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Step-by-Step Examples
Select an Example:
Basic Math
Long Arithmetic
Adding Using Long Addition
Long Subtraction
Long Multiplication
Long Division
Rational Numbers
Converting Regular to Scientific Notation
Arranging a List in Order
Expanded Notation
Prime or Composite
Comparing Expressions
Estimating
Converting to a Percentage
Operations with Fractions
Reducing Fractions
Finding the Reciprocal
Converting to a Decimal
Converting to a Mixed Number
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Ratios, Proportions, and Percents
Converting Ratios to Fractions
Comparing Ratios
Converting Percents to Decimal
Converting Percents to Fractions
Converting the Percent Grade to Degree
Converting the Degree to Percent Grade
Measurement, Area, and Volume
Finding the Area of a Rectangle
Finding the Perimeter of a Rectangle
Finding the Area of a Square
Finding the Perimeter of a Square
Finding the Area of a Circle
Finding the Circumference of a Circle
Finding the Area of a Triangle
Finding the Area of a Parallelogram
Finding the Area of a Trapezoid
Finding the Volume of a Box
Finding the Volume of a Cylinder
Finding the Volume of a Cone
Finding the Volume of a Pyramid
Finding the Volume of a Sphere
Finding the Surface Area of a Cube
Finding the Surface Area of a Cylinder
Finding the Surface Area of a Cone
Finding the Surface Area of a Pyramid
Factors, Fractions, and Exponents
Converting to a Fraction
Simple Exponents
Prime Factorizations
Finding the Factors
Simplifying Fractions
Unit Conversions
Converting Grams to Kilograms
Converting Grams to Pounds
Converting Grams to Ounces
Converting Feet to Inches
Converting Feet to Meters
Converting Feet to Miles
Converting Feet to Yards
Converting Inches to Feet
Converting Inches to Meters
Converting Inches to Miles
Converting Inches to yds
Converting Miles to Feet
Converting Miles to Kilometers
Converting Miles to Yards
Converting Kilometers to Miles
Converting Kilometers to Meters
Converting Meters to Feet
Converting Meters to Inches
Converting Ounces to Grams
Converting Ounces to Pounds
Converting Ounces to Tons
Converting Pounds to Grams
Converting Pounds to Ounces
Converting Pounds to Tons
Converting Yards to Feet
Converting Yards to Millimeters
Converting Yards to Inches
Converting Yards to Miles
Converting Yards to Meters
Converting Fahrenheit to Celsius
Converting Celsius to Fahrenheit
Data Measurement and Statistics
Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Minimum
Finding the Maximum
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Five Number Summary
Points and Line Segments
Finding a Point's Quadrant
Finding the Midpoint of a Line Segment
Distance Formula
Pre-Algebra
Variables, Expressions, and Integers
Arithmetic Operations
Combining Like Terms
Determining if the Expression is a Polynomial
Distributive Property
Comparing Expressions
Simplifying and Evaluating Expressions
Simplifying
Multiplication
Polynomial Addition
Polynomial Subtraction
Polynomial Multiplication
Polynomial Division
Simplifying Expressions
Evaluate
Multiplying Polynomials Using FOIL
Identifying Degree
Operations on Polynomials
Negative Exponents
Evaluating
Solving Equations
Solving by Adding/Subtracting
Solving by Multiplying/Dividing
Solving Containing Decimals
Multi-Step Equations and Inequalities
Solving for a Variable
Solving Linear Equations
Solving Linear Inequalities
Finding the Quadratic Constant of Variation
Factors, Fractions, and Exponents
Converting to a Fraction
Prime Factorizations
Finding the Factors
Simplifying Fractions
Simple Exponents
Operations with Fractions
Finding the Reciprocal
Converting to a Decimal
Converting to a Mixed Number
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Rational Numbers
Expanded Notation
Prime or Composite
Ratios, Proportions, and Percents
Converting Ratios to Fractions
Comparing Ratios
Converting Percents to Decimal
Converting Percents to Fractions
Converting the Percent Grade to Degree
Converting the Percent Grade to Slope
Converting the Degree to Percent Grade
Converting the Slope to Percent Grade
Points and Line Segments
Finding a Point's Quadrant
Finding the Midpoint of a Line Segment
Distance Formula
Finding Equations Using Slope-Intercept
Finding the Slope
Finding the Y Intercept
Linear Equations and Inequalities
Solving for a Variable
Calculating Slope and Y Intercept
Rewriting in Slope-Intercept Form
Solving Linear Equations
Finding Equations Using the Slope-Intercept Formula
Finding Equations Using Two Points
Finding a Perpendicular Line Containing a Given Point
Finding the Equation
Finding the Slope
Finding a Parallel Line Containing a Given Point
Finding a Parallel Line to the Given Line
Finding a Perpendicular Line to the Given Line
Finding Ordered Pair Solutions
Using a Table of Values to Graph an Equation
Finding the Equation Using Point-Slope Form
Unit Conversions
Converting Grams to Kilograms
Converting Grams to Pounds
Converting Grams to Ounces
Converting Feet to Inches
Converting Feet to Meters
Converting Feet to Miles
Converting Feet to Yards
Converting Inches to Feet
Converting Inches to Meters
Converting Inches to Miles
Converting Inches to yds
Converting Miles to Feet
Converting Miles to Kilometers
Converting Miles to Yards
Converting Kilometers to Miles
Converting Kilometers to Meters
Converting Meters to Feet
Converting Meters to Inches
Converting Ounces to Grams
Converting Ounces to Pounds
Converting Ounces to Tons
Converting Pounds to Grams
Converting Pounds to Ounces
Converting Pounds to Tons
Converting Yards to Millimeters
Converting Yards to Feet
Converting Yards to Inches
Converting Yards to Miles
Converting Yards to Meters
Converting Fahrenheit to Celsius
Converting Celsius to Fahrenheit
Measurement, Area, and Volume
Finding the Area of a Rectangle
Finding the Perimeter of a Rectangle
