Summary BASIC MATHS FORMULAE

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SOME IMPORTANT MATHEMATICAL FORMULAE
Circle : Area = π r2; Circumference = 2 π r.
Square : Area = x2 ; Perimeter = 4x.
Rectangle: Area = xy ; Perimeter = 2(x+y).
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Triangle : Area = (base)(height) ; Perimeter = a+b+c.
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3 2
Area of equilateral triangle = a .
4
4
Sphere : Surface Area = 4 π r2 ; Volume = π r3.
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2 3
Cube : Surface Area = 6a ; Volume = a .
1
Cone : Curved Surface Area = π rl ; Volume = π r2 h
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π
Total surface area = . r l + r π 2

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
am m n mn (ab)m = a m b m
1. am an = am + n 2. = a m − n . 3. (a ) = a . 4. .
an
m am −m = 1
a y
5.   = . 6. a 0 = 1, a ≠ 0 . 7. a x
m . 8. a = a ⇒ x = y
b b m a
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

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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.
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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, a+2d,-----------------------------are in A.P.
nth term, Tn = a + (n-1)d.
n
Sum to n terms, Sn = [ 2a + (n − 1)d ] .
2
If a, b, c are in A.P, then 2b = a + c.
GEOMETRIC PROGRESSION
a, ar, ar2 ,--------------------------- are in G.P.
a(1 − r n ) a(r n − 1)
Sum to n terms, Sn = if r < 1 and Sn = if r > 1.
1− r r −1
a
Sum to infinite terms of G.P, S∞ = .
1− r
If a, b, c are in A.P, then b2 = ac.
HARMONIC PROGRESSION
Reciprocals of the terms of A.P are in H.P
1 1 1
, , , ----------------- are in H.P
a a + d a + 2d
2ac
If a, b, c are in H.P, then b = .
a+c
MATHEMATICAL INDUCTION
n(n + 1)
1 + 2 + 3 + -----------------+n = ∑ n = .
2
n(n + 1)(2n + 1)
12+22 +32 + -----------------+n2 = ∑ n =
2
.
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S B SATHYANARAYANA
M. Sc., M.I.E ., M Phil .
9481477536