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Algebra 1
This is a list of all Virtual Nerd tutorials in Algebra 1, organized by topic.
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Getting Ready for Algebra
Foundations for Algebra
Variables and Expressions
Introduction to Algebraic Expressions
Translating Between Words and Math
- How Do You Write an Equation from a Word Problem?
- What Are Some Words You Can Use To Write Word Problems?
- How Do You Turn a Simple Expression into Words?
- How Do You Translate a Phrase with One Variable and Number Into a Mathematical Expression?
- How Do You Turn a Longer Verbal Phrase into an Algebraic Expression?
- How Do You Turn a More Complicated Expression into Words?
- How Do You Solve a Word Problem by Writing an Equation and Plugging in Values?
- How Do You Turn a Simple Equation into Words?
- How Do You Turn a More Complicated Equation into Words?
Representing and Comparing Real Numbers
Sets and Number Lines
- How Do You Find a Solution Set When You Have A Replacement Set?
- What's a Set?
- How Do You Graph a Set on a Number Line?
- What's a Venn Diagram, and How Do You Find the Intersection and Union of a Set?
- How Do You Name a Set That's Graphed on a Number Line?
- How Do You Find a Union and Intersection from a Venn Diagram?
Inequalities and Comparing Real Numbers
- What Are Some Words We Use When We Have Inequalities?
- What's an Inequality?
- How Do You Determine if a Value is a Solution to an Inequality?
- How Do You Graph the Intersection of Two Inequalities?
- How Do You Figure Out Which of Two Fractions is Bigger?
- How Do You Write an Inequality from a Number Line Graph?
- How Do You Solve a Word Problem By Writing an Inequality?
- How Do You Graph an Inequality or an Infinite Set on a Number Line?
- How Do You Put Real Numbers in Order?
- How Do You Graph the Union of Two Inequalities?
- How Do You Write Inequalities in Set Builder Notation?
Real Number Types and Properties
Types of Numbers
- What's Another Definition for an Integer?
- What are Consecutive Numbers?
- What's Another Definition for Prime and Composite Numbers?
- What's a Rational Number?
- What's an Irrational Number?
- What's a Prime Number?
- How Do Different Categories of Numbers Compare To Each Other?
- What's an Integer?
- What are Natural and Whole Numbers?
- What's a Real Number?
Real Number Properties
- What are the Inverse Properties of Addition and Multiplication?
- What Does Absolute Value Mean?
- What are the Identity Properties of Addition and Multiplication?
- What are the Commutative Properties of Addition and Multiplication?
- What are the Associative Properties of Addition and Multiplication?
- How Do You Find the Absolute Value of Positive and Negative Numbers?
- How Do You Use the Associative Property?
- What are the Multiplication Properties of 0 and -1?
- What Does Absolute Value Mean In the Real World?
Adding and Subtracting Real Numbers
Adding Real Numbers
- How Do You Add Fractions with Variables?
- How Do You Add Fractions with Different Denominators?
- How Do You Add a Negative Number to a Positive Number?
- How Do You Add Decimals?
- What are the Rules for Using Absolute Values to Add Integers?
- How Do You Add Two Negative Numbers?
- How Do You Add Fractions with the Same Denominator?
- What are Trailing Zeros?
- How Do You Find a Common Denominator and a Least Common Denominator?
Subtracting Real Numbers
- How Do You Subtract a Positive Number from a Negative Number?
- How Do You Subtract a Whole Number from a Fraction?
- How Do You Subtract Decimals?
- What is the Opposite, or Additive Inverse, of a Number?
- How Do You Rewrite Subtraction as Addition?
- How Do You Add and Subtract a Bunch of Numbers with Different Signs?
- How Do You Subtract Fractions with the Same Denominator?
- How Do You Subtract Fractions with Variables?
- How Do You Subtract Fractions with Different Denominators?
- How Do You Subtract a Negative Number from a Positive Number?
