MPORTANT MATHS FORMULAE
Algebra:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b) (a – b) = a2 – b2
- (x + a)(x + b) = x2 + (a + b)x + ab
- (x + a)(x – b) = x2 + (a – b)x – ab
- (x – a)(x + b) = x2 + (b – a)x – ab
- (x – a)(x – b) = x2 – (a + b)x + ab
- (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- (x + y + z) 2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
- (x + y – z) 2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
- (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
- (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
- x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
- x2 + y2 = 1212 [(x + y)2 + (x – y)2]
- (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
- x3 + y3 = (x + y) (x2 – xy + y2)
- x3 – y3 = (x – y) (x2 + xy + y2)
- x2 + y2 + z2 -xy – yz – zx = 1212 [(x-y)2 + (y-z)2 + (z-x)2]
Powers:
amxan = am+n
aman=am−naman=am−n
(am)n = amn
(ambn)p = ampb np
a-m = 1am1am
amn=am−−−√namn=amn
Rules of Zero:
a1 = a
a0 = 1
a*0 = 0
a is undefined
Linear Equation:
Linear equation in one variable ax + b = 0, x = – −ba−ba
Quadratic Equation: ax2 + bx + c = 0 x = −b±b2−4ac√2a−b±b2−4ac2a
Discriminant D = b2 – 4ac
Math Formulas:
When rate of discount is given Discount = MP∗Rate of Discount 100
Simple Interest = PTR100PTR100 where P = Principal, T = Time in years R = Rate of interest per annum
Principal = 100∗S.IR∗T100∗S.IR∗T
Rate = 100∗S.IP∗T100∗S.IP∗T
Time = 100∗S.IP∗R100∗S.IP∗R
Principal = Amount – Simple Interest
Discount = MP – SP
Trigonometry:
