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Mathematics Formula
Free educational resources
Algebra Formula
(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
a2 + b2 = (a + b)2 − 2ab
a2 + b2 = (a − b)2 + 2ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a − b)3 = a3 − b3 − 3ab(a − b)
a3 + b3 = (a + b)3 − 3ab(a + b)
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a2 − b2 = (a + b)(a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
a3 + b3= (a + b)(a2 − ab + b2)
a4 – b4 = (a2 – b2)(a2 + b2) = (a + b)(a + b)
(a2 + b2)
a4 + b4 = (a2 + b2)2 – 2a2b2 = (a2 + √2ab +
b2)(a2 – √2ab + b2)
a5 + b5 = (a + b)(a4 – a3b + a2b2 – ab3 + b4
)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
an − bn = (a − b)(an−1 + an−2 b + an−3 b2 +
··· + bn−1n−1)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
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c2 – ab – bc – ca)
If a + b + c = 0, then the above identity
reduces to a3 + b3 + c3 = 3abc
Statistics Math Formulas
SETS :
A = {2, 3, 4, 7, 8, 9, 12}
3∈A
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SUBSET:
B = {3, 8, 9} ⇒ B ⊆ A
C = {1, 5} ⇒ C ⊄ A
STATISTICS :
MEAN : The mean value is obtained the
arithmetic mean or average of a set of numbers
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is expected
value.
The mean value is calculated by adding up all
the values, and then dividing that sum by the
number of values .
Mean = Sum of all data values / Number of
data values
Symbolically ,
Where (read as ” x bar”) is the mean of the set
of x values, Σ x is the sum of all the x values,
and n is the number of x values.
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MEDIAN : The median is the middle value in
a set of values. So to find the midian you need
to order the numbers from largest to smallest
and then you have to choose the value in the
middle.
MODE : Mode is the value that the highest
frequency in the data set.means values that
occur most frequently and there can be more
than one mode in a set.
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and tips.
numerical
value
thatandoccurs
most of
the
times.
F (Xmode) = max
INTERSECTION :
In intersection A ∩ B of two sets A and B is
the set that contains all elements of B also
belong to A (or similarly all elements of B that
also belong to A) but no other elements. The
symbol intersection is inverted U.
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career and educational
resources, guides
tips. B
If Set
A containforelement
A = {1,2,3}
andandset
contains B = {2,3,4} and the element in having
common ares 2 and 3 and this intersection area
formed a new set containing 2 and 3.
UNION :
The union of two sets A and B includes all
elements which are members of either A or B.
If sets A and B have any elements in common
then this elements which are members of both
sets are only include one in the union.
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ForVisitexample
: for
Ifcareer
setsandAeducational
contains
theguides
elements
1,2, and 3 and set B contains 2,3 and 4 the
elements which are members of A or B are
1,2,3 and 4. This form a new set containing
1,2,3 and 4. when we write the union 2 and 3
are only listed once.
RELATIVE COMPLEMENT OF A IN B :
The relative complement of A in B denoted, B
\ A, is the set of elements in B but not in A.
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educational
Symbolically
:Bfor \career
A =and{x
| x ∈resources,
B ∧ xguides
∉ and
A}tips.
ABSOLUTE COMPLEMENT :
In a Set theory a complement of a set A refers
to things not in A.
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SYMMETRIC
DIFFERENCE
:
Operations on sets :
A∪A=A
A∩A=A
A∪B=B∩ A
A∩B=B∩A
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for career
and ∪
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(AVisit
∪ www.eduNgr.com
B) ∪ C = A
∪ (B
C) resources, guides and tips.
(A ∩ B) ∩ C = A ∩ (B ∩ C)
∪′ = ø
(A′)′ = A
A∩ø=ø
A∩U=A
A ∩ A′ = ø
(A ∪ B)′ = A′ ∩ B′
(A ∩ B)′ = A′ ∪ B′
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Geometry Formula
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P = Perimeter
A = Area
S = Side
d = diameter
P=4xs
A = S2
d = a x √2
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Rectangle
P = Perimeter
A = Area
d = diameter
P=2x(a+b)
A=axb
d = √a2 + b2
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Triangle
P = Perimeter
A = Area
P=a+b+c
A=bxh/2
A = √s(s-a)(s-b)(s-c);
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s =Visit
a www.eduNgr.com
+ b + c / 2for=career
p / and
2.educational resources, guides and tips.
α + β + γ = 180o
Circle
P = Perimeter
A = Area
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P =Visit2πr
A = πr2
π = 3.14
Parallelogram
P = (a + b) x 2
P = 2a + 2b
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A =Visitbh
= ab sinforαcareer and educational resources, guides and tips.