Finding the Area of a Square
Finding the Perimeter of a Square
Finding the Area of a Circle
Finding the Circumference of a Circle
Finding the Area of a Triangle
Finding the Area of a Parallelogram
Finding the Area of a Trapezoid
Finding the Volume of a Box
Finding the Volume of a Cylinder
Finding the Volume of a Cone
Finding the Volume of a Pyramid
Finding the Volume of a Sphere
Finding the Surface Area of a Cube
Finding the Surface Area of a Cylinder
Finding the Surface Area of a Cone
Finding the Surface Area of a Pyramid
Finding the Surface Area of a Sphere
Data Measurement and Statistics
Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Algebra
Algebra Concepts and Expressions
Solving for a Variable
Solving Graphically
Arithmetic Operations
Combining Like Terms
Simple Exponents
Distributive Property
Prime Factorizations
Finding the Factors
Finding the LCM of a List of Expressions
Finding the LCD of a List of Expressions
Determining if the Number is a Perfect Square
Finding the Domain
Finding the Domain Graphically
Evaluate
Evaluating the Difference Quotient
Dividing
Combining
Evaluating
Solving Using the Square Root Property
Determining if True
Points, Lines, and Line Segments
Finding a Point's Quadrant
Finding the Midpoint of a Line Segment
Distance Formula
Finding Equations Using Slope-Intercept
Finding the Start Point Given the Mid and End Points
Finding the End Point Given the Start and Mid Points
Finding the Slope
Finding the Y Intercept
Finding the Slope and Y-Intercept
Finding the Equation of the Parabola
Finding the Average Rate of Change
Finding the Slope of the Perpendicular Line to the Line Through the Two Points
Simplifying Polynomials
Simplifying
Multiplication
Polynomial Addition
Polynomial Subtraction
Polynomial Multiplication
Polynomial Division
Evaluate
Determining if the Expression is a Polynomial
Multiplying Polynomials Using FOIL
Operations on Polynomials
Simplifying Expressions
Negative Exponents
Rewriting Using Negative Exponents
Synthetic Division
Identifying Degree
Maximum Number of Real Roots/Zeros
Finding All Possible Roots/Zeros (RRT)
Finding All Roots with Rational Root Test (RRT)
Finding the Remainder
Evaluating a Function using Synthetic Division
Finding the Remainder Using Long Polynomial Division
Reordering the Polynomial in Ascending Order
Reordering the Polynomial in Descending Order
Finding the Leading Term
Finding the Leading Coefficient
Finding the Degree, Leading Term, and Leading Coefficient
Factoring Polynomials
Finding the GCF
Factoring Out Greatest Common Factor (GCF)
Identifying the Common Factors
Cancelling the Common Factors
Finding the LCM using GCF
Factoring Trinomials
Trinomial Squares
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring by Grouping
Factoring a Difference of Cubes
Determine if an Expression is a Factor
Determining if Factor Using Synthetic Division
Find the Factors Using the Factor Theorem
Determining if the Expression is a Polynomial
Determining if Polynomial is Prime
Determining if the Polynomial is a Perfect Square
Expand using the Binomial Theorem
Factoring over the Complex Numbers
Finding All Integers k Such That the Trinomial Can Be Factored
Linear Equations
Determining if Linear
Solving Linear Equations
Calculating Slope and Y Intercept
Rewriting in Slope-Intercept Form
Rewriting in Standard Form
Finding X and Y Intercepts
Finding Equations Using the Slope-Intercept Formula
Finding Equations Using the Point Slope Formula
Finding Equations Given Point and Y-Intercept
Finding the Constant Using Slope
Finding Equations Using Two Points
Finding a Perpendicular Line Containing a Given Point
Finding the Equation
Finding the Slope
Finding a Parallel Line Containing a Given Point
Finding the Slope of a Parallel Line
Finding a Parallel Line to the Given Line
Finding the Slope of a Perpendicular Line
Finding a Perpendicular Line to the Given Line
Finding Ordered Pair Solutions
Using a Table of Values to Graph an Equation
Finding the Equation Using Point-Slope Form
Absolute Value Expressions and Equations
Simplifying Absolute Value Expressions
Solving with Absolute Values
Finding the Vertex for the Absolute Value
Rewriting the Absolute Value as Piecewise
Radical Expressions and Equations
Calculating the Square Root
Simplifying Radical Expressions
Rationalizing Radical Expressions
Solving Radical Equations
Rewriting with Rational (Fractional) Exponents
Finding the Square Root End Point
Rational Expressions and Equations
Reducing
Cancelling the Common Factors
Rewriting in Standard Form
Simplifying Rational Expressions by Factoring
Operations on Rational Expressions
Determining if the Point is a Solution
Finding the Domain
Solving over the Interval
Finding the Range
Finding the Domain and Range
Solving Rational Equations
Adding Rational Expressions
Subtracting Rational Expressions
Multiplying Rational Expressions
Finding the Equation Given the Roots
Finding the Asymptotes
Finding the Constant of Variation
Finding the Equation of Variation
Systems of Equations
Substitution Method
Addition/Elimination Method
Graphing Method
Determining if the Point is a Solution
Determining Parallel Lines
Determining Perpendicular Lines
Finding the Constant of Variation
Dependent, Independent, and Inconsistent Systems
Finding the Intersection (and)
Using the Simplex Method for Constraint Maximization
Using the Simplex Method for Constraint Minimization
Finding the Union (or)
Finding the Equation with Real Coefficients
Solving in Terms of the Arbitrary Variable
Finding a Direct Variation Equation
Finding the Slope for Every Equation
Evaluating
Quadratic Equations
Quadratic Formula
Solving by Factoring
Solve by Completing the Square
Finding the Perfect Square Trinomial
Finding the Quadratic Equation Given the Solution Set
Finding a,b, and c in the Standard Form
Finding the Discriminant
