College Algebra

Absolute Value Equations

1. Solving an Absolute Value Equation (Where  the Variable is Outside The Absolute Value Sign)
2. Solving an Absolute Value Equation (Already Isolated)
3. Solving an Absolute Value Equation (Isolate First)
4. Solving an Absolute Value Equation (With No Solution)
5. Solving an Absolute Value Equation (Involving a Quadratic Polynomial)

Binomial Theorem

1. The Binomial Theorem Part 1
2. The Binomial Theorem Part 2

Cartesian Coordinate System (xy-plane)

1. Finding the Distance Between Two Points
2. Finding The Midpoint
3. Finding the Quadrant That a Midpoint Lies

Circles

1. Completing the Square
2. Writing the Equation of a Circle With Radius 2 and Center (4, 0)
3. Finding the Equation of a Circle
4. Find the Center of the Circle 2x^2 +2y^2 −4x+4y = 0
5. Find the Center and Radius of the Circle  x^2 +y^2 +6x−10y−2=0
6. Find the Center and Radius of the Circle x^2 +y^2 +10x−14y−7=0

Domain of a Function

1. Finding the Domain of a Rational Function
2. Finding the Domain of a Rational Function (Involving Factoring and Canceling) Part 1
3. Finding the Domain of a Function Involving a Square Root
4. Find the Domain of Function Involving a Square Root and a Fraction
5. Finding the Domain of a Sum of Function (Polynomial Plus Square Root) Part 1
6. Finding the Domain of a Sum of Function (Polynomial Plus Square Root) Part 2
7. Finding the Domain of a Logarithmic Function (Involves Factoring and an Inequality) Part 1
8. Finding the Domain of a Logarithmic Function (Involves Factoring and an Inequality) Part 2

Exponent and Radical Properties

1. Simplifying Exponents (Adding)
2. Simplifying Exponents (Adding and Negative Exponents)
3. Simplifying Exponents (Multiplying and Subtracting)
4. Exponent Properties (Distributing, Multiplying, and Adding)
5. Simplifying a Radical Expressions and Combing Like Terms

Exponential Functions and Equations

1. Properties of The Exponential Function
2. Solving an Exponential Equation With Base e
3. Solving an Exponential Equation Where The Bases Are The Same
4. Solving an Exponential Equation With Different Bases (Part 1)
5. Solving an Exponential Equation With Different Bases (Part 2)
6. Compound Interest Example: Inflation

Factoring

1. Factor by Grouping
2. Factoring a Difference of Squares
3. Factoring a Difference of Cubes
4. Factoring Polynomials Sum and Difference of Cubes – Beamer Style
5. Factoring a Difference of Cubes (Involving a Polynomial)
6. Factoring a Sum of Cubes (Involving a Monomial)
7. Factoring a Sum of Cubes (Involving a Polynomial)
8. Factoring a Polynomial of Degree 4 (Includes a Difference of Squares Twice)
9. Factoring a Degree 4 Polynomial (Using Substitution)
10. Factoring a Polynomial of Degree 8 (Includes Sum of Cube Formula)

Functions

1. Multiplication of Functions
2. Evaluation a Function on a Monomial
3. Evaluation a Function on x+h
4. Composition of Functions on a Real Number
5. Find the Input (Domain Element) Given The Output (Range Element)

Graphs

1. What it Means to Be a Point on The Graph of a Function
2. Using the Graph to Find The x Value(s) Given a y Value of Zero
3. Using The Graph to Find The x Value(s) Given a y Value
4. Finding The x Value(s) That Make The Function Positive
5. Determining When a Function Is Increasing Using The Graph of The Function
6. Where a Local Maximum Occurs (of a Continuous Function)
7. Finding the Local Maximum (of a Continuous Function)
8. Determining If a Graph is the Graph of a Function (If So Find Domain, Range, and Symmetry)

Inequality Problems

1. Solving an Inequality (with a Linear Polynomial)
2. Solving a Linear Inequality that Looks Quadratic (and FOIL)
3. Solving a Linear Inequality That Looks Quadratic (and Difference of Squares)
4. Solving Two Inequalities Simultaneously
5. Solving Two Inequalities Simultaneously (and Multiplying By a Negative)
6. Solving an Inequality (With a Difference of Squares)
7. Solving an Inequality (Involving a Difference of Squares) Part 1
8. Solving an Inequality (Involving a Difference of Squares) Part 2
9. Solving an Inequality (with a Difference of Squares Opposite Order) Part 1
10. Solving an Inequality (with a Difference of Squares Opposite Order) Part 2
11. Solving an Inequality (with a Degree 2 Polynomial) Part 1
12. Solving an Inequality (with a Degree 2 Polynomial) Part 2
13. Solving an Inequality with a degree 3 polynomial (Part 1)
14. Solving an Inequality with a degree 3 polynomial (Part 2)
15. Solving an Inequality (with a degree 3 polynomial and a repeated root)

