**What online resources are available for the Algebra portion of the Praxis 5161 Exam?**

An outstanding site is Paul's Online Notes. Here is a listing of all the material that is currently available in these notes.

Preliminaries

Solving Equations and Inequalities

Graphing and Functions

Common Graphs

Polynomial Functions

Exponential and Logarithm Functions

Systems of Equations

An excellent site for Algebra video tutorials is

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**Algebra Notes**Preliminaries

- Integer Exponents
- Rational Exponents
- Radicals
- Polynomials
- Factoring Polynomials
- Rational Expressions
- Complex Numbers

Solving Equations and Inequalities

- Solutions and Solution Sets
- Linear Equations
- Applications of Linear Equations
- Equations With More Than One Variable
- Quadratic Equations, Part I
- Quadratic Equations, Part II
- Quadratic Equations : A Summary
- Applications of Quadratic Equations
- Equations Reducible to Quadratic Form
- Equations with Radicals
- Linear Inequalities
- Polynomial Inequalities
- Rational Inequalities
- Absolute Value Equations
- Absolute Value Inequalities

Graphing and Functions

- Graphing
- Lines
- Circles
- The Definition of a Function
- Graphing Functions
- Combining functions
- Inverse Functions

Common Graphs

- Lines, Circles and Piecewise Functions
- Parabolas
- Ellipses
- Hyperbolas
- Miscellaneous Functions
- Transformations
- Symmetry
- Rational Functions

Polynomial Functions

- Dividing Polynomials
- Zeroes/Roots of Polynomials
- Graphing Polynomials
- Finding Zeroes of Polynomials
- Partial Fractions

Exponential and Logarithm Functions

- Exponential Functions
- Logarithm Functions
- Solving Exponential Equations
- Solving Logarithm Equations
- Applications

Systems of Equations

- Linear Systems with Two Variables
- Linear Systems with Three Variables
- Augmented Matrices
- More on the Augmented Matrix
- Nonlinear Systems

