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| MATHEMATICS Formulas, Graphs, Tables,
. . . < High School to University Level > |
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CONTENTS A
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ALGEBRA
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1
Real
Numbers
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The set of real
numbers
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Rational numbers or
fractions
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Absolute
value of a real number
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Properties of absolute value
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Properties of real numbers
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Recurring decimal
to fraction conversion
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Purely recurring
decimals
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Mixed
recurring decimals
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2 Exponentiation
- powers or indices, rules and properties
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Properties of
exponents
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The
rules for powers (or exponents)
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Radicals - Exponentiation with a fractional exponent
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Properties of radicals
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Rationalizing
denominator
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Algebraic
expressions - monomial, binomial, trinomial, . . . ,
polynomial
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Expanding
algebraic expression by removing parentheses or brackets
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The
square of binomial - the perfect square trinomial
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The
cube of binomial
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The
binomial expansion algorithm
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Factoring algebraic
expressions
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The
difference of two squares
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The
difference of two cubes
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The
sum of two cubes
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Ratios
and proportions
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The
geometric mean
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Percentage
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Percentage solved problems
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3
Percent
increase or decrease
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Percent increase or decrease solved problems
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Polynomial and/or
polynomial functions and equations
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Addition and subtraction of polynomials
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Multiplication
of polynomials
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Division
of polynomials
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3a Polynomial
functions' properties
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A polynomial function written in
general form represents translation of its source
(original) function
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Sigma
notation of the polynomial function
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Graphs of polynomial functions
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Zero polynomial
f(x)
= 0
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Constant function
f(x)
= a0
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Linear
function, the first degree polynomial f(x)
= a1x + a0
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The roots of a
polynomial or zero function
values, x-intercepts
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Linear
equation
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4
Quadratic
function, the second degree polynomial f(x)
= a2x2
+
a1x + a0
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Quadratic
equation, quadratic formula
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Cubic
function, the third degree polynomial f(x)
= a3x3
+ a2x2
+
a1x + a0
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The
graphs
of the source cubic functions - the classification criteria
diagram
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Translated
cubic functions
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Drawing a cubic function example
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5
Quartic
function, the fourth degree polynomial f(x) = a4x4
+ a3x3 + a2x2
+ a1x + a0
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Transformation of the quartic
polynomial from the general to the source form
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The
basic classification criteria applied to the source quartic
polynomial shows the diagram
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Graph
of the power function - translated power or monomial functions
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Drawing translated power or monomial
function example
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6
Polynomial functions'
coefficients and roots relations, Vietas formulas
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Polynomial
functions expressed by roots
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Graphing
polynomial
functions given their roots example
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7
Systems of linear equations - use of determinants
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Cramer’s
rule (using the determinant) to solve systems of linear equations
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Solving system
of two equations in two unknowns
using
Cramer's rule
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Solving system of three equations in three unknowns using
Cramer's rule
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Method of expanding a
determinant of a rank n
by cofactors, example
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Property
of a determinant use
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Absolute
value equations
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Solving absolute value
equations
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Inequalities
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Linear inequality
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Solving inequalities
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Compound or
double inequalities
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8
Rational
Inequalities
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Method of solving
rational inequalities
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Absolute value
inequalities
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Solving
linear inequalities with absolute value
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Systems
of linear inequalities
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Solving and graphing systems of
linear inequalities
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Systems of
linear inequalities in two variables
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Solving and graphing
systems of
linear inequalities in two variables
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Quadratic
inequalities
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Graphic solution of
quadratic inequalities
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9
Equations
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Equations
with rational expression
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Solving rational
equations
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Rational
equations - linear equations
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Rational
equations - quadratic equations
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Binomial
equations
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Solving binomial equations
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Equations
reducible to quadratic form, bi-quadratic equations
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Solving bi-quadratic
equations or equations reducible to quadratic
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Radical
or
irrational
equations
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Solving irrational
or radical
equations
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10 Exponential and
logarithmic functions and equations
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Exponential
and logarithmic functions (are mutually) inverse functions
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Inverse functions
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Graphs of inverse functions
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Exponential functions
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The
graph of the exponential
function
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The
graph of the logarithmic
function
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Translated logarithmic
and exponential functions
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