Finding the Quadratic Constant of Variation
Inequalities
Solving for a Variable
Determining if the Point is a Solution
Solving Linear Inequalities
Quadratic Inequalities
Rational Inequalities
Interval Inequalities
Converting from Interval to Inequality
Converting to Set Notation
Rewriting as a Single Interval
Relations
Determining if the Relation is a Function
Finding the Domain and Range of the Relation
Finding the Inverse of the Relation
Finding the Inverse
Determining if One Relation is the Inverse of Another
Determining if Surjective (Onto)
Determining if Bijective (One-to-One)
Determining if Injective (One to One)
Functions
Determining if Linear
Rewriting as an Equation
Rewriting as y=mx+b
Solving Function Systems
Find the Behavior (Leading Coefficient Test)
Finding Ordered Pair Solutions
Determining Odd and Even Functions
Describing the Transformation
Finding the Symmetry
Arithmetic of Functions
Composite Functions
Domain of Composite Functions
Finding Roots Using the Factor Theorem
Finding All Possible Roots/Zeros (RRT)
Determine if Injective (One to One)
Determine if Surjective (Onto)
Finding the Linear Function
Finding the Sum
Finding the Difference
Finding the Product
Finding the Quotient
Finding the Domain of the Sum of the Functions
Finding the Domain of the Difference of the Functions
Finding the Domain of the Product of the Functions
Finding the Domain of the Quotient of the Functions
Finding Roots (Zeros)
Identifying Zeros and Their Multiplicities
Finding the Bounds of the Zeros
Proving a Root is on the Interval
Finding the Average Rate of Change
Finding the Inverse Functions
Finding Maximum Number of Real Roots
Finding the Composition of Functions
Rewriting as a Function
Finding the Domain and Range
Determining if a Function is Rational
Determining if a Function is Proper or Improper
Maximum/Minimum of Quadratic Functions
Finding the slope
Complex Numbers and Vector Analysis
Finding All Complex Number Solutions
Rationalizing with Complex Conjugates
Vector Arithmetic
Logarithmic Expressions and Equations
Simplifying Logarithmic Expressions
Expanding Logarithmic Expressions
Evaluating
Rewriting in Exponential Form
Converting to Logarithmic Form
Exponential Expressions and Equations
Exponential Expressions
Exponential Equations
Converting to Radical Form
Matrices
Solving
Simplifying Matrices
Finding the Variables
Solving the System of Equations Using an Inverse Matrix
Finding the Dimensions
Multiplication by a Scalar
Multiplication
Subtraction
Finding the Determinant of the Resulting Matrix
Finding the Inverse of the Resulting Matrix
Finding the Identity Matrix
Finding the Scalar multiplied by the Identity Matrix
Addition
Simplifying the Matrix Operation
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of a 3x3 Matrix
Finding the Determinant of Large Matrices
Inverse of a 2x2 Matrix
Inverse of an nxn Matrix
Finding Reduced Row Echelon Form
Transposing
Finding the Adjoint
Finding the Cofactor Matrix
Null Space
Finding the Pivot Positions and Pivot Columns
Conic Sections
Identifying Conic Sections
Identifying Circles
Finding a Circle Using the Center and Another Point
Finding a Circle by the Diameter End Points
Finding the Parabola Equation Using the Vertex and Another Point
Finding the Properties of the Parabola
Finding the Vertex
Finding the Vertex Form of the Parabola
Finding the Vertex Form of an Ellipse
Finding the Vertex Form of a Circle
Finding the Vertex Form of a Hyperbola
Finding the Standard Form of a Parabola
Finding the Expanded Form of an Ellipse
Finding the Expanded Form of a Circle
Finding the Expanded Form of a Hyperbola
Vectors
Vector Addition
Vector Subtraction
Vector Multiplication by a Scalar
Finding the Variables
Finding the Length
Finding the Position Vector
Determining Column Spaces
Vector Spaces
Rewrite the System as a Vector Equality
Finding the Rank
Finding the Nullity
3d Coordinate System
Finding the Distance
Finding the Plane Parallel to a Line Giving four 3d Points
Finding the Intersection of the Line Perpendicular to Plane 1 Through the Origin and Plane 2
Finding the Equation of Variation
Eigenvalues and Eigenvectors
Finding the Eigenvalues
Finding the Characteristic Equation
Finding the Eigenvectors/Eigenspace of a Matrix
Linear Transformations
Proving a Transformation is Linear
Finding the Kernel of a Transformation
Projecting Using a Transformation
Finding the Pre-Image
Number Sets
Finding the Intersection of Sets
Finding the Union of Number Sets
Determining if a Set is a Subset of Another Set
Determining if Two Sets are Mutually Exclusive
Finding the Set Complement of Two Sets
Finding the Power Set
Finding the Cardinality
Finding the Cartesian Product of Two Sets
Determining if a Set is a Proper Subset of Another Set
Tables
Finding the Function Rule
Analytic Geometry
Finding the Square or Rectangle Area Given Four Points
Finding the Square or Rectangle Perimeter Given Four Points
Finding the Square or Rectangle Area Given Three Points
Finding the Square or Rectangle Perimeter Given Three Points
Finding the Equation of a Circle
Finding the Equation of a Hyperbola
Finding the Equation of an Ellipse
Trigonometry
Algebra Concepts and Expressions Review
Solving for a Variable
Synthetic Division
Polynomial Division
Partial Fraction Decomposition
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring Out Greatest Common Factor (GCF)
Factoring by Grouping
Factoring Trinomials
Finding the Domain
Dividing
Evaluate
Evaluating
Right Triangle Trigonometry
Finding an Angle Using another Angle
Pythagorean Theorem
Finding the Sine
Finding the Cosine
Finding the Tangent
Finding the Trig Value
Radian Measure and Circular Functions
Converting to Degrees, Minutes, and Seconds
Finding Trig Functions Using Identities
Finding Trig Functions Using the Right Triangle
Converting Radians to Degrees