Multiplying and Dividing Real Numbers
Multiplying Real Numbers
- How Do You Solve a Word Problem Where You Multiply and Subtract Whole Numbers and Fractions?
- How Do You Multiply and Divide Numbers with Different Signs?
- How Do You Multiply Decimals?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Multiply Fractions?
- How Do You Multiply a Whole Number by a Fraction?
Dividing Real Numbers
Powers and Square Roots
Simplifying Algebraic Expressions
Solving Linear Equations
One-Step Equations
Properties of Equality
Solving One-Step Equations
- How Do You Solve a Decimal Equation Using Division?
- How Do You Solve an Equation With Fractions With The Same Denominators Using Subtraction?
- How Do You Solve an Equation With Fractions With Different Denominators Using Addition?
- How Do You Solve an Equation by Guessing and Checking?
- How Do You Solve an Equation Using Division?
- How Do You Solve an Equation Where You're Multiplying Fractions?
- How Do You Solve a Word Problem Using an Equation Where You're Multiplying Fractions?
- How Do You Solve a Word Problem with an Equation Using Subtraction?
- How Do You Solve an Equation Using Multiplication?
- How Do You Solve a Decimal Equation Using Multiplication?
- How Do You Solve an Equation Using Addition?
- How Do You Solve a Word Problem with an Equation Using Multiplication?
- How Do You Solve a Decimal Equation Using Subtraction?
- How Do You Solve a Word Problem with an Equation Using Addition?
- How Do You Solve an Equation Using Subtraction?
- How Do You Solve an Equation With Fractions With Different Denominators Using Subtraction?
- How Do You Solve a Decimal Equation Using Addition?
- How Do You Solve an Equation With Fractions With The Same Denominators Using Addition?
- How Do You Solve a Word Problem with an Equation Using Division?
Two-Step and Multi-Step Equations
Solving Two-Step Equations
- How Do You Solve a Two-Step Equation by Multiplying by a Reciprocal?
- How Do You Solve a Two-Step Equation by Multiplying by -1 First?
- How Do You Solve a Two-Step Equation by Combining Like Terms?
- How Do You Solve a Word Problem Using a Two-Step Equation with Decimals?
- How Do You Solve a Two-Step Equation by Multiplying by -1?
- How Do You Solve a Two-Step Equation with Fractions by Multiplying Away the Fraction?
- How Do You Solve a Two-Step Equation with Fractions Using Reverse Order of Operations and Reciprocals?
- How Do You Solve a Two-Step Equation With a Negative Variable Term?
- How Do You Solve a Two-Step Equation by Distributing a Fraction First?
Solving Multi-Step Equations
- How Do You Solve for a Variable in a Fraction Using Multiplication First?
- How Do You Solve a Word Problem Using a Multi-Step Equation?
- How Do You Solve a Multi-Step Equation Using the Distributive Property?
- How Do You Use an Equation with Consecutive Numbers to Solve a Word Problem?
- How Do You Solve a Multi-Step Equation Using Order of Operations in Reverse?
Equations with Variables on Both Sides
Solving For a Variable and Working with Formulas
Solving For a Variable
Working with Formulas
- What is the Formula for Simple Interest?
- What's the Formula Connecting Distance, Speed, and Time?
- How Do You Solve a Formula For a Variable?
- How Do You Figure Out the Time Traveled if You Know the Distance and Speed?
- How Do You Use the Formula for Simple Interest?
- How Do You Solve an Opposite-Direction Travel Problem?
- How Do You Figure Out the Rate Traveled if You Know the Distance and Time?
- How Do You Solve a More Complicated Interest Problem?
- How Do You Find the Length of a Rectangle if You Know its Width and Area?
Ratios and Proportions
Proportion Definitions
Working with Proportions
- How Do You Write a Ratio From a Word Problem?
- How Do You Solve a Proportion Using Cross Products?
- How Do You Find Equivalent Ratios?
- How Do You Solve a Word Problem Using a Proportion?
- How Do You Solve a Proportion Using the Multiplication Property of Equality?
- How Do You Solve a Proportion by Finding an Equivalent Ratio?
- How Do You Know If Two Ratios are Proportional?
- How Do You Set Up a Proportion from a Word Problem?
Rates and Dimensional Analysis
- What are Rates and Unit Rates?
- What is Dimensional, or Unit Analysis?
- How Do You Use Dimensional Analysis to Convert Units on Both Parts of a Rate?
- How Do You Use Dimensional Analysis to Convert Units on One Part of a Rate?
- How Do You Use Unit Rates to Compare Rates?
- How Do You Convert a Rate To A Unit Rate?
- How Do You Solve a Word Problem Using Unit Rates?
Similar Figures and Indirect Measurement
- How Do You Find Missing Measurements of Similar Figures Using a Proportion?
- What is a Scale?
- How Do You Solve a Scale Model Problem Using a Scale Factor?
- What are Corresponding Parts in Similar Figures?
- What are Similar Figures?
- How Do You Find the Scale of a Model?
- How do you Figure Out if Two Figures are Similar?
- How Do You Use the Scale on a Map to Find an Actual Distance?
- How Do You Find a Scale Factor in Similar Figures?
- How Do You Solve a Problem Using Indirect Measurement with Shadows?
- What is a Scale Drawing?
- How Do You Find Missing Measurements of Similar Figures Using a Scale Factor?
- How Do You Figure Out What Size a Model Should Be if You Have a Scale?
Percents and Percent of Change
Percents and Percent Proportions
- How Do You Figure Out the Volume of a Solution Using Percents?
- What is the Percent Equation?
- How Do You Use a Proportion to Find What Percent a Part is of a Whole?
- How Do You Turn a Percent Into a Fraction?
- How Do You Solve a Word Problem Using a Percent Proportion?
- How Do You Set Up a Percent Proportion from a Word Problem?
- What's a Percent Proportion?
- How Do You Find the Intersection of Percent Data by Using a Venn Diagram?
- What's a Percent?
- How Do You Use a Proportion to Find a Whole?
- How Do You Turn a Decimal into a Percent?
- How Do You Turn a Fraction Into a Percent?
- How Do You Figure Out Sales Tax?
- How Do You Use an Equation to Find a Whole?
- How Do You Turn a Percent into a Decimal?
- How Do You Put Fractions, Decimals, and Percents in Order?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Use a Proportion to Find a Part of a Whole?
Percent of Change
Relations and Functions
The Coordinate Plane
Graphing in the Coordinate Plane
- What is an Ordered Pair?
- How Do You Identify Points on a Graph?
- Why Is It Called an Ordered Pair?
- What is the X-Axis?
- What are Quadrants in the Coordinate Plane?
- What are the Coordinate Axes?
- What is the Origin?
- What is the X-Coordinate?
- How Do You Plot Points in the Coordinate Plane?
- What is the Y-Axis?
- What is the Coordinate Plane?
- What is the Y-Coordinate?
Relations
Functions
Graphing Linear Equations
Transformations
Transformations of Linear Functions
Transformations of Figures in the Coordinate Plane
- What is a Translation?
- How Do You Use Coordinates to Translate a Figure Vertically?
- What is an Image?
- How Do You Rotate a Figure 90 Degrees Around the Origin?
- How Do You Use a Graph to Translate a Figure Diagonally?
- How Do You Use a Graph to Reflect a Figure Over the Y-Axis?
- How Do You Use Coordinates to Translate a Figure Horizontally?
- What is a Line of Reflection?
- What is a Rotation?
- How Do You Use a Graph to Reflect a Figure Over the X-Axis?
- What is a Transformation?
- How Do You Use a Graph to Translate a Figure Horizontally?
- How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?
- How Do You Use Coordinates to Reflect a Figure Over the X-Axis?
