important mathamatical formula for cbse

Important Mathematical Formulas

Maths Formulas
1. (a + b)(a – b) = a2 – b2
1. (a + b + c) 2 = a2 + b2 + c 2 + 2(ab + bc + ca)
1. (a ± b) 2 = a2 + b2± 2ab
1. (a + b + c + d) 2 = a2 + b 2 + c 2 + d2 + 2(ab +
ac + ad + bc + bd + cd)
1. (a ± b) 3 = a3 ± b3 ± 3ab(a ± b)
1. (a ± b)(a 2 + b2 m ab) = a3 ± b 3
1. (a + b + c)(a 2 + b2 + c 2 -ab – bc – ca) = a 3
+ b3 + c 3 – 3abc =
1/2 (a + b + c)[(a – b) 2 + (b – c) 2 + (c – a) 2]
1. when a + b + c = 0, a 3 + b3 + c 3 = 3abc
1. (x + a)(x + b) (x + c) = x 3 + (a + b + c) x 2 +
(ab + bc + ac)x + abc
1. (x – a)(x – b) (x – c) = x 3 – (a + b + c) x 2 +
(ab + bc + ac)x – abc
1. a4 + a 2b2 + b4 = (a 2 + ab + b 2)( a2 – ab +
b2)
1. a4 + b 4 = (a 2 – √2ab + b2 )( a2 + √2ab + b2 )
1. an + b n = (a + b) (a n-1 – a n-2 b + a n-3 b2
– a n-4 b 3 +…….. + b n-1 )
(valid only if n is odd)
1. an – bn = (a – b) (a n-1 + a n-2 b + a n-3 b2
+ a n-4 b3 +……… + b n-1 )
{where n ϵ N)
1. (a ± b) 2n is always positive while -(a ± b) 2n
is always negative, for any real values of a and b
1. (a – b) 2n = (b – a) 2” and (a – b) 2n+1 = – (b
– a) 2n+1
1. if α and β are the roots of equation ax 2 + bx
+ c = 0, roots of cx” + bx + a = 0 are 1/α and 1/
β.
if α and β are the roots of equation ax 2 + bx + c
= 0, roots of ax 2 – bx + c = 0 are -α and -β.
1.
n(n + l)(2n + 1) is always divisible by 6.
32n leaves remainder = 1 when divided by 8
n3 + (n + 1 ) 3 + (n + 2 ) 3 is always divisible by
9
102n + 1 + 1 is always divisible by 11
n(n 2 - 1) is always divisible by 6
n2+ n is always even
23n -1 is always divisible by 7
152n-1 +l is always divisible by 16
n3 + 2n is always divisible by 3
34n – 4 3n is always divisible by 17
n! + 1 is not divisible by any number between 2
and n
(where n! = n (n – l)(n – 2)(n – 3)…….3.2.1)
for eg 5! = 5.4.3.2.1 = 120 and similarly 10! =
10.9.8…….2.1= 3628800
1. Product of n consecutive numbers is always
divisible by n!.
1. If n is a positive integer and p is a prime,
then np – n is divisible by p.
1. |x| = x if x ≥ 0 and |x| = – x if x ≤ 0.
1. Minimum value of a2.sec 2Ɵ + b2.cosec 2Ɵ is (a
+ b) 2 ; (0° < Ɵ < 90°)
for eg. minimum value of 49 sec 2Ɵ + 64.cosec 2 Ɵ
is (7 + 8) 2 = 225.
2. among all shapes with the same perimeter a
circle has the largest area.
1. if one diagonal of a quadrilateral bisects the
other, then it also bisects the quadrilateral.
1. sum of all the angles of a convex
quadrilateral = (n – 2)180°
1. number of diagonals in a convex quadrilateral
= 0.5n(n – 3)
1. let P, Q are the midpoints of the nonparallel
sides BC and AD of a trapezium ABCD.Then,
ΔAPD = ΔCQB.