An Ordered Listing of the Lessons

• Why Do I Have to
• Take Algebra?
• Placement Tests
• Rounding
• Place Value
• Roman Numerals
• Number Properties
  (Distributive, Associative, Commutative, etc.)

• Number Bases
  (binary, octal, etc.)
• Factoring Numbers
• LCM and GCF
• Fractions
• (and fraction division: why does flip-n-multiply work?)

• Converting between Decimals, Fractions, and Percents
• Negative Numbers
• Number Types
• (natural, integer, etc.)
• Set Notation
• Geometric Formulas
• Absolute Value

• Variables
• Exponents: Basic Rules
• Order of Operations
• Evaluation
• Polynomials
• (Definitions & "like terms")
• Simplifying with Parentheses
• Polynomials: Adding
• and Subtracting
• Polynomials: Multiplying
• Simple Factoring
• such as "2x + 6 = 2(x + 3)
• Exponents: Negative
• Simplifying with Exponents
• Scientific Notation
• Engineering Notation
• Polynomials: Dividing
• x,y-Plane (plotting points, etc)
• Midpoint Formula
• Distance Formula
• Solving Linear Equations

• Solving Literal Equations
• Ratio and Proportion
• Cancelling (or
• Converting) Units

Translation: How to translate word problems from English into math

• "Age" Word Problems
• Geometry Word Problems
• "Coin" (money) Problems
• "Distance" d = rt
• (Uniform Rate) Problems
• Simple-Interest (I = Prt)
• "Investment" Problems
• "Mixture" Word Problems
• "Number" (Integer) Problems
• "Work" Word Problems
• "Percent of" Word Problems
• Slope of a Straight Line
• Graphing Linear Equations

• Slope and Graphing

Slope and y-intercept
(and their meaning in word problems)

• Straight-Line Equations
• such as "y = mx + b"
• x- and y-Intercepts
• Scatterplots & Regressions
• Solving Linear Inequalities
• such as "2x < 4"
• Graphing Linear Inequalities
• such as "y < 2x + 3"
• Graphing Absolute-
  • Value Equations
• Solving Absolute-
• Value Equations
• Radicals (square roots,
• cube roots, etc)
• Exponents: Fractional
• Solving Radical Equations
• Graphing Radical Equations

• Graphing Systems of
• Linear Inequalities
• Linear Programming
• Absolute-Value Inequalities
• Factoring Quadratics
• Special Factoring Formulas
• (difference of squares,
• sum of cubes, etc)
• Quadratic Formula
• Solving Quadratic Equations
• Graphing Quadratic Equations
• Quadratic Word Problems

• Quadratic Inequalities
• Solving Systems of Non-
• Linear Equations
• Functions
• Function Notation
• Function Transformations
• Variation
• (direct, inverse, joint)
• Rational Roots Test
• Remainder Theorem
• Factor Theorem
• Synthetic Division

• Descartes' Rule of Signs
• Solving/Factoring Polynomials
• Finding Polynomials
• from Their Zeroes
• Numeric Approx. of Zeroes
• Graphing Polynomials
• Completing the Square:
• circles
• ellipses
• solving quadratics
• finding the vertex
• Sequences and Series

• Complex Fractions
• Rational Expressions:
• Def's & Simplifying
• Adding Rational Expressions
• Multiplying Rat'l Expressions
• Asymptotes
• Graphing Rational Functions
• Solving Rational Equations
• Complex Numbers
• Partial Fraction
• Decomposition
• Function Composition
• Inverse Functions
• Exponential Functions
• Graphing Exponential
• Functions

• Solving Exponential Equations
• Logarithms
• Log Rules
• Graphing Log Functions
• Solving Log Equations
• Log & Exponential
• Word Problems
• Systems of Linear Equations
• System-of-Equation
• Word Problems
• Matrix Definitions
• Matrix Addition / Subtraction
• Matrix Multiplication
• Matrix Row Operations

• Inverse Matrices
• Determinants
• Minors & Cofactors
• Cramer's Rule
• Determinant Word Problems
• Next Number in a Sequence
• Factorials
• Binomial Theorem
• Induction Proofs
• Conics: Overview
  • Parabolas
  • Circles
  • Ellipses
  • Hyperbolas
  • Straight Lines

• Mean, Median,
• Mode, and Range
• Box-and-Whisker Plots
• Stem-and-Leaf Plots
• Venn Diagrams

Formatting Math as Text
(how to type math when e-mailing or posting questions on tutoring forums)

• How Do I Compute My Grade?
• Symmetry
• How Can 0.999...
• be Equal to 1?

• Conventions
• Pythagorean Theorem
• Greek Letters & Their Names
• Radians and Degrees
• Sectors, Areas, and Arcs
• Basic Trigonometric Ratios

• Quadrants and Angles
• Unit Circle
• Right-Triangle Word Probs
• Angles of Elevation / Depr.
• Special Angle Values
• Trig Functions & Graphs

• Advanced Trig Graphs
• Trigonometric Identities
• Evaluating Using Identities
• Proving Trig Identities
• Inverses of Trig Ratios
• Solving Trig Equations