Converting Degrees to Radians
Finding a Reference Angle
Finding a Supplement
Finding a Complement
Converting RPM to Radians per Second
Finding the Quadrant of the Angle
Graphing Trigonometric Functions
Graphing Sine & Cosine Functions
Graphing Other Trigonometric Functions
Amplitude, Period, and Phase Shift
Finding the Other Trig Values in a Quadrant
Simplifying Trigonometric Expressions
Finding the Exact Value
Finding the Value Using the Unit Circle
Expanding Trigonometric Expressions
Double Angle Formulas
Triple Angle Formulas
Expanding Using Sum/Difference Formulas
Simplify Using Pythagorean Identities
Simplify by Converting to Sine/Cosine
Inverting Trigonometric Expressions
Expanding Using DeMoivre's Theorem
Verifying Trigonometric Identities
Verifying Trigonometric Identities
Using Fundamental Identities
Solving Trigonometric Equations
Solving Standard Angle Equations
Complex Trigonometric Equations
Solving Equations over an Interval
Solving the Triangle
Complex Numbers
Finding All Complex Number Solutions
Complex Operations
Rationalizing with Complex Conjugates
Trigonometric Form of a Complex Number
Analytic Geometry in Polar Coordinates
Converting to Polar Coordinates
Graphing Circles
Graphing Limacons
Graphing Roses
Graphing Cardioids
Exponential and Logarithmic Functions
Simplifying Logarithmic Expressions
Expanding Logarithmic Expressions
Exponential Expressions
Exponential Equations
Vector Arithmetic
Vector Arithmetic
Vectors
Finding the Position Vector
Precalculus
Algebra Concepts and Expressions
Solving for a Variable
Solving Graphically
Polynomial Division
Finding the Remainder Using Long Polynomial Division
Synthetic Division
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring Out Greatest Common Factor (GCF)
Factoring by Grouping
Factoring Trinomials
Partial Fraction Decomposition
Finding the Perfect Square Trinomial
Finding a Perpendicular Line Containing a Given Point
Finding a Parallel Line Containing a Given Point
Reordering the Polynomial in Ascending Order
Finding the LCM of a List of Expressions
Finding the LCD of a List of Expressions
Determining if the Number is a Perfect Square
Evaluate
Combining
Finding the Domain
Dividing
Evaluating the Difference Quotient
Evaluating
Determining if True
Relations
Determining if the Relation is a Function
Finding the Domain and Range of the Relation
Finding the Inverse of the Relation
Finding the Inverse
Determining if One Relation is the Inverse of Another
Determining if Surjective (Onto)
Determining if Bijective (One-to-One)
Determining if Injective (One to One)
Functions
Determining if Linear
Rewriting as an Equation
Rewriting as y=mx+b
Find the Behavior (Leading Coefficient Test)
Finding Ordered Pair Solutions
Determining Odd and Even Functions
Describing the Transformation
Finding the Symmetry
Finding the Asymptotes
Difference Quotient
Finding Roots Using the Factor Theorem
Finding All Possible Roots/Zeros (RRT)
Finding Upper and Lower Bounds
Finding the Linear Function
Rewriting as a Function
Determining if a Function is Rational
Determining if a Function is Proper or Improper
Maximum/Minimum of Quadratic Functions
Finding the slope
Graphing
Operations on Functions
Evaluating Functions
Arithmetic of Functions
Composite Functions
Domain of Composite Functions
Finding the Sum
Finding the Difference
Finding the Product
Finding the Quotient
Finding the Domain of the Sum of the Functions
Finding the Domain of the Difference of the Functions
Finding the Domain of the Product of the Functions
Finding the Domain of the Quotient of the Functions
Finding Roots (Zeros)
Identifying Zeros and Their Multiplicities
Finding the Inverse Functions
Finding Maximum Number of Real Roots
Finding the Composition of Functions
Finding the Domain and Range
Points, Lines, and Line Segments
Finding a Point's Quadrant
Finding the Midpoint of a Line Segment
Distance Formula
Finding Equations Using Slope-Intercept
Finding the Start Point Given the Mid and End Points
Finding the End Point Given the Start and Mid Points
Finding the Slope
Finding the Y Intercept
Finding the Slope and Y-Intercept
Finding the Equation of the Parabola
Finding the Average Rate of Change
Finding the Slope of the Perpendicular Line to the Line Through the Two Points
Absolute Value Expressions and Equations
Simplifying Absolute Value Expressions
Solving with Absolute Values
Finding the Vertex for the Absolute Value
Rewriting the Absolute Value as Piecewise
Radical Expressions and Equations
Calculating the Square Root
Simplifying Radical Expressions
Rationalizing Radical Expressions
Solving Radical Equations
Rewriting with Rational (Fractional) Exponents
Finding the Square Root End Point
Rational Expressions and Equations
Reducing
Cancelling the Common Factors
Rewriting in Standard Form
Simplifying Rational Expressions by Factoring
Operations on Rational Expressions
Determining if the Point is a Solution
Finding the Domain
Solving over the Interval
Finding the Range
Finding the Domain and Range
Solving Rational Equations
Adding Rational Expressions
Subtracting Rational Expressions
Multiplying Rational Expressions
Finding the Equation Given the Roots
Finding the Asymptotes
Finding the Constant of Variation
Finding the Equation of Variation
Polynomial and Rational Functions
Simplifying Absolute Value Expressions
Solving with Absolute Values
Rationalizing Radical Expressions
Simplifying Radical Expressions
Solving Radical Equations
Reducing
Cancelling the Common Factors
Simplifying Rational Expressions by Factoring
Operations on Rational Expressions
Solving Rational Equations
Quadratic Inequalities
Rational Inequalities
Determining if the Expression is a Polynomial
Determining if Polynomial is Prime
Determining if the Polynomial is a Perfect Square
Finding the Leading Term
Finding the Leading Coefficient
Finding the Degree, Leading Term, and Leading Coefficient
