Ayush Agarwal 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  (a + b) 2  = a 2  + 2ab + b 2 (a – b) 2   = a 2  – 2ab + b 2 (a

                      Number System Natural Numbers - Counting numbers are called natural numbers.  •  The least natural number is 1.  • There are infinitely many natural numbers.  Whole Numbers - All natural numbers together with 0 form the collection of all whole numbers.  • The least whole number is 0.  • There are infinitely many whole numbers.  • Every natural number is a whole number.  • All whole numbers are not natural numbers, as 0 is a whole number which is not a natural number.  Integers -   All natural numbers, 0 and negatives of natural numbers form the collection of all integers.  • 0 is neither negative nor positive.  • There are infinitely many integers.  • Every natural number is an integer.  • Every whole number is an integer.  SSC previous year questions (Important)  Q. 1. Which of the following fraction is the greatest? 2/3 , 5/6 , 11/15 , and 7/8 A). 7/8 B). 11/15 C).  5/6 D). 2/3 Q. 2. If a number is as much greater than 31 as it is less than 75, then