- 1) This chapter is very important because numerical on simplification are based on concepts related decimal fraction, square and cube roots, H.C.F. and L.C.M., numbers, etc.
- 2) How to find H.C.F. and L.C.M.
- 3) Tricks to solve decimal fractions
- 4) Number system, types of numbers
- 5) How to find square root and cube root

- 1) (a - b)
^{2}= (a^{2}+ b^{2}- 2ab) - 2) (a + b)
^{2}= (a^{2}+ b^{2}+ 2ab) - 3) (a + b) (a – b) = (a
^{2}– b^{2}) - 4) (a
^{3}+ b^{3}) = (a + b) (a^{2}– ab + b^{2}) - 5) (a
^{3}- b^{3}) = (a - b) (a^{2}– ab + b^{2}) - 6) (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2 (ab + bc + ca) - 7) (a
^{3}+ b^{3}+ c^{3}– 3abc) = (a + b + c) (a^{2}+ b^{2}+ c^{2}– ab – bc – ac)

## Quick Tips and Tricks## 1) Virnaculum (Bar ‘¬¬–’):If a given expression contains a virnaculum (bar), then first simplify the given expression under virnaculum and then follow the rule of
## 2) ‘BODMAS Rule’:This rule is used to solve and find out the value of given expressions by performing the operations in a correct sequence.
- B: Bracket
- O: Order (i.e. power, square root etc.)
- D: Division (Left to right)
- M: Multiplication (Left to right)
- A: Addition (Left to right)
- S: Subtraction (Left to right)
## 3) Modulus of a real numberThe modulus of a real number or the absolute value is defined as follows: Modulus of x is written as |x| |

- Numbers
- Highest Common Factor And Least Common Multiple
- Decimal
- Fractions
- Simplification
- Surds And Indices
- Chain Rule
- Square Root And Cube Root
- Ratio And Proportion
- Pipes And Cisterns
- Boats and Streams
- Problems on Trains
- Alligation or Mixtures
- Time and Distance
- Geometry
- Time and Work
- Simple Interest
- Problem Solving

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- Ordering of Words
- Everyday Science
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- Ratios and Proportions: Definition and Examples
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