Circular Sector
L = πr = θ / 180 0
A = πr2 θ/360 0
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Pythagorean Theorem :
a2 + b2 = c2
c = √a2 + √b2
Circular Ring
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A = π (R2 – r2)
Sphere
2
S =Visit4πr
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2/3
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V =Visit4πr
Trapezoid
P=a+b +c+d
A=hx a+b/2
Rectangular
Box
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A = 2ab + 2ac + 2bc
V = abc
Right Circular Cone :
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A = πr2 + πrs
S = √r2 +√h2
V = 1 x πr2 h / 3
Cube
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A = 6l2
V = l3
Cylinder
A =Visit2πr(
r + h)
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2h
for career and educational resources, guides and tips.
V =Visitπrwww.eduNgr.com
Frustum of a Cone
V = 1 x πh (r2 + rR + R2) / 3
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Trigonometry Formula
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Trigonometry Function Formulas of a Right
Triangle :
sin α = a / c = opposite / hypotenuse
cos α = b / c = adjacent / hypotenuse
tan α = a / b = opposite / adjacent
cot α = b / a = adjacent / opposite
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resources,
secVisitα www.eduNgr.com
= c / b for career and educational
Cosec
α =guides
c / and
a tips.
Basic Formula :
sin2 α + cos2 α = 1
tan α . cot tan α = 1
tan α = sin α / cos α = 1 / cot tan α
cot tan α = cos α / sin α = 1 / tan α
1 + tan2 α = 1 / cos2 α = sec2 α
1 + cot tan2 α = 1 / sin2 α = cos sec2 α
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Trigonometric Table
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00
0
1
0
∞
1
∞
α
sin α
cos α
tan α
cot α
sec α
cosec α
300
1/2
√3/2
1/√3
√3
2/√3
2
450
√2/2
√2/2
1
1
√2
√2
600
√3/2
1/2
√3
1/√3
2
2/√3
900
1
0
∞
0
∞
1
1200
√3/2
-1/2
-√3
-1/√3
-2
2/√3
1800
0
-1
0
∞
-1
∞
2700
-1
0
∞
0
∞
-1
3600
0
1
0
∞
1
∞
Co-Ratios
900 – α
sin
-sin α
+cos α
cos
+cos α
+sin α
tan
-tan α
+cot α
cot
-cot α
+tan α
900 + α
+cos α
-sin α
-cot α
-tan α
1800 – α
+sin α
-cos α
-tan α
-cot α
1800 + α
-sin α
-cos α
+tan α
+cot α
2700 – α
-cos α
-sin α
+cot α
+tan α
2700 + α
-cos α
+sin α
-cot α
-tan α
3600k – α
-sin α
+cos α
-tan α
-cot α
3600k – α
+sin α
+cos α
+tan α
+cot α
-α
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Trigonometry Addition
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Formula:
sin(A + B) = sinA cosB + cosA sinB
sin(A – B) = sinA cosB – cosA sinB
cos(A + B) = cosA cosB – sinA sinB
cos(A – B) = cosA cosB + sinA sinB
tan (A + B) = tanA + tanB / 1 – tanA tanB
tan(A – B) = tanA – tanB / 1 + tanA tanB
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cot
(A+ B) =forcotA
cotB
– 1resources,
/ cotAguides
+ cotB
Product of Trigonometric
Functions:
sin α cos β = 1/2 [ sin (α + β) + sin(α – β)]
cos α cos β = 1/2 [ sin (α + β) + sin(α – β)]
cos α cos β = 1/2 [ cos (α + β) + cos(α – β)]
sin α sin β = 1/2 [ cos (α – β) + cos(α + β)]
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tips.
tan
α tan β = fortan
α and
+ educational
tan β / resources,
cot tanguides
α +andcot
tanβ = – tanα – tan β / cot tan α – cot tan β
Trigonometric Formula with t = tan(x/2)
sinx = 2t / 1 + t2
cos x = 1 – t2 / 1 + t2
tan x = 2t / 1 – t2
cot x = 1 – t2 / 2t
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Trigonometric
Relation Between Functions:
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Angle of a Plane Triangle :
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A, B, C are 3 angles of a triangle
sin A + sin B + sin c = 4 cos(A / 2) cos(B/2)
cos(C/2)
cosA + cos B + cos C = 4 sin(A/2) sin(B/2)
sin(C/2) + 1
sinA + sinB – sinC = 4sin (A/2) sin (B/2)
cos (C/2)
Sources
Visit the sources:
math-shortcut-tricks.com
byjus.com/math-formulas
mathportal.org/mathformulas.php
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