mathispower4u - Algebra 2

Polynomial Functions
Determining the Characteristics of Polynomial Functions

Determining the Equations of Polynomial Functions

Finding the Zeros of Polynomial Functions

Solving Polynomial Inequality

Ex 1: Solve a Polynomial Inequality in Factored Form
Ex 2: Solve a Polynomial Inequality in Factored Form
Ex: Solve a Polynomial Equation Using a Graphing Calculator (Approximate Solutions)
Ex: Solve a Polynomial Inequality Using Factor By Grouping (Degree 3)
Ex: Solve a Polynomial Inequality Using Factor Using GCF (Degree 3)
Ex: Solve a Polynomial Inequality Using Factor of a Trinomial (Degree 4)
Introduction to Odd and Even Functions
Ex 1: Determine if a Function is Odd, Even, or Neither
Ex 2: Determine if a Function is Odd, Even, or Neither
Determine if a Function is Even, Odd, or Neither Using a Graph (1)|
Determine if a Function is Even, Odd, or Neither Using a Graph (2)

Radicals Expressions, Equations, and Functions

Introduction to Radical Expressions

Introduction to Square Root and Perfect Squares
Introduction to Radicals
Using Rational Exponents
Approximate a Square Root to Two Decimal Places Using Trial and Error

Simplifying Radicals

Simplifying Radicals
Simplify Square Roots (Perfect Square Radicands)
Simplify a Variety of Square Expressions (Simplify Perfectly)
Simplify Square Roots with Variables (perfect squares)
Simplify Square Roots of Decimals (Perfect Square Decimals)
Simplify Perfect Nth Roots
Simplify Square Roots (Not Perfect Square Radicands)
Simplify Square Roots in the Form a*sqrt(b) (not perfect squares)
Simplify Square Roots with Variables
Simplify Cube Roots (Perfect Cube Radicands)
Simplify Cube Roots (Not Perfect Cube Radicands)
Simplifying Radical Expressions Without Fractions
Simplifying Radical Expressions With Fractions
Order of Operations with a Fraction Containing a Square Root
Ex: Simplify Square Roots - Perfect Roots
Ex: Simplify Perfect Nth Roots - Radicals
Ex: Simplify Square Roots - Not Perfect Roots
Ex: Simplify Square Roots of Variable Expressions - Absolute Value Needed
Ex: Simplify a Radical Expression containing Square Roots in the Numerator and Denominator
Simplify Cube Roots with Variables (not perfect cubes)
Ex: Simplify Radicals with the Same Radicand and Different Indexes
Ex: Simplify a Radical Containing a Fraction - Perfect Root
Ex: Simplify Radicals with Variables - Perfect Roots
Simplify Nth Roots with Variables
Ex 1: Simplifying Perfect Nth Roots Containing Variables
Ex 2: Simplifying Perfect Nth Roots Containing Variables
Ex: Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots
Ex: Simplify Radicals with Negative Radicands and Odd Indexes
Simplify Radicals with Variables (Large Index and Exponents)
Ex: Simplify Radicals with Variables - Not Perfect Roots
Evaluating Radical Expressions on the TI83/84
Evaluating Radicals on the TI-84
Approximating Square Roots Using Division (No Calculator Required)

Multiplying Radicals

Introduction to Multiplying Radicals
Multiplying Radical Expressions with Variables Using Distribution
Multiplying Binomial Radical Expressions with Variables
Multiplying Radicals Containing Variables
Multiplying Binomials with Radicals
Multiplying Conjugates of Radical Expressions
Review of Multiplying Radicals
Ex: Multiply Square Roots
Ex 1: Multiply Radicals
Ex 2: Multiply Radicals
Ex: Multiply Radicals with Variables
Multiply Two Radicals with Variables (Index 4 and 5) Perfect Roots
Ex: Radicals Raised to Powers
Ex: Distribution with Square Roots
Ex: Multiply Binomials with Square Roots
Ex: Square Binomials With Square Roots
Ex: Multiply Radical Conjugates - Square Roots
Square a Binomial with a Square Root of a Variable Expression
Multiply two Binomial Radical Expressions with Variables (Conjugates)

Dividing Radicals

Performing Operations with Rational Exponents

Adding and Subtracting Radicals

Adding Radicals (Basic With No Simplifying)
Adding Radicals That Requires Simplifying
Simplify and Add Square Roots: sqrt(a^2*c)+sqrt(b^2*c)
Subtracting Radicals (Basic With No Simplifying)
Subtracting Radicals That Requires Simplifying
Adding and Subtracting Radicals
Ex: Evaluate the Square Root of a Sum and the Sum of Square Roots on a Calculator
Ex: Add and Subtract Square Roots - No Simplifying
Ex: Add and Subtract Square Roots
Ex: Add and Subtract Square Roots Containing Variables
Subtract Square Expressions with a Variable - Simplifying Required
Add Square Root Expressions with Variables
Add and Subtract Square Root Expressions with Variables (Adv)