Factoring Polynomials
Finding the GCF
Factoring Out Greatest Common Factor (GCF)
Identifying the Common Factors
Cancelling the Common Factors
Factoring Trinomials
Trinomial Squares
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring by Grouping
Factoring a Difference of Cubes
Determine if an Expression is a Factor
Determining if Factor Using Synthetic Division
Find the Factors Using the Factor Theorem
Determining if Polynomial is Prime
Determining if the Polynomial is a Perfect Square
Expand using the Binomial Theorem
Finding All Integers k Such That the Trinomial Can Be Factored
Conic Sections
Identifying Conic Sections
Identifying Circles
Finding a Circle Using the Center and Another Point
Finding a Circle by the Diameter End Points
Finding the Parabola Equation Using the Vertex and Another Point
Finding the Properties of the Parabola
Finding the Vertex
Finding the Vertex Form of the Parabola
Finding the Vertex Form of an Ellipse
Finding the Vertex Form of a Circle
Finding the Vertex Form of a Hyperbola
Finding the Standard Form of a Parabola
Finding the Expanded Form of an Ellipse
Finding the Expanded Form of a Circle
Finding the Expanded Form of a Hyperbola
Exponential and Logarithmic Functions
Simplifying Logarithmic Expressions
Expanding Logarithmic Expressions
Exponential Expressions
Exponential Equations
Evaluating
Rewriting in Exponential Form
Converting to Logarithmic Form
Converting to Radical Form
Trigonometry
Converting Radians to Degrees
Converting Degrees to Radians
Right Triangle Trigonometry
Graphing Sine & Cosine Functions
Graphing Other Trigonometric Functions
Amplitude, Period, and Phase Shift
Solving Equations over an Interval
Converting RPM to Radians per Second
Finding a Reference Angle
Finding a Supplement
Finding a Complement
Finding the Quadrant of the Angle
Analytic Trigonometry
Using Fundamental Identities
Solving Standard Angle Equations
Double Angle Formulas
Triple Angle Formulas
Finding the Quadrant of the Angle
Inequalities
Solving for a Variable
Determining if the Point is a Solution
Solving Linear Inequalities
Quadratic Inequalities
Rational Inequalities
Interval Inequalities
Converting from Interval to Inequality
Converting to Set Notation
Rewriting as a Single Interval
Linear Equations
Determining if Linear
Solving Linear Equations
Calculating Slope and Y Intercept
Rewriting in Slope-Intercept Form
Rewriting in Standard Form
Finding X and Y Intercepts
Finding Equations Using the Slope-Intercept Formula
Finding Equations Using the Point Slope Formula
Finding Equations Given Point and Y-Intercept
Finding the Constant Using Slope
Finding Equations Using Two Points
Finding a Perpendicular Line Containing a Given Point
Finding the Equation
Finding the Slope
Finding a Parallel Line Containing a Given Point
Finding the Slope of a Parallel Line
Finding a Parallel Line to the Given Line
Finding the Slope of a Perpendicular Line
Finding a Perpendicular Line to the Given Line
Finding Ordered Pair Solutions
Using a Table of Values to Graph an Equation
Finding the Equation Using Point-Slope Form
Systems of Equations
Substitution Method
Addition/Elimination Method
Determining Parallel Lines
Determining Perpendicular Lines
Graphing Method
Determining if the Point is a Solution
Finding the Constant of Variation
Dependent, Independent, and Inconsistent Systems
Finding the Intersection (and)
Finding the Union (or)
Finding the Equation with Real Coefficients
Solving in Terms of the Arbitrary Variable
Finding a Direct Variation Equation
Finding the Slope for Every Equation
Quadratic Equations
Quadratic Formula
Solving by Factoring
Solve by Completing the Square
Finding the Perfect Square Trinomial
Finding the Quadratic Equation Given the Solution Set
Finding a,b, and c in the Standard Form
Finding the Discriminant
Finding the Quadratic Constant of Variation
Matrices
Solving
Simplifying Matrices
Finding the Variables
Solving the System of Equations Using an Inverse Matrix
Finding the Dimensions
Multiplication by a Scalar
Multiplication
Subtraction
Finding the Determinant of the Resulting Matrix
Finding the Inverse of the Resulting Matrix
Finding the Identity Matrix
Finding the Scalar multiplied by the Identity Matrix
Addition
Simplifying the Matrix Operation
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of a 3x3 Matrix
Finding the Determinant of Large Matrices
Inverse of a 2x2 Matrix
Inverse of an nxn Matrix
Finding Reduced Row Echelon Form
Transposing
Finding the Adjoint
Finding the Cofactor Matrix
Null Space
Sequences and Series
Arithmetic Sequences/Progressions
Geometric Sequences/Progressions
Finding the Next Term of the Sequence
Finding the nth Term
Finding the Sum of First n Terms
Expanding Series Notation
Finding the Sum of the Series
Finding the Sum of the Infinite Geometric Series
Analytic Geometry in Rectangular Coordinates
Finding the Midpoint of a Line Segment
Distance Formula
Calculating Slope and Y Intercept
Identifying Conic Sections
Identifying Circles
Analytic Geometry in Polar Coordinates
Converting to Polar Coordinates
Converting to Rectangular Coordinates
Graphing Circles
Graphing Limacons
Graphing Roses
Graphing Cardioids
Limits and an Introduction to Calculus
Evaluating Limits Approaching a Value
Evaluating Limits Approaching Infinity
Vectors
Vector Addition
Vector Subtraction
Vector Multiplication by a Scalar
Finding the Variables
Finding the Length
Finding the Position Vector
Determining Column Spaces
Finding the Angle Between the Vectors
Number Sets
Finding the Intersection of Sets
Finding the Union of Number Sets
Determining if a Set is a Subset of Another Set
Determining if Two Sets are Mutually Exclusive
Finding the Set Complement of Two Sets
Finding the Power Set
Finding the Cardinality
Finding the Cartesian Product of Two Sets
Determining if a Set is a Proper Subset of Another Set