An excellent site for Algebra video tutorials is

__http://patrickjmt.com/__**ALGEBRA videos**__Arithmetic Basics: Long Division of Numbers____Arithmetic Basics: Finding the Percent of a Number____Arithmetic Basics: Multiplying Decimals____Arithmetic Basics: Dividing Decimals____Arithmetic Basics: Converting Decimals into Fractions____Fractions – Adding and Subtracting____Fractions: Adding and Subtracting – Numerical and Variable Examples____Fractions: Adding and Subtracting Fractions with Different Denominators____Fractions – Multiplying and Dividing____Basic Math: Dividing Fractions____Comparing Fractions using Inequalities – Ex 1____Comparing Fractions using Inequalities – Ex 2____Fractions: Multiplying, Reducing, Adding and Subtracting____Simplifying Complex Fractions – Ex 1____Simplifying Complex Fractions – Ex 2____Simplifying Complex Fractions – Ex 3____Partial Fraction Decomposition – Example 1____Partial Fraction Decomposition – Example 2____Partial Fraction Decomposition – Example 4____Partial Fraction Decomposition – Example 5____Partial Fraction Decomposition – Example 6____Averages and Word Problems – Basic Example____Averages: Finding an Average Grade You Need to Make to Bring Your Grade up to a Desired Amount____Averages: What Grade do I Need on the Final to Pass the Class?!____Radical Notation and Simplifying Radicals____Radicals: Simplifying Radical Expressions Involving Variables – Ex 1____Simplifying Numbers under Square Roots____Rationalize the Denominator____Rationalizing the Denominator – Ex 1____Rationalize the Denominator – Harder Example____Rationalizing the Denominator – Ex 3____Factoring a Number____Factoring a Number____Greatest Common Factor, GCF____Least Common Multiple____An Intro to Solving Linear Equations: What Does it Mean to be a Solution?____An Intro to Solving Linear Equations: Solving some Basic Linear Equations____An Intro to Solving Linear Equations: Solving some Basic Linear Equations, Ex 2____Solving Linear Equations____Solving Linear Equations – Example 1____Solving a Basic Linear Equation – Example 2____Solving a Basic Linear Equation – Example 3____Direct Variation / Direct Proportion – Ex 1____Direct Variation / Direct Proportion – Ex 2____Direct Variation / Direct Proportion – Ex 3____Slope of a Line____Equation of a Line: Point-Slope Form____Graphing a Line Using a Point and Slope____Linear Functions: Graphing by Finding X,Y Intercept____An Introduction To Solving Inequalities – Ex 1____An Introduction To Solving Inequalities – Ex 2____An Introduction To Solving Inequalities – Ex 3____Fundamental True/False Questions about Inequalities!____Solving Word Problems Involving Inequalities – Ex 1____Solving Word Problems Involving Inequalities – Ex 2____Solving Word Problems Involving Inequalities – Ex 3____Using Interval Notation to Express Inequalities – Ex 1____Using Interval Notation to Express Inequalities – Ex 2____Interval Notation – A basic question!____Writing Compound Inequalities Using Interval Notation – Ex 1____Writing Compound Inequalities Using Interval Notation – Ex 2____Writing Compound Inequalities Using Interval Notation – Ex 3____Absolute Value: Evaluating Numbers____Absolute Value: Evaluating Expressions – Ex 1____Absolute Value: Evaluating Expressions – Ex 2____Absolute Value: Evaluating Expressions – Ex 3____Matching Number Lines with Absolute Value Inequalities – Ex 1____Solving Absolute Value Equations – Ex 1____Solving Absolute Value Equations – Ex 2____Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 1____Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 2____Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 3____Solving Absolute Value Inequalities – Ex 1____Solving Absolute Value Inequalities – Ex 2____Solving Absolute Value Inequalities – Ex 3____Solving Absolute Value Inequalities, MORE Ex 1____Solving Absolute Value Inequalities, MORE Ex 2____Solving Linear Absolute Value Equations and Inequalities____Graphing Systems of Linear Inequalities – Ex 1____Graphing Systems of Linear Inequalities – Ex 2____Solving Linear Compound Inequalities – Ex 1____Solving Linear Compound Inequalities – Ex 2____Solving Linear Compound Inequalities – Ex 3____Exponents: Basic Properties____Exponents: Basic Problems – Ex 1____Exponents: Basic Problems – Ex 2____Exponents: A Few True/False Questions____Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 1____Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 2____Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 3____Exponents: Applying the Rules of Exponents – Basic Ex 1____Exponents: Applying the Rules of Exponents – Basic Ex 2____Exponents: Applying the Rules of Exponents – Basic Ex 3____Exponents: Applying the Rules of Exponents – Basic Ex 3____Exponents: Negative Exponents____Negative Exponents – Basic Rules and Examples____Exponents: Simplifying Expressions with Negative Exponents – Ex 1____Exponents: Simplifying Expressions with Negative Exponents – Ex 2____Exponents: Simplifying Expressions with Negative Exponents – Ex 3____Exponents: Numbers Raised to Fractional Exponents____Exponents: Evaluating Numbers Raised