MATHEMATICS   Formulas, Graphs, Tables, . . .  < High School to University Level >
CONTENTS A
  ALGEBRA
  1    Real Numbers
         The set of real numbers
         Rational numbers or fractions
         Absolute value of a real number

         Properties of absolute value

         Properties of real numbers
         Recurring decimal to fraction conversion
         Purely recurring decimals
         Mixed recurring decimals
   2   Exponentiation - powers or indices, rules and properties  
         Properties of exponents
         The rules for powers (or exponents)
         Radicals - Exponentiation with a fractional exponent
         Properties of radicals
         Rationalizing denominator
         Algebraic expressions - monomial, binomial, trinomial, . . . , polynomial
         Expanding algebraic expression by removing parentheses or brackets
         The square of binomial - the perfect square trinomial
         The cube of binomial
         The binomial expansion algorithm
         Factoring algebraic expressions
         The difference of two squares
         The difference of two cubes
         The sum of two cubes
         Ratios and proportions
         The geometric mean
         Percentage
         Percentage solved problems
  3    Percent increase or decrease
         Percent increase or decrease solved problems
         Polynomial and/or polynomial functions and equations
         Addition and subtraction of polynomials
         Multiplication of polynomials
         Division of polynomials
  3a  Polynomial functions' properties
         A polynomial function written in general form represents translation of its source (original) function
         Sigma notation of the polynomial function
         Graphs of polynomial functions
         Zero polynomial   f(x) = 0
         Constant function  f(x) = a0
         Linear function, the first degree polynomial  f(x) = a1x + a0
         The roots of a polynomial or zero function values, x-intercepts
         Linear equation
  4    Quadratic function, the second degree polynomial   f(x) = a2x2 + a1x + a0
         Quadratic equation, quadratic formula
      Cubic function, the third degree polynomial   f(x) = a3x3 + a2x2 + a1x + a0
         The graphs of the source cubic functions - the classification criteria diagram
         Translated cubic functions
         Drawing a cubic function example
  5    Quartic function, the fourth degree polynomial  f(x) = a4x4 + a3x3 + a2x2 + a1x + a0
         Transformation of the quartic polynomial from the general to the source form
         The basic classification criteria applied to the source quartic polynomial shows the diagram
      Graph of the power function - translated power or monomial functions
         Drawing translated power or monomial function example
  6    Polynomial functions' coefficients and roots relations, Vietas formulas
         Polynomial functions expressed by roots
         Graphing polynomial functions given their roots example
  7    Systems of linear equations - use of determinants
         Cramer’s rule (using the determinant) to solve systems of linear equations
      Solving system of two equations in two unknowns using Cramer's rule
      Solving system of three equations in three unknowns using Cramer's rule
         Method of expanding a determinant of a rank n by cofactors, example
         Property of a determinant use
         Absolute value equations
         Solving absolute value equations
         Inequalities
      Linear inequality
         Solving inequalities
      Compound or double inequalities
  8    Rational Inequalities
         Method of solving rational inequalities
      Absolute value inequalities
         Solving linear inequalities with absolute value
      Systems of linear inequalities
         Solving and graphing systems of linear inequalities
      Systems of linear inequalities in two variables
         Solving and graphing systems of linear inequalities in two variables
      Quadratic inequalities
         Graphic solution of quadratic inequalities
  9    Equations
      Equations with rational expression
         Solving rational equations
      Rational equations - linear equations
         Rational equations - quadratic equations
      Binomial equations
         Solving binomial equations
      Equations reducible to quadratic form, bi-quadratic equations
         Solving bi-quadratic equations or equations reducible to quadratic
      Radical or irrational equations
         Solving irrational or radical equations
 10  Exponential and logarithmic functions and equations
         Exponential and logarithmic functions (are mutually) inverse functions
         Inverse functions
         Graphs of inverse functions
         Exponential functions
         The graph of the exponential function
         The graph of the logarithmic function
         Translated logarithmic and exponential functions
 
 
 
 
 
 
 
 
 
 
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