Calculus
Algebra Concepts and Expressions
Solving for a Variable
Polynomial Division
Synthetic Division
Partial Fraction Decomposition
Dividing
Finding the Domain
Finding the Range
Finding the Domain and Range
Finding the Asymptotes
Quadratic Inequalities
Rational Inequalities
Solving Linear Inequalities
Converting from Interval to Inequality
Functions
Determining if the Point on the Graph
Solving Function Systems
Find the Behavior (Leading Coefficient Test)
Determining Odd and Even Functions
Finding the Symmetry
Finding the Asymptotes
Difference Quotient
Finding the Anti-Derivative
Graphing
Operations on Functions
Evaluating Functions
Checking if Continuous Over an Interval
Arithmetic of Functions
Composite Functions
Finding Roots (Zeros)
Identifying Zeros and Their Multiplicities
Finding the Inverse Functions
Finding the Composition of Functions
Finding the slope
Polynomial and Rational Functions
Simplifying Absolute Value Expressions
Solving with Absolute Values
Simplifying Radical Expressions
Rationalizing Radical Expressions
Solving Radical Equations
Simplifying Rational Expressions by Factoring
Operations on Rational Expressions
Solving Rational Equations
Exponential and Logarithmic Functions
Simplifying Logarithmic Expressions
Expanding Logarithmic Expressions
Exponential Expressions
Exponential Equations
Sequences and Series
Arithmetic Sequences/Progressions
Geometric Sequences/Progressions
Finding the Next Term of the Sequence
Finding the nth Term
Finding the Sum of First n Terms
Expanding Series Notation
Convergence of Infinite Series
Finding the Sum of the Series
Finding the Sum of the Infinite Geometric Series
Evaluating Limits
Evaluating Limits Approaching a Value
Evaluating Limits Approaching Infinity
Using the Limit Definition to Find the Tangent Line at a Given Point
Derivatives
Finding the nth Derivative
Finding the Derivative Using Product Rule
Finding the Derivative Using Quotient Rule
Finding the Derivative Using Chain Rule
Finding the Derivative
Implicit Differentiation
Using the Limit Definition to Find the Derivative
Evaluating the Derivative
Finding where dy/dx is Equal to Zero
Finding the Linearization
Applications of Differentiation
Finding a Tangent Line to a Curve
Checking if Differentiable Over an Interval
The Mean Value Theorem
Finding the Inflection Points
Find Where the Function Increases/Decreases
Finding the Critical Points of a Function
Find Horizontal Tangent Line
Evaluating Limits with L'Hospital Rule
Local Maxima and Minima
Finding the Absolute Maximum and Minimum on the Given Interval
Finding Concavity using the Second Derivative
Using the Limit Definition to Find the Tangent Line at a Given Point
Finding the Derivative
Integrals
Finding the Integral
Evaluating Definite Integrals
Evaluating Indefinite Integrals
Substitution Rule
Rewriting as a Single Interval
Applications of Integration
Finding the Arc Length
Finding the Average Value of the Derivative
Finding the Average Value of the Equation
Finding Area Between Curves
Finding the Volume
Finding the Average Value of the Function
Finding the Root Mean Square
Techniques of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration by Partial Fractions
Parametric Equations and Polar Coordinates
Eliminating the Parameter from the Function
Converting to Polar Coordinates
Graphing Circles
Graphing Limacons
Graphing Roses
Graphing Cardioids
Statistics
Algebra Review
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring Out Greatest Common Factor (GCF)
Factoring by Grouping
Factoring Trinomials
Finding the Perfect Square Trinomial
Finding a Perpendicular Line Containing a Given Point
Finding the Slope
Finding a Parallel Line Containing a Given Point
Average Descriptive Statistics
Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Geometric Mean
Finding the Quadratic Mean (RMS)
Finding the Minimum
Finding the Maximum
Finding the Mid-Range (Mid-Extreme)
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Interquartile Range (H-Spread)
Finding the Midhinge
Finding the Five Number Summary
Dispersion Statistics
Finding the Standard Deviation
Finding the Skew of a Data Set
Finding the Range of a Data Set
Finding the Variance of a Data Set
Finding the Class Width
Probability
Solving Combinations
Solving Permutations
Finding the Probability of Both Independent Events
Finding the Probability of Both Dependent Events
Finding the Probability for Both Mutually Exclusive Events
Finding the Probability for Both not Mutually Exclusive Events
Finding the Conditional Probability for Independent Events
Determining if Given Events are Independent/Dependent Events
Determining if Given Events are Mutually Exclusive Events
Finding the Probability of Both not Mutually Exclusive Events
Finding the Conditional Probability Using Bayes's Rule
Finding the Probability of the Complement
Probability Distributions
Describing Distribution's Two Properties
Finding the Probability of x
Finding the Expectation
Finding the Standard Deviation
Finding the Variance
Finding the Probability of a Binomial Distribution
Finding the Probability of the Binomial Event
Finding the Mean
Frequency Distribution
Finding the Relative Frequency
Finding the Percentage Frequency
Finding the Upper and Lower class Limits
Finding the Class Boundaries
Finding the Class Width
Finding the Midpoints
Finding the Mean
Finding the Variance
Finding the Standard Deviation
Finding the Cumulative Frequency
Finding the Median Class Interval
Finding the Modal Class
Creating a Grouped Frequency Distribution Table
Finding the Data Range
Normal Distributions
Finding Probability from a Normal Distribution
Finding a z-Score for a Normal Distribution
Approximating Using Normal Distribution
Finding Probabilities using the Central Limit Theorem
Finding the Probability of the z-Score Range