- How Do You Rotate a Figure 270 Degrees Around the Origin?
- How Do You Make a Figure Larger Using a Dilation?
- How Do You Use a Graph to Translate a Figure Vertically?
- What is a Dilation?
- What is a Reflection?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
Arithmetic Sequences
Analyzing Linear Equations
Rate of Change and Slope
Defining Slope
- What is Rate of Change?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- What Does Undefined Slope Mean?
- What Does 0 Slope Mean?
- What Does Positive Slope Mean?
- What's the Formula for Slope?
- What Does Negative Slope Mean?
- What Does the Slope of a Line Mean?
- How Do You Find the Rate of Change Between Two Points in a Table?
Finding Slopes
- How Do You Graph a Line If You're Given the Slope and a Single Point?
- How Do You Find the X-Coordinate of a Point on a Line If You Have Another Point and the Slope?
- How Do You Find the Slope of a Line from Two Points?
- How Do You Find the Slope of a Line from a Graph?
- How Do You Find the Slope of a Ramp If You Know the Rise and Run?
Using Intercepts
Slope-Intercept Form
Working with Slope-Intercept Form
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Table?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept?
- How Do You Find the Y-Intercept of a Line If You Have Another Point and the Slope?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have Two Points?
- What's Slope-Intercept Form of a Linear Equation?
- How Do You Put an Equation in Slope-Intercept Form Into Standard or Point-Slope Form?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- How Do You Graph a Line If You're Given the Slope and the Intercept?
- How Do You Write the Equation of a Line in Slope-Intercept Form from a Word Problem?
Point-Slope Form and Standard Form
Working with Point-Slope Form
- How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point?
- What's Point-Slope Form of a Linear Equation?
- How Do You Write an Equation of a Line in Point-Slope Form and Standard Form If You Have Two Points?
- How Do You Put an Equation in Point-Slope Form Into Standard or Slope-Intercept Form?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Use Point-Slope Form to Write an Equation from a Table?
Working with Standard Form
Direct Variation
Direct Variation Definitions
Using Direct Variation
- How Do You Write an Equation for Direct Variation Given a Point?
- How Do You Solve a Word Problem Using the Direct Variation Formula?
- How Do You Write an Equation for Direct Variation from a Table?
- How Do You Use the Formula for Direct Variation?
- How Do You Find the Constant of Variation from a Direct Variation Equation?
Parallel and Perpendicular Lines
Scatter Plots and Correlation
Solving and Graphing Linear Inequalities
Solving Inequalities Using Addition and Subtraction
Solving Inequalities Using Multiplication and Division
Solving Inequalities Using Multiplication
- How Do You Solve an Inequality Where You're Multiplying Negative Fractions?
- What's the Multiplication Property of Inequality?
- How Do You Use Multiplication with Positive Numbers to Solve an Inequality Word Problem?
- How Do You Solve an Inequality with Negative Numbers Using Multiplication?
- How Do You Use Multiplication with Negative Numbers to Solve an Inequality Word Problem?
- How Do You Solve a Word Problem Using an Inequality Where You're Multiplying Negative Fractions?
- How Do You Solve an Inequality with Positive Numbers Using Multiplication?
- How Do You Solve an Inequality Where You're Multiplying Positive Fractions?
- How Do You Solve a Word Problem Using an Inequality Where You're Multiplying Positive Fractions?
Solving Inequalities Using Division
- How Do You Solve an Inequality with Positive Numbers Using Division?
- How Do You Use Division with Positive Numbers to Solve an Inequality Word Problem?
- How Do You Solve an Inequality with Negative Numbers Using Division?
- What's the Division Property of Inequality?
- How Do You Solve a Decimal Inequality Using Division?
- How Do You Solve a Decimal Inequality Using Division with Negative Numbers?
- How Do You Use Division with Negative Numbers to Solve an Inequality Word Problem?
