Math -
Formula Sheet
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Math Formula Sheet
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General Information
a
Symbols, and relationships in mathematics
Number theory
ℕ
⊂
ℤ
⊂
ℚ
⊂
ℝ
⊂
ℂ
Number Sets
ℙ
=
{
2
,
3
,
5
,
7
,
…
}
Prime Numbers - Prime Factorization
a
|
m
⇔
n
·
a
=
m
Divisibility Rules
(
m
;
n
)
=
l
;
[
m
;
n
]
=
k
Greatest Common Divisor (factor) - Least Common Multiple
a
b
+
c
d
=
a
d
+
b
c
b
d
Operations with rational numbers
Binomial theorem
a
+
b
n
Binomial theorem
Combinatorics
P
n
=
n
!
Permutations
C
n
k
=
(
n
k
)
Combination
V
n
k
=
n
!
(
n
−
k
)
!
Variation
Sets
A
∪
B
;
A
∩
B
;
A
B
Operations on Sets
A
∪
B
=
B
∪
A
Fundamental laws of set algebra
A
∪
B
∪
C
Cardinality of sets
A
×
B
Cartesian product
ρ
⊆
A
x
A
Relation
Logic
P
∨
Q
;
P
⇒
Q
Logical Operations and Truth Tables
a
∨
b
=
b
∨
a
Properties of Logical Operators
Graph Theory
Graph Theory - definitions, relationships
Algebra
Polynomials
a
+
b
2
Special Binomials
Progressions
a
n
=
a
a
+
(
n
−
1
)
d
Arithmetic progression
a
n
=
a
1
⋅
q
n
−
1
Geometric progression
Logarithm
l
o
g
a
b
=
c
⇔
a
c
=
b
Logarithm
l
o
g
a
x
=
l
o
g
b
x
l
o
g
b
a
Changing the base of a logarithm
Exponents
a
·
a
·
a
=
a
3
Powers
Roots
a
n
=
b
⇒
b
n
=
a
Roots
Proportionality
a
:
b
=
c
:
d
Direct and Inversely Proportion
Inequalities
f
x
<
g
x
Inequalities
Equations
a
x
2
+
b
x
+
c
=
0
Quadratic equation
a
x
3
+
b
x
2
+
c
x
+
d
=
0
Cubic Equations
x
n
=
a
Irrational and transcendental equations
Complex numbers
z
=
a
+
i
b
;
i
=
-
1
Complex Numbers
z
1
±
z
2
Adding and Subtracting Complex Numbers
z
1
·
z
2
;
z
1
z
2
Multiplying and Dividing Complex Numbers
z
n
Power of complex numbers
z
k
=
a
+
i
b
n
Roots of complex numbers
Kamatni račun
k
=
T
·
p
100
Interest calculation,
Matrices
C
=
A
+
B
Definition, adding & subtracting of matrices
C
=
A
·
B
Multiplying matrices
Geometry
Trigonometry
a
s
i
n
α
=
b
s
i
n
β
=
c
s
i
n
γ
Law of Sines
c
2
=
a
2
+
b
2
−
2
a
b
c
o
s
2
γ
Law of Cosines
s
i
n
(
2
α
)
Trigonometric identities of double angles
s
i
n
2
α
+
c
o
s
2
α
=
1
Trygonometry Identities of same angle
s
i
n
α
2
Trigonometric identities of half angles
s
i
n
(
α
±
β
)
Identities for the sum and difference of two angles
s
i
n
α
±
s
i
n
β
Sum and difference of trigonometric functions
s
i
n
α
=
a
c
Trigonometric Values of Special Angles
Two-dimensional geometric shapes
Angle Bisector Theorem
The inscribed angle theorem
Convex - Concave polygons, functions
Regular and Irregular Polygons
Thales Theorem
Triangle
Special Triangles - Right Triangle, Equilateral Triangles, Isosceles Triangles
Quadrilateral
Squere
Rectangle
Rhombus
Parallelogram
Kite
Trapezoid
Circle
Circular sector
Circular segment
Three-dimensional geometric shapes
Cube
Sphere
Cone
Prism
Pyramide
Platonic solids
Cylinder
Vectors
a
→
·
b
→
=
|
a
→
|
|
b
→
|
c
o
s
α
Scalar Product of Vectors
c
→
=
a
→
×
b
→
Vector Product of Vectors
Analytical Geometry 2D
d
=
|
P
1
P
2
|
¯
Distance between two points
x
2
+
y
2
=
r
2
Circle
y
=
m
x
+
b
Linear equation
x
2
a
2
-
y
2
b
2
=
1
Hyperbole
x
2
a
2
+
y
2
b
2
=
1
Ellipse
y
2
=
2
p
x
Parabola
Analytical Geometry 3D
a
x
+
b
y
+
c
z
+
d
=
0
Plane
Mathematical analysis
Important functions
y
=
a
x
+
b
Linear polynomial function
y
=
a
x
2
+
b
x
+
c
Quatratic polynomial function
y
=
a
x
3
+
b
x
2
+
c
x
+
d
Cubic polynomial function
y
=
1
x
Rational function
y
=
x
2
k
,
k
∈
ℕ
Root function with even radical
y
=
x
2
k
+
1
,
k
∈
ℕ
Root function with odd radical
y
=
a
x
Exponential function
y
=
log
a
x
Logarithmic function
y
=
sin
x
Sine function
y
=
cos
x
Cosine function
y
=
tg
x
Tangent function
y
=
ctg
x
Cotangent function
y
=
|
x
|
Absolute value functions
Function Transformations
f
(
x
+
c
)
Variable and function value transformations
Limits
l
i
m
x
→
x
0
f
x
=
a
Limit of a function
Dervation
d
f
x
d
x
=
f
'
x
Table of Derivatives
(
f
·
g
)
′
=
f
′
·
g
±
f
·
g
′
Differentiation rules
T
x
Taylor Series
Integration
∫
f
x
d
x
=
F
x
+
C
Table of Integrals
∫
c
f
(
x
)
d
x
=
c
∫
f
(
x
)
d
x
Integration Rules
∫
a
b
f
x
d
x
=
F
b
-
F
a
Definite Integrals
Probability and Statistics
Probability
∑
i
=
1
n
A
i
=
Ω
Events, Operations with events, Complete system of events
P
A
=
A
Ω
Probability of an event
P
A
|
B
=
P
A
∩
B
P
B
Conditional Probability
P
A
=
∑
i
=
1
n
P
A
|
B
i
·
P
B
i
Law of Total Probability
P
B
i
|
A
=
P
A
|
B
i
·
P
B
i
P
A
Bayes’ Theorem
F
x
=
P
ξ
<
x
Discrete Probability Variable - Distribution Function
Statistics
A
=
∑
x
i
i
=
1
n
n
Measures of Central Tendency
x
=
x
1
+
x
2
+
x
3
+
.
.
.
.
+
x
n
n
Statistics