Solving Radical Equations

Solving Radical Equations with One Radical
Solve a Radical Equation with One Cube Root (Fraction Answer)
Solve a Radical Equation with One Square Root (Fraction Answer)
Solve a Basic Radical Equation Given Function Notation
Solve a Radical Equation Given Function Notation
Solving Radical Equations with Two Radicals
Ex 1: Solve a Basic Radical Equation - Square Roots
Ex 2: Solve Radical Equations - Square Roots
Ex 3: Solve Radical Equations - Square Roots
Ex 4: Solve Radical Equations - Square Roots
Ex 5: Solve Radical Equations - Two Square Roots
Ex 6: Solve Radical Equations - Two Square Roots
Ex 7: Solve Radical Equations - Two Square Roots
Ex: Solve a Radical Equation with One Radical: Factoring and Extraneous Solution
Ex: Solve a Radical Equation with Two Radicals: a*sqrt(b)=sqrt(d)
Solve a Radical Equation with a Cube Root
Ex: Solve Radical Equations - Cube Roots / Fourth Roots
Solve Basic Equations with Rational Exponents: Are There Solutions
Solve Basic Equations with Rational Exponents Using Two Steps: One Solution x^(a/b)=c (odd a)
Solve Basic Equations with Rational Exponents Using Two Steps: Two Solutions x^(a/b)=c, even a)
Solve Equations with Rational Exponents by Factoring Using Substitution
Solve Equations with Negative Rational Exponents: a(x-b)^(-1/3)=c
Solve Equations with Positive Rational Exponents: Two Solutions? (ax+b)^(1/2)-c=x
Solve Equations with Rational Exponents (One Solution)
Solve Equations with Rational Exponents (Two Solutions)
Solving Equations with Rational Exponents: One and Two Solutions
Solve an Equation with a Rational Exponent (x+b)^(c/d)=f (One Solution)
Solve an Equation with a Rational Exponent (x+b)^(c/d)=f (Two Solutions)
Ex: Solving an Equation with Rational Exponents Using Reciprocal Powers
Solve a Radical Equation Given Function Notation (Extraneous Sol)

Radical Equation Applications

Radical Equation Application - Vehicle Speed from Skid Mark Length
Application: Evaluate a Square Function (Safe Speed)
Application: Solve a Square Root Equation (Year of Obesity Percent)
Ex: Radical Equation Application - Obesity Percentage
Ex: Radical Function Application Finding Inputs and Outputs (Speed and Length of Skids)
Ex: Radical Function Outputs and Inputs Application - BMI
Ex: Radical Function Outputs and Inputs Application - Pendulum
Ex: Rational Function Outputs and Inputs Application - Average Cost
Kinetic Energy - Radical Equation Application
Volume of a Cone -Radical Equation Application
Volume of a Cone -Radical Equation Application (Special Formula)

Performing Operations with Complex Numbers

Complex Numbers
Ex: Determine a Real, Imaginary, and Complex Number
Simplify Square Roots to Imaginary Numbers
Write Number in the Form of Complex Numbers
Complex Number Operations
Ex: Simplify Complex Numbers
Ex : Simplify Imaginary and Complex Numbers
Ex: Simplify, Add, and Subtract Imaginary and Complex Numbers
Ex 1: Adding and Subtracting Complex Numbers
Ex 2: Adding and Subtracting Complex Numbers
Ex 1: Simplify and Multiply Complex Numbers
Ex 2: Multiply Complex Numbers
Ex 3: Multiply Complex Numbers
Ex: Multiplying Complex Conjugates
Ex: Subtract and Multiply Complex Number
Multiply Three Complex Numbers
Cube a Complex Number
Simplifying Powers of i (Method of Dividing by 4)
Ex: Raising the imaginary unit i to powers
Ex: Dividing Complex Numbers
Simplify a Quotient of Imaginary Numbers
Complex Number Operations on the TI-84

Using the Pythagorean Theorem

The Pythagorean Theorem
Ex: Determine if a Triangle is a Right Triangle Given the Length of 3 Sides
Ex: Determine the Length of the Hypotenuse of a Right Triangle
Ex: Determine the Length of the Leg of a Right Triangle
Ex: Pythagorean Theorem App - Find the Width of a Laptop
Ex: Determine the Distance Between Two Points Using the Pythagorean Theorem
Ex: Find the Shortest Distance Between Two Locations North and West
Use The Pythagorean Theorem to Determine the Diagonal of a TV

Using the Distance Formula / Midpoint Formula

The Distance Formula
Distance Formula App: Find the Closest Boat
Ex: Midpoint of a Segment
Ex: Find the Endpoint of a Segment Given the Midpoint and One Endpoint
Ex: Determine the Distance Between Two Points (length of segment)

Graphing the Square Root Function with Transformations

Rational Expressions, Equations, and Functions

Simplifying Rational Expressions

Simplifying Rational Expressions
Simplify and Give the Domain of Rational Expressions
Simplify Rational Expressions: (linear/quad) and (quad/quad)
Ex 1: Simplifying Rational Expressions – Monomials
Ex 2: Simplifying Rational Expressions
Ex 3: Simplifying Rational Expressions
Ex 4: Simplifying Rational Expressions
Ex: Find Values Where a Rational Expression is Undefined

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Solving Rational Equations

Solving Rational Equations
Solve Basic Rational Equations
Solve Rational Equations with Like Denominators
Solve a Rational Equation: (x-a)/x-b/c=d/x
Solve a Rational Equation: a/(x+b)=-c/(x+d) - No Cross Products
Ex 1: Solve Rational Equations Algebraically by Clearing Fractions and Solve Graphically
Ex 2: Solve Rational Equations Algebraically by Clearing Fractions and Solve Graphically
Ex 1: Solving Rational Equations
Ex 2: Solving Rational Equations
Ex 3: Solving Rational Equations
Ex 4: Solving Rational Equations
Ex 5: Solving Rational Equations
Ex: Solve a Rational Equation
Ex: A Rational Equation with No Solution
Ex 1: Solve Equations with Fractions (Alternative Method)
Ex 2: Solve Equations with Fractions (Alternative Method)
Ex 1: Solve a Rational Equation (Alternative Method)
Ex 2: Solve a Rational Equation (Alternative Method)
Ex: Solve a Rational Equation - Alternative Method
Solve A Rational Equation (No Solution) x/(3x-9)-6=1/(x-3)
Given f(x)=3/x-4/(3x), Solve f(x)=-7 (Rational Equation)

