Algebra 2 Explained

Study Notes for Solving Linear Equations Part 1

Practice Test for Solving Linear Equations Part 1.

This quiz will test your knowledge of how to solve a linear equation in one variable using the four step process.

Study Notes for Solving Linear Equations Part 2

Practice Test for Solving Linear Equations Part 2.

This quiz will test your knowledge of how to solve a linear equation in one variable with fractions and decimals.

This lecture explains how to convert a repeating decimal into a fraction.

Study Notes for Repeating Decimal to Fraction

Practice Test for Repeating Decimal to Fraction.

This quiz will test your knowledge of how to convert a repeating decimal into a fraction.

This lecture explains how to solve an equation for a given variable.

Study Notes for Solving Literal Equations.

Practice Test for Solving Literal Equations.

This quiz will test your knowledge of how to solve an equation for a specified variable.

This lecture explains the basics of a word problem. This lecture will cover:

• Phrase Translation to Algebraic Expressions/Equations

• Interpretation of key words to arithmetic operators

• Solving Basic Word Problems

Study Notes for Applications of Linear Equations Part 1

Practice Test for Applications of Linear Equations Part I.

This quiz will test your knowledge of how to translate phrases into algebraic expressions and equations.

This lecture explains how to solve a word problem when a linear equation in one variable is involved. This lecture will cover:

• Six Step Procedure to Solve a Word Problem with Linear Equations

• Solving "Sums of Quantities Problems"

• Solving "% Markup and Markdown Problems"

• Solving  "Simple Interest Problems I=prt"

Study Notes for Applications of Linear Equations Part 2.

Practice Test for Applications of Linear Equations Part 2.

This quiz will test your knowledge of how to solve a word problem with linear equations involved.

This lecture continues to explain how to solve a word problem when a linear equation in one variable is involved. This lecture will cover:

• Six Step Procedure to Solve a Word Problem with Linear Equations

• Solving "Motion Word Problems d=rt"

• Solving "Mixture Word Problems"

Study Notes for Applications of Linear Equations Part 3.

Practice Test for Applications of Linear Equations.

This quiz will test your knowledge of how to solve a word problem with linear equations involved.

This lecture explains how to write an interval or range of values using interval notation. This lecture will cover:

• Interval Notation

• Set Builder Notation

• Graphing Intervals on a Number Line

Study Notes for Interval Notation.

Practice Test for Interval Notation.

This quiz will test your knowledge of how to write intervals using interval notation.

This lecture explains how to solve a linear inequality in one variable. This lecture will cover:

• Writing the solution in Interval Notation and Graphing the Interval on a Number Line

• Addition Property of Inequality

• Multiplication Property of Inequality

• Solving any Linear Inequality in one Variable

Study Notes for Solving Linear Inequalities.

Practice Test for Solving Linear Inequalities, if you need any help please post your question in the Q&A. I am glad to help.

This quiz will test your knowledge of how to solve linear inequalities.

This lecture explains how to solve a compound inequality. This lecture will cover:

• Solving Compound Inequalities with "or"

• Solving Compound Inequalities with "and"

• Graphing Solutions for Compound Inequalities using the Number Line

  
  

Study Notes for Solving Compound Inequalities.

Practice Test for Solving Compound Inequalities.

This quiz will test your knowledge of how to solve a compound inequality with "and" or "or".

This lecture explains how to solve absolute value equations. This lecture will cover:

• The concept of Absolute Value

• Compound Equations with "or"

• Special Case Scenarios with No Solution

Study Notes for Solving Absolute Value Equations.

Practice Test for Solving Absolute Value Equations.

This quiz will test your knowledge of how to solve absolute value equations.

This lecture explains how to solve absolute value inequalities. This lecture will cover:

• The concept of Absolute Value

• Compound Inequalities with "and"

• Compound Inequalities with "or"

Study Notes for Solving Absolute Value Inequalities.

Practice Test for Solving Absolute Value Inequalities.