Finding the Probability of a Range in a Nonstandard Normal Distribution
Finding the z-Score
t-Distributions
Finding the P-Value
Finding a t-Value for a Confidence Level
Finding the Critical t-Value
Hypothesis Testing
Setting the Alternative Hypothesis
Setting the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Alternative Hypothesis
Testing a Claim about the Mean
Testing a Claim using the t-Test
Testing a Claim about the Mean (Two-Tailed Test)
Testing a Claim from a Small Sample
Estimation and Sample Size
Finding Sampling Distribution
Finding Standard Error
Finding the Maximum Error
Finding the Confidence Level
Determining Sample Size Required for Stated Confidence Level
Finding the Confidence Level for a Small Sample
Finding the Maximum Error for a Small Sample
Correlation and Regression
Finding the Linear Correlation Coefficient
Determining if the Correlation is Significant
Finding a Regression Line
Finite Math
Polynomials and Expressions
Simplifying
Synthetic Division
Polynomial Division
Finding the Remainder Using Long Polynomial Division
Reducing
Cancelling the Common Factors
Evaluate
Identifying Degree
Multiplying Polynomials Using FOIL
Negative Exponents
Operations on Polynomials
Simplifying Expressions
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring Out Greatest Common Factor (GCF)
Trinomial Squares
Factoring by Grouping
Factoring a Difference of Cubes
Factoring Trinomials
Maximum Number of Real Roots/Zeros
Finding All Possible Roots/Zeros (RRT)
Finding All Roots with Rational Root Test (RRT)
Ratios, Proportions, and Percents
Converting Percents to Decimal
Converting Percents to Fractions
Converting the Percent Grade to Degree
Converting the Degree to Percent Grade
Equations and Inequalities
Interval Inequalities
Converting from Interval to Inequality
Solve by Completing the Square
Finding the Domain
Finding the Range
Finding the Domain and Range
Finding the Asymptotes
Solving by Factoring
Solving Rational Equations
Quadratic Formula
Quadratic Inequalities
Rational Inequalities
Solving Linear Inequalities
Finding the Discriminant
Finding the Quadratic Constant of Variation
Linear Functions and Points
Calculating Slope and Y Intercept
Solving Linear Equations
Solving Radical Equations
Finding the Midpoint of a Line Segment
Distance Formula
Finding a Point's Quadrant
Finding Equations Using the Slope-Intercept Formula
Finding Equations Using Slope-Intercept
Finding Equations Using Two Points
Finding a Perpendicular Line Containing a Given Point
Finding the Equation
Finding the Slope
Finding a Parallel Line Containing a Given Point
Finding the Equation Using Point-Slope Form
Functions
Find the Behavior (Leading Coefficient Test)
Determining Odd and Even Functions
Arithmetic of Functions
Composite Functions
Finding Roots Using the Factor Theorem
Finding All Possible Roots/Zeros (RRT)
Determine if Injective (One to One)
Determine if Surjective (Onto)
Finding the Linear Function
Finding the Sum
Finding the Difference
Finding the Product
Finding the Quotient
Finding the Domain of the Sum of the Functions
Finding the Domain of the Difference of the Functions
Finding the Domain of the Product of the Functions
Finding the Domain of the Quotient of the Functions
Finding Roots (Zeros)
Identifying Zeros and Their Multiplicities
Finding the Bounds of the Zeros
Proving a Root is on the Interval
Finding the Average Rate of Change
Finding the Inverse Functions
Finding Maximum Number of Real Roots
Finding the Composition of Functions
Rewriting as a Function
Finding the Domain and Range
Determining if a Function is Rational
Determining if a Function is Proper or Improper
Maximum/Minimum of Quadratic Functions
Relations
Determining if the Relation is a Function
Finding the Domain and Range of the Relation
Finding the Inverse of the Relation
Determining if Surjective (Onto)
Determining if Bijective (One-to-One)
Matrices
Finding the Dimensions
Multiplication by a Scalar
Multiplication
Subtraction
Finding the Identity Matrix
Finding the Scalar multiplied by the Identity Matrix
Addition
Simplifying the Matrix Operation
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of a 3x3 Matrix
Finding the Determinant of Large Matrices
Inverse of a 2x2 Matrix
Inverse of an nxn Matrix
Finding Reduced Row Echelon Form
Transposing
Finding the Adjoint
Finding the Cofactor Matrix
Systems of Linear Equations
Substitution Method
Determining Parallel Lines
Determining Perpendicular Lines
Cramer's Rule
Solving using Matrices by Elimination
Solving using Matrices by Row Operations
Solving using an Augmented Matrix
Mathematics of Finance
Finding the Simple Interest Received
Finding the Present Value with Compound Interest
Finding the Simple Interest Future Value
Finding the Future Value with Continuous Interest
Average Descriptive Statistics
Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Geometric Mean
Finding the Quadratic Mean (RMS)
Finding the Minimum
Finding the Maximum
Finding the Mid-Range (Mid-Extreme)
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Interquartile Range (H-Spread)
Finding the Midhinge
Finding the Five Number Summary
Probability
Solving Combinations
Solving Permutations
Finding the Probability of Both Independent Events
Finding the Probability for Both Mutually Exclusive Events
Finding the Conditional Probability for Independent Events
Determining if Given Events are Mutually Exclusive Events
Finding the Probability of Both not Mutually Exclusive Events
Finding the Probability for Both not Mutually Exclusive Events
Finding the Probability of the Complement
Dispersion Statistics
Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Standard Deviation
Finding the Minimum
Finding the Maximum
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Five Number Summary
Statistical Distributions
Describing Distribution's Two Properties