to Fractional Exponents____Exponents: Evaluating Numbers with Rational Exponents by using Radical Notation – Basic Ex 1____Exponents: Multiplying Variables with Rational Exponents – Basic Ex 1____Exponents: Multiplying Variables with Rational Exponents – Basic Ex 2____Polynomial… or NOT?! Recognizing Polynomials, the degree and some Terminology____Symmetry – A Quick Discussion for Testing if a Polynomial is Even / Odd____Polynomials: Adding and Subtracting____Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 1____Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 2____Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 3____Polynomials: Multiplying – Slightly Harder Ex 1____Polynomials: Multiplying – Slightly Harder Ex 2____Polynomials: Multiplying – Slightly Harder Ex 3____Polynomials: Multiplying – Slightly Harder Ex 4 – Cubing Binomials____Polynomials: Multiplying – Slightly Harder Ex 5 – Cubing Binomials____Polynomials: Multiplying – Slightly Harder Ex 6____Long Division of Polynomials____Long Division of Polynomials – A slightly harder example____Synthetic Division____Synthetic Division – Ex 2____The Remainder Theorem – Example 1____The Remainder Theorem – Example 2____Factoring Trinomials (A quadratic Trinomial) by Trial and Error____Factoring Trinomials by Trial and Error – Ex 2____Factoring Trinomials: Factor by Grouping – Ex 1____Factoring Trinomials: Factor by Grouping – Ex 2____Factoring Trinomials: Factor by Grouping – Ex 3____Factoring Perfect Square Trinomials – Ex1____Factoring Perfect Square Trinomials – Ex 2____Factoring Perfect Square Trinomials – Ex3____Factoring the Difference of Two Squares – Ex 1____Factoring the Difference of Two Squares – Ex 2____Factoring the Difference of Two Squares – Ex 3____Factoring Sums and Differences of Cubes____Factoring Sums and Differences of Cubes – Ex 3____Factoring Using the Great Common Factor, GCF – Ex 1____Factoring Using the Great Common Factor, GCF – Ex 2 – Factoring Out Binomials____Finding all the Zeros of a Polynomial – Example 1____Finding all the Zeros of a Polynomial – Example 2____Finding all the Zeros of a Polynomial – Example 3____Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 1____Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 2____Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 3____Rational Roots Test____Descartes’ Rule of Signs____The Conjugate Pair Theorem – Example 1____The Conjugate Pair Theorem – Example 2____Quadratic Equations – Factoring and Quadratic Formula____Solving Quadratic Equations by Factoring – Basic Examples____Solving Quadratic Equations by Factoring – Another Example____Factoring by Grouping____Factoring by Grouping – Ex 1____Factoring By Grouping – Ex 2____Quadratic Equations – Completing the Square____Completing the Square – Solving Quadratic Equations____Completing the Square: Solving Quadratic Equations – Ex 2____Completing the Square to Solve Quadratic Equations: More Ex 1____Completing the Square to Solve Quadratic Equations: More Ex 2____Completing the Square to Solve Quadratic Equations: More Ex 3____Completing the Square to Solve Quadratic Equations: More Ex 4____Completing the Square to Solve Quadratic Equations: More Ex 5____Completing the Square to Solve Quadratic Equations: More Ex 6____Quadratic Formula____Quadratic Formula: How to Derive____Solving Quadratic Equations using the Quadratic Formula – Ex 1____Solving Quadratic Equations using the Quadratic Formula – Ex 2____Solving Quadratic Equations using the Quadratic Formula – Ex 3____Quadratic Equations: Using the Discriminant____Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 1____Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 2____Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 3____Graphing Quadratic Functions – Ex 1____Solving Fancy Quadratics – Ex 1____Solving Fancy Quadratics – Ex 2____Solving Fancy Quadratics – Ex 3____Solving a Geometry Word Problem by Using Quadratic Equations – Ex 1____Solving a Geometry Word Problem by Using Quadratic Equations – Ex 2____Solving a Geometry Word Problem by Using Quadratic Equations – Ex 3____Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 1____Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 2____Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 3____Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 1____Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 2____Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 3____Solving a Projectile Problem Using Quadratics – Ex 1____Solving a Projectile Problem Using Quadratics – Ex 2____Solving a Projectile Problem Using Quadratics – Ex 3____More Word Problems Using Quadratic Equations – Ex 1____More Word Problems Using Quadratic Equations – Ex 2____More Word Problems Using Quadratic Equations – Example 3____Solving Quadratic Inequalities – The Basics____Solving Quadratic Inequalities____Solving Quadratic Inequalities – A Common Mistake____Solving Quadratic Inequalities – Ex 1____Solving Quadratic Inequalities – Ex 2____Solving Quadratic Inequalities – Ex 3____Solving Quadratic Inequalities, More Ex 1____Solving Quadratic Inequalities, More Ex 2____Solving Quadratic Inequalities, More Ex 3____Solving Quadratic Inequalities, More Ex 4____Solving Quadratic Inequalities – More Examples____Rational Expressions and Domain____Finding the Domain of an Expression Involving Fractions – Ex 1____Finding the Domain of an Expression Involving Fractions – Ex 2____Finding the Domain of an Expression Involving Fractions – Ex 3____Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Example 1____Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Ex 2____Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Ex 3____Finding the Domain of a Function Algebraically (No graph!)