Important Formulas of Maths

        

               Key Points and Useful Formulas for Exams 

     Important Formulas For Board Exams

                                                          Number system 

Prime numbers - A prime number is defined as a number that has no factor other than 1 and itself.

Co-prime numbers- co-primes are considered in pairs and two numbers are co-prime if they have no common factors other than 1.

Twin prime numbers - Twin prime numbers are the prime numbers whose difference is always equal to 2. For example, the difference between 5 and 7 is 2, and hence 5 and 7 are twin prime numbers.

Composite numbers - 

All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers. 

HCF and LCM 

About Fraction 

° HCF =       HCF of Numerators /LCM of Denominators 

° LCM =  LCM of Numerators / HCF of Denominators

• Product of two Numbers = L.C.M. × H.C.F 

Keys/ Formulas 

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 = 1/2 [(x-y)² + (y-z)² + (z-x)²]

Exponents /Powers:

a^mxaⁿ  = a^m+n

(a^m)ⁿ  =  a^mn

(a^mbⁿ)^p =   a^mpb ^np

                                                     ^{Quadrilateral} 

. What is quadrilateral? 

   A plane, closed figure bounded by four line segments is called quadrilateral. There are different types of quadrilaterals, they are trapezium, parallelogram, rhombus, rectangle, square. 

•What is the sum of all the interior angles of a quadrilateral? 

The sum of all the interior angles of a quadrilateral is 360 degree. 

^{Quadrilateral Chart} 

                      ^{Trigonometric Table} 

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