Linear Equations

1. Solving a Linear Equation Involving Fractions
2. Solving an equation involving fractions with no solution (Part 1)
3. Solving an equation involving fractions with no solution (Part 2)
4. Solving a Linear Equation that looks Quadratic

Lines

1. Determine The Slope of a Line From a Diagram
2. Determine the Equation of a Line From a Diagram
3. Finding the Slope and y Intercept of a Vertical Line
4. Finding the Slope and y Intercept of a Line
5. Equation of a Line Given a Point and the Slope
6. Equation of a Line Given the x and y Intercept
7. Equation of a Line Which is Parallel to a Given Line Though a Given Point (Quadrant IV)
8. Equation of a Line Which is Parallel to a Given Line Though a Given Point (Quadrant I)
9. Equation of a Line Which is Perpendicular to a Given Line Through a Given Point (Part 1)
10. Equation of a Line Which is Perpendicular to a Given Line Through a Given Point (Part 2)

Logarithmic Problems

1. Using The Definition of Log to Convert From Exponential Form to Logarithmic Form
2. Inverses: Logarithm and Exponential
3. Logarithm: Change of Base Formula
4. Writing as a Sum and/or Difference of Logarithms (Division Inside Log)
5. Write as a Single Log (Coefficients, Addition, and Subtraction)
6. Write as a Single Log (Don’t Forget to Cancel)
7. Solving a Logarithmic Equation (Inverse Property)
8. Solving a Logarithmic Equation (Definition of Log and a Linear Equation)
9. Solving a Logarithmic Equation (Using The Definition of Log and Factoring a Quadratic) Part 1
10. Solving a Logarithmic Equation (Using The Definition of Log and Factoring a Quadratic) Part 2
11. Solving a Logarithmic Equation (Definition of Log, a Quadratic, and Extraneous Solutions) Part 1
12. Solving a Logarithmic Equation (Definition of Log, a Quadratic, and Extraneous Solutions) Part 2
13. Uninhibited Growth: Solving For Time (In The Exponent)
14. Uninhibited Growth (Finding Growth Constant and Using General Formula)

Multiply Variable Equations

1. Solving a Forumla (Involving Two variables)
2. Solving a Forumla (Involving Three Variables)

One-to-One Functions

1. Horizontal Line Test to Determine If a Function is One-To-One
2. Finding the Inverse of a One-to-One Function

Piecewise Functions

1. Evaluation of a Piecewise Function
2. Evaluation of a Piecewise Function and Adding
3. Finding The x and y Intercept(s) of a Piecewise Function by Graphing

Quadratic Equation

1. The Discriminant Gives The Number of Real Solutions
2. Solving a Quadratic Equation by Factoring
3. Finding the Largest Solution of a Quadratic Equation by Factoring
4. Finding the Smallest Solution of a Quadratic Equation by Factoring
5. Solving an Equation Involving Fractions (and Using the Quadratic Formula)

Quadratic Functions

1. Finding The Vertex of a Parabola (Also Opens Up vs. Opens Down)
2. Finding The Axis of Symmetry For a Parabola (Quadratic Function)
3. Finding The Maximum Value of a Quadratic Function (Parabola)
4. Finding The Minimum Value of a Quadratic Function (Parabola)
5. Determining When a Quadratic Function is Increasing Using The Graph
6. Maximizing a Quadratic Profit Function

Rational Functions

1. Using Long Division to Simplify The Rational Expression (x^2-1) / (x+1)
   

Symmetry

1. Symmetry With Respect to the x-axis
2. Checking For Symmetry of an Equation
3. Determine The Symmetry of The Graph With Equation x + y^2 – 9 = 0
4. Determining if a Function is Even or Odd (Algebraically)

System of Linear Equations

1. Solving a System of Linear Equations Using The Elimination Method
2. Solving a System of Linear Equations With No Solution
3. System of Equations With Infinitely Many Solutions

Transformations

1. Transformation of a Function (Up/Down, Left/Right)
2. Transformation of a Function (Up, Reflected Over the x and y axis)
3. Transformation of a Function (Up, Reflected Over y-axis, and Right)

Variation Problems

1. Direct Variation Problem (General Formula)
2. Direct Variation Word Problem (Pendulum)
3. Direct and Inverse Variation Word Problem (Volume)
4. Direct and Inverse Variation Word Problem (Weight)

Word Problems

1. Word Problem: Working Together to Paint
2. Word Problem: Working Together to Split a cord of Firewood
3. Word Problem: Mixture of Cheeses (Part 1)
4. Word Problem: Mixture of Cheeses (Part 2)
5. Word Problem: Simple Interest (Part 1)
6. Word Problem: Simple Interest (Part 2)
7. Word Problem: System of Equations (Elimination Method)
8. Word Problem: Acid Mixture
9. Word Problem: Distance