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# Formulae and Shortcuts - making life easier!

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TIME AND WORK

• If A can do a piece of work in x days, then A’s one day’s work=1/x
• If the ratio of time taken by A and B in doing a work is x:y, then, ratio of work done is 1/x :1/y=y:x. And the ratio in which the wages is to be distributed is y:x
• If A can do a work in x days and B can do the same work in y days, then A and B can together do the work in (xy)/(x+y) days
• If “a” men or “b” women can do a piece of work in x days, then “m” men and “n” women can together finish the work in (abx)/(an+bm) days
• If A is x times efficient than B, and working together, they finish the work in y days, then Time taken by A=y(x+1)/(x), Time taken by B=y(x+1)
• If A and B can finish a work in “x” and “ax” days respectively, that is if A is “a” times efficient than B, then working together, they can finish the work in (ax)/(a+1) days
• If A and B working together can complete a work in x days, whereas B working alone can do the same work in y days, ten, A alone will complete the work in (xy)/(y-x) days.
• Pipe A can fill a tank in x hrs and B can empty a tank in y hrs.If both pipes are opened together, the tank will be filled in (xy)/(y-x) hrs
• A pipe can fill a cistern in x hrs but due to leakage in the bottom, it is filled in y hrs, then the time taken by the leak to empty the cistern is (xy)/(y-x) hrs

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Very ingenious idea ,

Keep going.

Ruchi

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Most of you will know all the formulae given below. This is just to give a comprehensive list (all these can be found in http://math.about.com )

Rectangle:

Area = lw

Perimeter = 2l + 2w

Parallelogram:

Area = bh

Triangle

Area = 1/2 of the base X the height = 1/2 bh

Perimeter = a + b + c

Trapezoid

Perimeter = P = a + b1 + b2 + c

Circle:

The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius ® is the distance from the center to a point on the circle. (Pi = 3.14)

d = 2r

c = pd = 2 pr

A = pr2

(p=3.14)

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Rectangular Solid

Volume = lwh

Surface = 2lw + 2lh + 2wh

Prisms

Volume = Base area X Height

Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)

Cylinder

Volume = pr2 h

Surface = 2prh

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Pyramid

V = 1/3 bh

b is the area of the base

Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.

Cones

Volume = 1/3 pr2 x height = 1/3 pr2h

Surface = pr2 + prs = pr2 + pr http://math.about.com/library/graphics/coneformula.gif

Sphere

Volume = 4/3 pr^3

Surface area = 4pr^2

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I think ETS pundits will reconsider their questions if they viewed this thread. Suja, remarkable contribution - keep it.
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Great job coolgal and puzoo. Keep it up..:tup:

I think ETS pundits will reconsider their questions if they viewed this thread. Suja, remarkable contribution - keep it.

Thanks Dimas, and I wanted to ask you this... why dont you write something on math fundementals and concepts that people tend to misconstrue? I know it is not easy to think in terms of what others might find difficult, but why dont you just try? You know the one about square root, it is still being discussed in atleast one of the threads all the time... You or xeley or manwithmission, or someone who doesnt have GRE very soon can do this. It requires a very clear idea of the fundamentals (which i am not sure i have). I myself get confused often with very basic concepts of mathematics. But I shall anyhow try doing it once my GRE is over (which is on this friday and is hence keeping me busy all the time). What say...? :hmm:

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Nice suggestion. I belive that the wealth of information in the GRE and GMAT math is sufficient for 850/800. I don't know what are the most common misconceptions in math, but I recommend everybody to allot three days to work these forums before the circus day. Let me know if anybody needs a specific topic.
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Distance of a Point from a Line

The perpendicular distance d of a point P (x 1, y 1) from the line ax +by +c = 0 is given by:

d =| ax1 +by1 +c|/[http://www.ilovemaths.com/sqrt.gif(a² +b²)]

http://www.ilovemaths.com/images/12/geo/675.gif

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Pyramid

V = 1/3 bh

b is the area of the base

Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.