Solving Applications using Rational Equations

Solving Direct and Inverse Variation Problems

Direct Variation
Basic Direct Variation with Decimals
Direct Variation Application: Currency Conversion
Ex: Direct Variation Application - Aluminum Can Usage
Inverse Variation
Direct and Inverse Variation
Inverse Variation: Square of x
Inverse Variation: The Square Root of x.
Inverse Variation Application: Water Temperature and Depth
Ex 1: Inverse Variation
Ex 2: Inverse Variation - Change of Variables
Ex 3: Inverse Variation - Fractional Variation Constant
Ex: Inverse Variation Application - Number of Workers and Job Time
Ex: Inverse Variation Application - Loudness and Distance
Joint Variation: Determine the Variation Constant (Volume of a Cone)

Determining Key Components of Rational Functions

Graphing Rational Functions

Graphing the Basic Rational Function f(x)=1/x
Graphing Rational Functions
Ex 1: Graphing Rational Functions
Ex 2: Graphing Rational Functions
Ex 3: Graphing Rational Functions
Ex 4: Graphing Rational Functions
Ex 5: Graphing Rational Functions
Ex 6: Graphing Rational Functions
Graphing Reflections of the Basic Rational Function f(x)=1/x
Graphing Translations of the Basic Rational Function f(x)=1/x
Ex 1: Graph Two Translations of the Basic Rational Function f(x)=1/x
Ex 2: Graph Two Translations of the Basic Rational Function f(x)=1/x

Determining Equations of Rational Functions

Ex 1: Find the Equation of Rational Function From a Graph with a Hole
Ex 2: Find the Equation of Rational Function From a Graph with a Hole
Ex 3: Find the Equation of Rational Function From a Graph
Ex 4: Find the Equation of Rational Function From a Graph (Squared Intercept)
Ex 5: Find the Equation of Rational Function From a Graph (Squared VA)
Ex 6: Find the Equation of Rational Function From a Graph (Squared Intercept / VA)
Rational Function Application - Concentration of a Mixture

Solving Rational Inequalities

Solving Rational Inequalities
Solve a Rational Inequality in the Form: a/(x-b)<=c
Solve a Rational Inequality in the Form: (ax-b)/(cx+d)<e
Solve a Rational Inequality in the Form: (ax-b)/(cx+d)>=e/d
Solve a rational Inequality Given Using Function Notation: (x-a)/(x-b)>0
Solve a rational Inequality Given Using Function Notation: (x-a)/(x-b)<=0
Ex 1: Solving Rational Inequalities
Ex 2: Solving Rational Inequalities
Ex 3: Solving Rational Inequalities
Ex 4: Solving Rational Inequalities
Ex 5: Solve a Rational Inequality

Performing Partial Fraction Decomposition

Ex: Setting Up Partial Fraction Decomposition
Ex 1: Partial Fraction Decomposition (Linear Factors)
Ex 2: Partial Fraction Decomposition (Linear Factors)
Ex 3: Partial Fraction Decomposition (Repeated Linear Factors)
Ex 4: Partial Fraction Decomposition (Repeated Linear Factors)
Ex 5: Partial Fraction Decomposition (Linear and Quadratic Factors)
Ex 6: Partial Fraction Decomposition (Repeating Quadratic Factors)
Ex: Partial Fraction Decomposition - Degree 2 / Degree 3

Exponential and Logarithmic Expressions, Equations, and Functions

Determining Composite Functions and Composite Function Values

Composite Functions
Ex: Evaluate Functions and Composite Function in Context of a Story (Graphing Calculator)
Ex: Intro Composite Function Notation Application Problem
Ex: Evaluate Composite Functions Using Tables of Values
Ex: Evaluate Composite Functions from Graphs
Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule
Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule
Determine f(g(x)) and g(f(x)) with Linear and Quadratic Functions
Determine f(f(x)) and g(g(x)) with Linear and Quadratic Functions
Determine Composite Functions (Linear and Quadratic)
Determine Composite Function Values (Linear and Quadratic)
Determine all Four Composite Functions of Two Linear Functions
Ex: Find and Evaluate a Composition of Three Functions
Ex: Decompose Functions
Ex 1: Composite Function Values
Ex 2: Composite Function Values
Ex 1: Composition of Functions
Ex 1: Find Composite Function Values
Ex 2: Find Composite Function Values With Fractions
Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule
Ex 2: Determine Composite Function Values Using Table, Graph, and Function Rule
Composite Function Values on the TI-84
Ex 1: Domain of a Composite Function
Ex 2: Domain of a Composite Function
Ex 3: Domain of a Composite Function
Ex 4: Domain of a Composite Function
Composition of Two Function and the Domain
Composition of Three Function and the Domain
Ex: Find a Composition of Functions Involving Rational Functions
Ex: Domain of a Quotient and Composite Functions
Ex: Domain of Composite Function From Graphs
Ex: Inverse Function Notation and Reciprocal of a Function

