Course Resources Math 1630

Chapter 1 – Linear Equations and Functions

1.1 Solution of Linear Equations and Inequalities in One Variable

• Evaluate a formula using substitution
• Algebra: Linear Equations 2 : solving equations of the form AX+B=C
• Equations 2: slightly more complicated equations
• Solving Equations 1
• Two-Step Equations
• Solving Equations 2
• Equations with Variables on Both Sides
• Multi-step equations 2
• Solving Equations with the Distributive Property
• Solving equations with the distributive property 2
• Algebra: Linear Equations 3
• Algebra: Linear Equations 4: Solving linear equations with variable expressions in the denominator
• Equation Special Cases
• Averages: Introduction to averages and algebra problems involving averages.
• Interpreting Inequalities (concept no example)
• One-Step Inequalities
• One-Step Inequalities 2
• Inequalities Using Addition and Subtraction
• Inequalities Using Multiplication and Division
• Inequalities on a number line -- Kahn Academy
• Solving Inequalities
• Writing and using inequalities 2
• Writing and using inequalities 3
• Multi-Step Inequalities
• Multi-Step Inequalities 2
• Inequalities -- word problems
• Applying the Metric System
• Rational Equations
• Solving Rational Equations 2

1.2 Functions

• Functional Relationships 1
• Testing if a relationship is a function
• Domain of a function
• Relations and Functions
• Graphical Relations and Functions
• Domain and Range of a Function
• Domain and Range of a Function Given a Formula
• Domain of a Radical Function
• Evaluating Functions
• Sum of Functions
• Difference of Functions
• Product of Functions
• Quotient of Functions
• A more formal understanding of functions
• Linear Function Graphs

1.3 Linear Functions

• X and Y intercepts
• X and Y intercepts 2
• Slope of a line
• Slope Example
• Slope and Rate of Change
• Graphical Slope of a Line
• Slope of a Line 2
• Slope of a Line 3
• Graphing a line in slope intercept form
• Graphing using X and Y intercepts
• Graphs Using Slope-Intercept Form
• Linear Equations in Slope Intercept Form
• Equation of a line 1
• Equation of a line 2
• Equation of a Line hairier example
• Equation of a line 3
• Converting to slope-intercept form
• Point-slope and standard form
• Parallel Lines
• Parallel Lines 2
• Parallel lines 3
• Perpendicular Lines
• Perpendicular lines 2
• Word Problem Solving 4

1.4 Graphs and Graphing Utilities

• Plotting (x,y) relationships
• Graphs of Linear Equations

1.6 Applications of Linear Functions in Business and Economics

• Interpreting Linear Graphs

 

Chapter 2 – Quadratics and Special Functions

2.1 Quadratic Equations

• Factoring Special Products
• Quadratic Formula 1
• Quadratic Formula 2
• Quadratic Formula 3
• Quadratic Equations in Standard Form
• Simple Quadratic Equation
• Applying the Quadratic Formula
• Solving Rational Equations 3
• Extraneous Solutions to Rational Equations
• Application Problem with Quadratic Formula
• Discriminant for Types of Solutions for a Quadratic
• Discriminant of Quadratic Equations

2.2 Quadratic Functions; Parabolas

• Graphing a Quadratic Function
• Quadratic Functions 2
• Graphing a Quadratic Function

2.5 Modeling: Fitting Curves to Data with Graphing Utilities

• Fitting a Line to Data-- Concept -- not using TI-84

 