Cones

Volume = 1/3 pr2 x height = 1/3 pr2h

Surface = pr2 + prs = pr2 + pr http://math.about.com/library/graphics/coneformula.gif

Sphere

Volume = 4/3 pr^3

Surface area = 4pr^2

great work by gre gal and suja and others....[clap]

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1. Simple Interest = PNR/100

where, P --> Principal amount

N --> time in years

R --> rate of interest for one year

2. Compound interest (abbreviated C.I.) = A -P =

http://www.ilovemaths.com/images/12/comm/ci2.gif

where A is the final amount, P is the principal, r is the rate of interest compounded yearly and n is the number of years

3. When the interest rates for the successive fixed periods are r1 %, r2 %, r3 %, ..., then the final amount A is given by A =

http://www.ilovemaths.com/images/12/comm/ci4.gif

4. S.I. (simple interest) and C.I. are equal for the first year (or the first term of the interest period) on the same sum and at the same rate.

5. C.I. of 2nd year (or the second term of the interest period) is more than the C.I. of Ist year (or the first term of the interest period), and C.I. of 2nd year -C.I. of Ist year = S.I. on the interest of the first year.

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1. Mean.
(i) Mean (for ungrouped data) = http://www.ilovemaths.com/images/910/central/2.gif where x1, x2, x3, ..., xn are the observations and n is the total no. of observations.
(ii) Mean (for grouped data) = http://www.ilovemaths.com/images/910/central/3.gif, where x1, x2, x3, ..., xn are different variates with frequencies f1, f2, f3, ..., fn respectively.
(iii) Mean for continuous distribution.
Let there be n continuous classes, yi be the class mark and fi be the frequency of the ith class, then
mean = http://www.ilovemaths.com/images/910/central/4.gif (Direct method)
Let A be the assumed mean, then
mean = A +http://www.ilovemaths.com/images/910/central/6.gif, where di = yi -A (Short cut method)
If the classes are of equal size, say c, then
mean = A +c x http://www.ilovemaths.com/images/910/central/5.gif, where ui = http://www.ilovemaths.com/images/910/central/7.gif (Step deviation method)

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1. Median.
(i) Median is the central value (or middle observation) of a statistical data if it is arranged in ascending or descending order.
(ii) Let n be the total number of observations, then
Median =http://www.ilovemaths.com/images/910/central/8.gif
2. Quartiles
(i) Lower Quartile =http://www.ilovemaths.com/images/910/central/9.gif
(ii) Upper Quartile =http://www.ilovemaths.com/images/910/central/10.gif
(iii) Inter quartile-range = upper quartile -lower quartile
3. Mode.
(i) Mode (or modal value) of a statistical data is the variate which has the maximum frequency.
(ii) The class with maximum frequency is called the modal-class.

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.....

More formulae:

PROGRESSION:

Sum of first n natural numbers: 1 +2 +3 + .... + n = [n(n+1)]/2

Sum of first n odd numbers: 1 + 3 + 5 + .... upto n terms = n^2

Sum of first n even numbers: 2 + 4 + 6 + ... upto n terms = n(n+1)

ARITHMETIC PROGRESSION

nth term of an Arithmetic progression = a + (n-1)d

Sum of n terms in an AP = s = n/2 [2a + (n-1)d]

where, a is the first term and d is the common differnce.

If a, b and c are any three consequtive terms in an AP, then 2b = a + c

GEOMETRIC PROGRESSION

nth term of a GP is = a[r^(n-1)]

sum of n terms of a GP:

s = a [(r^n - 1)/(r-1)] if r > 1

s = a [(1 - r^n)/(r-1)] if r

sum of an infinite number of terms of a GP is

s(approx.) = a/ (1-r) if r

If a, b and c are any three consequtive terms in a GP, then b^2 = a + c

If a, b and c are any three consequtive terms in a GP, then b^2 = ac

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manwiththemission 2005,

i did not understand the last one i.e. root A : root B. A & B are two points, how their root could be possible?

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If a, b and c are any three consequtive terms in a GP, then b^2 = a + c

If a, b and c are any three consequtive terms in a GP, then b^2 = ac

Oh my! thanks a lot nirmala! I didnt notice that typo.

Can somebody suggest me how i can remove that post? As it is right at the beginning, some people might get misled and ....what if they dont see this correction? I am worried. Please help me out.:(

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suja u r just doing great.......
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LINES - BASICS:

1. The equation of X axis: y =0

2. The equation of Y axis: x = 0

3. Equation of straight line parallel to X axis: y =a, where a is any constant

4. Equation of straight line parallel to Y axis: x =a, where a is any constant

5. Equation of a straight line through a given point (x1, y1) and having a given slope m: y -y1 = m (x - x1)

6. Equation of a straight line through a given point (0, 0) and having a given slope m: y = m x

7. Equation of a straight line with a slope m and y-intercept c is: y = mx + c

8. Equation of a straight line passing through two points (x1, y1) and (x2, y2) is:

(y -y1)/(y2 - y1) = (x -x1)/(x2 -x1)