Determining Inverse Functions

Inverse Functions
Determine if Two Linear Functions Are Inverses (1)
Determine if Two Linear Functions Are Inverses (2)
Determine if a Relation Given as a Table is a One-to-One Function
Determine if Sets of Ordered Pairs Represent One-to-One Function
Ex 1: Determine if the Graph of a Relation is a One-to-One Function
Ex 2: Determine if the Graph of a Relation is a One-to-One Function
Determine if Two Linear Functions Are Inverses Using Composition of Functions
Ex 1: Determine if Two Functions Are Inverses
Ex 2: Determine if Two Functions Are Inverses Ex: Find an Inverse Function From a Table
Ex: Function and Inverse Function Values Using a Table
Ex: Function and Inverse Function Values Using a Graph
Graph the Inverse Function Given the Graph of a Linear Function
Graph the Inverse Function Given the Graph of a Cubic Function
Graph the Inverse Function Given the Graph of a Exponential Function
Ex: Restrict the Domain to Make a Function 1 to 1, Then Find the Inverse
Ex: Find Inverse Function Values Without Finding the Inverse Function
Ex: Function and Inverse Function Values
Ex: Find the Inverse of a Square Root Function with Domain and Range
Ex: Find the Inverse of a Rational Function
Ex: Find the Inverse of a Rational Function and an Inverse Function Value
Determine the Inverse Function of a Rational Function: f(x)=a/(x+b)+c
Ex 1: Determine If Two Functions Are Inverses
Ex 2: Determine If Two Functions Are Inverses
Determine the Inverse Function of a Square Root Function and State the Domain and Range
Determine the Inverse Function of a Quadratic Function with Domain Restriction and State the Domain and Range
Determine the Inverse Function of a Cube Root Function and State the Domain and Range
Ex 1: Find the Inverse of a Function
Ex 2: Find the Inverse of a Function
Ex: Find the Inverse Function of an Exponential Function

Using the Definition of a Logarithm

Introduction to Logarithms
Ex: Write Exponential Equations as Logarithmic Equations
Ex: Write Logarithmic Equations as Exponential Equations
Ex: Write Exponential Equations as Logarithmic Equations - Variables
Ex: Write Logarithmic Equations As Exponential Equations - Variables
Ex: Write Exponential Equations with base 10 as Common Logarithmic Equations
Ex: Write Exponential Equations as Logarithmic Equations - Natural Logarithms
Use the Definition of a Logarithm to Show the Zero Exponent and Identity Property
Ex 1: Evaluate Logarithms Without a Calculator - Whole Numbers
Ex: Evaluate Logarithmic Expressions without a Calculator - Different Bases
Ex: Evaluate Logarithmic Expressions without a Calculator - Common Log
Ex: Solve a Basic Exponential Equation with Base Ten Using Logarithm Definition
Ex: Solve a Exponential Equation with Base Ten Using Logarithm Definition (Multiple Steps)
Ex: Solve a Basic Exponential Equation with Base e Using Logarithm Definition
Ex: Solve a Exponential Equation with Base e Using Logarithm Definition (Multiple Steps)
Ex 2: Evaluate Logarithms Without a Calculator - Fractions
Ex: Evaluate Common Logarithms on a Calculator
Ex: Evaluate Common Logarithms Without a Calculator
Ex: Evaluate Common Logarithms on the Calculator
Ex: Evaluate Natural Logarithms on the Calculator
Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form)
Ex: Determine the Value of a Number on a Logarithmic Scale (Exponential Form)
Ex: Plot Numbers on a Logarithmic Scale
Ex: Determine the Difference in Order of Magnitude to Two Quantities
Ex: Determine the Difference in Order of Magnitude to Two Quantities (Application)

Graphing Logarithmic Functions

Using the Properties Logarithms

Evaluating Logarithmic Expressions

Ex 1: Evaluate a Logarithmic Expression Using the Properties of Logarithms
Ex 2: Evaluate a Logarithmic Expression Using the Properties of Logarithms
Simplify Logarithmic Expression by Converting to Exponential Equations with a Common Base
Solve an Exponential Equation with Log Exponents with the Same Bases: Logarithm Property
Solve Basic Log Equations by Writing Equivalent Exponential Equations to Then Discover Log Properties
Ex: Simplify Log Expression with the Base and Base of the Number are the Same
Simplify Exponential Expressions with Logarithmic Exponents Using Log Properties
Simplify Exponential and Logarithmic Expressions Using Log Properties
Simplify Expressions with Logarithmic Exponents Using Logarithmic Properties
Ex: Evaluate Exponential Expressions with Logarithmic Exponents
Logarithm Review
Logarithms: Change of Base Formula
Use the Change of Base Formual to Evaluate Logarithms.
Ex: Change of Base Formula to Evaluate Logarithmic Expressions
Ex: Change of Base Formula to Solve Basic Exponential Equations
Ex: Evaluate Logarithmic Functions Using the Change of Base Formula
Evaluate Logarithms of any Base on the TI-84 (Not using Change of Base)

Solving Logarithmic Equations

Solving Applications Using Logarithmic Equations

Logarithm Application: Magnitude of an Earthquake
How to Compare the Intensity of Two Earthquakes
Logarithm Application: Intensity of Two Sounds (Decibels)
Determine the Decibels of a Sound Given the Intensity (No Calculator)
Determine the Magnitude of an Earthquake Given the Intensity (Using a Calculator)
Ex: Logarithmic Function Application - Test Scores
Ex: Logarithm Application - pH
Ex: Exponential Function Application with Logarithms
Ex: Logarithmic Function Application - pH (Outputs and Inputs)
Ex: Logarithmic Function Application - Preston Curve (Outputs and Inputs)
Logistic Function Application: A Fish Population

Solving Exponential Equations Without Logarithms

Solving Exponential Equations With Logarithms

Solving Applications of Exponential Growth and Decay

Solving Applications Using Exponential Equations / Compounded and Continuous Interest / Exponential Regression

