Cube  If any number multiply by itself three time, then result is know as Cube . We denote the Cube of x by x 3 Example :  x × x × x = x 3 2×2×2 = 2 3  = 8 Cube root The is a given number x is the number whose Cube is x .  We denote the Cube root of x by ∛x . Example : ∛x×x×x = x ∛8 =∛2×2×2 = 2  1) Rule : Cube of that number which is made by 1 . Example : 1) 11 3 Step I       11×11×11 Step II  = 121×11→  1 / 1+2 / 2+1 / 1 Step III  =                   1 /3 /3 /1                 =                    1331 2) 111 3 Step I       111×111×111 Step II  =  12321×111 Step III  =  1/ 1+2 / 1+2+3 / 2+3+2 / 3+2+1 / 2+1 / 1 Step IV   =  1/ 3/ 6 /7 /6 /3 /1                 =   1367631 3) 1111 3 + Step I        1111×1111×1111 Step II  =    1234321×1111 Step III  =    1/ 1+2 / 1+2+3 / 1+2+3+4 / 2+3+4+3/ 3+4+3+2/ 4+3+2+1/ 3+2+1 / 2+1 / 1 Step IV   =     1 /3 /6 /10 /12 /12/ 10 /6 /3 /1                  =     1371330631 2) Rule : Cube of that number which is made by 2 . Example :  1) 22 3 Step I       2

Important Formula  : Cuboid :      Let Length = l       Breadth = b       Height = h      then i) Volume of Cuboid = (l X b X h ) cube units. ii) Whole Surface Area of Cuboid = 2(lb X bh X hl ) sq. units iii) Length of  Diagonal of Cuboid = √ l 2 + b 2 + h 2   units. Cube: Let each edge of Cube be a units . Then, i) Volume of the  Cube = a 3 cubic units. ii) Whole surface of the Cube = 6a 2  sq. units. iii) Diagonal of the Cube = √3a units. Cylinder : Let radius of base be r & height or length be h . i) Volume of the Cylinder =  πr 2 h cubic units. ii) Curved surface area of the Cylinder = 2πrh sq. units iii) Total surface area of the  Cylinder = 2πr 2  + 2πrh                                                        = 2πr( r + h ) Cone : Let radius of base = r , height = h  & slant height = l. i) l = √  h 2 + r 2                                                            1                      ii) Volume of the   Cone =    -------πr 2 h sq. units.                       

Fo rmulas on Area                                                                                      1 1) Area of Triangle = --------- X base X heigh t                                                  2 2) Area of Triangle = √s(s-a)(s-b)(s-c) where a, b, c are sides of Triangle                                                 a+b+c and semi perimeter S = -----------------------                                                  2                                                                             √ 3    3) Area of an equilateral Triangle = ------------ X (Side ) 2                                                                                4                                                                              (x + y + z ) 2 4) Area of an Equilateral Triangle = -------------------                                                                                   √ 3    Where x, y, z are Perpendiculars .                                                              

 Average or mean   Number which show the central value of a set of given numbers. Formula Sum of observations ----------------------------------- Number of observations 1) Rule : If each one of some given numbers is multiplied by k, then their average or mean is multiplied by k._ 2) Rule: If each one of some given numbers is increased by k, then their average or mean is increased by k.  3) Rule : A man cover a distance from A to B at u km/hr and returns back to A at uniform speed of v km/hr, then the speed during the whole distance 2uv/(u+v) km/hr. Example 1) Find the average of first 4 prime numbers. Solution:       2+3+5+7 =   -----------------------           4 = 17/4 = 4.25 2)Find the average of first 18 multiples of 6 . Solution:                      Sum of  multiples of 6  Average = ------------------------------------------                        Number of multiple of 6                  6(1+2+3+.............+18) =     ----------------------------------------------              

  Decimal Fractions : Fractions a/b in which the denominators are powers of 10 are called decimal fraction . 1/10, 1/100, 1/1000 etc. are respectively the tenth ,hundredth, and thousandth part of 1 . 6/10 is 6 tenths, written as 0.6 (called decimal 6 ) 19/100 is 19 hundredths written as 0.19 ( called decimal one nine ) 13/100 is 13 hundredths written as 0.13 ( called decimal one three )   1/100 is 1 hundredths written as 0.01 (called decimal zero one ) 122/100 is 122 hundredths written as 1.22 ( called one decimal two two) Example : 1) what is eighty-five hundredths in a fraction ? Solution : 1/100 is hundredth part of 1 , We can write eighty-five hundredths in a fraction 85/100. 2)What is 8 hundredths ? Solution : 1/100 is hundredth part of 1, We can write 8 hundredths in fraction 8/100. Convert a Decimal Into a fraction : Rule : In the denominator, put 1 under the decimal point and annex with it as many zeros a as is the number of digits after the decimal point. Now , remove th

In this page we show some method of subtraction that save your time in exam i) Borrowing and Paying Back Method  It is faster method of subtraction, we also known as equal addition Method . Example : 92 - 55 = 37 ,                97-60 = 37 428-179=249,            449-200=249 2826- 1875=951,   2951-2000=951 ii) Double Column Method of Addition And Subtraction Example    +7165              - 1354               +7834        - 4321 +1432 --------- 11556 --------- Explain  step 1    take first double column 32-21=11, 11+34=45, 45-54= -9, -9+65=56 step 2     take second double column 14-43= -29, -29+78 = 49, 49- 13 = 36, 36+ 79 = 115 Thus Answer 11556 iii) Vinculum  Method Example + 3725 -  6783 + 2502 -  8712 + 1226 -  8713 ----------- -16755 ----------- Explain step 1  take first double column 25-83=-58, -58+2=-56, -56-12=-68,  -68+26= -42, -42-13=-55 step 2  take second double column 37-67=-30, -30+25=-5, -5-87=--92, -92+12=-80, -80-57=-167 thus Answer -16755  iv) Austrian Method of Subt