____Rational Expressions: Writing in Lowest Terms – Ex 1____Rational Expressions: Writing in Lowest Terms – Ex 2____Rational Expressions: Adding and Subtracting____Rational Expressions: Adding and Subtracting. Ex 1____Rational Expressions: Adding and Subtracting. Ex 2____Rational Expressions: Multiplying and Dividing. Ex 1____Rational Expressions: Multiplying and Dividing. Ex 2____Rational Expressions: Multiplying and Dividing. Ex 3____Rational Equations: Solving____Solving a Basic Rational Equation – Ex 1____Solving a Basic Rational Equation – Ex 2____Solving a Basic Rational Equation – Ex 3____Solving a Basic Rational Equation – Ex 4____Solving a Basic Rational Equation – Ex 5____Graphing Some Basic Rational Functions – Example 1____Graphing a Rational Function – Example 1____Graphing a Rational Function – Example 2____Graphing a Rational Function – Example 3____Graphing a Rational Function – Example 4____Rational Functions: Shortcut to Find Horizontal Asymptotes____Rational Functions: Vertical Asymptotes____Rational Functions: Slant Asymptotes____Find Asymptotes of a Rational Function (Vertical and Oblique/Slant)____Find Asymptotes of a Rational Function (Vertical and Oblique/Slant), Ex 2____Graphing a Rational Function that has an Oblique/Slant Asymptote and a Vertical Asymptote____Rational Inequalities: Solving____Solving a Rational Inequality – Ex 1____Solving a Rational Inequality – Ex 2____Solving a Rational Inequality – Ex 3____Solving a Rational Inequality, More Examples – Ex 1____Solving a Rational Inequality, More Examples – Example 2____Solving a Rational Inequality, More Examples – Example 3____Piecewise Defined Functions: Graphing____Graphing a Piece-Wise Defined Function – Another Example____Piecewise Functions: Find the Formula from a Graph – Ex 1____Piecewise Functions: Find the Formula from a Graph – Ex 2____Evaluating Piecewise Defined Functions____Functions: Adding and Subtracting____Functions: Multiplying and Dividing____Composition of Functions____Finding Functions that Form a Particular Composite Function____The Vertical Line Test____X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 1____X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 2____The Difference Quotient – Example 1____The Difference Quotient – Example 2____Graphing the Greatest Integer or Floor Function____Solving an Equation for a Specified Variable____Solving Equations Involving Square Roots____Solving an Equation Involving a Single Radical (Square Root) – Ex 1____Solving an Equation Involving a Single Radical (Square Root) – Ex 2____Solving an Equation Involving a Single Radical (Square Root) – Ex 3____Solving an Equation Containing Two Radicals – Ex 1____Solving an Equation Containing Two Radicals – Ex 2____Solving an Equation Containing Two Radicals – Ex 3____Solving Equations Involving Rational Exponents____Solving an Equation Involving Rational Exponents – Ex 1____Solving an Equation Involving Rational Exponents – Ex 2____Solving an Equation Involving Rational Exponents – Ex 3____The Cartesian Coordinate System – A few basic questions____Basic Graphs that Every Algebra Student Should Know!!____Graphing Equations by Plotting Points – Example 1____Graphing Equations by Plotting Points – Example 2____Graphing Equations by Plotting Points – Example 3____Finding Domain and Range of a Function using a Graph____Domain and Range From a Graph____Local Max/Min, Inc/Dec: On a Graph____Finding Limits From a Graph____Horizontal and Vertical Graph Transformations____Horizontal And Vertical Graph Stretches and Compressions Part 1 of 3____Horizontal And Vertical Graph Stretches and Compressions Part 2 of 3____Graph Transformations about the X-axis and Y-axis____Graphing Using Graph Transformations – Ex 1____Graphing Using Graph Transformations – Ex 2____Inverse Functions – The Basics!