Chapter 1- Linear Equations and Functions

1.5 Solutions of Systems of Linear Equations

• Testing a solution for a system of equations
• Solving Linear Systems by Graphing
• Solving systems by graphing 2
• Solving systems by graphing 3
• Consistent and Inconsistent Systems
• Independent and Dependent Systems
• Solving systems by substitution 1
• Solving systems by substitution 2
• Solving systems by substitution 3
• Solving Linear Systems by Substitution
• Solving systems by elimination
• Solving systems by elimination 2
• Solving systems by elimination 3
• Solving Systems of Equations by Elimination
• Solving Systems of Equations by Multiplication
• Mixture problems 2
• Mixture problems 3
• Graphing Systems of Equations
• Graphical Systems Application Problem
• The Substitution Method
• Substitution Method 2
• Substitution Method 3
• Addition Elimination Method 1
• Addition Elimination Method 2
• Addition Elimination Method 3
• Addition Elimination Method 4

 

Chapter 3 – Matrices

3.3 Gauss-Jordan Elimination: Solving Systems of Equations

• Gauss-Jordan Elimination with a 2x2 matrix
  YouTube
• Matrices: Reduced Row Echelon Form 1
• Matrices: Reduced Row Echelon Form 2
• Matrices: Reduced Row Echelon Form 3

3.4 Inverse of a Square Matrix; Matrix Equations

• Inverse Matrix (part 1)
• Inverting matrices (part 2)
• Inverting Matrices (part 3)
• Matrices to solve a system of equations
• Singular Matrices: When and why you can't invert a matrix.

 

Chapter 4 – Inequalities and Linear Programming

4.1 Linear Inequalities in Two Variables

• Graphing Linear Inequalities Part 1
  YouTube
• Solving and graphing linear inequalities in two variables 1
• Graphing Linear Inequalities in Two Variables Example 2
• Graphing Linear Inequalities in Two Variables Example 2
  (same problem as 2, different explanation)
• Graphing linear inequalities in two variables 3
• Graphing Inequalities
• Graphing Inequalities 1
• Graphing Inequalities 2
• Graphing Systems of Inequalities
• Graphing systems of inequalities 2
• Graphical System of Inequalities

4.2 Linear Programming: Graphical Methods

• Linear Programming -- patrickJMT
  YouTube

4.3 The Simplex Method: Maximization

• Simplex Method - Finding a Maximum Word Problem Example, Part 1 of 5 -- patrickJMT
  YouTube
• Simplex Method - Finding a Maximum Word Problem Example, Part 2 of 5 - patrickJMT
  YouTube
• Simplex Method - Finding a Maximum Word Problem Example, Part 3 of 5 -- patrickJMT
  YouTube
  (note about video part 3 – Some of our faculty do ask you to find the pivot elements, but none of our faculty ask you to solve the Simplex by hand at this point you would put it into the calculator and get the final tableau. So only watch until 2:07)
• Simplex Method - Finding a Maximum Word Problem Example, Part 5 of 5 -- patrickJMT
  YouTube

 

Chapter 5 – Exponential and Logarithmic Functions

Review of Exponents: for those that have forgotten your exponents here is a set of videos to watch as a review:

• Negative Exponent Intuition: Intuition on why a^-b = 1/(a^b) (and why a^0 =1)
• Zero, Negative, and Fractional Exponents
• Exponent Rules Part 1 : Introduction to exponent rules
• Exponent Rules Part 2
• Exponent Properties 1
• Exponent Properties 2
• Exponent Properties 3
• Exponent Properties 4
• Exponent Properties Involving Products
• Exponent Properties Involving Quotients
• Rational Exponents and Exponent Laws

5.1 Exponential Functions

• Graphing Exponential Functions

5.2 Logarithmic Functions and Their Properties

• Introduction to Logarithms
• Logarithm of a Power
• Sum of Logarithms with Same Base
• Introduction to logarithm properties
• Introduction to logarithm properties (part 2)
• Change of Base Formula
• Solving Logarithmic Equations
• Proof: log a + log b = log ab
• Proof: A(log B) = log (B^A), log A - log B = log (A/B)
• Natural Logarithm with a Calculator

 

Chapter 6 – Mathematics of Finance

6.2 Compound Interest; Geometric Sequences

• Compound Interest - More than Once Per Year - Part 2
  patrickJMT