Mathe Formulae

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1

SOME IMPORTANT MATHEMATICAL FORMULAE

Circle
: Area = π r2; Circumference = 2 π r.
Square : Area = x2 ; Perimeter = 4x.
Rectangle: Area = xy ; Perimeter = 2(x+y).
1
Triangle : Area = (base)(height) ; Perimeter = a+b+c.
2
3 2
Area of equilateral triangle = a .
4
4
Sphere : Surface Area = 4 π r2 ; Volume = π r3.
3
2
3
Cube
: Surface Area = 6a ; Volume = a .
1
Cone
: Curved Surface Area = π rl ; Volume = π r2 h
3
π r l + π r2
Total surface area = .
Cuboid : Total surface area = 2 (ab + bh + lh); Volume = lbh.
Cylinder : Curved surface area = 2 π rh; Volume = π r2 h
Total surface area (open) = 2 π rh;
Total surface area (closed) = 2 π rh+2 π r2 .
SOME BASIC ALGEBRAIC FORMULAE:

1.(a + b)2 = a2 + 2ab+ b2 .
2. (a - b)2 = a2 - 2ab+ b2 .
3.(a + b)3 = a3 + b3 + 3ab(a + b).
4. (a - b)3 = a3 - b3 - 3ab(a - b).
2
2
2
2
5.(a + b + c) = a + b + c +2ab+2bc +2ca.
6.(a + b + c)3 = a3 + b3 + c3+3a2b+3a2c + 3b2c +3b2a +3c2a +3c2a+6abc.
7.a2 - b2 = (a + b)(a – b ) .
8.a3 – b3 = (a – b) (a2 + ab + b2 ).
9.a3 + b3 = (a + b) (a2 - ab + b2 ).
10.(a + b)2 + (a - b)2 = 4ab.
11.(a + b)2 - (a - b)2 = 2(a2 + b2 ).
12.If a + b +c =0, then a3 + b3 + c3 = 3 abc .
INDICES AND SURDS m n mn (ab)m = a m b m am 1. am an = am + n 2.
= a m − n . 3. (a ) = a
. 4.
.
an m am
−m = 1
a
5.   =
.
6. a 0 = 1, a ≠ 0 .
7. a
. 8. a x = a y ⇒ x = y m am
b
b
9. a x = b x ⇒ a = b 10. a ± 2 b = x ± y , where x + y = a and xy = b.

S B SATHYANARAYANA
M. Sc., M.I.E ., M Phil .
9481477536

2
LOGARITHMS
a x = m ⇒ log m = x (a > 0 and a ≠ 1) a 1. loga mn = logm + logn.
m
2. loga   = logm – logn.
n
3. loga mn = n logm. log a
4. logba =
.
log b
5. logaa = 1.
6. loga1 = 0.
1
7. logba =
.
log a b
8. loga1= 0.
9. log (m +n) ≠ logm +logn.
10. e logx = x.
11. logaax = x.
PROGRESSIONS
ARITHMETIC PROGRESSION a, a + d,…...

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