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Preliminary Topics

Absolute Value
Factoring Numbers
Fractions

Geometric Formulas
LCM and GCF
Metric Conversions
Negative Numbers
  

 

Number Bases
   (binary, octal, etc.)
Number Properties
   (Distributive, Associative,
   Commutative, etc.)
Number Types 
   (natural, integer, real, etc.)
  

 

Converting between
   Decimals, Fractions,
   and Percents

Place Value
Roman Numerals

Rounding
   (and
significant digits)
Set Notation  
 

Beginning Algebra Topics

Canceling Units
Distance Formula
Engineering Notation
Evaluation
Exponents:
  Basic rules
  Negative exponents
  Fractional exponents
Graphing Overview
Graphing Absolute Value
Graphing Linear Equations
Graphing Radical Equations
Graphing Linear Inequalities
  (of the form "y < 2x + 3")
Inequalities Overview
  (three solution methods)
Inequalities: Linear
  (such as "2x < 4")
  

 

Intercepts
Midpoint Formula
Order of Operations
Polynomials

  (definitions & "like terms")
Polynomials: Adding &
  Subtracting
Polynomials: Multiplying
Polynomials: Dividing

Radicals
  (square roots, cube roots,
  rationalizing denominators,
  etc.)
Ratio & Proportion
Scatterplots & Regressions
Scientific Notation
Simple Factoring
  like "2x + 6 = 2(x + 3)"
 

 

Simplifying with Exponents
Simplifying with Parentheses
Slope of a straight line
Slope and Graphing
Slope and y-intercept
  (their meaning in the
  context of word problems)
Solving Absolute Value
   Equations
Solving Linear Equations
Solving Literal Equations
Solving Radical Equations
Straight-line equations
  (y = mx + b)
Variables
x,y-Plane
  (plotting points, etc.)
   
 

Intermediate Algebra Topics

Completing the Square:
  circles
  ellipses
  solving quadratics
  finding the vertex
Descartes' Rule of Signs
Domain and Range
Even and Odd Functions
Factor Theorem
Factoring Polynomials
Factoring Quadratics
Finding Polynomials from
   Their Zeroes
Function Notation
Functions
Function Transformations  
 
  

 

Graphing Quadratic
   Equations
   Deriving Vertex Formula
Graphing Systems of
   Linear Inequalities
Inequalities: Absolute Value

Inequalities: Quadratic
Linear Programming
Numerical Approximation
  
of Zeroes
Operations on Functions
Piecewise Functions:
  definition of
  graphing of
Polynomial Graphs

Rational Roots Test
Remainder Theorem 
  

 

Quadratic Formula
  Deriving the Quad. Formula
Sequences and Series
Solving Polynomials
Solving Quadratic Equations
Solving Systems of
   Non-Linear Equations
Special Factoring Formulas
  (difference of squares,
  sums and differences of
  cubes, etc.)
Symmetry
Synthetic Division
Variation
  (direct, inverse, & joint)
Vertical Line Test
  
  

Advanced Algebra Topics

Asymptotes
Binomial Theorem

Complex Fractions
Complex Numbers
Composition of Functions
Conics: Overview
  Parabolas
  Circles
  Ellipses
  Hyperbolas

Cramer's Rule
Determinants
Exponentials
Graphing Exponential
   Equations
Graphing Logarithmic
   Equations
    

 

Graphing Rational Equations
Induction Proofs
Inequalities: Polynomial
Inequalities: Rational
   Expressions
Inverse Functions
Logarithms
Log Rules
Matrix Definitions
Matrix Addition
  and Subtraction
Matrix Multiplication
Matrix Row Operations
Matrix Inversion
Minors and Cofactors
  

 

Next Number in a
   Sequence
Partial-Fraction
   Decomposition
Rational Expressions:
   Simplifying
Rational Expressions:
   Adding
Rational Expressions:
   Multiplying
Solving Exponential
   Equations
Solving Logarithmic
   Equations

Solving Rational Equations
Solving Systems of
   Linear Equations
       

Solving Word Problems

Translation: How to translate word problems from English into mathematical equations
 
"
age" word problems
"
area/volume/perimeter"
  geometry word problems
"
coin" (money) problems
  
  

 

"distance"
  d = rt word problems
"
investment"
   simple interest I = Prt
"
mixture" problems
"
number" (integer) problems
"
work" problems
Determinant Word Problems

  

 

Exponential and Logarithmic
   
word problems
"Percent of" word problems
  (including increase /
  decrease problems)
Quadratic word problems
  (including projectile motion)
Systems-of-equations
   word problems
      

Appendix

"The Bible says pi = 3"
Books:  Reviews, etc.
Box-and-Whisker Plots
Calculators
  (what to look for, what to buy)
Factorials
  

 

Formatting Math as Text
  (how to type math when
   e-mailing or posting
   questions on tutoring
   forums)
  
How Can 0.999... = 1?

 

How Do I Compute
   My Grade?
Mean, Median, and Mode

Placement Tests
Stem-and-Leaf Plots
Venn Diagrams 
Why Do I Have to
  Take Algebra?   

...and the beginnings of trig

Advanced Trig Graphs
Angles of Elevation / Depr.
Basic Trigonometric Ratios
Conventions
Evaluating Using Identities
Greek Letters & Their Names 

 

Inverses of Trig Ratios
Proving Trig Identities
Pythagorean Theorem
Quadrants and Angles
Radians and Degrees
Right-Triangle Word Probs

 

Sectors, Areas, and Arcs
Solving Trig Equations
Special Angle Values
Trig Functions & Graphs
Trigonometric Identities
Unit Circle

 

 

 

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