Multi-Step Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities
Graphing Inequalities in Two Variables
Graphing Inequalities in the Coordinate Plane
- What's a Boundary?
- How Do You Graph a Greater Than Inequality on the Coordinate Plane?
- How Do You Figure Out Whether a Boundary is a Part of the Graph of an Inequality?
- What's a Half-Plane?
- How Do You Determine if an Ordered Pair is a Solution to a Linear Inequality?
- What is a Linear Inequality?
- How Do You Figure Out a Situation That a Graph Represents?
- How Do You Solve and Graph Inequalities from a Word Problem?
Systems of Equations and Inequalities
Solving Systems of Equations By Graphing
Solving Systems of Equations Using Substitution
Solving Systems of Equations Using Elimination
Elimination by Addition and Subtraction
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Use a System of Linear Equations to Find Coordinates on a Map?
- How Do You Solve a Word Problem Using the Elimination by Subtraction Method?
Elimination by Multiplication
Solving Special Systems
Systems of Inequalities
Exponents and Exponential Functions
Properties of Exponents
Monomials and Polynomials
Monomials
- What's a Monomial?
- How Do You Take the Power of a Monomial?
- How Do You Solve a Word Problem by Dividing Monomials?
- How Do You Find the Degree of a Monomial?
- How Do You Solve a Word Problem by Taking a Monomial to a Power?
- How Do You Find the Volume of a Box Whose Sides are Monomials?
- How Do You Take a Monomial to a Power?
- How Do You Divide Monomials Using Quotient of Powers?
- How Do You Multiply Monomials?
Polynomials
Scientific Notation
Working with Scientific Notation
- How Do You Convert From Decimal Notation to Scientific Notation?
- How Do You Order Numbers in Scientific Notation?
- What's Scientific Notation?
- How Do You Solve a Word Problem by Multiplying with Scientific Notation?
- How Do You Convert From Scientific Notation to Decimal Notation?
- How Do You Multiply Two Numbers Using Scientific Notation?
Exponential Functions
Exponential Growth and Decay
Geometric Sequences
Polynomials and Factoring
Adding and Subtracting Polynomials
Multiplying Polynomials
Special Products of Polynomials
Factors and Greatest Common Factors
Factors
Greatest Common Factors
- How Do You Find the Greatest Common Factor If There are No Common Factors?
- How Do You Factor the Greatest Common Factor out of a Polynomial?
- How Do You Find the Greatest Common Factor of Monomials?
- How Do You Find the Greatest Common Factor of Two Numbers Using Prime Factorization?
- How Do You Find the Greatest Common Factor of Three Numbers?
Factoring Trinomials
Factoring Special Products
Choosing Factoring Strategies and Solving Polynomial Equations
Quadratic Equations and Functions
Graphing Quadratic Functions
Graphs of Quadratic Functions
- What is the Minimum of a Quadratic Function?
- What is a Parabola?
- What is the Vertex of a Quadratic Function?
- How Do You Find the Axis of Symmetry for a Quadratic Function?
- How Do You Graph a Quadratic Function?
- How Do You Find the a, b, and c Values of a Quadratic Function?
- What is a Quadratic Function?
- What is the Maximum of a Quadratic Function?
- How Do You Determine if the Vertex of a Quadratic Function Will be a Maximum or Minimum?
- How Do You Find the Vertex of a Quadratic Function?
- What is the Axis of Symmetry of a Quadratic Function?
- How Do You Make a Table for a Quadratic Function?
Transforming Quadratic Graphs
Solve Quadratics by Graphing
Solve Quadratics by Factoring and with Square Roots
Completing the Square
The Quadratic Formula and the Discriminant
Solving Quadratics Using the Quadratic Formula
Using the Discriminant
- How Do You Find The Discriminant of a Quadratic Equation With 2 Solutions?
- How Do You Find The Discriminant of a Quadratic Equation With No Solutions?
- How Do You Find The Discriminant of a Quadratic Equation With 1 Solution?
