Sample Material of Online Coaching For SSC CGL (Tier - 2) - Simplification

Sample Material SSC CGL TIER-2 Online Coaching

Numerical Aptitude (Chapter - Simplification)

In simplification of an expression there are certain laws which should be strictly adhered to. These laws are as follows:

‘VBODMAS’ Rule

This rule gives the correct sequence in which the mathematical operation are to be executed so as to find out the value of a given expression.

Here, ‘V’ stands for Vicnaculum (or Bar), ‘B’ stands for ‘Bracket’, ‘O’ stands for ‘Of’, ‘D’ stands for ‘Division’, ‘M’ stands for ‘Multiplication’, ‘A’ stands for ‘Addition’ and ‘S’ stand for ‘Subtraction’.

(a) Here, ‘VBODMAS’ gives the order of simplification. Thus, the order of performing the mathematical operations in a given expression are

  1. First : Virnaculum or line bracket or bar
  2. Second: Bracket
  3. Third: Of
  4. Fourth: Division
  5. Fifth: Multiplication
  6. Sixth: Addition &
  7. Seventh: Subtraction
  8. The above order should strictly be followed.

(b) There are four types of brackets.

  1. Square brackets [ ]
  2. Curly brackets { }
  3. Circular brackets ( )
  4. Bar or Virnaculum –

Thus, in simplifying an expression all the brackets must be removed in the order ‘–’, ‘( )’, ‘{ }’ and ‘[ ]’.

Basic Formulae

(i) (a + b)2 = a2 + 2ab + b2

(ii) (a – b)2 = a2 – 2ab + b2

(iii) (a + b)2 – (a – b)2 = 4ab

(iv) (a + b)2 + (a – b)2 = 2(a2 + b2)

(v) (a2 – b2) = (a + b) (a – b)

(vi) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

(vii) (a3 + b3) = (a + b) (a2 – ab + b2)

(viii) (a3 – b3) = (a – b) (a2 + ab + b2)

(ix) (a3 + b3 + c3 – 3abc) = (a + b + c), (a2 + b2 + c2 – ab – bc – ca)

(x) a3 + b3 + c3 = 3abc, if a + b + c = 0

:: Home Assignment for Practice ::

1. What is of 3?

(a) 6
(b) 3
(c) 1/2
(d) 1/3

2. What is 10 + 8 equal to?

(a) 2
(b) 18
(c) 10
(d) 8

3. Multiply 0.932 by 100.

(a) 932
(b) 9.32
(c) 93.2
(d) 9320

4. Divide 0.045 by 100.

(a) 0.0045
(b) 0.00045
(c) 0.000045
(d) 0.45

5. If 2x = 5 and 3y = 8, then is equal to

(a) 5/18
(b)5/16
(c)5/12
(d)5/8

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SSC Combined Graduate Level Exam
Mathematics