Thursday, August 24, 2017

102-Tool to calculate difference between two dates

Blog-102

Click on the following link:


Now we will learn very useful tool to calculate the difference between to two dates in years, months and days. Now we calculate our age today. Its very interesting software.

Click on the following Figure:

Tool to calculate difference between two dates

Simply enter the data in Start Date and End date fields. Here your start date is smaller than end date. It becomes very easy to calculate your age in years/Months/days. by using this software. So many times we need to calculate the difference between two date such as "At what age I completed my Graduation" or "What is the difference between me and my mother". This is very easy tool to calculate such difference.

Click on the following link to check the difference between two dates:

Tool to get difference between two dates

 ANIL SATPUTE

Friday, August 11, 2017

101-GRE Math Test - Important Key points and formulas Part - 6

Blog-101

In continuation of Blog-100, we will see all the important formulas and useful statements which are to be used in Math test of GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued)

4) (x - a) (x - b) = x (x - b) - a (x - b)
                         = x 2 - b x - a x + ab
                         = x 2 - (a + b) x + ab
Generally we call x 2 as the first term, (a + b) x as the middle term and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "+" so factorize the product of the coefficient of first term (here it is 1) and the last term in such a way that the SUM of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x 2 - 10 x + 21.

a) Step-1: Here sign of the last term 21 is "+"
b) Step-2: The coefficient of the first term is 1 and the last term is 21 , so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "+", their addition is -3 - 7 = -10 which is the coefficient of the middle term.  
                         = x 2 - 10 x + 21
                         = x 2 - (3 + 7) x + (3 x 7)
                         = x 2 - 3 x - 7 x + (3 x 7)
                         = x (x - 3) - 7 (x - 3)
                         = (x - 3) (x - 7)
c) Step-3: So the factors of x 2 - 10 x + 21 are (x - 3) and (x - 7) 

Example-2:

Factorize: 8 x 2 - 14 x + 5.

a) Step-1: Here sign of the last term 5 is "+"
b) Step-2: The coefficient of the first term is 8 and the last term is 5 , so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2 and 5 and as the sign of the last term is "+", so, we take two factor in such a way that their sum will be 14. Here 2, 2, 2 and 5 will give us 4 and 10. So, here addition is -4 - 10 = -14 which is the coefficient of the middle term.  

                         = 8 x 2 - 14 x + 5
                         = 8 x 2 - (4 + 10) x + 5
                         = 8 x 2 - 4 x - 10 x + 5
                         = 4 x (2 x - 1) - 5 (2 x - 1)
                         = (4 x - 5) (2 x - 1)
c) Step-3: So the factors of 8 x 2 - 14 x + 5 are (2 x - 1) and (4 x - 5).

In the next part we will see some important formulae.

 ANIL SATPUTE

Thursday, August 10, 2017

100-GRE Math Test - Important Key points and formulas Part - 5

Blog-100

In continuation of Blog-99, we will see all the important formulas and useful statements which are to be used in Math test of GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued)

3) (x - a) (x + b) = x (x + b) - a (x + b)
                          = x 2 + b x - a x - ab
                          = x 2 - (a - b) x - ab
Generally we call x 2 as the first term, (a + b) x as the middle term and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "-" so factorize the product of the coefficient of first term (here it is 1) and the last term in such a way that the DIFFERENCE of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x 2 - 4 x - 21.

a) Step-1: Here sign of the last term 21 is "-"
b) Step-2: The coefficient of the first term is 1 and the last term is 21 , so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "-", their subtraction is 3 - 7 = -4 which is the coefficient of the middle term. (Note: Here, the coefficient of the middle term is positive so we took it as 3 - 7).  

                         = x 2 - 4 x - 21
                         = x 2 + (3 - 7) x - (3 x 7)
                         = x 2 + 3 x - 7 x - (3 x 7)
                         = x (x + 3) - 7 (x + 3)
                         = (x - 7) (x + 3)
c) Step-3: So the factors of x 2 - 4 x - 21 are (x + 3) and (x - 7) 

Example-2:

Factorize: 8 x 2 - 18 x - 5.

a) Step-1: Here sign of the last term 5 is "-"
b) Step-2: The coefficient of the first term is 8 and the last term is 5 , so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2 and 5 and as the sign of the last term is "-", so, we take two factor in such a way that their difference will be 18. Here 2, 2, 2 and 5 will give us 2 and 20. So, here subtraction is 2 - 20 = -18 which is the coefficient of the middle term.  

                         = 8 x 2 - 18 x - 5
                         = 8 x 2 + (2 - 20) x - 5
                         = 8 x 2 + 2 x - 20 x - 5
                         = 2 x (4 x + 1) - 5 (4 x + 1)
                         = (2 x - 5) (4 x + 1) 
c) Step-3: So the factors of 8 x 2 - 18 x + 5 are (2 x - 5) and (4 x + 1).

In the next part we will see remaining 1 types in detail. These 1 types are given below.

