Course Resources Math 1710

Chapter 1 – Introduction to Functions and Graphs

• Distance Formula (Section 1.2)
• Midpoint Formula (Section 1.2)

1.3 Functions and Their Representations

• 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
• A more formal understanding of functions
• Linear Function Graphs

1.5 Functions and Their Rates of Change

• Interpreting Linear Graphs
• Slope of a line
• Slope Example
• Slope and Rate of Change
• Graphical Slope of a Line
• Slope of a Line 2
• Recognizing Linear Functions (1.4/1.5)
• Newton Leibniz and Usain Bolt: Why we study differential calculus

 

Chapter 2 – Linear Functions and Equations

2.1 Linear Functions and Models (treat as a review)

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

2.2 Equations of Lines (treat as a review)

• X and Y intercepts - Khan Academy
• X and Y intercepts 2
• Slope and Y-intercept Intuition - Khan Academy
• 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

2.3 Linear Equations (treat as a review)

• Applying the Metric System

2.4 Linear Inequalities (treat as a review)

• One-Step Inequalities
• One-Step Inequalities 2
• Inequalities Using Addition and Subtraction
• Inequalities Using Multiplication and Division
• Multi-Step Inequalities
• Writing and using inequalities -- Word Problem involving Absolute ValueInequity
• Writing and using inequalities 2
• Writing and using inequalities 3
• Multi-Step Inequalities 2
• Inequalities -- word problems
• Compound Inequalities
• Compound Inequalities 2
• Compound Inequalities -- (2 inequalities)
• Compound Inequalities 3
• Compound Inequalities 4

2.5 Absolute Value Equations and Inequalities

• Absolute Value Equations
• Absolute Value Inequalities
• Absolute value inequalities Example 1
• Absolute Value Inequalities Example 2
• Absolute value inequalities example 3
• Absolute Inequalities 2

 

Chapter 3 – Quadratic Functions and Equations

3.1 Quadratic Functions and Models

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

3.2 Quadratic Equations and Problem Solving

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

3.3 Complex Numbers

• Number Sets
  (Section 1.1)
• Number Sets 1
• Number Sets 2
• Number Sets 3
• Introduction to i and Imaginary Numbers
• Calculating i Raised to Arbitrary Exponents
• i as the Principal Root of -1 (a little technical)
• Imaginary Roots of Negative Numbers
• Complex Conjugates Example
• Adding Complex Numbers
• Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Complex Roots from the Quadratic Formula

 

Chapter 4 – More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

• Terms coefficients and exponents in a polynomial
  ( review)
• Simply a polynomial
  (review)
• Polynomials1
• Recognizing Odd and Even Functions
• Connection between even and odd numbers and functions

4.3 Division of Polynomials

• Polynomial divided by monomial
• Polynomial Division
• Dividing polynomials 1
• Dividing polynomials with remainders

4.6 Rational Functions and Models

• Rational Equations
• Multiplying and Dividing Rational Expressions 1 (review of rational)
• Multiplying and Dividing Rational Expressions 2 (review of rational)

4.7 More Equations and Inequalities

• Solving Rational Equations 2
• Solving Rational Equations 3
• Applying Rational Equations 1
• Applying Rational Equations 2
• Applying Rational Equations 3
• Extraneous Solutions to Rational Equations
• Direct Variation 1
• Proportionality Constant for Direct Variation
• Direct Variation Application
• Direct Variation Models
• Rational Inequalities 2
• Direct and Inverse Variation
• Recognizing Direct and Inverse Variation
• Direct Inverse and Joint Variation
• Inverse Variation Application

4.8 Radical Equations and Power Functions

Chapter 5 – Exponential and Logarithmic Functions

5.1 Combining Functions

• Sum of Functions
• Difference of Functions
• Product of Functions
• Quotient of Functions

5.2 Inverse Functions and Their Representations

• Introduction to Function Inverses
• Function Inverse Example 1
• Function Inverses Example 2
• Function Inverses Example 3
• Linear Algebra: Introduction to the inverse of a function

5.3 Exponential Functions and Models

• Graphing Exponential Functions

5.4 Logarithmic Functions and Models

• Introduction to Logarithms

5.5 Properties of Logarithms

• Logarithm of a Power
• Sum of Logarithms with Same Base
• Introduction to logarithm properties
• Introduction to logarithm properties (part 2)
• Using Multiple Logarithm Properties to Simplify
• 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 9 – Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables (emphasize solutions of non-linear systems.)

• Testing a solution for a system of equations
• Consistent and Inconsistent Systems
• Independent and Dependent Systems
• Solving Linear Systems by Graphing
• Solving systems by graphing 2
• Solving systems by graphing 3
• 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
• Systems of Three Variables
• Systems of Three Variables 2
• Three Equation Application Problem

9.2 Systems of Inequalities in Two Variables (optional)

• Solving and graphing linear inequalities in two variables 1
• Graphing Linear Inequalities in Two Variables Example 2
  (same problem as 2, differentexplanation)
• 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
• Testing Solutions for a System of Inequalities

9.4 -9.6 An Introduction to Matrices (Selected topics from Sections 9.4-9.6) (as time permits)

• Inverse Matrix (part 1)
• Inverting matrices (part 2)
• Inverting Matrices (part 3)
• Matrices to solve a system of equations