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
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
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 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
9    Equations Equations with rational expression
Solving rational equations Rational equations - linear equations Binomial equations
Solving binomial equations Equations reducible to quadratic form, bi-quadratic equations Radical or irrational equations
10
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    