Compounded Interest
Continuous Interest Formula
Determine the Total Return of an Investment as Percent
Ex 1: Compounded Interest – Quarterly
Compounded Interest: Solve for Principal (Present Value)
Ex 2: Compounded Interest with Logarithms
Ex: Find Exponential Growth Rate and Make Prediction of a Future Home Value
Continuous Interest Formula - Derivation
Effective Yield for Compounded Interest
Compounded Interest (Slightly Different Form of Equation): Find Future Value
Effective Yield for Continuous Interest
Effective Interest Rate (Effective Yield)
Ex 1: Continuous Interest
Ex 2: Continuous Interest with Logarithms
Ex 3: Continuous Interest with Logarithms and Doubling Time
Continuous Interest - Find the Initial Investment Needed
Ex: Perform Exponential Regression on a Graphing Calculator
Perform Exponential Regression and Make Predictions Using Desmos
Using Desmos in Log Mode to Perform Exponential Regression (Decay)
Ex: Exponential Regression Application on the TI84 (Decreasing Polio Case)
Ex: Exponential Decay Regression Model (Declining Population)
Ex: Exponential Growth Regression Model (Investment Account)
Ex: Comparing Linear and Exponential Regression
Ex: Find an Exponential Function for a Semi-Log Graph
Ex: Newton's Law of Cooling - Exponential Function App
Newton's Law of Cooling Application: A Cup of Soup is Cooling
Exponential Function App. With Logs (y=ae^(kt))- Radioactive Dye
Ex: Compounded Interest with Different Compounding

Using the Properties of Hyperbolic Functions

Introduction to Hyperbolic Functions
Prove a Property of Hyperbolic Functions: (sinh(x))^2 - (cosh(x))^2 = 1
Prove a Property of Hyperbolic Functions: (tanh(x))^2 + (sech(x))^2 = 1
Prove a Property of Hyperbolic Functions: sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y)
Prove a Property of Hyperbolic Functions: (sinh(x))^2=(-1+cosh(2x))/2

Function Transformations
Determining Transformations of Functions

Graphing and Finding Equations of Transformed Absolute Value Functions

Graphing and Finding Equations of Transformed Square Root Functions

Graphing and Finding Equations of Transformed Quadratic and Exponential Functions

Sequences and Series
Sequences

Series

Arithmetic Series
Sequences on the TI84 Graphing Calculator
Geometric Series
Determine the Partial Sum of an Arithmetic Series Given in Sigma Notation
Determine the Partial Sum of an Geometric Series Given in Sigma Notation
Geometric Series: Find Partial Sum and Term Need Given an Allowable Error
Determine the Sum of an Arithemetic Sequence (Series) Given using Sigma (Summation) Notation
Write a Sum Using Sigma (Summation) Notation Using Pattern Recognition
Use Summation Properties and Formulas to Evaluate Sigma Notation: Form: sum(i)
Use Summation Properties and Formulas to Evaluate Sigma Notation: Form: sum(i^2)
Use Summation Properties and Formulas to Evaluate Sigma Notation: Form: sum(i^3)
Find a Partial Sum Using Summation Formula: Sum (Constant), Sum(4i)
Find a Partial Sum Using Summation Formula: Sum(2i^2), Sum(4i^3)
Use Summation Properties and Formulas to Evaluate Sigma Notation: Sum(25a+19b)
Use Summation Properties and Formulas to Evaluate Sigma Notation: Sum(-3k^2+5k+7)
Use Summation Properties and Formulas to Evaluate Sigma Notation: Sum(9(i^2-4i+2))
Find a Partial Sum Using Summation Formula Sum(5i^3-2i)
Find a Partial Sum Using Summation Formula: Sum((2-3i)^2)
Ex 1: Find a Sum Written in Summation / Sigma Notation
Ex 2: Find a Sum Written in Summation / Sigma Notation
Ex: Write a Sum Using Summation / Sigma Notation
Ex 1: Find the Partial Sum of an Arithmetic Series
Ex 2: Find the Sum of an Arithmetic Series
Sum of Arithmetic Sequence Given 4th and 12th Term
Ex 1: Find the Partial Sum of an Geometric Series
Ex 2: Find the Sum of an Geometric Series
Introduction to Sigma Notation
Ex: Sigma Notation - Summation Involving a Quadratic
Ex: Sigma Notation - Summation Involving Sine
Sequences and Series on the TI84
Write a Given Finite Arithmetic Series Using Sigma (Summation) Notation (d>0)
Write a Given Finite Arithmetic Series Using Sigma (Summation) Notation (d<0)
Write a Given Finite Geometric Series Using Sigma (Summation) Notation
Evaluate Sigma Notation Using Formulas (Constant and i)
Evaluate Sigma Notation Using Formulas (i squared and I cubed)

Infinite Series

Infinite Geometric Series
Ex 1: Find the Sum of an Infinite Geometric Series
Ex 2: Find the Sum of an Infinite Geometric Series
Write a Repeating Decimal as a Geometric Series and Write as a Simplified Fraction (Ex 1)
Write a Repeating Decimal as a Geometric Series and Write as a Simplified Fraction (Ex 2)
Ex: Arithmetic Series Application - Number of Auditorium Seats
Ex: Geometric Series Application - Total Income with Doubling Pay

Mathematical Induction

Using the Binomial Theorem / Combinations

Ex 1 :Simplify Expressions with Factorials
Ex 2: Simplify Expressions with Factorials Containing Variables
Zero Factorial: Why is 0! = 1?
Ex: Evaluate Combinations
Evaluate Combinations by Hand (No Calculator)
Ex 1: The Binomial Theorem Using Combinations
Ex 2: The Binomial Theorem Using Combinations
Ex 3: The Binomial Theorem Using Combinations
Ex: Find a Single Term in a Binomial Expansion
Ex 1: The Binomial Theorem Using Pascal's Triangle
Ex 2: The Binomial Theorem Using Pascal's Triangle
Ex 3: The Binomial Theorem Using Pascal's Triangle
The Binomial Theorem Using Pascal’s Triangle

Using Augmented Matrices

Determining Inverse Matrices

The Identity Matrix
2 x 2 Inverse Matrix Formula
Inverse Matrices Using Augmented Matrices
Inverse Matrices on the Graphing Calculator
Ex: Find the Inverse of a 2x2 Matrix Using a Formula
Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix
Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix
Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix

