Some quick maths formulas which we should know:- Formulas 1. Sum of first n natural numbers = n(n+1)/2 2. Sum of the squares of first n natural numbers = n(n+1)(2n+1)/6 3. Sum of the cubes of first n natural numbers = [n(n+1)/2]^2 4. Sum of first n natural odd numbers = n^2 5. Average = (Sum of items)/Number of items _________________ AP & GP Arithmetic Progression (A.P.): An A.P. is of the form a, a+d, a+2d, a+3d, … Where a is called the ‘first term’ and d is called the ‘common difference’ 1. nth term of an A.P. tn = a + (n-1)d 2. Sum of the first n terms of an A.P. Sn = n/2[2a+(n-1)d] or Sn = n/2(first term + last term) Geometrical Progression (G.P.): A G.P. is of the form a, ar, ar2, ar3, … where a is called the ‘first term’ and r is called the ‘common ratio’. 1. nth term of a G.P. tn = arn-1 2. Sum of the first n terms in a G.P. Sn = a|1-rn|/|1-r| _______________ PERMUTATIONS AND COMBINATIONS : nPr = n!/(n-r)! nPn = n! nP1 = n nCr = n!/(r! (n-r)!) nC1 = n nC0 = 1 = nCn nCr = nCn-r nCr = nPr/r! Number of diagonals in a geometric figure of n sides = nC2-n _________________ TESTS OF DIVISIBILITY : A number is divisible by 2 if it is an even number. A number is divisible by 3 if the sum of the digits is divisible by 3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4. A number is divisible by 5 if the units digit is either 5 or 0. A number is divisible by 6 if the number is divisible by both 2 and 3. A number is divisible by 8 if the number formed by the last three digits is divisible by 8. A number is divisible by 9 if the sum of the digits is divisible by 9. A number is divisible by 10 if the units digit is 0. A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places, is divisible by 11. _______________ H.C.F and L.C.M : H.C.F stands for Highest Common Factor. The other names for H.C.F are Greatest Common Divisor (G.C.D) and Greatest Common Measure (G.C.M). The H.C.F. of two or more numbers is the greatest number that divides each one of them exactly. The least number which is exactly divisible by each one of the given numbers is called their L.C.M. Two numbers are said to be co-prime if their H.C.F. is 1. H.C.F. of fractions = H.C.F. of numerators/L.C.M of denominators L.C.M. of fractions = G.C.D. of numerators/H.C.F of denominators Product of two numbers = Product of their H.C.F. and L.C.M. ________________ PERCENTAGES : If A is R% more than B, then B is less than A by R / (100+R) * 100 If A is R% less than B, then B is more than A by R / (100-R) * 100 If the price of a commodity increases by R%, then reduction in consumption, not to increase the expenditure is : R/(100+R)*100 If the price of a commodity decreases by R%, then the increase in consumption, not to decrease the expenditure is : R/(100-R)*100 ________________ PROFIT & LOSS : Gain = Selling Price(S.P.) – Cost Price(C.P) Loss = C.P. – S.P. Gain % = Gain * 100 / C.P. Loss % = Loss * 100 / C.P. S.P. = (100+Gain%)/100*C.P. S.P. = (100-Loss%)/100*C.P. If CP(x), Gain(y), Gain%(z). Then y = x*z/100. [Same in case of Loss] _________________ RATIO & PROPORTIONS: The ratio a : b represents a fraction a/b. a is called antecedent and b is called consequent. The equality of two different ratios is called proportion. If a : b = c : d then a, b, c, d are in proportion. This is represented by a : b :: c : d. In a : b = c : d, then we have a* d = b * c. If a/b = c/d then ( a + b ) / ( a – b ) = ( c + d ) / ( c – d ). _________________ TIME & WORK : If A can do a piece of work in n days, then A’s 1 day’s work = 1/n If A and B work together for n days, then (A+B)’s 1 days’s work = 1/n If A is twice as good workman as B, then ratio of work done by A and B = 2:1 ____________________ PIPES & CISTERNS : If a pipe can fill a tank in x hours, then part of tank filled in one hour = 1/x If a pipe can empty a full tank in y hours, then part emptied in one hour = 1/y If a pipe can fill a tank in x hours, and another pipe can empty
Posted on: Fri, 12 Dec 2014 06:06:40 +0000
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