MTH 131 - Algebra and Trigonometry

Unit 1: Basic Algebraic Operations Overview

Unit 2: Functions

Unit 3: Linear Equations

Unit 4: Factoring Fractions

Unit 5: Quadratic Equations

Unit 6: Exponents and Radicals

Unit 7: Exponential and Logarithmic Functions

Unit 8: Variation

Unit 9: Trigonometric Functions

Unit 10: Trigonometric Functions of Any Angle

Unit 11: Vectors and Oblique Triangles

Unit 12: Graphing Trig Functions

Unit 13: Trig Identities

Unit 1: Basic Algebraic Operations Overview

- Commutative Law of Addition
- Commutative Law of Multiplication
- Associative Law of Addition
- Associative Law of Multiplication
- The Distributive Property
- Law of Exponents: Multiplication (LEM)
- Law of Exponents: Division (LED)
- Law of Exponents: Powers (LEP)
- Simplifying Rational Expressions Using Exponent Laws - Example
- Law of Exponents: Extension of LEP 1
- Law of Exponents: Extension of LEP 2
- Law of Exponents: Negative Exponents
- Introduction to Roots
- Finding Cube Roots
- Simplifying a Polynomial (collecting like terms)
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Monomials
- Multiplying Monomials by Polynomials
- Multiplying Binomials
- Multiplying Polynomials
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial 1
- Dividing a Polynomial by a Monomial 2
- Dividing a Polynomial by a Binomial
- Dividing Polynomials with Remainders
- Solving a Linear Equation Example 1
- Solving a Linear Equation Example 2
- Solving a Linear Equation Example 3
- Solving a Linear Equation Example 4
- Solving a Linear Equation Example 5
- Rearrange a Formula to Isolate a Specific Variable

Unit 2: Functions

- Introduction to Functions 1
- Introduction to Functions 2
- Introduction to Functions 3
- Introduction to Functions 4
- Evaluate a Formula or Function Using Substitution
- Domain of a Function
- Domain and Range of a Function 1
- Domain and Range of a Function 2
- Domain and Range of a Function 3
- The Coordinate Plane
- Plotting (x,y) Coordinates
- Finding the Length of a Line Segment or Finding the Distance Between Two Points (Distance Formula)
- Graphing a Basic Function
- Graphing a Quadratic Function

Unit 3: Linear Equations

- Checking if a Point is (or is not) a Solution in a Linear System
- Finding Slope from a Graph
- Finding Slope When Given Two Points (or Ordered Pairs) Example 1
- Finding Slope When Given Two Points (or Ordered Pairs) Example 2
- Graphing a Linear Function by the X and Y Intercept Method
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 1
- Graphing a Linear Function (Line) by the Slope Y-Intercept Method Example 2
- Solving Linear Systems by Graphing
- Solving Linear Systems by Substitution Method Example 1
- Solving Linear Systems by Substitution Method Example 2
- Solving Linear Systems by Elimination (Addition) Method Example 1
- Solving Linear Systems by Elimination (Addition) Method Example 2

Unit 4: Factoring Fractions

- Binomial Squared (Special Products in Algebra)
- Difference of Squares (Special Products in Algebra)
- Finding The Greatest Common Factor (GCF)
- More GCF Examples
- Common Factoring Example
- More Common Factoring Examples
- Factoring Easy Trinomials (Trinomial with a Leading One Coefficient)
- Factor by Grouping (Triple Common Factor)
- Factoring Hard Trinomials (Trinomials with a Non-One Coefficicent)
- Factoring a Trinomial with a Common Factor First
- Factoring a Perfect Square Trinomial

Unit 5: Quadratic Equations

- Solving Quadratics by Factoring Example 1
- Completing the Square
- Completing the Square to Solve Quadratics
- Quadratic Formula 1
- Quadratic Formula 2
- Quadratic Formula 3
- Quadratic Formula 4
- Graphing a Quadratic

Unit 6: Exponents and Radicals

- Law of Exponents: Multiplication (LEM)
- Law of Exponents: Division (LED)
- Law of Exponents: Powers (LEP)
- Simplifying Rational Expressions Using Exponent Laws - Example
- Law of Exponents: Extension of LEP 1
- Law of Exponents: Extension of LEP 2
- Law of Exponents: Negative Exponents
- Rational Exponents and Exponent Laws
- Simplifying Expressions With Rational Exponents
- Simplifying Radical Expressions Example 1
- Simplifying Radical Expressions Example 2
- Simplifying Radical Expressions Example 3
- How to Rationalize a Denominator
- Addition of Radical Expressions
- Subtraction of Radical Expressions
- Adding and Subtracting Radical Expressions
- Multiplying Rational Expressions Example 1
- Multiplying Rational Expressions Example 2
- How to Rationalize a Denominator

Unit 7: Exponential and Logarithmic Functions

- Graphing Exponential Functions
- Solving Basic Logarithms and Exponentials
- Logarithm Properties (Sum and Difference Properties)
- Logarithm Properties (Multiple Property and Change of Base)
- Proof of the Sum Property of Logarithms
- Proof of the Difference and Multiple Property of Logarithms
- Change of Base Formula
- Simplifying Logarithms
- Calculating a Logarithm with a Calculator
- Logarithmic Equations
- Solving Logarithmic Equations

Unit 8: Variation

- Introduction to Ratios
- Understanding Proportions
- Ratios as Fractions
- Simplifying Rates and Ratios
- Finding an Unknown in a Proportion
- Finding Unit Rates
- Finding Unit Prices

Unit 9: Trigonometric Functions

- Language and Notation in Geometry
- Angle Basics
- Measuring Angles in Degrees
- Radians and Degrees
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 1
- Using SOH CAH TOA and Pythagoreans Theorem to Solve Right Angle Triangles Part 2

Unit 10: Trigonometric Functions of Any Angle

Unit 11: Vectors and Oblique Triangles

- Introduction to Scalars and Vectors
- Visualizing Vectors in Two Dimensions
- Vector Addition and Subtraction Examples
- Proof: Law of Sines
- Proof: Law of Cosines

Unit 12: Graphing Trig Functions

- Graphs of Trigonometric Functions - Sine
- Graphs of Trigonometric Functions - Cosine
- Graphs of Trigonometric Functions - Tangent
- Graphing Trigonometric Functions: Transformations
- Finding the Trigonometric Equation From the Graph 1
- Finding the Trigonometric Equation From the Graph 2

Unit 13: Trig Identities

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