Using The Matrix Equation

Ex: Write a System of Equations as a Matrix Equation (3x3)
Ex 1: Solve the Matrix Equation AX=B (2x2)
Ex 2: Solve the Matrix Equation AX=B (2x2)
Ex: Solve the Matrix Equation AX=B (3x3)
Matrix Equations
Ex 1: Solve a System of Two Equations Using a Matrix Equation
Ex 2: Solve a System of Two Equations Using a Matrix Equation
Ex: Solve a System of Three Equations Using a Matrix Equation
LU Decomposition Using Elementary Matrices
LU Decomposition - Shortcut
Solve a System of Linear Equations Using LU Decomposition
Perform Linear Regression Using Matrices
Solve a 3x3 System Using a Matrix Equation (Desmos Matrix Calc)
Solve a 2x2 System Using a Matrix Equation (Desmos Matrix Calc)

Finding and Using Determinants

Determinants
Determinants
Ex: Determinant of a 2x2 Matrix
Ex: Solve an Equation Involving a Determinant
Determinants of Triangular Matrices
Ex 1: Determinant of 3x3 Matrix - Diagonal Method
Ex 2: Determinant of 3x3 Matrix - Diagonal Method
Find the Minors and Cofactors of a 2 by 2 Matrix
Find the Minors and Cofactors of a 3 by 3 Matrix
Find the Cofactor Matrix and Adjoint Matrix (2 by 2)
Find the Cofactor Matrix and Adjoint Matrix (3 by 3)
Ex 1: Determinant of 3x3 Matrix - Cofactor Method
Ex 2: Determinant of 3x3 Matrix - Cofactor Method
Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 2
Ex: Find a 3x3 Determinant using Cofactor Expansion on Row 3
Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)
The Determinant of a 4 by 4 Matrix Using Cofactor Expansion (Expansion by Minors)
Determinants on the Graphing Calculator
Cramer’s Rule
Solve a System of Two Equations with Two Unknowns Using Cramer's Rule
Ex: Solve a System of Two Equations Using Cramer's Rule
Ex: Solve a System of Three Equations Using Cramer's Rule
Application of Cramer's Rule for a 2 by 2: Mixed Paint
Application of Cramer's Rule for a 2 by 2: Types of Cards
Solve a System of Linear Equations Using Cramer's Rule (4 by 4)
Area Using Determinants
Ex: Find the Area of a Triangle on the Coordinate Plane Using a Determinant
Ex: Determine if a 2x2 Matrix is Invertible (nonsingular) Using a Determinant
Ex: Determine if a 3x3 Matrix is Invertible (nonsingular) Using a Determinant
Ex: Determine a Value in a 2x2 Matrix To Make the Matrix Singular
Ex: Determine a Value in a 3x3 Matrix To Make the Matrix Singular
Properties of Determinants 1
Properties of Determinants 2
Desmos Matrix Calc: The Determinant of a Matrix

Linear Programming

Introduction to Linear Programming
Ex: Find the Maximum and Minimum of an Objective Function Given the Feasible Region Using Linear Programming
Ex: Find the Minimum of an Objective Function Given Constraints Using Linear Programming (unbounded)
Ex: Find the Maximum of an Objective Function Given Constraints Using Linear Programming (bounded)
Ex: Use Linear Programming to Maximize Profit from Two Crops
Ex: Use Linear Programming to Maximize Income from Two Desserts
Ex: Use Linear Programming to Maximize Profit from Two DVD Players
Linear Programming: Max Profit from Tubing Production (Desmos Graph)

The Simplex Method

Perform Matrix Row Operations Using the TI84 Matrix Menu
Perform Matrix Row Operations Using the TI84 Home Screen
Introduction to the Simplex Method: Standard Maximization (2 variables)
Using Simplex Method an a Standard Maximization Problem (3 variables)
Ex: Simplex Method - Set Up Initial Tableau From a Word Problem (Standard Max)
Ex: Simplex Method - Set Up Initial Tableau Given Objective Function and Constraints (Standard Max)
Ex: Simplex Method - Interpret the Final Tableau
Ex: Simplex Method - Given a Tableau, Determine the Pivot Column and Pivot Row
Ex: Simplex Method - Determine the Active Variables and the Basic Solution
Ex: Simplex Method - Perform the Pivot Operation Given a Tableau
Solving a Standard Minimization Problem Using The Simplex Method (Duality)
Ex 1: Determine a Dual Problem Given a Standard Minimization Problem
Ex 2: Determine a Dual Problem Given a Standard Minimization Problem
Ex 1: Interpret the Final Tableau of a Dual Problem
Ex 2: Interpret the Final Tableau of a Dual Problem

Counting and Probability
Counting Principle

The Counting Principle
Ex: Determine the Number of Possible Outfits - Counting Principle
Ex: Determine the Number of Three Letter Codes - Counting Principle
Ex: Determine the Outcomes Rolling Colored Dice - Counting Principle
Ex: Determine the Number of Possible License Plates - Counting Principle
Ex: Determine the Number of Ways to Complete a True/False Test - Counting Principle

Permutations and Combinations

Permutations
Ex: Evaluate a Combination and a Permutation - (n,r)
Ex: Evaluate a Combination and a Permutation - (n,1)
Ex: Determine the Number of Ways Six Runners Can Finish - Counting/Permutation
Ex: Determine the Possible Number of 4 Color Striped Flags (Permutation)
Ex: Determine the Possible Number of of Ways 255 Contestants can Win 3 Prizes (Permutation)
Ex1: Determine the Number of Permutations With Repeated Items
Ex2: Determine the Number of Permutations With Repeated Items
Combinations
Ex: Determine the Number of Ways 6 Books can be Selected from 9 Books (Combination)
Ex: Determine the Number of Ways 3 Varieties can be Selected from 12 (Combination)
Ex: Determine the Number of 4 Topping Pizzas from 14 Toppings (Combination)
Ex: Determine the Number of 4 Card Hands from 52 Cards
Solving Counting Problems

