# Mathematics in Review Video Series

## Outline

• Arithmetic
• Number Theory
• Commutative Properties of Addition and Multiplication
• Associative Properties of Addition and Multiplication
• Additive and Multiplicative Inverse Properties
• Additive and Multiplicative Identity Properties
• Zero Property of Multiplication
• Distributive Properties (non-algebraic)
• Number Systems
• Definition of Closure
• Whole and Natural Numbers
• Definition
• Arithmetic of Whole and Natural Numbers (retaining closure)
• Prime Factorization
• Exponents on (a.k.a. Powers of) Natural Numbers
• Square Roots of Natural Numbers (retaining closure)
• Natural-numbered Roots of Natural Numbers (retaining closure)
• Order of Operations (retaining closure)
• Estimation Techniques
• Applications
• Integers
• Definition
• Arithmetic of Integers (retaining closure)
• Exponents on Integers (retaining closure)
• Natural-numbered Roots on Integers (retaining closure)
• Definition of Absolute Value
• Absolute Value of Integers
• Estimation Techniques
• Applications
• Rational Numbers
• Definition
• Mixed Numbers, Proper, and Improper Fractions
• Simplification of Rational Numbers
• Arithmetic of Rational Numbers
• Converting Between Mixed and Fractional Form
• Converting Between Decimals and Fractions
• Rounding and Truncation
• Definition and Simplification of Compound Fractions
• Exponents on Rational Numbers
• Natural-numbered Roots of Rational Numbers (retaining closure)
• Rational Exponents (retaining closure)
• Application: Ratios and Proportions
• Application: Percent
• Application: Scientific Notation
• Estimation Techniques
• Irrational Numbers
• Simplification
• The Four Operations
• Rationalizing Numerators and Denominators
• Applications
• Pythagorean Theorem
• pi: Area and Circumference of a Circle
• Real Numbers
• Complex Numbers
• i
• The Four Operations
• Units of Measurement
• Unit Conversion
• Unit Analysis
• Finance
• Simple Interest
• Compound Interest
• Statistics
• Mean, Median, and Mode
• Geometry
• Lines and Angles
• Points
• Lines
• Rays
• Line Segments
• Triangles
• Angles and Angle Sums
• Perimeter and Area
• Similar Triangles
• Perimeter and Area
• Circles
• Circumference and Area
• Combined Figures
• Perimeter and Area
• Set Theory
• Standard Set Notation
• Set-builder Notation
• Intervals
• Algebraic Expressions
• Variables
• Addition and Subtraction
• Like Terms
• Review: Distributive Property
• Multiplication and Division
• Review: Order of Operations
• Evaluation for Given Values
• Exponents
• Whole Number Exponents
• Laws of Exponents - Product with Same Base
• Laws of Exponents - Quotient with Same Base
• Laws of Exponents - Quotient to a Power
• Laws of Exponents - Negative Powers
• Laws of Exponents - Power to a Power
• Laws of Exponents - Product to a Power
• Laws of Exponents - Zero Power
• Laws of Exponents - Quotient with a Negative Power
• Review: Order of Operations
• Formulas
• Distance, Rate, and Time
• Profit, Cost, and Revenue
• Review: Geometry
• Polynomials
• Review: The Four Operations
• Review: The Distributive Property
• Division by a Monomial
• Long Division
• Synthetic Division
• Factoring
• GCF
• Difference of Squares
• Grouping
• Sums and Differences of Cubes
• Trinomials with Unit Lead Coefficient
• Trinomials with Non-unit Lead Coefficient
• Rational Expressions
• Determine Undefined Values
• Simplify
• Multiplication and Division
• Addition and Subtraction of Rational Expressions
• Like and unlike denominators
• Finding the LCD
• Simplifying Complex Fractions
• Simplifying Square Roots of Variables
• Simplifying nth Roots of Variables
• Simplifying nth Roots of a Variable Raised to the nth Power
• Review: The Four Operations
• Review: Rationalizing Numerators and Denominators
• Functions
• Definition of a Function
• Function Notation
• Point-plotting
• Determining the Domain of a Function
• Determining the Range of a Function
• The Arithmetic of Functions
• Composition of Functions
• Inverse Functions
• Algebraic Equations
• Linear
• Equality Property of Arithmetic
• Solving Linear Equations in One Variable
• Solving Absolute Value Equations
• Applications
• Identities and Contradictions
• Solving Linear Equations in Two Variables
• Point-plotting
• Tables
• Slope
• Intercepts
• Graphing: The Intercept Method
• Graphing: The Slope-intercept Form
• Standard Form
• Point-slope Form
• Parallel and Perpendicular Lines
• Linear Functions: Domain and Range
• Formulas
• Review: Evaluate for a Given Set of Variables
• Solve for a Given Variable
• Mixture Problems
• Investment Problems
• Graphing Using Point-plotting
• Tables
• Solving by Factoring
• Solving by Extraction of Roots
• Solve by Completing the Square
• Solve Using the Quadratic Formula
• Solve Quadratic-like Equations
• Graph Using Completing the Square and Vertex Form
• Graph Using Intercepts
• Optimization Problems
• Quadratic Functions: Domain and Range
• Rational
• Solve Rational Equations
• Applications
• Variation
• Direct
• Inverse
• Joint
• Rational Functions: Domain and Range
• Solve Radical Equations Involving One Radical Expression
• Solve Radical Equations Involving More Than One Radical Expression
• Radical Functions: Domain and Range
• Exponentials and Logarithms
• Definitions
• Graphs
• Properties of Exponentials and Logarithms
• Solving Exponential and Logarithmic Equations
• Applications
• Algebraic Inequalities
• Linear
• One Variable
• Solve and Graph Simple Inequalities
• Solve and Graph Compound Inequalities
• Solve and Graph Absolute Value Inequalities
• Two Variables
• Solve and Graph
• Systems
• 2x2
• Geometric Method
• Substitution Method
• Elimination Method
• Inconsistent and Dependent Systems
• 3x3
• See above
• Inequalities
• Conic Sections
• Graphing Circles
• Distance and Midpoint Formulas
• Graphing Parabolas
• Ellipses
• Hyperbolas
• Translation of Axes