This quiz will test your knowledge of how to solve absolute value inequalities.

This lecture introduces the linear equation in two variables. This lecture will cover:

• Solving a Linear Equation in two variables for a given variable

• Completing a table of values

• Plotting Ordered Pairs on the Cartesian Coordinate Plane

Study Notes for Linear Equations in two variables.

Practice Test for Linear Equations in two Variables.

This quiz will test your knowledge of how to work with linear equations in two variables.

This lecture explains how to graph a linear equation in two variables. This lecture will cover:

• Creating a table of ordered pairs

• Plotting Ordered Pairs

• Graphing Linear Equations

• Finding the x-intercept

• Finding the y-intercept

• Using the Intercept Method

• Graphing Vertical Lines

• Graphing Horizontal Lines

Graphing Linear Equations Study Notes.

Practice Test for Graphing Linear Equations.

This quiz will test your knowledge of how to graph a linear equation in two variables.

This lecture explains how to find the slope of a line. This lecture will cover:

• Slope Formula

• Finding Slope from a Graph

• Finding the Slope of a Horizontal Line

• Finding the Slope of a Vertical Line

• Slope-Intercept Formula - Finding the Slope from the Equation of the Line

The Slope of a Line Study Notes.

Practice Test for the Slope of a Line.

This quiz will test your knowledge of how to find the slope of a line.

This lecture continues to explain concepts related to slope. This lecture will cover:

• Graph a Line quickly using Slope-Intercept Form of the Line

• How to Determine if two Lines are Parallel

• How to Determine if two Lines are Perpendicular

Study Notes for More on Slope.

Practice Test for More on Slope.

This quiz will continue to test your knowledge of slope. We will determine if two lines are parallel (same slope), perpendicular (slopes have a product of -1) or neither.

This lecture explains how to algebraically manipulate a linear equation in two variables into different forms. This lecture will cover:

• Point-Slope Form - used with known slope and one point or two points given

• Slope-Intercept Form - used to immediately know the slope and y-intercept

• Standard Form

Study Notes for Forms of a Line.

Practice Test for Forms of a Line.

This quiz will test your knowledge of how to algebraically manipulate a linear equation in two variables into different forms: standard form, point-slope form, and slope-intercept form.

This lecture explains how to sketch the solution for a linear inequality in two variables. This lecture will cover:

• Drawing the Boundary Line

• Graphing a Linear Inequality in two Variables using the Test Point Method

• Graphing a Linear Inequality in two Variables by Solving for y

Study Notes for Linear Inequalities in two Variables.

Practice Test for Linear Inequalities in two Variables.

This quiz will test your knowledge of how to sketch the graph of a linear inequality in two variables.

This lecture explains how to determine if a relation represents a function.

Study Notes for Relations and Functions.

Practice Test for Relations and Functions.

This quiz will test your knowledge of how to determine if a relation represents a function.

This lecture explains how to use the vertical line test to visually determine if the graph of a relation represents a function.

Study Notes for Function Vertical Line Test.

Practice Test for Functions Vertical Line Test.

This quiz will test your knowledge of how to determine if the graph of a relation represents a function using the vertical line test.

This lecture explains how to work with functions, when function notation is used.

Study Notes for Function Notation.

Practice Test for Function Notation.

This quiz will test your knowledge of how to write and solve function problems using function notation.

This lecture explains how to solve variation problems. This lecture will cover:

• Direct Variation

• Direct Variation as a Power

• Inverse Variation

• Inverse Variation as a Power

• Joint Variation

• Variation Word Problems

Study Notes for Variation.

Practice Test for Variation.

This quiz will test your knowledge of how to solve a variation problem: direct variation, inverse variation, and joint variation.

This lecture explains how to systems of linear equations in two variables using graphing.

Study Notes for Solving Linear Systems by Graphing.

Practice Test for Solving Linear Systems by Graphing.

This quiz will test your knowledge of how to solve a system of linear equations using the graphing method.

