Wednesday 19 June 2019

Mathematics Class 6 ( state Board) - Textbook solved Questions


MATHEMATICS ( Class 6 )


TEXTBOOK  SOLUTIONS







BUY STUDY GUIDES CLICK BELOW

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Friday 14 June 2019

SSC class 10 ( Science & Technology ) Textbook solved questions


SYLLABUS

 Free Text Book can be downloaded http://ebalbharati.in/main/publicHome.aspx

PART 1 : 

1. Gravitation
2. Periodic classification of Elements
3. Chemical Reaction and equations 
4. Effects of Electric current
5. Heat
6. Refraction of Light 
7. Lenses 
8. Metallurgy
9. Carbon Compounds
10. Space missions

PART 2 :

1. Heridity and evolution
2. Life process in living organisms
3. Environment management
4. Towards Green energy 
5. Animal classification 
6. Introduction to microbiology 
7. Cell biology and biotechnoology
8. Social health
9. Disaster management

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Tuesday 11 June 2019

Mathematics Fundamentals ( EASY MULTIPLICATION ) - Multiply numbers easily and accurately in seconds

Introduction

Everyone is familiar with the normal procedure of multiplication 



In this lesson we shall learn the easy methods of multiplication from different techniquies around the world such Indian vedic maths , oriental Stick Method , magic square method ..etc

Remember these tricks  first for easy multiplication 

 1 .multiplication by 1 : (write number as it is) .  Eg ( 9 X 1 = 9  ) 

 2 .multiplication by 2 : (double the number ) .  Eg ( 9*2 = double  of  9)  =  18

 3. multiplication by 3 : ( double number & add the same number )              Eg ( 9*3 = double of 9 ie 18  and add 9 = 18 + 9 = 27 ) 

 4 . multiplication by 4 ( double number & double it again)  
    eg ..( 9*4 = double of 9 is 18 and double of 18 =  36 ) 

 5 . multiplication by 5 ( place zero after number and then divide by 2 ) 
Eg : 9*5 = ( place zero  after 9  so it becomes 90 and then divide by 2  i.e 90/2 = 45) 

 6. multiplication by 6 ( multiply number by 5 and then add the number  to it ) 

Eg : 9 *  6   = ( 9 * 5)  + (  9 ) =   45+ 9 = 54  

 7 . multiplication by 7 ( multiply by 5 and add the number ( doubled) 

Eg ..9*7 = ( 9*5 + 9(doubled) = 9*5 + 18 = 45+18 = 63

 8. multiplication by 8 ( double , double ,double ,)  3 times ...... 

 Eg : 9 * 8 = ( double 9 = 18 , double 18=36 , double 36 = 72 

 9. multiplication by 9 ( place zero after the number and  then substract the same number . )

 Eg : 9 * 9 = ( place zero  after 9 so it becomes 90 and then substarct  9)  = 90 - 9 = 81 

 10.  multiplication by 10 : Just place a zero after the number
1.Multiply any 2 Digit numbers under 20 in your head 

Example 1 : 13 X 12

1. add first number and last digit of second number as shown 
      (shaded in yellow and blue ) 
            
           13 X  12    =  ( 13 +2) = 15 

2. place  a zero in front of the result( 15 )  we get 15( place zero here)  so it becomes 150 

3. mulitply the last digits of both the numbers

    13    X 12     (  i.e 3*2 = 6 ) 
                      
4 .  add result of step ( 2 & 3) i.e 150 + 6 =    156      ....answer      


Wow ..So easy isnt it ...with little practice you can master this technique

lets see another example .......................

Example 2 : 19  X  17 

1. add first number and last digit of second number as shown 
      (shaded in yellow and blue ) 


        19  X   17      = ( 19 + 7 ) = 26 


2. place  a zero in front of the result( 26 )   i.e  26( place zero here)  so it becomes 260 


3. mulitply the last digits of both the numbers

  19 X 17  (  i.e 9*7 = 63 ) 

4.  add result of step ( 2 & 3) i.e 260 + 63 =    323  ....answer     
2. Base Method of Vedic Math

Multipling when numbers are near the base numbers like (10 ,50, 100)

Example 1 : 13 * 13 

solution :

13 * 13

now 13 is 3 more  from  base 10 ,i.e 13 = ( 10 + 3 )
 so write numbers as shown below 

 13    3 
13    3
                                   
                                                                      
step 1 : 

Multiply both numbers shaded in yellow i.e( 3*3 = 9 ) 
that is the answers last number 


step 2: 