Probability

The Binomial Theorem

The Binomial Theorem using Combinations
Ex 1: The Binomial Theorem Using Combinations
Ex 2: The Binomial Theorem Using Combinations
Ex 3: The Binomial Theorem Using Combinations

Conic Sections

Introduction to Conic Section

Introduction to Conic Sections

Graphing and Writing Equations of Circles

Conic Sections: The Circle
Ex: Write the Standard Form of a Circle From a Graph
Determine the Standard Equation of a Circle from a Graph (Whole Number Radius)
Determine the Standard Equation of a Circle from a Graph (Center at the Origin, Irrational Radius)
Determine the Standard Equation of a Circle from a Graph (Center NOT the Origin, Irrational Radius)
Find the Center and Radius of a Circle Given the Equation in Standard Form
Graph a Circle on the X-axis or Y-axis Given the Equation in Standard Form
Ex: Graph a Circle in Standard Form
Graph a Circle: Write the Equation in Standard form x^2+y^2-10y+16=0
Graph a Circle: Write the Equation in Standard form x^2-2x+y^2+4y+4=0
Graph a Circle: Write the Equation in Standard form 2x^2+2y^2+16x-12y+18=0
Ex 1: Write the General Equation of a Circle in Standard Form
Ex 2: Write the General Equation of a Circle in Standard Form (Fractions)
Ex 3: Write General Equation of a Circle in Standard Form (Coefficent Not 1)
Ex 4: Write General Equation of a Circle in Standard Form (Coefficent Not 1 and Fractions)
Ex: Find Standard Equation of a Circle Given Center and Point on the Circle
Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Ex 2: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Ex : Find the Intercepts of a Circle
Ex: Intersection of a Line and a Circle - Applications
Ex: Find a Point on the Unit Circle Given One Coordinate
Ex 1: Find a Point of Intersection of a Line and a Circle
Ex 2: Find a Point of Intersection of a Line and a Circle

Graphing and Writing Equations of Ellipses

Graphing and Writing Equations of Parabolas

Conic Sections: The Parabola part 1 of 2
Conic Sections: The Parabola part 2 of 2

Graphing and Writing Equations of Hyperbolas

Conic Sections: The Hyperbola part 1 of 2
Conic Sections: The Hyperbola part 2 of 2
Match Equations of Hyperbolas to Graphs
Match Equations of Hyperbolas to Graphs
Graphing Hyperbolas Given the Equation in Standard Form
Convert the Equation of a Hyperbola from General Form to Standard Form - Horizontal
Convert the Equation of a Hyperbola from General Form to Standard Form - Vertical
Write the General Form of a Hyperbola in Standard Form and Graph (Origin Center)
Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal)
Ex 2: Conic Section - Graph a Hyperbola with Center at the Origin (Vertical)
Ex 3: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Horizontal)
Ex 4: Conic Section - Graph a Hyperbola with Center NOT at the Origin (Vertical)
Ex: Find the Equation of a Hyperbola Given the Center, Focus, and Vertex
Determining the Type of Conic Section from General Form

Set Theory

Sets and Venn Diagrams In Class Exercises
Introduction to Set Theory
Finite and Infinite Sets
Introduction to Subsets
Sets: Elements Of and Subsets
Determining Subsets Using a Venn Diagram
Determine the Cardinality of Sets From a List of Set
Set Operations and Venn Diagrams - Part 1 of 2
Set Operations and Venn Diagrams - Part 2 of 2
Solving Problems Using Venn Diagrams
Ex: Find the Union and Intersection of Two Sets Using a Venn Diagram
Ex: Find the Union and Intersection of Two Sets Without a Venn Diagram
Ex: Find the Intersection of a Set and A Complement Using a Venn Diagram
Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (long)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (long)
Ex: Determine Cardinality of the Intersection of Two Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Two Sets Without Using Venn Diagram
Ex: Determine Cardinality of Various Sets Given a Venn Diagram of Three Sets
Ex: Determine Cardinality of the Intersection of Three Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Three Sets Without Using Venn Diagram
Problem Solving with Venn Diagrams: Cardinality of a Universal Set
Use a Venn Diagram to Determine the Cardinality of a Set: n(not C and not D)
Ex: Find the Number of Element in the Intersection of Two Sets Using a Venn Diagram
Ex: Set Problem Solving - Find the Number of Element in the Intersection of Two Sets Using a Formula
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex 2: Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 2: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex: Determine How Many Elements in a Set With a Venn Diagram (Movies)
Ex: Determine How Many Elements in a Set Without a Venn Diagram (Movies)
Ex 1: Problem Solving With Venn Diagrams (Cardinality of Intersection)
Ex 2: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)
Ex 3: Problem Solving With Venn Diagrams (Cardinality of Complement of (A Union B)
Ex 4: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)
Determine the Number Elements in a Set From a Venn Diagram
Use a Venn diagram to Determine Cardinality of Sets (Level 1)
Use a Venn diagram to Determine Cardinality of Sets (Level 2)
Find Complement, Union, and Intersection of 2 Sets as Lists
Find the Intersections and Union of Three Sets as Lists
Venn Diagrams and Percentages: Survey Results Social Media
Venn Diagrams and Cardinality: Tea or Coffee Survey Results
Determine Cardinality of Sets Using a Venn Diagram
Determine Cardinality of Sets Using a Completed Venn Diagram: 3 Subjects
Determine Cardinality of Sets Using a Completed Venn Diagram: Vehicles
Determine the Cardinality of an Intersection of Two Sets
Complete a Venn Diagram With Cardinality: Math, English, History
Complete a Venn Diagram With Cardinality: Brand, Color, Size
Complete a Venn Diagram From Survey: Coffee and Tea
Determine the Cardinality of an Universal Set Using a Venn Diagram
Determine the Cardinality of a Set Given Cardinality of Union and Intersection

