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Quant formulae and shortcuts for Bank PO and SSC

Quant formulae and shortcuts for Bank PO and SSC

Here we are presenting some most important Quant formulae and shortcuts for Bank PO and SSC. This quant cheat sheet can be very handy for the last minute revision before the exam.

  1. HCF & LCM

LCM × HCF = Product of the Numbers

  1. Algebra
  • a2 – b2 = (a – b)(a + b)
  • (a+b)2 = a2 + 2ab + b2
  • a2 + b2 = (a – b)2 + 2ab
  • (a – b)2 = a2 – 2ab + b2
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  • (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a – b)3 = a3 – 3a2b + 3ab2 – b3
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  • a4 – b4 = (a – b)(a + b)(a2 + b2)
  • (a + b + c)3 = a3 + b3 + c3 + 3(b+c)(c+a)(a+b)
  • a3 + b3 + c3 -3abc = (a+b+c) (a2 + b2 + c2 – ab – bc – ca)
  • If (a+b+c) = 0, a3 + b3 + c3 = 3abc
  1. Surds and Indices
  • (am)(an) = am+n
  • (ab)m= ambm
  • (am)n= amn
  • a0= 1
  • (am)/(an) = (am-n)
  • (am) = 1/ (a-m)
  1. Progressions:

In an Arithmetic progression (AP) with first term  and common difference  ,

  • Nth term of AP = 
  • Sum of n terms of AP = 

In a Geometric Progression (GP) with first term  and common ratio  ,

  • Nth term of GP = 
  • Sum of n terms of GP = 
  • For an infinite GP where , sum of the series is 

Harmonic Progression: A series in which reciprocal terms are in AP. Harmonic mean of two numbers  and  is given by 

  1. Percentages
  • Effective percentage of x% and y% =  . If there is a percentage decrease, the value is used with a negative sign.
  1. Profit & Loss

  1. Simple & Compound Interest

Watch Trick on Simple & Compound Interest

  1. Alligations and Mixtures

Direct formula for removal and replacement in mixtures:

‘x’ amount of milk is there in the vessel and ‘a’ is taken out and replaced with water. If the process is repeated ‘n’ times, then the quantity of milk remaining in the vessel = 

  1. Time Speed Distance
  • Distance = Speed x Time
  • Average speed = 
  • Speed conversion from km/hr to m/s

  • Speed conversion from m/s to km/hr

  • If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is 
  • If a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the 
  • If two persons A and B start at the same time in opposite direction from two points and after passing each other, they complete the journey in ‘a’ and ‘b’ hrs respectively, then

           

  • A Man covers a certain distance at x km/h and gets late/early by ‘a’ minutes. When he travels at y km/h, he reaches ‘b’ minutes late/early. Distance travelled in this case is given by

        

[Difference of time should be taken by accounting late and early in the problem]
  • If the speed of boat in still water is ‘u’ km/h and speed of the stream is ‘v’ km/h, then
    • Downstream speed = (u+v) km/h
    • Upstream speed = (u-v) km/hr
  • If the speed downstream is ‘a’ km/hr and speed upstream is ‘b’ km/hr, then
    • Speed of boat in still water = km/h
    • Speed of stream = km/h
  1. Time & Work, Wages, pipes & Cisterns
  • If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in [pq / (p+q)] days
  • MDH formula: where M= no. of men, D= no. of days, H= no. of hours per day and W= amount of work.
  1. Permutations/Combinations
  • Number of permutations of ‘n’ things, taken ‘r’ at a time is given by:

  • Number of combinations of ‘n’ things, taken ‘r’ at a time is given by:

  • If there are ‘n’ objects, out of which ‘p’ are alike of one kind, ‘q’ are alike of second kind, ‘r’ are alike of third kind, and remaining all are different, then permutations is given by 
  • Circular permutations: the number of circular permutations of n different things taken all at a time is given by (n-1)!, if clockwise and anti-clockwise orders are taken as different.
  • In case of a garland or necklace, no. of circular permutations become  x (n-1)! , as clockwise and anti-clockwise arrangements are treated as same.
  1. Probability

Probability means chance of occurrence of an event. In its basic form, probability is calculated as:

Probability =

Eg. If two coins are tossed, probability of both heads is 1/4. This is because the total cases are (HH),(HT),(TH),(TT) out of which favourable cases is only (HH).

All the exam questions can be solved by just remembering this formula. You can log on to www.examformula.com to better understand the concept and exam problems.

Quant formulae and shortcuts for Bank PO and SSC

  1. Trigonometry

Pythagoras Theorem:   , where ‘a’ and ‘b’  are perpendicular and base and c is the hypotenuse

Trigonometry Identities:

Formulas involving co-function identities:

sin(90−x)=cosx

cos(90−x)=sinx

tan(90−x)=cotx

cot(90−x)=tanx

Sum/ difference formulas:

Double Angle Formulas:

Formulas involving Product Identities:

Formulas for Sum to Product Identities:

  1. Mensuration

2D FIGURES:

Rectangle:

  • Area = length x breadth
  • Perimeter = 2 × (Length + Breadth)
  • Length of the Diagonal = 

Square:

  • Area =
  • Perimeter =
  • Length of Diagonal =

Parallelogram:

  • Area = 
  • Perimeter = 2 × (Length + Breadth)

Triangle:

  • Area =

Area (using heron’s formula) =  ; where s (semi-perimeter) = 
where a,b,c  are sides of the triangle

  • Area of equilateral triangle = 

Trapezium:

  • Area =
  • Area =
  • Perimeter =

Circle:

  • Area =
  • Circumference =
  • Area of sector =
  • Length of an arc =

3D FIGURES:

Cuboid:

  • Volume =
  • Total surface Area =
  • Length of diagonal =

Cube:

  • Volume =
  • Total surface area =
  • Length of leading diagonal =

Cylinder:

  • Volume =
  • Curved Surface Area =
  • Total Surface Area =

Cone:

  • Volume =
  • Curved surface Area =
  • Total Surface Area =
  • Slant Height =

Sphere:

  • Volume =
  • Surface Area =

Hemisphere:

  • Volume =
  • Curved Surface Area =
  • Total Surface Area =

Prism:

  • Volume =
  • Lateral Surface Area =
  • Total Surface Area =

Pyramid:

  • Volume =
  • Total Surface Area =
  1. Linear & Quadratic Equations
  • Roots of equations  are:

  • is called the Discriminant (denoted by ‘D’). The value of D tells about the nature of roots of the equation:
    • If D>0, the equation has two real and distinct roots
    • If D=0, the equation has two real and equal roots
    • If D<0, the equation has no real roots
  • Sum of roots = , product of roots =
  1. Coordinate Geometry
  • Distance Formula: Distance between two points (x1, ,y1) and (x2 ,y2) is given by:

  • Section Formula: The point which divides the line joining two points (x1, ,y1) and (x2 ,y2) internally is:

The point which divides the line joining two points (x1, ,y1) and (x2 ,y2) externally is:

  • Mid point:

  • Slope of a line:

  • Angle between two lines: For two lines, y1=m1x1+c1 and y2=m2x2+c2 which make angles , the slopes are given by

Angle between the lines is:

Watch Video on Coordinate Geometry

  1. Simplification
  • BODMAS Rule: The rule says that you have to solve any mathematical expression in correct sequence. The sequence of BODMAS is as follows:

B = Bracket

O = Order (Powers, Square Roots, etc.)

DM = Division and Multiplication (left-to-right)

AS = Addition and Subtraction (left-to-right)

If some formulae are left, we will cover it in the upcoming articles. Hope you enjoyed this compilation. Stay tuned for more and share with your friends!

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