching

 

A Family of Quadratic Functions with the Vertex at the Given Point

The Factored Form of a Quadratic Function

 

The Meaning of the Factored Form of a Quadratic Function and Its Graphical Representation

 

The Quadratic Function as a Product of Two Linear Functions - Part I

 

The Quadratic Function as a Product of Two Linear Functions - Part II

Exploring Parameters in Different Families of Quadratic Functions

 

Exploring Parameter  B  in the Family of Functions  y = x2 + Bx

 

Exploring Parameter  k  in the Family of Quadratic Functions   y = k(x2 + px + q)

 

Exploring Parameter  A  in the Family of Quadratic Functions   y = Ax2 + Bx + C

 

Exploring Parameter  C  in the Family of Quadratic Functions   y = Ax2 + Bx + C

 

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OTHER FUNCTIONS

 

Power and Polynomial Functions

 

Power Function

 

Polynomial Function - General

 

Different Third Degree Polynomial Functions and their Graphs

 

Different Forth Degree Polynomial Functions and their Graphs

 

Exploring Parameter  a  in Function  f(x) = (x - 5)(x - a)(x + 3)

 

Extrema of Third Degree Polynomial Function

 

Extrema and x-Intercept Points of Fourth Degree Polynomial Function

 

Rational Functions - Introduction

 

Types of Rational Functions

 

Exponential and Logarithmic Functions

 

Introduction

 

The Family of Exponential Functions  y = ax

 

The Mathematical Constant  e  and its Meaning

 

Two Families of Functions:  y = eax  and  y = kex

 

Logarithmic Function

 

Exploring the Properties of Function ex

 

Examples of Exponential Growth

 

Absolute Value and Integer Functions

 

Absolute Value Function

 

Integer Function

 

Discrete Variable Functions

 

Function of Discrete Variable

 

Sequence and Sum

 

Inverse Functions

 

Square Power and Square Root Functions

 

Cube Power and Cube Root Functions

 

Exponential and Logarithmic Functions

 

Sine and Arcsine Functions

 

Inequalities and Linear Programming

 

Inequalities in One Variable

 

Inequalities in Two Variables

 

Inequalities of Functions

 

Solving a Problem of Linear Programming

 

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EXPLORING FUNCTIONS

 

Functions Evaluation

 

The Necessity of a Unique Name for a Function

 

The Use of a Function Name for Evaluating Functions

 

The Use of Existing Function Name for Defining New Function

 

x-Intercept, Extrema and Inflection Points

 

The Meaning of the  x-Intercept Point

 

The Sign of a Function

 

The Point of Maximum

 

A Steepness and Tangent Slopes in the Vicinity of the Maximum Point

 

The Point of Minimum

 

A Steepness and Tangent Slopes in the Vicinity of the Minimum Point

 

Increasing Function

 

Different Combinations of Positive / Negative and Increasing / Decreasing Regions of a Function

 

Local and Global Extrema

 

Inflection Point - Introduction

 

General Rules of Functions' Graphs

 

Translation

 

Horizontal Translation

 

Examples of Horizontal Translation

 

Vertical Translation

 

Examples of Vertical Translation

 

Combined Translation

 

Examples of Combined Translation

 

The Translation of Function Graph - Summary

 

A Pencil of Straight Lines

 

The Locus of Vertex Points of a Translated Quadratic Function

 

The Translation of an Exponential Function's Graph

 

The Translation of a Circle

 

Reflection

 

The Reflection of Points over the Axes

 

The Reflection of Points through the Origin

 

The Reflection of Points - Summary

 

The Meaning of the Reflection of a Function Graph

 

The Reflection of an Even Function Graph

 

The Reflection of an Odd Function Graph

 

Reflection of Function Graph - Summary

 

Additional Examples of Reflection

 

Shrinking/Stretching

 

Quadratic Function's Graph

 

Exponential Function's Graph

 

The sine Function's Graph

 

Shrinking/Stretching of Function Graph - Summary

 

Applications

 

Reflection of Figures

 

Finding a Polynomial Function

 

Drawing a sine Function's Graph

 

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Discontinuity of Functions

 

Types of Discontinuity

 

Exploring Rational Functions

 

More Examples of Rational Functions

 

Trigonometric Functions

 

Operations with Functions

 

Two Linear Functions

 

Addition & Subtraction

 

Multiplication

 

Division

 

Square Root of Product

 

Linear and Quadratic Functions

 

Addition & Subtraction

 

Multiplication

 

Division

 

Square Root of Product

 

Two Trigonometric Functions

 

Addition & Subtraction

 

Other Operations

 

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  Copyright 1995-2013 Dr. Joseph Dalin, All rights reserved.