Study Notes for Solving Linear Systems by Substitution.

Practice Test for Solving Linear Systems by Substitution.

This quiz will test your knowledge of how to solve a system of linear equations using the substitution method.

This lecture explains how to solve systems of linear equations in two variables using elimination.

Study Notes for Solving Linear Systems by Elimination.

Practice Test for Solving Linear Systems by Elimination.

This quiz will test your knowledge of how to solve a system of linear equations using the elimination method.

This lecture explains how to a system of linear equations in three variables.

Study Notes for Solving Linear Systems in 3 Variables.

Practice Test for Systems of Equations - 3 Variables

This quiz will test your knowledge of how to solve a system of equations with variables.

This lecture explains how to solve application problems that involve setting up a system of linear equations. This lecture will cover:

• Sums of Quantities Word Problems

• Motion Word Problems

• Production Word Problems

Study Notes for Applications of Linear Systems.

Practice Test for Applications of Linear Systems.

This quiz will test your knowledge of how to solve word problems when a system of linear equations is involved.

This lecture explains how to solve a system of linear equations in two variables using matrix methods. This lecture will cover:

• Setting up an Augmented Matrix

• Elementary Row Operations

• Row Echelon Form

• Reduced Row Echelon form

Study Notes for Solving Linear Systems using Matrix Methods Part 1

Practice Test for Matrix Methods I.

This quiz will test your knowledge of how to solve a system of linear equations in two variables using matrix methods.

This lecture explains how to solve a system of linear equations in three variables using matrix methods. This lecture will cover:

• Setting up an Augmented Matrix

• Elementary Row Operations

• Row Echelon Form

• Reduced Row Echelon form

Study Notes for Matrix Methods Part 2.

Practice Test for Matrix Methods Part II.

This quiz will test your knowledge of how to solve a system of linear equations in 3 variables using matrix methods.

This lecture explains how to sketch the Graph for a System of Linear Inequalities. This lecture will cover:

• Review of Graphing Linear Inequalities in two Variables

• Finding the Overlap between two Graphs on the Coordinate Plane

• Special Case Scenarios with No Solution

Study Notes for Graphing Systems of Linear Inequalities.

Practice Test for Graphing Systems of Linear Inequalities.

This quiz will test your knowledge of how to sketch the graph for a system of linear inequalities.

This lecture will review the various rules of exponents This lecture will cover:

• Product Rule for Exponents

• Quotient Rule for Exponents

• Negative Exponents

• Zero as an Exponent

• Power Rules for Exponents

Study Notes for Exponent Rules.

Practice Test for Exponent Rules.

This quiz will test your knowledge of how to use the various rules of exponents: product rule, quotient rule, power to power rule, exponent of zero, power rules, and negative exponents.

This lecture explains how to add and subtract polynomials. This lecture will cover:

• Finding the degree of a polynomial

• Writing a polynomial in standard form

• Like Terms

• Adding Polynomials

• Subtracting Polynomials

Study Notes for Adding and Subtracting Polynomials.

Practice Test for Adding and Subtracting Polynomials.

This quiz will test your knowledge of how to add and subtract polynomials.

This lecture explains how to multiply polynomials. This lecture will cover:

• Finding the product of a monomial and a polynomial

• Finding the product of two polynomials

• Finding the product of two binomials using FOIL

• Finding the product of more than two polynomials

Study Notes for Multiplying Polynomials.

Practice Test for Multiplying Polynomials.

This quiz will test your knowledge of how to multiply polynomials.

This lecture explains how to quickly multiply commonly occuring polynomial products. This lecture will cover:

• Finding the product of a binomial squared

• Finding the product of the sum and difference of the same two terms

• Finding the product of a binomial cubed

Study Notes for Special Polynomial Products.

Practice Test for Special Polynomial Products.

This quiz will test your knowledge of special polynomial products.

