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linkinpark
- Master | Next Rank: 500 Posts
- Posts: 124
- Joined: Tue Dec 22, 2009 8:32 am
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Hi BTG members following is my collection of mathematics formulas that I've come across so far, this list might grow so I may update the original thread should the need be, pardon my formatting I'm lazy for that
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* Any factorial > 2 is divisible by 3 atleast
* for lines to be parallel, coefficients in front of x have to be equal and other coefficients have to differ
e.g. y = 0.48 - x/3 and y = 10 - x/3 are two parallel lines
* Standar Deviation of a set is 0 if all elements are equal.
* In one hour, the hour hand moves by 360/12 = 30 degrees. In one minute, the hour hand moves by 30/60 = 1/2 degrees.
* Any traingle inscribed in circle with diameter as one side is right traingle
* individual contribution vs overall contribution change percentage
* In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, \
then the standard deviation is 0.
* sqr(1) or 1^any power = 1 and sqr or any power of 0 = 0
* If 5 noble knights are to be seated at a round table, then how many different ways can they be seated? Fix a knight in a spot to arrange the rest.
The formula is (N-1)! , or (5-1)! = 4!
* Range of set = max element - min element
* d = a sqrt{3} , where a is the length of a side and d is the cube's diagonal
* radius of circle in equi triangle = r = side * root 3/6
* general linear equation in two variable ax + by + c = 0 represents a line, slope = -a/b and
* If a line has a positive slope, it definitely goes through sectors 1 and 3.
* If a line has a negative slope, it definitely goes through sectors 2 and 4.
** 'overtaking' problem, the first thing that should strike us is that the distance traveled by both trains is the same at the time of overtaking.
** a 'meeting' problem, there are two things that should strike you. First, since they are starting at the same time, when they meet,
the time for which both will have been cycling will be the same. Second, the total distance traveled by the will be equal to the sum
of their individual distances.
** Since this is a question on round trip, the first thing that should strike us is that the distance going and coming back will be the same.
Now, we are required to find out the boats speed in calm water. So let us assume it to be 'b'.
Now if speed of the current is 3 mph, then the speed of the boat while going downstream and upstream will be 'b + 3' and 'b - 3' respectively.
In the first row, we have the speed of the boat in terms of 'b' and we are given the time.
==================== sequence and series
in geometric sequence
nth term an = an-1 * r
an = a1 * r^n-1
in arithmetic sequence
nth term an = an - 1 + d
an = a1 + (n-1)d
sum in geometric series
Sn = a1*(1-r^n)/(1-r)
in arithmetic series sum =n/2(first term + last term) = n/2[2*first term + (n-1)d]
number of terms = [last term - first term] + 1 "Add one before you are done".
number of odd/even terms = [(last term - first term )/ 2 ] + 1
*If the question is to find the number of odd integers between 2 and 30, then your first term is 3, and your last term is 29.
They must be odd to fit in the set you are asked to analyze.
*If the question is find the number of even integers between 3 and 29, then your first term is 4, and your last term is 28.
(1) The mean and the medium of any arithmetic sequence is equal to the average of the first and last terms.
(2) The sum of an arthritic sequence is equal to the mean (average) times the number of terms.
(3) The product of n consecutive integers is always divisible by n! So, 4x5x6 (4*5*6=120) is divisible by 3!
(4) If you have an odd number of terms in consecutive set, the sum of those numbers is divisible by the number of terms.
(5) number four (above) does not hold true for consecutive sets with an even amount of terms.
===========================
** radius of circle inscribed in square = half the side of square
** diagonal of sqr = root 2 * side
** from n>3 points you can form nc3 triangles
For mixture related problems do google a document by Sureshbala I've lost that URL, its nice way to hit those questions in a faster way.
I know many of experts are there on this forum but I thought at least 1 person might find these helpful.
Cheers
====================================================================
* Any factorial > 2 is divisible by 3 atleast
* for lines to be parallel, coefficients in front of x have to be equal and other coefficients have to differ
e.g. y = 0.48 - x/3 and y = 10 - x/3 are two parallel lines
* Standar Deviation of a set is 0 if all elements are equal.
* In one hour, the hour hand moves by 360/12 = 30 degrees. In one minute, the hour hand moves by 30/60 = 1/2 degrees.
* Any traingle inscribed in circle with diameter as one side is right traingle
* individual contribution vs overall contribution change percentage
* In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, \
then the standard deviation is 0.
* sqr(1) or 1^any power = 1 and sqr or any power of 0 = 0
* If 5 noble knights are to be seated at a round table, then how many different ways can they be seated? Fix a knight in a spot to arrange the rest.
The formula is (N-1)! , or (5-1)! = 4!
* Range of set = max element - min element
* d = a sqrt{3} , where a is the length of a side and d is the cube's diagonal
* radius of circle in equi triangle = r = side * root 3/6
* general linear equation in two variable ax + by + c = 0 represents a line, slope = -a/b and
* If a line has a positive slope, it definitely goes through sectors 1 and 3.
* If a line has a negative slope, it definitely goes through sectors 2 and 4.
** 'overtaking' problem, the first thing that should strike us is that the distance traveled by both trains is the same at the time of overtaking.
** a 'meeting' problem, there are two things that should strike you. First, since they are starting at the same time, when they meet,
the time for which both will have been cycling will be the same. Second, the total distance traveled by the will be equal to the sum
of their individual distances.
** Since this is a question on round trip, the first thing that should strike us is that the distance going and coming back will be the same.
Now, we are required to find out the boats speed in calm water. So let us assume it to be 'b'.
Now if speed of the current is 3 mph, then the speed of the boat while going downstream and upstream will be 'b + 3' and 'b - 3' respectively.
In the first row, we have the speed of the boat in terms of 'b' and we are given the time.
==================== sequence and series
in geometric sequence
nth term an = an-1 * r
an = a1 * r^n-1
in arithmetic sequence
nth term an = an - 1 + d
an = a1 + (n-1)d
sum in geometric series
Sn = a1*(1-r^n)/(1-r)
in arithmetic series sum =n/2(first term + last term) = n/2[2*first term + (n-1)d]
number of terms = [last term - first term] + 1 "Add one before you are done".
number of odd/even terms = [(last term - first term )/ 2 ] + 1
*If the question is to find the number of odd integers between 2 and 30, then your first term is 3, and your last term is 29.
They must be odd to fit in the set you are asked to analyze.
*If the question is find the number of even integers between 3 and 29, then your first term is 4, and your last term is 28.
(1) The mean and the medium of any arithmetic sequence is equal to the average of the first and last terms.
(2) The sum of an arthritic sequence is equal to the mean (average) times the number of terms.
(3) The product of n consecutive integers is always divisible by n! So, 4x5x6 (4*5*6=120) is divisible by 3!
(4) If you have an odd number of terms in consecutive set, the sum of those numbers is divisible by the number of terms.
(5) number four (above) does not hold true for consecutive sets with an even amount of terms.
===========================
** radius of circle inscribed in square = half the side of square
** diagonal of sqr = root 2 * side
** from n>3 points you can form nc3 triangles
For mixture related problems do google a document by Sureshbala I've lost that URL, its nice way to hit those questions in a faster way.
I know many of experts are there on this forum but I thought at least 1 person might find these helpful.
Cheers
530->480->580
when posting a question don't post OA(even masked) before some discussion.
when posting a question don't post OA(even masked) before some discussion.
