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

                               EXPONENTS Exponents - An exponent refers to a number that how many times to use the number in a mathematical operation like multiplication, division etc.  Exponents is also termed as power.  Power - An expression that represents repeated multiplication of the same number is called a power. Special cases when the exponent is 0 or 1 :- Case 1.  When the power is 0 a^0 = 1 67^0 = 1 Case 2. When the power is 1  a^1 = a 9^1 = 9                     Laws of Exponents The following identities hold for all integer exponents :- Practice Questions:- 1.Find out the value of (2/5) 3  ?   2.What is the power of a number when squared? 3. Simplify: (3/2) 2  + (2/3) 2  + (5/4) 2 4.  If 4 x  = 64, then 3 2x  = ? 5. Divide x 5  by x 2     Thank you for visiting  Keep sharing  Join us now :-  Instagram