>>> SOME QUICK MATHS FORMULAS y TIME & DISTANCE :- Distance = Speed * Time 1 km/hr = 5/18 m/sec 1 m/sec = 18/5 km/hr Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is 2xy/(x+y) kmph. PROBLEMS ON TRAINS :- Time taken by a train x metres long in passing a signal post or a pole or a standing man is equal to the time taken by the train to cover x metres. Time taken by a train x metres long in passing a stationary object of length y metres is equal to the time taken by the train to cover x+y metres. Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u>v, then time taken by the faster train to cross the slower train = (x+y)/(u-v) hours. Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph. If two trains of length x km and y km are moving in the opposite directions at u kmph and v kmph, then time taken by the trains to cross each other = (x+y)/(u+v)hours. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then A’s speed : B’s speed = (√b : √a) SIMPLE & COMPOUND INTERESTS :- Let P be the principal, R be the interest rate percent per annum, and N be the time period. Simple Interest = (P*N*R)/100 Compound Interest = P(1 + R/100)^N – P Amount = Principal + Interest when rate of interest time n principal are constant den principal=(C.I.-S.I.)*(100/R)^N LOGARITHMS :- If a^m = x , then m = loga(x). Properties : logx(x) = 1 logx(1) = 0 loga(x*y) = loga(x) + loga(y) loga(x/y) = log ax – log ay loga(x) = 1/logx(a) loga(x^p) = p(loga(x)) loga(x) = logb(x)/logb(a) Note : Logarithms for base 1 does not exist. AREA & PERIMETER :- Shape Area Perimeter Circle ∏ (Radius)2 2∏(Radius) Square (side)2 4(side) Rectangle length*breadth 2(length+breadth) Area of a triangle = 1/2*Base*Height or Area of a triangle = √ (s(s-(s-b)(s-c)) where a,b,c are the lengths of the sides and s = (a+b +c)/2 Area of a parallelogram = Base * Height Area of a rhombus = 1/2(Product of diagonals) Area of a trapezium = 1/2(Sum of parallel sides) (distance between the parallel sides) Area of a quadrilateral = 1/2(diagonal)(Sum of sides) Area of a regular hexagon = 6(√3/4)(side)2 Area of a ring = ∏(R2-r2) where R and r are the outer and inner radii of the ring. Area of a circle=πr^2 or πd^2/4 Area of semi-circle=πr^2/2 Area of a quadrant of a circle=πr^2/4 Area enclosed by two concentric circles=π(R^2- r^2) Area of a sector=Ɵ/180 degree *πr No of revolutions completed by a rotating wheel in 1 minute=distance moved in 1 minute/ circumference VOLUME & SURFACE AREA :- Cube : Let a be the length of each edge. Then, Volume of the cube = a3 cubic units Surface Area = 6a2 square units Diagonal = √ 3 a units Cuboid : Let l be the length, b be the breadth and h be the height of a cuboid. Then Volume = lbh cu units Surface Area = 2(lb+bh+lh) sq units Diagonal = √ (l2+b2+h2) Cylinder : Let radius of the base be r and height of the cylinder be h. Then, Volume = ∏r2h cu units Curved Surface Area = 2∏rh sq units Total Surface Area = 2∏rh + 2∏r2 sq units Cone : Let r be the radius of base, h be the height, and l be the slant height of the cone. Then, l2 = h2 + r2 Volume = 1/3(∏r2h) cu units Curved Surface Area = ∏rl sq units Total Surface Area = ∏rl + ∏r2 sq units Sphere : Let r be the radius of the sphere. Then, Volume = (4/3)∏r3 cu units Surface Area = 4∏r2 sq units Hemi-sphere : Let r be the radius of the hemi-sphere. Then, Volume = (2/3)∏r3 cu units Curved Surface Area = 2∏r2 sq units Total Surface Area = 3∏r2 sq units Prism : Volume = (Area of base)(Height) ALGEBRA :- 1.(a+b)^2=a^2+2ab+b^2 2.(a-b)^2=a^2-2ab+b^2 3.(a+b)^2=(a-b)^2+4ab 4.(a-b)^2=(a+b)^2-4ab 5.a^2-b^2=(a+b)(a-b) 6.(a + b)3= a3+ b3+ 3ab(a + b) 7.a3+ b3= (a + b)3− 3ab(a + b);(a+b)^3-3ab(a +b) 8.(a − b)3= a3− b3− 3ab(a − b) 9.a3− b3= (a − b)3+ 3ab(a − b);(a-b)^3+3ab(a- b) 10.a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2- ab-bc-ac) =(a+b+c)*1/2*[(a-b)^2+(b-c)^2+(c-a)^2] 11.if a+b+c=0 then a^3+b^3+c^3=3abc 12.(a+b+c)^3=a^3+b^3+c^3+3(b+c)(c+a)(a+b) 13.a^2+b^2=(a+b)^2-2ab=(a-b)^2+2ab 14.(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca) 15.. a^n− b^n= (a − b)(a^n−1+ a^n−2*b + a^n −3*b^2+ …..+b^n−1)
Posted on: Tue, 26 Aug 2014 15:06:48 +0000
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