9. Equation of a straight line whose x and y intercepts are a and b is:

x/a + y/b = 1

10. The length of the perpendicular drawn from origin (0,0) to the line Ax + By + C =0 is :

C/ sqrt(A^2 + B^2)

11. Length of the perpendicular from (x1, y1) to the line Ax + By + C =0 is:

Ax1 + By1 +C / sqrt(A^2 + B^2)

12. The point of intersection of two lines a1x + b1y +c1 = 0 and a2x + b2y +c2 = 0 is :

([b1*c2 - b2*c1]/[a1*b2 - a2*b1], [c1*a2 - c2*a1]/[a1*b2 - a2*b1])

13. The condition for concurrency of three lines a1x + b1y +c1 = 0, a2x + b2y +c2 = 0 and a3x + b3y +c3 = 0 is (in determinant form)

| a1 b1 c1 |

| a2 b2 c2 | = 0

| a3 b3 c3 |

14. The angle between two lines y = m1x + c1 and y = m2x + c2 is tan inverse of the modulus of :

[(m1 - m2)/(1 + m1*m2)]

15. Condition for parallelism of two lines with slopes m1 and m2 is m1 = m2

16. Condition for perpendicularity of two lines with slopes m1 and m2 is m1*m2 =-1

CIRCLES:

17. General equation of a circle with centre (x1, y1) and radius r is:

(x - x1)^2 + (y - y1)^2 = r^2

18. The equation of a circle whose diameter is the line joining the points (x1, y1) and (x2, y2) is :

(x - x1)(x - x2) + (y - y1)(y - y2) = 0

19. The equation of the tangent to the circle x^2 + y^2 = a^2 (where a is the radius of the circle) at the point (x1, y1) on it is :

x*x1 + y*y1 + a^2

20. The condition for y = mx + c to be a tangent to the circle x^2 + y^2 = a^2 is :

c^2 = a^2 (1 + m^2)

source: Higher secondary first year Maths text book (TNSB)

suja u r just doing great.......
Thanks goodgirl!

Can somebody tell me why i dont see any of the pictures that were accompanying some of the formulae? Also, for some formulae I had given the formula itself as a picture due to difficulties in formatting and they are also gone... Is this a temporary problem or should I post them again? :(

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manwiththemission 2005,

i did not understand the last one i.e. root A : root B. A & B are two points, how their root could be possible?

It is Speed of train A: Speed of train B = sqrt(b) : sqrt(a)

@Sujatha and others

Keep the good work going.

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Goodgirl,

Sorry for being late. Anyways,

If 2 trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then

(A's speed) : (B's speed) = (root(b) : root(a))

where a and b number of seconds.

Hope you do get it goodgirl . All the best :)

Btw, thanks manasi for helping her on behalf of me.

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hey guys ...when r u ppl giving gre...

it seems mansi has been here from a long time ...also manwithmission ...when r u guys havin gre...mine is in nov..m pretty tense rt now. wanna do lots of maths practise ...m almost done with vocabs...but doin engg simultaneously...so m not havin much time to study...guys just wanna ask u one thing ..if i give my gre in nov.. will i be able to apply bfor the deadlines for applications..

hey suja u r doing a godly job ...u gonna hav millions of blessings...keep doing the godly work!!!

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gazeup, you keyboard don't has all the letters? :rolleyes:;)
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Normally, 1st week of December is the date for some of the Institutions I suppose. It's always better to get ready with your applications as early as possible. By the way, I m taking it on October 24 and I will be ready with my SOP, Recos and other stuff b4 that so that once I get my score results, I will start applying right way. When are you taking it in November? That matters a lot. First week of November is fine. Manasi is taking it on Sep 16. It also depends on the universities you r applying to. Most of the universities I m applying to (Atleast the most important ones) are mid Jan. Anyways, All the best dude. There's no substitute for HARDWORK. Simple as that!
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Hi,

Can anyone explicitly tell me whether one needs to study topics like 'Analytical Geometry' and 'Matrices and Determinants' for GRE? I haven't seen them in any of the normal GRE prep books. However, when someone discusses it in the GRE Maths forum , I get petrified. I am a non maths student. Please help.....suja, are you reading this??

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I won't . It is out of GRE for sure.

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