This lecture explains how to divide polynomials using long division. This lecture will cover:

• Dividing a polynomial by a monomial

• Polynomial Long Division

• Polynomial Long Division with Remainders

• Polynomial Long Division with Missing Terms

Study Notes for Polynomial Long Division.

Practice Test for Polynomial Long Division

This quiz will test your knowledge of how to divide polynomials using long division.

Study Notes for Synthetic Division.

Practice Test for Synthetic Division.

This quiz will test your knowledge of how to divide polynomials using synthetic division.

This lecture explains how to perform operations with polynomial functions. This lecture will cover:

• Function Notation

• Adding Polynomial Functions

• Subtracting Polynomial Functions

• Multiplying Polynomial Functions

• Dividing Polynomial Functions

Study Notes for Operations on Functions.

Practice Test for Operations on Functions.

This quiz will test your knowledge of how to perform operations with functions: adding, subtracting, multiplying, and dividing.

This test will cover all material from Lesson 1 - Lesson 39. Please use the Q&A if you get stuck.

Good luck :)

This lecture explains how to factor out the Greatest Common Factor (GCF) from a polynomial. This lecture will cover:

• Finding the GCF

• Factoring out the GCF

• Checking the result of factoring using the Distributive Property

Study Notes for Factoring out the Greatest Common Factor.

Practice Test for Factoring out the Greatest Common Factor.

This quiz will test your knowledge of how to factor out the Greatest Common Factor (GCF).

This lecture explains how to factor a four term polynomial using the grouping method.

Study Notes for Factoring by Grouping.

Practice Test for Factoring by Grouping.

This quiz will test your knowledge of how to factor a four term polynomial using grouping.

This lecture explains how to factor trinomials into the product of two binomials when the leading coefficient is 1.

Study Notes for how to factor trinomials.

Practice Test for Factoring Trinomials.

This quiz will test your knowledge of how to factor trinomials when the leading coefficient is 1.

This lecture explains how to factor trinomials into the product of two binomials when the leading coefficient is not 1. In this lecture we will present the first of two methods known as the AC method or the factoring by grouping method. 

Study Notes for Factoring Trinomials using the AC Method.

Practice Test for Factoring Trinomials AC Method.

This quiz will test your knowledge of how to factor trinomials with a leading coefficient that is not 1, using the AC Method.

This lecture explains how to factor trinomials into the product of two binomials when the leading coefficient is not 1. In this lecture we will present the second of two methods known as the Reverse FOIL method. 

Study Notes for Factoring Trinomials using Reverse FOIL.

Practice Test for Factoring Trinomials Reverse FOIL.

This quiz will test your knowledge of how to factor trinomials with a leading coefficient that is not 1, using reverse FOIL.

This lecture explains how to factor polynomials using substitution.

Study Notes for Factoring Polynomials.

Practice Test for Factoring Polynomials (Substitution).

This quiz will test your knowledge of how to factor polynomials using substitution.

This lecture explains how to quickly factor commonly occuring polynomials. This lecture will cover:

• Factoring Perfect Square Trinomials

• Factoring the Difference of two Squares

• Factoring the Sum/Difference of Cubes

Study Notes for Special Factoring.

Practice Test for Special Factoring.

This quiz will test your knowledge of how to factor trinomials using special factoring formulas.

This lecture explains how to solve a polynomial equation using factoring and the zero product property.

Study Notes for Solving Polynomial Equations by Factoring.

Practice Test for Solving Polynomial Equations.

This quiz will test your knowledge of how to solve polynomial equations by factoring.

This lecture gives an introduction to Rational Expressions. This lecture will cover:

• The definition of a Rational Expression

• Simplifying Rational Expressions

• Finding the Restricted Value(s) for a Rational Expression

Study Notes for Simplifying Rational Expressions.

Practice Test for Simplifying Rational Expressions.

This quiz will test your knowledge of how to simplify rational expressions. This quiz will also test your ability to find the restricted value(s) for a rational expression

This lecture explains how to multiply and divide rational expressions.

Study Notes for Multiplying Rational Expressions.

Practice Test for Multiplying Rational Expressions.

This quiz will test your knowledge of how to Multiply Rational Expressions.

This lecture explains how to add and subtract rational expressions. This lecture will cover:

• Finding the LCD for a group of rational expressions

• Adding/Subtracting Rational Expressions with a common denominator

• Adding/Subtracting Rational Expressions without a common denominator

Study Notes for Adding Rational Expressions.

Practice Test for Adding Rational Expressions.

This quiz will test your knowledge of how to add  and subtract rational expressions.

This lecture explains how to simplify a complex rational expressions. This lecture will cover:

• Finding the LCD for a group of rational expressions

• Simplifying a Complex Rational Expression using the LCD method

  
  

Study Notes for Complex Rational Expressions.

Practice Test for Complex Rational Expressions.

This quiz will test your knowledge of how to simplify complex rational expressions.

This lecture explains how to solve rational equations. This lecture will cover:

• Finding the LCD for a group of rational expressions

• Solving Rational Equations

• How to Find and Reject Extraneous Solutions

Study Notes for Solving Rational Equations.

Practice Test for Solving Rational Equations.

This quiz will test your knowledge of how to solve rational equations (equations with rational expressions).

This lecture explains how to setup and solve word problems that involve rational expressions. This lecture will cover:

• Work Rate Problems

• Motion Word Problems

Study Notes for Applications of Rational Expressions.

Practice Test for Applications of Rational Expressions.

This quiz will test your knowledge of how to solve a word problem with rational expressions involved.

This lecture gives an introduction to radical expressions. This lecture will cover:

• Finding the square root of a number

• Finding the cube root of a number

• Finding higher level roots

• Sign rules for radicals

Study Notes for Evaluating Radical Expressions.

Practice Test for Evaluating Radical Expressions.

This quiz will test your knowledge of how to evaluate radical expressions and work with fractional exponents.

This lecture explains how to simplify, multiply, and divide radical expressions. This lecture will cover:

• Product Rule for Radicals

• Quotient Rule for Radicals

• How to Simplify a Radical

Study Notes for Simplifying Radicals.

Practice Test for Simplifying Radicals.

This quiz will test your knowledge of how to simplify radicals.

This lecture explains how to find the distance between two points on the coordinate plane using the distance formula.

Study Notes for the Distance Formula.

Practice Test for The Distance Formula.

This quiz will test your knowledge of how to find the distance between two points using the distance formula.

This lecture explains how to add and subtract radical expressions. This lecture will cover:

• How to identify Like Radicals

• Adding/Subtracting Radicals

• Simplifying Radicals

Study Notes for Adding and Subtracting Radical Expressions.

Practice Test for Adding and Subtracting Radicals.

This quiz will test your knowledge of how to add and subtract radical expressions.

This lecture explains how to rationalize the denominator. This lecture will cover:

• Rationalizing the Denominator with a Square Root

• Rationalizing the Denominator with a Cube Root

• Rationalizing the Denominator with a Higher Level Root

Study Notes for Rationalizing the Denominator.

Practice Test for Rationalizing the Denominator.

This quiz will test your knowledge of how to rationalize the denominator.

This lecture continues to explain how to rationalize the denominator. In this lecture, we will cover the process of rationalizing a binomial denominator. This lecture will cover:

• Finding the Conjugate of the denominator

• Multiplying and Simplifying Radicals

• Rationalizing a Binomial Denominator

Study Notes for Rationalizing a Binomial Denominator.

Practice Test for Rationalizing a Binomial Denominator.

This quiz will test your knowledge of how to rationalize a binomial denominator.

This lecture explains how to Solve Radical Equations. This lecture will cover:

• Squaring Property of Equality

• Solving Equations with Radicals

• Finding and Rejecting Extraneous Solutions

Study Notes for Solving Radical Equations.

Practice Test for Solving Radical Equations.

This quiz will test your knowledge of how to solve radical equations (equations with radicals).