- What is the Discriminant?
- How Do You Use The Discriminant to Determine the Number of Solutions of a Quadratic Equation?
Comparing Linear, Quadratic, and Exponential Models
Radical Expressions and Equations
Simplifying Radical Expressions
Operations with Radical Expressions
Graphs of Square Root Functions
Solve Radical Equations
The Pythagorean Theorem
Using The Pythagorean Theorem
Trigonometric Ratios
- How Do You Find the Tangent of an Angle in a Right Triangle?
- What is the Tangent Ratio?
- How Do You Find a Missing Side of a Right Triangle Using Tangent?
- What is the Sine Ratio?
- How Do You Find a Missing Side of a Right Triangle Using Sine?
- How Do You Find the Cosine of an Angle in a Right Triangle?
- How Do You Find the Sine of an Angle in a Right Triangle?
- How Do You Find a Missing Side of a Right Triangle Using Cosine?
- How Do You Solve a Problem Using an Angle of Elevation?
The Distance and Midpoint Formulas
Rational Expressions and Functions
Inverse Variation
Rational Functions
Rational Expressions
Simplifying Rational Expressions
- What's an Algebraic Fraction?
- How Do You Reduce Common Factors in a Rational Expression?
- What's a Rational Expression?
- How Do You Simplify a Polynomial Over a Polynomial Using Opposite Binomial Factors?
- How Do You Simplify an Algebraic Fraction by Canceling Common Factors?
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Divide Monomials Using the Greatest Common Factor?
- Why is it Called a Rational Expression?
Excluded Values
Multiplying and Dividing Rational Expressions
Dividing Polynomials
Adding and Subtracting Rational Expressions
Adding and Subtracting with Like Denominators
Adding and Subtracting with Unlike Denominators
- How Do You Subtract Two Rational Expressions with Different Denominators?
- How Do You Find the Least Common Denominator of Two Rational Expressions?
- What's the Least Common Denominator?
- How Do You Add Two Rational Expressions with Different Denominators?
- How Do You Find the Least Common Multiple of Monomials?
Mixed Expressions and Complex Fractions
Solve Rational Equations
Solving Rational Equations
- How Do You Solve a Rational Equation by LCD Multiplication?
- How Do You Solve a Rational Equation?
- What's a Rational Equation?
- How Do You Solve a Rational Equation With Binomials in the Denominator?
- How Do You Solve a Rational Equation by Adding Fractions?
- How Do You Solve a Word Problem with a Rational Equation?
Special Rational Equations
Probability and Data Analysis
Simple Probability and Odds
Simple Probability
- What is the Complement of an Event?
- How Do You Find the Probability of the Complement of an Event?
- How Do You Find the Probability of a Simple Event?
- What is an Outcome?
- What is Probability?
- How Do You Determine All the Possible Outcomes of an Experiment?
- What is Experimental Probability?
- What is a Sample Space?
- How Do You Use a Simulation to Solve a Problem?
Permutations and Combinations
Permutations
- What is a Factorial?
- What is a Permutation?
- How Do You Find a Number of Permutations Using the Fundamental Counting Principle?
- How Do You Use the Fundamental Counting Principle to Count the Number of Outcomes in a Sample Space?
- What is the Fundamental Counting Principle?
- How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?
Combinations
Probability of Compound Events
Sampling Methods and Displaying Data
Measures of Central Tendency and Dispersion
Measures of Central Tendency
- What is a Weighted Average?
- How Do You Find an Average?
- How Do You Find the Mode of a Data Set?
- How Do You Find the Mean of a Data Set?
- What is the Mean of a Data Set?
- How Do You Find the Mode of a Data Set Where All The Numbers are Different?
- What is the Median of a Data Set?
- How Do You Find the Mode of a Data Set When There is More Than One Mode?
- What is the Mode of a Data Set?
- How Do You Find the Median of a Data Set?
Measures of Dispersion
Frequency and Histograms