13    3
13    3

     
add the  numbers shaded in green , that is the first part of the answer i.e ( 13 + 3 = 16) 


step 3 : 

combine result from step 2 ( purple shaded ) step 1 green shaded 
i.e ( 16 9 )      = 169 ....answer 


Example 2 : 103 * 103 

solution 

here both numbers of near base 100 , so 

103 is 3 more than 100  i.e ( 103 = 100 + 3 ) , so write like this 

                 103  3
                 103  3


Step 1 : 

Multiply both numbers shaded in yellow shown  as above 
i.e ( 3*3 = 09)    PS* ( since base is 100 write 3*3 as 09) 

This is answers last number 

Step 2 : 

                 103      3

                 103      3

add the numbers shaded in green , i.e ( 103 + 3 = 106 ) 

This gives first part of the answer ....

Step 3 : 

combine result from step 2( purple shaded)  & 1( blue shaded) 

i.e  10609  =  10609 ....answer 
  


Stick Method Of Multiplication

CLICK HERE 


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Saturday 1 June 2019

Mathematics Fundamentals ( EASY ADDITION ) - add numbers easily and accurately in seconds


Introduction

Everyone is familiar with the normal procedure of addition ( add numbers and carry if the number is greater than 9 )  



In this lesson we shall learn the easy methods of addition from different techniquies around the world such Indian vedic maths , oriental Stick Method ,Chinese abacus etc.
Method 1 ( Using Vedic Mathematics principle)

This Method uses the basic Units , Tens , hundred principle for addition 

Seperate the Numbers into its units , tens and hundred place and then add.

Example 1 : 88 + 11

Solution : 

1. seperate the numbers into unit , tens place 

( units place shaded blue ,tens place in yellow ) 
    
    88 = ( 80 + 8) 

    11 = ( 10 + 1) 

2. Add the tens place & then the units place 

 = 80+10+8+1 = 99 ...answer 


Example 2 : 43 +23+ 66

solution :  
( units place shaded blue ,tens place in yellow )

 1.seperate the numbers into unit , tens place 

43 = 40 + 3  , 23 = 20 + 3 , 66 = 60 + 6 

2. Add the tens place & then the units place 

40 + 20 + 60 + 3+3+6     = 120 + 12     = 132  ...answer 

Example 3 : 233 + 145 + 69

 solution :  
( units place shaded blue ,tens place in yellow, hundreds in orange )

1.seperate the numbers into its unit , tens  & hundreds place 

 233 = 200 + 30 + 3  , 145 =100 + 40 + 5 , 69 = 60 + 9
2.  Add the hunderd place , tens place & then the units place 

  = 200+ 100 + 30+40+60 +3+5+9  = 447 ...answer 
VERY EASY METHOD ...WITH SOME PRACTICE YOU CAN ADD NUMBERS IN YOUR HEAD ...

Practice Problems : 
1.77 + 45         2. 501 + 135               3. 65 +166 + 7


Method 2 ( Using CARRY at last  method )

This is a very fast method of adding numbers . In the method we first add numbers as it is ( no carry ) ..  and then we carry numbers on the final result 

 but this method  needs lot of practice and you should know the concept of carry.. 

 Example 1 :   45 + 69  

 1. Add the numbers ( dont carry write as it is ) 
    
    now 5 + 9 = 14 , 4 + 6 = 10 , see below 


4   5  
6   9  
10 / 14

2.  write the result and then carry ( always left to right ) 

    our result :: 10 / 14 ... carry the 1 ( marked yellow towards left & add to that 0 before it )  = 1 0 / 1 4  = 1 ( 0+1) 4 = 114 .... answer 
Example 2  :   87 + 65 

 1. Add the numbers ( dont carry write as it is ) 
   
    now 8 + 6  = 14  ,  7 + 5 = 12 
8   7
6   5
14 / 12

2.  write the result and then carry ( always left to right ) 

our result :  14 / 12  ( carry 1 to left towards 4) so 1 ( 4+1)  2  

 = 152 ...answer 


 Example 3  :   245 +  569

1. Add the numbers ( dont carry write as it is ) 
  
     2 + 5 = 7   ,   4 + 6 =10  ,  9+5 = 14  
2   4   5 
 5   6   9  

                                                                 
                                                                    7 / 1 0 / 14

2.  write the result and then carry ( always left to right ) 

our result ::  7 / 10 / 14 = ( carry 1 towards 0 , and other 1 towards 7 

i.e    :   ( 7 +1 ),(  0+1) , 4 = 814 ....answer 


Method 3 : ( Using the Chinese Stick Method )


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