4) (x - a) (x - b) = x 2 - (a + b) x + ab     

Wednesday, August 9, 2017

99-GRE Math Test - Important Key points and formulas Part - 4

Blog-99

In continuation of Blog-98, we will see all the important formulas and useful statements which are to be used in Math test of GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued)

2) (x + a) (x - b) = x (x - b) + a (x - b)
                          = x 2 - b x + a x - ab
                          = x 2 + a x - b x - ab
                          = x 2 + (a - b) x - ab
Generally we call x 2 as the first term, (a + b) x as the middle term and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "-" so factorize the product of the coefficient of first term (here it is 1) and the last term in such a way that the DIFFERENCE of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x 2 + 4 x - 21.

a) Step-1: Here sign of the last term 21 is "-"
b) Step-2: The coefficient of the first term is 1 and the last term is 21 , so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "-", their subtraction is 7 - 3 = 4 which is the coefficient of the middle term. (Note: Here, the coefficient of the middle term is positive so we took it as 7 - 3).  

                         = x 2 + 4 x - 21
                         = x 2 + (7 - 3) x - (3 x 7)
                         = x 2 + 7 x - 3 x - (3 x 7)
                         = x (x + 7) - 3 (x + 7)
                         = (x - 3) (x + 7)
c) Step-3: So the factors of x 2 + 4 x - 21 are (x - 3) and (x + 7) 

Example-2:

Factorize: 8 x 2 + 18 x - 5.

a) Step-1: Here sign of the last term 5 is "-"
b) Step-2: The coefficient of the first term is 8 and the last term is 5 , so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2 and 5 and as the sign of the last term is "-", so, we take two factor in such a way that their difference will be 18. Here 2, 2, 2 and 5 will give us 2 and 20. So, here subtraction is 20 - 2 = 18 which is the coefficient of the middle term.  

                         = 8 x 2 + 18 x - 5
                         = 8 x 2 + (20 - 2) x - 5
                         = 8 x 2 + 20 x - 2 x - 5
                         = 4 x (2 x + 5) - 1 (2 x + 5)
                         = (2 x + 5) (4 x - 1) 
c) Step-3: So the factors of 8 x 2 + 18 x + 5 are (2 x + 5) and (4 x - 1).

In the next part we will see remaining 2 types in detail. These 2 types are given below.

3) (x - a) (x + b) = x 2 - (a - b) x - ab
4) (x - a) (x - b) = x 2 - (a + b) x + ab     

Tuesday, August 8, 2017

98-GRE Math Test - Important Key points and formulas Part - 3

Blog-98

In continuation of Blog-97, we will see all the important formulas and useful statements which are to be used in Math test of GRE.

Factorization (Continued):

b) Factorization of Polynomial: 

Here following 4 possibilities can be studied to understand the factorization in better way.

1) (x + a) (x + b) = x (x + b) + a (x + b)
                          = x 2 + b x + a x + ab
                          = x 2 + a x + b x + ab
                          = x 2 + (a + b) x + ab
2) (x + a) (x - b) = x (x - b) + a (x - b)
                          = x 2 - b x + a x - ab
                          = x 2 + a x - b x - ab
                          = x 2 + (a - b) x - ab

3) (x - a) (x + b) = x (x + b) - a (x + b)
                          = x 2 + b x - a x - ab
                          = x 2 - a x + b x - ab
                          = x 2 - (a - b) x - ab

Note: Here formulae 2 and 3 are of same type. the coefficient of the middle term is the difference of the Constance and the sign is to be taken of the greater Constance. 

4) (x - a) (x - b) = x (x - b) - a (x - b)
                          = x 2 - b x - a x + ab
                          = x 2 - a x - b x + ab
                          = x 2 - (a + b) x + ab

Now we will study these types in detail:

1) (x + a) (x + b) = x (x + b) + a (x + b)
                          = x 2 + b x + a x + ab
                          = x 2 + a x + b x + ab
                          = x 2 + (a + b) x + ab
Generally we call x 2 as the first term, (a + b) x as the middle term and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "+" so factorize the product of the coefficient of first term (here it is 1) and the last term in such a way that the SUM of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x 2 + 10 x + 21.

a) Step-1: Here sign of the last term 21 is "+"
b) Step-2: The coefficient of the first term is 1 and the last term is 21 , so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "+", their addition is 3 + 7 = 10 which is the coefficient of the middle term.  

                         = x 2 + 10 x + 21
                         = x 2 + (3 + 7) x + (3 x 7)
                         = x 2 + 3 x + 7 x + (3 x 7)
                         = x (x + 3) + 7 (x + 3)
                         = (x + 3) (x + 7)
c) Step-3: So the factors of x 2 + 10 x + 21 are (x + 3) and (x + 7) 

Example-2:

Factorize: 8 x 2 + 14 x + 5.

a) Step-1: Here sign of the last term 5 is "+"
b) Step-2: The coefficient of the first term is 8 and the last term is 5 , so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2 and 5 and as the sign of the last term is "+", so, we take two factor in such a way that their sum will be 14. Here 2, 2, 2 and 5 will give us 4 and 10. So, here addition is 4 + 10 = 14 which is the coefficient of the middle term.  

                         = 8 x 2 + 14 x + 5
                         = 8 x 2 + (4 + 10) x + 5
                         = 8 x 2 + 4 x + 10 x + 5
                         = 4 x (2 x + 1) + 5 (2 x + 1)
                         = (4 x + 5) (2 x + 1)
c) Step-3: So the factors of 8 x 2 + 14 x + 5 are (2 x + 1) and (4 x + 5).
In the next part we will see remaining 3 types in detail. These 3 types are given below.

2) (x + a) (x - b) = x 2 + (a - b) x - ab
3) (x - a) (x + b) = x 2 - (a - b) x - ab
4) (x - a) (x - b) = x 2 - (a + b) x + ab