____Inverse of a Function____Finding the Inverse of a Function or Showing One Does not Exist, Ex 2____Finding the Inverse of a Function or Showing One Does not Exist, Ex 3____Finding the Inverse of a Function or Showing One Does not Exist, Ex 4____Solving a Linear System of Equations by Graphing____Linear System of Equations: Row Reducing – Part 1____Linear System of Equations: Row Reducing – Part 2____Linear System of Equations: Solving using Substitution____Linear System of Equations: Solving using Elimination by Addition____Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 1____Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 2____Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 3____Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 1____Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 2____Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 3____Solving a Dependent System of Linear Equations involving 3 Variables____Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 1____Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 2____Cramer’s Rule to Solve a System of 3 Linear Equations – Example 1____Cramer’s Rule to Solve a System of 3 Linear Equations – Example 2____The Distance Formula____The Distance Formula and Finding the Distance Between Two Points – Example 1____The Distance Formula and Finding the Distance Between Two Points – Example 2____The Midpoint Formula____The Midpoint Formula – Finding the Midpoint____Collinearity and Distance: Determining if Three Points are Collinear, Example 1____Collinearity and Distance: Determining if Three Points are Collinear, Example 2____Collinearity and Distance: Determining if Three Points are Collinear, Example 3____Word Problem: Distance, Rate, and Time____Pythagorean Theorem____Word Problems Using the Pythagorean Theorem – Ex 1____Word Problems Using the Pythagorean Theorem – Ex 2____Word Problems Using the Pythagorean Theorem – Ex 3____Word Problem Involving Perimeter of a Triangle – Ex 1____Word Problem Involving Perimeter of a Triangle – Ex 2____Word Problem Involving the Perimeter of a Rectangle – Ex 1____Word Problem Involving the Perimeter of a Rectangle – Ex 2____Coterminal Angles – Example 1____Coterminal Angles – Example 2____Coterminal Angles – Example 3____Finding the Quadrant in Which an Angle Lies – Example 1____Finding the Quadrant in Which an Angle Lies – Example 2____Finding the Quadrant in Which an Angle Lies – Example 3____Adding and Subtracting Complex (Imaginary) Numbers____Rewriting Radicals using Complex Numbers____Rewriting Powers of ‘ i ‘ – Ex 1____Rewriting Powers of ‘ i ‘ – Ex 2____Complex Numbers: Graphing, Adding, Subtracting____Complex Numbers: Multiplying and Dividing____Complex Numbers: Multiplying – Ex 1____Complex Numbers: Multiplying – Ex 2____Complex Numbers: Dividing – Ex 1____Complex Numbers: Dividing – Ex 2____Complex Numbers: Dividing – Ex 3____Conic Sections: Parabolas, Part 1____Conic Sections: Parabolas, Part 2 (Directrix and Focus)____Conic Sections: Parabolas, Part 3 (Focus and Directrix)____Conic Sections: Parabolas, Part 4 (Focus and Directrix)____Conic Sections: Parabolas, Part 5 (Focus and Directrix)____Graphing a Parabola____Conic Sections: Hyperbolas, An Introduction____Conic Sections: Hyperbolas, An Introduction – Graphing Example____Finding the Equation for a Hyperbola Given the Graph – Example 1____Conic Sections: Graphing Ellipses – Part 1____The Center-Radius Form for a Circle – A few Basic Questions, Example 1____The Center-Radius Form for a Circle – A few Basic Questions, Example 2____Finding the Center-Radius Form of a Circle by Completing the Square – Example 1____Finding the Center-Radius Form of a Circle by Completing the Square – Example 2____Finding the Center-Radius Form of a Circle by Completing the Square – Example 3____Identifying a Conic from an Equation by Completing the Square, Ex 1____Identifying a Conic from an Equation by Completing the Square, Ex 2____Identifying a Conic from an Equation by Completing the Square, Ex 3____Matrices: Basic Matrix Operations (add, subtract, multiply by constant)____Matrices: Multiplying a Matrix by another Matrix____Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 1____Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 2____Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 3____Logarithms: Properties of Logarithms – Part 1____Logarithms: Properties of Logarithms – Part 2____Properties of Logarithms____Solving Logarithmic Equations – Example 1____Solving Logarithmic Equations – Example 2____Change of Base Formula for Logarithms____Solving Exponential Equations____Exponential Function From a Graph____Word Problem: Exponential Growth____Factoring Trigonometric Expressions, Example 1____Factoring and Simplifying Trigonometric Expressions – Example 2____Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2____Binomial Theorem – Ex 1____Binomial Theorem – Ex 2____Arithmetic Sequences: A Quick Intro____Arithmetic Sequences: Finding a General Formula Given Two Terms____Finding the Sum of a Finite Arithmetic Series____Proof by Induction – Example 1____Proof by Induction – Example 2____Proof by Induction – Example 3____Understanding Simple Interest and Compound Interest____Deriving the Annual Compound Interest Formula____Compound Interest – More than Once Per Year____Compound Interest – More than Once Per Year – Part 2____Finding an Interest Rate to Match Certain Financial Goals, Ex 1____Finding an Interest Rate to Match Certain Financial Goals, Ex 2____Finding an Interest Rate to Match Certain Financial Goals, Ex 3____Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement – Ex 2____Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement – Ex 3__

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