Ayush Agarwal Maths

Compound Interest - compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. Applications of Compound Interest  1. In increase or decrease in population.  2. The growth of bacteria when the rate of growth is known.  3. Depreciation in the values of machines.  Important Facts :  1. When time is given in days, we convert it to year by dividing it by 365. 2. When time is given in months, we convert it to year by dividing it by 12. 3. When dates are given, the day on which the sum is borrowed is not included but the day on which money is returned is included, while counting the number of days. Remark - negative sign of rate indicates the depreciation.  Practice Questions  1.Find the compound interest on ₹ 5000 at 8% per annum for 2 years, compounded annually?  2.Find the amount of ₹18000 for 3 years, compounded annually at 10% per annum. Also, find the compound interest.  3.The compound interest on Rs. 30,000 at 7% pe

Simple interest -  Simple interest  is  interest  calculated on the principal portion of a loan  to a savings account.

Direct proportion - Two quantities x and y are said to be in direct proportion if whenever the value of x increases or decreases, then the value of y increases or decreases in such a way that the ratio x/y remains constant. 

          SQUARES AND SQUARE ROOTS   Square number - The square of a number is the product of the number with the number itself.  A given number is a perfect square if its prime factors can be expressed in pairs of equal factors.  A perfect square number is never negative. For example - 8^2 = (8×8) = 64 Facts About Squares -  1. A number ending in 2, 3, 7 or 8 is never a perfect square.  2. A number ending in an odd number of zeros is never a perfect square.  3. The square of an even number is always even.  4. The square of an odd number is always odd.  5. The ending digits of a square number is 0, 1, 4, 5, 6, or 9 only.  Note:- It is not necessary that all numbers ending with digits 0, 1, 4, 5, 6, or 9 are square numbers.  Important Facts-  1. Numbers ending in an even number of zeros are not necessarily perfect squares. Eg- 3700, 290000, 47000000.   Practice Questions :-  1. Find the square of 54 ?  2. What least number must be added to 5607 to mak