Summary list of math formulas

MATHEMATICS FORMULA LIST
FOR CLASS XII (For I Term Paper)
Factoring Formulas
2
a  b  a 2  2ab  b 2

a 2  b 2  ( a  b)( a  b)
3
a  b  a 3  3a 2b  3ab 2  b3
3
a b  a 3  3a 2b  3ab 2  b3


a 3  b 3  ( a  b)(a 2  ab  b 2 )
2
a  b  c  a 2  b 2  c 2  2ab  2bc  2ca

1 2 2 2
a 2  b 2  c 2  ab  bc  ca 
  a  b    b  c    c  a  
2


a3  b3  c 3  3abc   a  b  c  a 2  b 2  c 2  ab  bc  ca 
Area and Volume


Circle : C  2 r   D, where C is circumference, r is radius and D is diameter
A   r 2 , where A is the area
1
Triangle: A b h, where b is the base and h is the perpendicular height
2
a bc
A  s  s  a  s  b  s  c  ; where s  (Heron’s Formula)
2

3 2
Equilateral Triangle A   side 
4
Parallelogram: A  base×corresponding height

2
Square A   side  ; Perimeter = 4 x side

Rectangle A  lb ; Perimeter = 2  l  b 

1
Rhombus A  d1 d 2
2

1
Trapezium : A (a  b)h, where a and b are the lengths of the parallel sides
2
and h is the perpendicular height

1 | Page

, Cuboid ( length = l , breadth = b , height = h )
(i ) V  lbh (ii ) CSA  2h  l  b  (iii) TSA  2  lb  bh  lh  (iv) Diagonal  l 2  b 2  h 2

Cube (side = a )
(i ) V  a 3 (ii) CSA  4a 2 (iii ) TSA  6a 2 (iv) Diagonal  3 a

Cylinder (radius = r , height = h)
(i ) V   r 2 h (ii ) CSA  2 rh (iii ) TSA  2 r  r  h 

Cone (radius = r , height = h , slant height  l )
1
(i ) V   r 2 h (ii) CSA   rl (iii ) TSA   r  r  l  (iv) l  r 2  h 2
3
Sphere (radius = r )
4
(i ) V   r 3 (ii) A  4 r 2
3
Hemi-Sphere (radius = r )
2
(i )V   r 3 (ii) CSA  3 r 2 (iii ) TSA  4 r 2
3
Polygon
Sum of all the angles in a n-sided polygon : 1800  (n – 2)
180 0   n  2 
Each angles of a n-sided regular polygon :
n
Quadratic Formula

If ax 2  bx  c  0, then b  b 2  4ac
x
2a
b c
Sum of roots   ; Product of roots 
a a
Logarithmic Function
log a x  y  x  a y ; x  0, a 0 , a  1


(i) log a 1  0 (ii ) log a a  1
x 
(iii ) log a  xy   log a x  log a y (iv ) log a    log a x  log a y
y 
m
(v) log a x n  n log a x (vi ) log an x m  log a x
n
1 log c a
(vii ) log a x  (viii ) logb a 
log x a log c b
(ix ) If a 1 then x  y  log a x  log a y
( x ) If 0  a  1 then x  y  log a x  log a y


2 | Page