Regression

Introduction to Regression Analysis
Linear Regression – Example 1, Example 2
Quadratic Regression – Example 1, Example 2
Perform Quadratic Regression and Make Predictions Using Desmos
Interpret a Quadratic Function Model: Fuel Consumption
Ex 1: Cubic Regression on the TI84 – Natural Gas Consumption
Ex 2: Cubic Regression on the TI84 - Total Sales
Exponential Regression – Example 1, Example 2
Ex: Exponential Decay Regression Model (Declining Population)
Ex: Exponential Growth Regression Model (Investment Account)
Logarithmic Regression
Logistic Regression

Financial Mathematics (See more under Math for Liberal Arts library)

Simple Interest Formula
Compounded and Continuous Interest
Effective Yield
Effective Yield on the TI84
Derive the Value of an Annuity Formula (Compounded Interest)
Determining the Value of an Annuity
Determining the Value of an Annuity Using the TI84
Determining the Monthly Saving Required to Reach a Financial Goal
Determining the Monthly Saving Required to Reach a Financial Goal on the TI84
Ex 1: Find a Monthly Mortgage Payment with a Down Payment
Ex 2: Find a Monthly Mortgage Payment with a Down Payment and Points
Ex: Comparing Two Installments Loans (Car Loans)
Ex: Simple Interest Discounted Loan
Determining the Monthly Payments for a Loan
Determining the Monthly Payments for a Loan on the TI84

Graphing Calculator
Basics: Evaluating Expressions and Determining Function Values

Graphing Calculator Basics
The Table Feature of the Graphing Calculator
Evaluating Radical Expressions on the TI83/84
Determine Function Values Using Function Notation on the TI84

Graphing Functions and Determining Key Components of Functions

Graphing Lines on the Graphing Calculator
Determining the Intersection of Two Graph on the TI83/84
Determining Relative Extrema on the Graphing Calculator
Determine Function Values Using Function Notation on the TI84
Determine the value of the derivative function on the graphing calculator
Determining the value of a definite integral on the graphing calculator
Determining the Intersection of Two Graph on the TI83/84
Determining the Zeros or Roots of a Polynomial Function on the TI83/84
From a Graph Determine Where a Quadratic Function is Increasing and Decreasing
Determining When a Polynomial Function is Increasing and Decreasing
Determine Max/Mins and Incr/Decr Intervals Using a Free Online Graph Calc (MathAS)
Determining the Zeros or Roots of a Polynomial Function on the TI83/84
Ex: Quadratic Function Application Using a Graphing Calculator - Rocket Launch
Ex 1: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2: The Zero Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 1: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial
Ex 2: The Intersection Feature of the TI84 to Find Rational Zeros of a Polynomial

Solving Equations on the Graphing Calculator

Solving Linear Equations Graphically
Ex: Solve a Linear Equation in One Variable Graphically using the TI84
Ex: Solve a Linear Inequality in One Variable Graphically using the TI84
Ex: Solving Absolute Value Equations on the Graphing Calculator
Ex 1: Solve a Quadratic Equation Graphically on Calculator
Ex 2: Solve a Quadratic Equation Graphically on Calculator
Ex: Determine How a Final Exam Score Affect a Course Grade using the TI84 (Weighted Averages)
Solving Polynomial Equations Graphically

Logarithms on the Graphing Calculator

Ex: Evaluate Common Logarithms on a Calculator
Ex: Evaluate Common Logarithms on the Calculator
Ex: Evaluate Natural Logarithms on the Calculator
Ex: Change of Base Formula to Evaluate Logarithmic Expressions
Ex: Change of Base Formula to Solve Basic Exponential Equations
Ex: Evaluate Logarithmic Functions Using the Change of Base Formula
Ex: Solve an Exponential Equation Graphically on the TI84
Ex: Perform Exponential Regression on a Graphing Calculator
Ex: Comparing Linear and Exponential Regression
Sequences and Series on the TI84
Sequences and Series on the TI84

Matrices on the Graphing Calculator

Augmented Matrices on the Graphing Calculator
Matrix Multiplication on the Graphing Calculator
Inverse Matrices on the Graphing Calculator
Ex 1: Solve a System of Two Equations Using a Matrix Equation
Ex 2: Solve a System of Two Equations Using a Matrix Equation
Ex: Solve a System of Three Equations Using a Matrix Equation
Determinants on the Graphing Calculator
Ex: Solve a System of Three Equations Using Cramer's Rule

Regression on the Graphing Calculator

Ex 1: Create a Scatter Plot and then Perform Linear Regression on the Calculator
Ex 2: Creating a Scatter Plot and Performing Linear Regression on the Calculator
Linear Regression – Example 1, Example 2
Ex: Matching Correlation Coefficients to Scatter Plots
Quadratic Regression – Example 1, Example 2
Perform Quadratic Regression and Make Predictions Using Desmos
Ex: Quadratic Regression on the TI84 - Stopping Distance
Exponential Regression – Example 1, Example 2
Perform Exponential Regression and Make Predictions Using Desmos
Logarithmic Regression
Logistic Regression
Regression and Systems of Equations: Application

Financial Mathematics on the Graphing Calculator

Loan Information on the TI83/84
Effective Yield on the TI84
Determining the Value of an Annuity Using the TI84
Determining the Monthly Payments for a Loan on the TI84
Determining the Monthly Saving Required to Reach a Financial Goal on the TI84

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