Advance Math Formulas

By Abhishek Tomar on Aug 31, 2009 with Comments 0

Speed And Distance

Speed = distance/ Time

Average Speed = 2(a+b)/ab or (Total Distance/Total Time)/2

Upstream and Downstream

Upstream = ( Current – Still )/2

Downstream = ( Current – Still ) /2

Series

1 + 2 +3 + 4 + 5 ….. = ( n ( n + 1 ) ) / 2

1² + 2² +3² + 4² + 5² ….. = ( n (n+1)(2n+)) / 6

1³ + 2³ +3³ + 4³ + 5³ ….. = ( n² (n + 1)² ) / 4

1 + 3 + 5 + 7 …. = n²

2 + 4 + 6 + 8…. = n ( n + 1 )

Number of Terms = ( Last term – First Term ) / Difference ) + 1

Arithmetic Progression

n^th Term = a + (n – 1) d

Sum Of n^th Term = n/2 ( 2a + (n-1) d)

Mid Term a, b, c….. b = (a + c) / 2

Geometric Progression

n^th Term = ar^(n-1)

Sum Of n^th Term = a ( 1 – rⁿ) / (1 – r)

Mid Term a, b, c….. b² = ac

Harmonic Progression

Mid Term a, b, c….. b = (2 ac) / a + c

Square Root ( trick )

Square Root of 29 = nearest root ( Remainder ) / 2 ( nearest root )

eg: 5 ( 4 / 10 )

Explanation : 5² = 25 : 29 – 25 = 4 : 2 x 5 = 10;

Cube Root ( Trick )

Cube Root of 12,167 = 23

Explanation : group three digest in, one starting from right to left. So we get 167 one group and 12 other group. Now 167 last digest is 7 and cube of 3 is 27 so the last digit is 7 we have a match so we take 3, Now we have 12 nearest to which cube 2³ = 8 so we take , we get 23.

1³ + 6³ + 8³ = 9³

3³ + 4³ + 5³ = 6³

Sets

(A U B) = A + B – ( A n B )

(A U B) =A + B

A = (A – B ) + ( A n B )

B = (B – A ) + ( A n B )

(A U B) = (A – B ) + ( A n B ) + (B – A )

LCM and GCM

LCM X GCM = a X b

Ratio

(a + b) /b :: (c + d) /d

(a – b) /b :: (c – d) /d

(a + b) / (a – b) :: (c + d) / (c – d)

Simple Interest

Simple Interest = (P X R X T )/ 100

Installment basis : Present Worth = (P X 100 ) / (100 + R X T)

Compound Interest = P+ I = P ( 1 + (R/100) ) ^Time

Installment basis : Present Worth =Principle / (R/100) ) ^Time

Coordinate Geometric

Length of 2 point = point P (x₁,y₁) and point Q (x₂,y₂) == √ ( x_{2 –} x₁ )² + ( y₂ – y₂)²

Mid Point = ( x_{2 –} x₁ ) / 2 , ( y₂ – y₂) / 2

Divide Line in M : N ratio = ( Mx₂ + Nx₂ ) / M+N , ( My₂ + Ny₂ ) / M+N

Centroid of triangle = (X₁ + X₂ + X₃ ) / 3 , (Y₁ + Y₂ + Y₃ ) / 3

Slope = M= y₂ – y₁ / x₂ – x₁

Equation of straight line = y – y₁ = M ( X – X₁)

Parallel Line = M₁ =M₂

Perpendicular Line = M₁M₂ = -1

Area of Triangle = 1/2 (X₁(Y₂ – Y₃) + X₂(Y₃-Y₁) + X₃(Y₁-Y₂) )

Complementary Angle

2 Angle whose Sum = 90 that is (90 – x) & x = 90

Supplementary Angle

2 Angle whose Sum = 180 that is (180 – x) & x = 180

Polygons

Sum of Interior angle = (2n – 4) 90

Number of sides = 360 / exterior Angles