Important Formulas

 IMPORTANT MATHS FORMULAE

Algebra:

1. (a + b)2 = a2 + 2ab + b2

2. (a – b)2  = a2 – 2ab + b2

3. (a + b) (a – b) = a2 – b2

4. (x + a)(x + b)  = x2 + (a + b)x + ab

5. (x + a)(x – b)  = x2 + (a – b)x – ab

6. (x – a)(x + b)  = x2 + (b – a)x – ab

7. (x – a)(x – b)  = x2  – (a + b)x + ab

8. (a + b)3  = a3 + b3 + 3ab(a + b)

9. (a – b)3  =  a3 – b3 – 3ab(a – b)

10. (x + y + z) 2  = x2 + y2 + z2 + 2xy + 2yz + 2xz

11. (x + y – z) 2  =  x2 + y2 + z2 + 2xy – 2yz – 2xz

12. (x – y + z)2  = x2 + y2 + z2 – 2xy – 2yz + 2xz

13. (x – y – z)2  = x2 + y2 + z2 – 2xy +  2yz – 2xz

14. x3 + y3 + z3 – 3xyz  = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)

15. x2 + y2  = 1212 [(x + y)2 + (x – y)2]

16. (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

17. x3 + y3 = (x + y) (x2 – xy + y2)

18. x3 – y3  = (x – y) (x2 + xy + y2)

19. 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:

Probability

P(E) =   Number of outcomes favorable to E

Total Number of Possible Outcomes

Mensuration