Finding the Probability of x
Finding the Expectation
Finding the Standard Deviation
Finding the Variance
Finding Probability from a Normal Distribution
Finding a z-Score for a Normal Distribution
Approximating Using Normal Distribution
Finding the Probability of a Binomial Distribution
Finding the Probability of the Binomial Event
Finding the Mean
Frequency Distribution
Finding the Upper and Lower class Limits
Finding the Class Boundaries
Finding the Class Width
Finding the Midpoints
Finding the Mean
Finding the Variance
Finding the Standard Deviation
Finding the Cumulative Frequency
Finding the Relative Frequency
Finding the Median Class Interval
Finding the Modal Class
Creating a Grouped Frequency Distribution Table
Finding the Data Range
Normal Distributions
Finding Probabilities using the Central Limit Theorem
Finding the Probability of the z-Score Range
Finding the Probability of a Range in a Nonstandard Normal Distribution
Finding the z-Score
Finding the P-Value
Finding a t-Value for a Confidence Level
Finding the Critical t-Value
t-Distributions
Finding the P-Value
Finding a t-Value for a Confidence Level
Finding the Critical t-Value
Hypothesis Testing
Setting the Alternative Hypothesis
Setting the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Alternative Hypothesis
Testing a Claim about the Mean
Testing a Claim using the t-Test
Testing a Claim about the Mean (Two-Tailed Test)
Testing a Claim from a Small Sample
Estimation and Sample Size
Finding Sampling Distribution
Finding the Maximum Error
Finding the Confidence Level
Determining Sample Size Required for Stated Confidence Level
Finding the Confidence Level for a Small Sample
Finding the Maximum Error for a Small Sample
Correlation and Regression
Finding the Linear Correlation Coefficient
Determining if the Correlation is Significant
Finding a Regression Line
Vectors
Vector Addition
Vector Subtraction
Vector Multiplication by a Scalar
Finding the Position Vector
Linear Algebra
Introduction to Matrices
Multiplication by a Scalar
Multiplication
Subtraction
Addition
Complex Numbers
Complex Operations
Rationalizing with Complex Conjugates
Trigonometric Form of a Complex Number
Matrices
Solving
Simplifying Matrices
Finding the Variables
Solving the System of Equations Using an Inverse Matrix
Finding the Dimensions
Multiplication by a Scalar
Multiplication
Subtraction
Finding the Determinant of the Resulting Matrix
Finding the Inverse of the Resulting Matrix
Finding the Identity Matrix
Finding the Scalar multiplied by the Identity Matrix
Addition
Simplifying the Matrix Operation
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of a 3x3 Matrix
Finding the Determinant of Large Matrices
Inverse of a 2x2 Matrix
Inverse of an nxn Matrix
Finding Reduced Row Echelon Form
Transposing
Finding the Adjoint
Finding the Cofactor Matrix
Null Space
Finding the Pivot Positions and Pivot Columns
Systems of Linear Equations
Substitution Method
Cramer's Rule
Solving using Matrices by Elimination
Solving using Matrices by Row Operations
Solving using an Augmented Matrix
Vectors
Vector Addition
Vector Subtraction
Vector Multiplication by a Scalar
Finding the Variables
Finding the Norm in Real Vector Space
Finding the Norm in Complex Vector Space
Finding the Length
Linear Independence and Combinations
Linear Independence of Real Vector Spaces
Determining if a Vector is an Element of the Set
Basis
Dimension
Vector Spaces
Rewrite the System as a Vector Equality
Finding the Null Space
Finding the Rank
Finding the Nullity
Eigenvalues and Eigenvectors
Finding the Eigenvalues
Finding the Characteristic Equation
Finding the Eigenvectors/Eigenspace of a Matrix
Linear Transformations
Proving a Transformation is Linear
Finding the Kernel of a Transformation
Projecting Using a Transformation
Finding the Pre-Image
Number Sets
Finding the Intersection of Sets
Finding the Union of Number Sets
Determining if a Set is a Subset of Another Set
Determining if Two Sets are Mutually Exclusive
Finding the Set Complement of Two Sets
Finding the Power Set
Finding the Cardinality
Finding the Cartesian Product of Two Sets
Determining if a Set is a Proper Subset of Another Set
Chemistry
Unit Conversion
Converting Grams to Kilograms
Converting Grams to Pounds
Converting Grams to Ounces
Converting Feet to Inches
Converting Ounces to Grams
Converting Ounces to Pounds
Converting Ounces to Tons
Converting Pounds to Grams
Converting Pounds to Ounces
Converting Fahrenheit to Celsius
Converting Celsius to Fahrenheit
Atomic Structure
Finding the Number of Protons
Finding the Number of Electrons
Finding the Number of Neutrons
Finding the Mass of a Single Atom
Finding the Electron Configuration
Finding the Atomic Mass
Finding the Atomic Number
Molecules and Compounds
Finding the Empirical/Simplest Formula
Finding the Number of Mols
Finding the Mass Percentages
Finding the Number of Molecules in a Certain Mass
Determining the Type of Ion
Finding Oxidation Numbers
Finding the Empirical Formula
Chemical Equations and Reactions
Balancing Chemical Equations
Balancing Burning Reactions
Balancing Chemical Equations with Water as a Product
Stoichiometry
Finding the Mass given a Mass
Finding the Volume given a Volume
Finding the Mass given a Volume
Finding the Volume given a Mass
Behavior of Gases
Using the Combined Gas Law
Finding the Density at STP
Dalton's Law of Partial Pressures
Thermochemistry
Finding the Calories Required to Heat Water
Finding the Specific Heat
Finding the Mass Required to Heat Water
Solutions and Concentrations
Finding the Concentration
Finding the Mass of a Solute
Finding the Moles of a Solute
Determining if the Compound is Soluble in Water
Acids and Bases
Finding the pH of a Strong Acid
Finding the pH of a Strong Base
Finding the pH of a Weak Acid
Finding the pH of a Weak Base
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